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WASI user manual - eLib

1. Pre Fit Infrared from 760 to a00 nm steps fio nm max Iterations 100 Pre Fit Blue from 380 to 450 nm steps fio nm max Iterations 100 Fig 4 11 The register card Remote sensing reflectance for deep water of the pop up window Fit tun ing If a downwelling irradiance measurement is available the number of fit parameters for Rys A can be reduced by 4 a B y 5 In this case the box use Ed measurement should be marked with a hook and the measured spectrum has to be specified Most of the initial values are taken from the parameter list in the main window However for some parameters an automatic determination is possible for a B y 6 if an Ed measurement is available for CL and o from a pre fit in the Infrared and for Co Y S and Q from a pre fit in the Blue For doing so the box automatic determination of initial values has to be marked with a hook Subsequently the wavelength intervals steps and maximum number of iterations have to be specified for each pre fit If max Iterations is set to 0 or 1 the corresponding pre fit is not performed 4 4 4 Remote sensing reflectance of shallow water For inversion of remote sensing reflectance spectra also the 8 steps of Table 4 3 are per formed The only difference to the case of irradiance reflectance is that all R spectra are re placed by the corresponding R spectra 52 WASI manual version 3 4 4 5 Downwelling irradiance
2. 002035 002057 002081 002104 002128 002152 002176 002201 002226 002251 002277 004880 004942 005006 005070 005135 005201 005268 005336 005404 005474 005544 007951 008057 008164 008272 008382 008493 008605 008719 008834 008951 009069 OO OO O OO OO HO OL O 0 O DO O O O 0 0 O_O O O OS Or SD 0 0 0 0 0 O OGO 0 Fig 3 9 The first lines and the first 6 columns of the file SPEC FWD of the spectra series of Fig 3 8 The parameter values and input files used for calculating the spectra are documented by a copy of the WASI INI file which is stored automatically in the directory of the spectra The values of the iterated parameters are tabulated in the file CHANGES TXT An example of that file is given in Fig 3 10 34 WASI manual version 3 This file was generated by the program WASI Version 3 Latest update 29 May 2005 List of parameter values which differ from one spectrum to the next Common parameter set of all spectra in file WASI INI All spectra are the results of forward calculations Spectra Irradiance reflectanc Spectrum ClO C_L BO1 fwd 0 B02 fwd 0 B03 fwd 0 B04 fwd 000 B05 fwd 000 B06 fwd 000 B07 fwd 000 B08 fwd 000 B09 fwd 000 B10 fwd 000 Bll fwd 000 B12 fwd 000 B13 fwd 000 B14 fwd 000 B15 fwd 000 000 000 000 000 000 000 000 000 000 000
3. 4 16 where 1 R A A R A exp 2K 4 A z5 f 1 A exp 2K A z The conversion from optical units Bo to gravimetric units Cr Cs uses eq 4 8a or 4 8b as for deep water NA 4 17 Simulations of Albert 2004 showed that for zg gt 2 m the accuracy is typically better than 20 for Cr Cs lt 5 mg l and better than 40 for CL Cs lt 25 mg l if 760 nm is taken as ref erence wavelength which is used as default in WASI Such accuracy is sufficient for initialis ing Cr and Cs Step 3 Because eq 4 14 cannot be solved analytically for Co and Y an intermediate step is required to estimate the total absorption of all water constituents awc This is done iteratively by the method of nested intervals which is described in the following At wavelengths of non negligible absorption of water constituents the values of R and Kg de pend on awc When R is calculated using eq 4 1a and Ka using eq 2 5 values for by and a 50 WASI manual version 3 have to be assigned first by is calculated using eq 2 4 for its critical parameters Cr and Cs the values from step 2 are taken a is calculated using eq 2 3 the value of awc in that equa tion is treated as unknown and determined iteratively as follows In the first step R and Kg are calculated using a start value Ay for awc in eq 2 3 and with these R and Ky values Re 1s calculated using eq 4 14 In the next steps Ao is replaced in a systematic
4. 000 000 000 000 000 0 UN 0 UN DUNN UN DUN 0 0 0 ad o Db ds SI NINNIN Fig 3 10 The file CHANGES TXT of the spectra series of Fig 3 8 WASI manual version 3 35 4 Inverse mode Inverse modeling is the determination of model parameters for a given spectrum More pre cisely those values of the model parameters must be determined for which the correspon dence between fit curve and given spectrum is maximal Three modes of operation are implemented for inverse modeling of spectra e Single spectrum mode Inversion is performed for a single spectrum which the user loads from file After calculation an overlay of imported spectrum and fit curve is automatically shown on screen and resulting fit values number of iterations and residuum are dis played This mode allows to inspect the results for individual measurements It is useful for optimizing the choice of initial values and the fit strategy before starting a batch job e Batch mode A series of spectra from file is inverted After each fit an overlay of im ported spectrum and fit curve is automatically shown on screen This mode is useful for processing large data sets e Reconstruction mode Combines forward and inverse modes Inversion is performed for a series of forward calculated spectra which are not necessarily read from file The model parameters can be chosen differently for forward and inverse calculations This mode is useful for performing sensiti
5. A is nearly spectrally flat at overcast sky but clearly not for clear sky conditions Thus eq 2 13a should be used in general and eq 2 13b at most for days with overcast sky WASI manual version 3 15 2 5 Irradiance reflectance The ratio of upwelling irradiance to downwelling irradiance in water R A E A Ea A is called irradiance reflectance Mobley 1994 It is an apparent optical property AOP and depends not only on the properties of the medium but also on the geometric distribution of the incoming light 2 5 1 Deep water A suitable parameterization which separates to a large extent the parameters of water and of the illumination was found by Gordon et al 1975 R A f A 2 14 The function A which is given by eq 2 8 depends only on inherent optical properties of the water body absorption and backscattering The factor f comprises the illumination de pendencies It can be treated either as an independent parameter with a default value of 0 33 according to Gordon et al 1975 or the relationship of Albert and Mobley 2003 can be used 2 15 f 0 1034 1 3 3586 6 5358 4 6638 0 1 24121 cos O n 0 sun is the sun zenith angle in water Eq 2 15 takes into consideration the fact that f depends not only on the geometric structure of the light field expressed by the parameter O sun but also on the absorption and scattering properties of the water Some alter
6. a 002 Retedionfcorofupetingedaree le 1066 oceicentofatonaion WASI manual version 3 81 Appendix 5 Input spectra The following table summarizes the 28 spectra which can be imported from files For each a default spectrum is provided in the WASI software package and stored in the directory WASI DATA The user can replace the default spectra by changing the corresponding file description in the WASLINI file No WASI Symbol Units Description ae po fremente sms T e Je fems TT 7 ao A m mg Specific absorption of phytoplankton class no 0 Default Mixture of species typical for Lake Constance aP 1 ar A m mg Specific absorption of phytoplankton class no 1 Default Cryptophyta type L aP 2 a2 A m mg Specific absorption of phytoplankton class no 2 Default Cryptophyta type H aP 3 as A Specific absorption of phytoplankton class no 3 Default Diatoms aP 4 as A Specific absorption of phytoplankton class no 4 Default Dinoflagellates aP 5 as A Specific absorption of phytoplankton class no 5 Default Green algae Normalized absorption of non chlorophyllous particles Normalized absorption of Gelbstoff R A Irradiance reflectance sev Je Weis ofchamasativersen _ g g g Edi Y E gt y bL A ES Normalized backscattering coefficient of large particles o a y A E gt o A E d 82 WASI manual version 3 Appendix 6 Spectrum
7. and ratioing that equation for two wavelengths yields the following ratio Ra ASD ab Ya A CdA RA 4 10 O Yray A2 Co aAa MOD a a ba R A W 2 b 2 Since all functions on the right hand side of this equation are known Ra can be calculated Division of nominator and denominator of the center expression by Co leads to an equation which has as single unknown parameter the ratio Y Co Rewriting this equation yields the fol lowing expression Y _ Ry apQ a A 4 11 Co ay A R ay A The ratio of Gelbstoff to phytoplankton concentration is calculated using this equation It is a matter of optimisation to determine the best suited wavelengths and A By inserting Y Y Co Co into eq 4 9 and solving eq 4 9 for Co the following expression is obtained p Dv As ROA ag 210 0 E ay A3 b 2 C 4 12 Eq 4 12 is used to calculate the phytoplankton concentration It is a matter of optimisation to determine the best suited wavelength A3 Gelbstoff concentration is then calculated using eq 4 13 with the results from eqs 4 11 and 4 12 WASI manual version 3 47 ves 4 13 Co It has been investigated how the accuracy of the ratio Y Co and of the Co and Y values de pends on the choice of the wavelengths A 22 and 43 on the errors of Cr determination from step 1 and on suspended matter concentration The results of these studies are as follows e should be chosen below
8. xo highest x coordinate displayed 3 9E 5 yu lowest y coordinate displayed 0 050 yo highest y coordinate displayed 380 xub lowest x coordinate calculated 900 xob highest x coordinate calculated L dxb wavelength interval for calculation 400 Norm_min lower boundary for normalisation nm 800 Norm_max upper boundary for normalisation nm 3 1416 Ed factor multiplicator of spectrum E_down 0 10000 E0_factor multiplicator of spectrum E0 3 1416 Rrs_factor multiplicator of spectrum R_rs 0 calc_mode calculation mode l invers 0 2 batch 3 spec_type type of spectrum 0 E_d 1 L_up 2 R_rs 3 R 4 R_surf 5 a 6 K_d 7 R_bottom 0 Model_R R model 0 f bb a bb 1 f bb a al Model_R_rsA R_rs above surface is a function of 0 R_rs 0 1 R 2 both 0 Model_R_rsB R_rs model below surface 0 f_rs bb a bb 1 f_rs bb a 2 R Q 4 Model_f f model 0 const 1 Kirk 2 Morel Gentili 3 Sath Platt 4 Albert Mobley 0 Model_f_rs f_rs model 0 Albert 1 f 0 L bottom_fill bottom surface type adjusted to yield sum of weights 1 00E1FFFF clPlotBk color of plot background Flags 0 FALSE 1 TRUE 0 flag_SubGrid draw subgrid flag_Grid draw grid flag_Autoscale autoscale plot flag_ShowName display filename flag_ShowPath display path 0 flag_INI save INI file automatically 0 flag_sv_table save forward spectra as table 0 flag_save_t save calculation time 0 flag_mul
9. 0 100 to 10 ug l in 7 steps which are equidistant on a logarithmic scale and Gelbstoff absorp tion at 440 nm C_Y is iterated from 0 100 to 1 m in 4 steps which are equidistant on a lin ear scale i e absorption values of 0 1 0 4 0 7 and 1 0 m are taken Spectra are calculated for each combination hence the number of generated spectra is 7 4 28 3 3 2 3 Iteration over 3 parameters When 3 parameters should be iterated these parameters their range of variation and the num ber of steps must be specified analogously to iterating 1 or 2 parameters This is illustrated in Fig 3 7 Parameter from to steps log Fig 3 7 Iteration over 3 parameters In the example of Fig 3 7 phytoplankton concentration C_P and Gelbstoff absorption C_Y are iterated as in Fig 3 6 but additionally the concentration of large suspended particles C_L is iterated from 1 to 5 mg l in 5 steps which are equidistant on a linear scale i e concen 32 WASI manual version 3 trations of 1 2 3 4 and 5 mg l are taken Spectra are calculated for each combination hence the number of generated spectra is 7 4 5 140 3 3 3 Data storage Calculated spectra are stored automatically if saving is activated in the Forward calculation settings pop up window shown in Fig 3 2 Each spectrum is stored in a separate file the file names are Bnr fwd with nr file number The extension fwa indicates that the spectra are the result of forward calculations The
10. 0 5 m and below 12 for Y lt 1 m Hence for sensors equipped with two or more channels above 820 nm and for moderate Gelbstoff concentrations the analytical equations are well suited to determine initial values of Cr and f The conversion from optical units Bo to gravimetric concentrations Cr Cs is based on eq 2 4 assuming br A 1 Accordingly it is Bo by A bp w A CL bpL Cs bps X X 8 If Cs 0 Cr is calculated as Ge 4 8a Sa bp L Otherwise i e for Cs 0 the user defined ratio r s C Cs is retained hence the initial val ues of Cr and Cs are calculated as follows 46 WASI manual version 3 B 0 C 4 8b C bi x n r bi sd fn di r Ag LS C can be determined in that way with an accuracy in the order of 1 Gege and Albert 2005 Step 2 A non iterative procedure based on two channels was found to be practicable for cal culating the initial concentrations of phytoplankton and Gelbstoff at an accuracy in the order of 30 Gege and Albert 2005 If suspended matter concentration and the factor f are known with little error e g from step 1 the concentrations Co and Y can be determined analytically from two wavelengths A and Az The equations of determination are obtained from the irradi ance reflectance model described in chapter 2 5 1 by A RA f a l ay Y a3 A C a A b A 4 9 Resolving the equation for the sum Y ay A Co ao A
11. 2000 Flugzeuggest tzte Fernerkundung von Wasserinhaltsstoffen am Bodensee PhD thesis DLR Forschungsbericht 2000 40 134 p N G Jerlov 1976 Marine Optics Elsevier Scientific Publ Company J H Jerome R P Bukata J E Bruton 1990 Determination of available subsurface light for photochemical and photobiological activity J Great Lakes Res 16 3 436 443 J T O Kirk 1984 Dependence of relationship between inherent and apparent optical prop erties of water on solar altitude Limnol Oceanogr 29 350 356 J T O Kirk 1991 Volumen scattering function average cosines and underwater lightfield Limnol Oceanogr 36 455 467 Z P Lee K L Carder C D Mobley R G Steward J S Patch 1998 Hyperspectral re mote sensing for shallow waters I A semianalytical model Appl Optics 37 6329 6338 C D Mobley B Gentili H R Gordon Z Jin G W Kattawar A Morel P Reinersman K Stamnes R H Stavn 1993 Comparison of numerical models for computing underwater light fields Appl Optics 32 7484 7504 C D Mobley 1994 Light and Water Academic Press 592 pp WASI manual version 3 71 C D Mobley 1999 Estimation of the remote sensing reflectance from above surface meas urements Appl Optics 38 7442 7455 A Morel 1974 Optical Properties of Pure Water and Pure Sea Water In Jerlov N G Steemann Nielsen E Eds Optical Aspects of Oceanography Academic Press London 1 24
12. P Gege 2000 Gaussian model for yellow substance absorption spectra Proc Ocean Optics XV conference October 16 20 2000 Monaco P Gege 2001a A software tool for simulation and analysis of optical in situ spectra Proc 4th Berlin Workshop on Ocean remote sensing Berlin Germany May 30 to June 1 2001 P Gege 2001b The water colour simulator WASI A software tool for forward and inverse modeling of optical in situ spectra Proc IGARSS Sydney Australia 9 13 July 2001 P Gege 2002 Error propagation at inversion of irradiance reflectance spectra in case 2 wa ters Ocean Optics XVI Conference November 18 22 2002 Santa Fe USA P Gege 2004 The water color simulator WASI an integrating software tool for analysis and simulation of optical in situ spectra Computers amp Geosciences 30 523 532 P Gege A Albert 2005 A tool for inverse modeling of spectral measurements in deep and shallow waters In L L Richardson and E F LeDrew Eds Remote Sensing of Aquatic Coastal Ecosystem Processes Kluwer book series Remote Sensing and Digital Image Proc essing accepted H R Gordon O B Brown M M Jacobs 1975 Computed Relationships between the In herent and Apparent Optical Properties of a Flat Homogeneous Ocean Applied Optics 14 417 427 H R Gordon 1989 Can the Lambert Beer law be applied to the diffuse attenuation coeffi cient of ocean water Limnol Oceanogr 34 8 1389 1409 T Heege
13. The below water calculation is done using eq 2 4 which requires additionally the parameters of the irradiance model Parameter beta Start gamma delta IV above water Sa Fig 6 1 Settings of the spectrum type Downwelling irradiance in the main window Left Drop down list with Downwelling irradiance selected as spectrum type and above water check box Parameter CF 48 C_ch C_d C_df C_g ak Eas EX cati 5 n T_W alpha beta gamma delta nue f RARA Value 0 300 0 0140 1 00 18 0 0 400 0 100 0 100 0 330 Center Parameter list for above water calculation Right Parameter list for in water calculation 58 WASI manual version 3 6 2 Irradiance reflectance The spectrum type Irradiance reflectance is activated by selecting this type in the main win dow from the drop down list above the Start button see Fig 6 2 left After the spectrum type is selected one of the two parameter lists shown in Fig 6 2 is displayed if the check box shallow water below the Start button is not marked the short list is displayed Fig 6 2 center otherwise the long list is displayed Fig 6 2 right Only 25 of the 36 parameters of the shallow water model can be displayed simultaneously for displaying the hidden parame ters the scroll bar to the right of the Value fields has to be moved up or downwards Parameter Yalue CIO jso cn pinza Ca jo cIa po C4 jo CIS pezzi
14. This eq was used for example by Lee et al 1998 for comparing simulated remote sensing reflectance spectra above and below the surface and calculating the conversion factors for which they found as typical values 1 0 1 0 Y nw 0 518 and o Q 1 562 The factor Q which is difficult to assess in practice can be avoided by replacing in the denominator Q Ris by R Cel aa 2 200 n GER WwW Ri The three equations 2 20a 2 20b and 2 20c are formally identical The first term on the right hand side of each equation describes reflection in the water the second at the surface Frequently the first term alone is called remote sensing reflectance e g Mobley 1994 In WASI the reflection at the surface is also included in the Rss definition It is calculated using eq 2 13a or 2 13b and can easily be excluded by setting the reflection factor o equal to Zero The factors o or and o are the reflection factors for Ea Lu and E respectively o depends on the radiance distribution and on surface waves Typical values are 0 02 to 0 03 for clear sky conditions and solar zenith angles below 45 and 0 05 to 0 07 for overcast skies Jerlov 1976 Preisendorfer and Mobley 1985 1986 It is set to o 0 03 by default o can either be calculated as a function of Oy using eq 2 12 or a constant value can be taken o is 18 WASI manual version 3 in the range of 0 50 to 0 57 with a value of 0 54 being typical Je
15. as described in section 4 1 3 Otherwise there are two options either the results from the previous fit are taken as start values for the subsequent fit or some start values are determined from the spectrum itself Which of these options is taken is specified individually for each spectrum type in the register card Settings for individual spectra types However determination of start values from the spectrum itself is not possible for every spectrum type If there is no register card for a specific spectrum type or if the reg ister card does not include a box labeled automatic determination of initial values the re sults from the previous fit are taken as start values Fig 4 8 shows as an example the register card for the spectrum type Irradiance reflec tance Automatic determination of initial values is activated i e the initial values are de termined from the spectra themselves The implemented algorithms for automatic determina tion and the relevant user interfaces are described in chapter 4 3 Optimisation of inversion 42 WASI manual version 3 E Settings for all spectrum types Initial values Final Fit Residual Weights Wavelength range from 400 to 800 nm Data interval fi channels Maximum number of iterations 1000 Settings for individual spectrum types Irradiance i Iradiance reflectan E Remote sensing reflectance d t Y Analytic estimate of C_L ias at 870 2 15 0 nm JV Analytic estimate of
16. forward calculation The abbreviation fwd in the heading of this column means value of forward calculation the heading s second line specifies the parameter name If more than one parameter is iterated similar columns are added In the example of Fig 5 3 11 values of the parameter nue 1 000 0 800 1 were taken for forward calculation Since the other model parameters were hold constant for the series of forward calculations these are not in cluded in this file their values are documented in the WASI INI file as indicated in the header information All subsequent columns summarize the results which were obtained by fitting the forward calculated spectra The column headed Inversion Iterations shows the required number of iterations of the fit routine see 4 2 4 The next column Residuum lists the residuals which are a measure for the correspondence between the forward calculated spectrum and the fit curve see 4 2 3 1 The next columns tabulate the resulting values of the fit parameters The abbreviation inv in their heading means value of inverse calculation the heading s second line specifies the parameter name Each parameter for which in the parameter list the corresponding check box Fit is marked with a hook is represented by such a column In the example of Fig 5 3 these are the parameters alpha beta gamma The specific results of the reconstruction mode are tabulated in the last colums These col umns
17. 2 3 Small particles Backscattering by small particles is calculated as the product of concentration Cs specific backscattering coefficient by s and a normalized scattering function A As The exponent n which determines the spectral shape depends on particle size distribution n is typically in the order of 1 Sathyendranath et al 1989 and by s in the order of 0 005 m g for As 500 nm Default values in WASI are n 1 and by s 0 0042 m g The empirical data given in Sathyendranath et al 1989 correspond to by s 0 015 m g however the cal culations in that paper were done using by s 0 0042 m g personal communication Sathyendranath 12 WASI manual version 3 2 3 Attenuation The diffuse attenuation coefficient of irradiance E is defined as K 1 E dE dz where z is the depth Similarly the attenuation coefficient of radiance L is defined as k 1 L dL dz Attenuation is an apparent optical property AOP and depends not only on the properties of the medium but additionally on the geometric distribution of the illuminating light field 2 3 1 Diffuse attenuation for downwelling irradiance The most important attenuation coefficient is Kg which describes attenuation for downwel ling vector irradiance Gordon 1989 has shown for Case 1 waters that the geometric struc ture of the light field can be corrected and the corrected attenuation coefficient U K is to a high degree of accura
18. A Morel 1980 In water and remote measurements of ocean colour Boundary Layer Mete orology 18 177 201 A Morel Gentili 1991 Diffuse reflectance of oceanic waters its dependence on Sun angle as influenced by the molecular scattering contribution Appl Optics 30 4427 4438 J L Mueller R W Austin 1995 Volume 25 of Ocean Optics Protocols for SeaWiFS Vali dation Revision 1 S B Hooker E R Firestone and J G Acker eds NASA Tech Memo 104566 NASA Goddard Space Flight Center Greenbelt Md J A Nelder R Mead 1965 A simplex method for function minimization Computer J 7 308 313 G Nyquist 1979 Investigation of some optical properties of seawater with special reference to lignin sulfonates and humic substances PhD Thesis G teborgs Universitet 200 p K F Palmer D Williams 1974 Optical properties of water in the near infrared J Optical Soc of America 64 1107 1110 N Pinnel 2005 Spectral discrimination of submerged macrophytes in lakes using hyper spectral remote sensing data Ph D thesis Limnological Institute of the Technical University Munich in preparation R W Preisendorfer C D Mobley 1985 Unpolarized irradiance reflectances and glitter patterns of random capillary waves on lakes and seas by Monte Carlo simulation NOAA Tech Memo ERL PMEL 63 Pacific Mar Environ Lab Seattle WA 141 pp R W Preisendorfer C D Mobley 1986 Albedos and glitter patterns of a
19. Ky k wA za N 2 19 Ana REO exp K 0 K 20 Zp The first term on the right hand side is the reflectance of a water layer of thickness zp the second term the contribution of the bottom Bottom reflectance R A is calculated using eq 2 22 Ka Kuw and kug account for attenuation within the water layer and are calculated using WASI manual version 3 17 eqs 2 5 2 9 and 2 10 respectively The empirical constants are set to Ars 1 1576 and Ars 1 0389 according to Albert and Mobley 2003 and cannot be changed by the user 2 6 3 Above the surface The remote sensing reflectance above the water surface is related to radiance and irradiance spectra in water as follows POLL e R A L A Ny OL L A Ny 0 L A E A E A E A E A o E A RA Eq 2 29 was used to replace L A and eq 2 24 to express Eq A in terms of Ey A and Eu A The first term on the right hand side describes reflection in the water the second at the surface By using Lu A Eu A Q multiplying numerator and denominator of the first term with R A E A where R A Eu A Ea A and expressing the second term as R s A according to eq 2 13a the following equation is obtained 1 0 1 0 R RA 2 20a nm Qs RA OT WwW R A Replacing R A by Rys A according to eq 2 17a yields the following relationship Pe ONE Oi O aos 2 20b n l 0 Q RLA i WwW R A
20. Sini ian 80 Appendix 5 Input spectra a silice 81 Appendix 6 SPETTA PES ss tai id 82 WASI manual version 3 5 1 Introduction The Water Colour Simulator WASI is a software tool for analyzing and simulating the most common types of spectra that are measured by ship borne optical instruments It summarises the experiences from 15 years of experimental and theoretical work performed mainly at Lake Constance by DLR s Inland Water Group Early versions were presented and distributed on CD ROM on conferences Gege 2001a 2001b The deep water version is described in Gege 2004 the shallow water version in Gege and Albert 2005 The spectrum types and major calculation options are listed in Table 1 1 A more comprehen sive summary including the fit parameters is given in Appendix 6 WASI can be used to gen erate the spectra of Table 1 1 Forward mode or to analyze such spectra Inverse mode Both modes can be combined effectively for performing sensitivity studies Reconstruction mode The three modes of operation are described in chapter 3 forward mode chapter 4 inverse mode and chapter 5 reconstruction mode Model options are depicted in chapter 6 program options in chapter 7 The installation of WASI is described in Appendix 1 Spectrum type Model options Absorption Of water constituents Of natural water bodies Attenuation For downwelling irradiance Specular reflectance Wavelength dependent Constant Irradian
21. absolute differences logarithmic g In m In f 6 relative differences logarithmic g 11 In f In m Table 4 1 Methods for calculating residuals g weight of channel i m measurement of channel i f fit of channel i 4 2 4 Definition of fit region and number of iterations Which part of the spectrum is fitted and which data interval is taken for calculating the residuals is specified in the Final fit register card of the Fit tuning menu as shown in Fig 4 7 The pop up window is accessed from the menu bar via Options Invers calculation Fit tuning see Fig 7 1 The maximum number of iterations forces the fit routine to stop the number should be set high enough that a forced stop is exceptional Settings for all spectrum types Initial values Final Fit Residual Weights Wavelength range from 400 to 800 nm Data interval fi channels Maximum number of iterations 1000 Fig 4 7 The register card Final fit of the pop up window Fit tuning WASI manual version 3 41 4 3 Inversion of a series of spectra 4 3 1 Selection of spectra A series of spectra is selected for inversion as follows e the path of the input spectra is set in the menu Options directories field Read spec tra e the path for storing the results is set in the menu Options directories field Save re sults input line Inversion e reading of spectra is activated in the menu Options Invers
22. absorp tion If pure water absorption is included check box is marked with a hook the absorption spectrum of the water body is calculated using eq 2 3 Otherwise no hook absorption of the water constituents alone is calculated using eq 2 1 Parameters of the absorption model are the concentrations of the 6 phytoplankton classes C C i i 0 1 5 the concentration of non chlorophyllous particles X C_X Gelbstoff concentration Y C_Y and eventually Gelbstoff exponent S and water temperature T T_W T is model parameter if pure water absorption is included it is not required for calculating absorption of the water constituents Whether S is model parameter or not depends on the choice of the specific Gelbstoff absorption spectrum ay A It can either be read from file or it can be calculated during run time using eq 2 2 The selection is done in the Absorption register card of the pop up window Model options which is shown in Fig 6 6 The corresponding boxes exponential function and specific absorption from file are exclusive i e exact one of both is marked with a hook The input field Normalize absorption spectrum at nm specifies the wavelength o where ay A is normalised 7 Most spectrum types included in WASI depend on the absorption of the water body For all types which use absorption implicitely the absorption spectrum includes pure water i e absorption is calculated accordi
23. calculation Data in out field Input mark the box read spectra with a hook e the file characteristics of the input spectra are set in the menu Options Invers calcula tion Data in out field Input specify file extension number of header lines in the files column of x values column of y values e saving of fit spectra is activated or deactivated in the menu Options Invers calculation Data in out field Output select or deselect the box save all spectra As a result of inversion the fit results are stored in the table FITPARS TXT This table is gen erated at the specified path irrespective whether saving of spectra is activated or deactivated If saving of spectra is activated for each input spectrum a file is generated which lists the spectral values of input and fit curve The file names are identical to the input file names but the file extensions are set to INV 4 3 2 Definition of initial values When a series of spectra shall be inverted the initial values can either be chosen identically for every spectrum or they are determined individually The selection of the method is done in the Initial values register card of the pop up window Fit tuning menu as shown in Fig 4 8 The pop up window is accessed from the menu bar via Options Invers calculation Fit tuning If the box identical for all spectra is marked with a hook the initial values for every spec trum are taken from the parameter list
24. domains Limnol Oceanogr 26 43 53 H Buiteveld J H M Hakvoort M Donze 1994 The optical properties of pure water SPIE Vol 2258 Ocean Optics XII 174 183 M S Caceci W P Cacheris 1984 Fitting Curves to Data Byte May 1984 340 362 K L Carder G R Harvey P B Ortner 1989 Marine humic and fulvic acids their effects on remote sensing of ocean chlorophyll Limnol Oceanogr 34 68 81 C Cox W Munk 1954 Statistics of the sea surface derived from sun glitter J Marine Res 13 198 227 C Cox W Munk 1956 Slopes of the sea surface deduced from photographs of sun glitter Bulletin Scripps Inst Oceanogr Univ Calif 6 401 488 P Gege 1994 Gew sseranalyse mit passiver Fernerkundung Ein Modell zur Interpretation optischer Spektralmessungen PhD thesis DLR Forschungsbericht 94 15 171 p P Gege 1995 Water analysis by remote sensing A model for the interpretation of optical spectral measurements Technical Translation ESA TT 1324 231 pp July 1995 P Gege 1998a Correction of specular reflections at the water surface Ocean Optics XIV November 10 13 1998 Kailua Kona Hawaii USA Conference Papers Vol 2 P Gege 1998b Characterization of the phytoplankton in Lake Constance for classification by remote sensing Arch Hydrobiol Spec Issues Advanc Limnol 53 p 179 193 Dezember 1998 Lake Constance Characterization of an ecosystem in transition 70 WASI manual version 3
25. interface The appearance of WASI s graphical user interface GUI depends slightly on the spectrum type Fig 3 1 shows the GUI at the example of the spectrum type Remote sensing reflec tance The GUI consists of 8 elements 1 Drop down list for selecting the spectrum type The user selects one of the spectrum types from Table 1 1 If the spectrum type is changed the parameter list 3 is updated in the way that only the parameters relevant for the selected type are displayed and accordingly the model options 5 are updated 2 Check box for switching between forward and inverse mode In the forward mode this box is not checked wast Water color simule_or Dj xj File Display Options Help Parameter Value cia 2 00 5 A i Remote sensing reflectance sr 1 simulated spectra qn fo qe fo ca fo 0 014 4 fo CIS fo 0 012 CL E 00 CS fo 0 010 CX fo CY fo 300 0 0080 S 6 fo 0140 pren n fo CZ Tw fia 0 0 0060 A N Q ls UU n 0 0040 sigma_L fo 01000 apha 0 200 beta fo 109 400 500 600 700 800 gemme fo 100 wavelength run alta fo Remote sensing reflectance nz SS n TENS Parameter from to steps log a pha n my f 7 E NARA E fori i Start T invert spectra C10 y 1 8 00 le r gomme TT shallow wat n fea z F TERRAS none y 0100 fi fio n TT wavelength dependent s lections z TT calculate sigma_L from viewing angle Fig 3 1 Graphical user interface of the forward mode 1 Drop down
26. irradiance in air Ea through ESO 1 0 Ed 07 Ey A 2 24 o is the reflection factor for downwelling irradiance in air o for upwelling irradiance in wa ter and E is the upwelling irradiance in water Using the irradiance reflectance R E Eq yields the following expression l o E 1 07 RA EL 2 25 This equation is used in WASI for calculating Eg A R A is calculated using eq 2 14 Ea A can either be calculated according to eq 2 23 or a measured spectrum can be taken Making use of measurements is useful for reducing the number of fit parameters when up welling radiance spectra are inverted Default values of the reflection factors are o 0 03 and o 0 54 Downwelling irradiance below the surface in shallow water Eg A is also calculated using eq 2 25 but using R A instead of R A WASI manual version 3 23 2 9 Sky radiance The same parameterization as for Eq A is also implemented for L A EXA 0 ta B OA y QUA 8 te A lt Eo A 2 26 The functions Eo A taQ O A 9 A Am and tc A are those of eq 2 23 Parameters of Ls A are the weights a B y which represent the relative intensities of the four above mentioned light sources for a radiance sensor and the exponent v This model of L A has been included for modeling specular reflection at the water surface Its usefulness has been demonstrated Gege 1998b Capillary waves at the wa
27. list of Fig 4 1 For the example of Fig 4 1 these are the parameters of the remote sensing reflectance model The acronym a check box and a value is depicted for each parameter The check box Fit is used for selecting whether the parameter is treated as constant no hook or as fit parameter hook during inversion In the example of Fig 4 1 the parameters C 0 C_L and sigma L will be fitted while all other parameters will be kept con stant The entry in the Value field has a different meaning before inversion is started and after it is finished Before the initial values are displayed afterwards the fit results are shown More details about the fit parameters contains the pop up window Fit parameters Fig 4 4 It is accessed from the menu bar via Options Inverse calculation Fit parameters see Fig 7 1 It has six register cards which sort the parameters according to the categories Illumina tion Surface Reflectance Algae classes Shallow water and Miscellaneous Fig 4 4 shows as example the register card Miscellaneous WASI manual version 3 39 For each parameter the Fit parameters pop up window displays a description the physical units and the acronym furtheron it shows a check box for determining whether the parameter is fit variable or constant and it specifies the start value and minimum and maxium values that are allowed for the fit routine The user can change the settings of the Fit check box and
28. reflectance of shallow water Inversion of a shallow water irradiance reflectance spectrum determines in addition to the parameters of deep water several parameters related to the bottom bottom depth zg and areal fractions f of up to 6 bottom albedo spectra The analytic function R 2 used for inversion is given by eq 2 16 Since it consists of as much as 21 parameters it is very important to ini tialise the fit parameters with realistic values Otherwise the probability is large that the Sim plex gets lost in the high dimensional search space up to 22 dimensions and hence the fit provides completely wrong results Albert 2004 developed the well working methodology of Table 4 3 to increase step by step the number of estimated parameters and he implemented it in WASI 48 WASI manual version 3 Step determine algorithm Procedure Determine a first estimate of zg from an analytic equation at a wavelength interval in the red ee ee Determine a first estimate of C and Cs from an analytic equation at a wavelength in the Infrared using the zg value from step 1 awcl A Estimate the total absorption spectrum of all water constituents for intervals a wavelength interval in the visible using nested intervals The required values of Zg C and Cs are taken from steps 1 and 2 Bed Determine a first estimate of Co and Y by fitting the spectrum awc A of step 3 e The eA fractions of all bottom types are set equal N number of considered bottom
29. s major optical classes cryptophyta type L cryptophyta type H diatoms dinoflagellates and green algae Gege 1994 1995 1998b The spectrum ao A labeled phytoplankton in Fig 2 1 is a weighted sum of these five spectra and represents a mixture which can be considered as typical for Lake Constance It was calculated by Heege 2000 using phytoplankton absorp tion spectra and pigment data from 32 days in 1990 and 1991 and he validated it using 139 irradiance reflectance and 278 attenuation measurements from 1990 to 1996 Non chlorophyllous particles Absorption is calculated as the product of concentration X and specific absorption ax A The spectrum ax A provided with WASI is shown in Fig 2 2 left It is taken from Prieur and Sathyendranath 1981 and normalized to 1 at the refer ence wavelength Ao 440 nm Gelbstoff dissolved organic matter Gelbstoff absorption is the product of concentration Y and specific absorption ay A The spectrum ay A can either be read from file or calculated using the usual exponential approximation Nyquist 1979 Bricaud et al 1981 ay A exp S A Ao 2 2 where S denotes the spectral slope and Ao is a reference wavelength with ay normalized to 1 Default values are A 440 nm and S 0 014 nm which can be considered representative of a great variety of water types Bricaud et al 1981 Carder et al 1989 Derived from above water re
30. the Options menu see Fig 7 1 Four yes no decisions can be made e The check box save INI file automatically selects whether or not the file WASI INI is updated automatically at program termination e The check box multiply spectrum Ed with factor allows to multiply automatically each downwelling irradiance spectrum Eq A which is read from file with a factor whose value 68 WASI manual version 3 de General options Ox TT multiply spectrum Ed with factor 3 1 416 Y multiply spectrum EO with factor jo 0000 T multiply spectrum Ars with factor 3 1 416 casi Fig 7 4 The pop up window General options is set in the adjacent input field This is useful if E4 A was measured as radiance upwell ing from a horizontally oriented diffuse reflecting panel Lup A In this case it is Eg A x P Lip A where p is the panel s reflectance The conversion factor is set to n 3 1416 by default which corresponds to p 1 The check box multiply spectrum EO with factor allows to multiply automatically the spectrum of the extraterrestrial solar irradiance Eo A with a conversion factor This is useful if the spectrum Eo A is given in other units than the other irradiance spectra For example the spectrum Eo A provided with WASI is given in units of JW cm sr while the common units in WASI are mW m sr This leads to a conversion factor of 0 1 The check box multiply spectrum Rrs with factor allows to mul
31. without user interaction and finally WASI is terminated automatically after the calculations are finished This mode of operation is useful for combining WASI with another program For example WASI has been combined with a radiative transfer simulation program for the atmosphere 6S to estimate the influence of errors in atmospheric correction on the retrieval of phytoplankton Gelbstoff and suspended matter from MERIS and MODIS data Pyh lahti and Gege 2001 WASI manual version 3 7 2 Models 2 1 Absorption 2 1 1 Water constituents Absorption of a mixture of water constituents is the sum of the components absorption coef ficients ae SC 220 X az A Y ay 0 Q 1 i 0 A denotes wavelength Three groups of absorbing water constituents are considered phyto plankton non chlorophyllous particles and Gelbstoff Phytoplankton The high number of species that occur in natural waters causes some vari ability in phytoplankton absorption properties This is accounted for by the inclusion of 6 spe cific absorption spectra a A If no phytoplankton classification is performed the spectrum ao A is selected to represent the specific absorption of phytoplankton C indicates pigment concentration where pigment is the sum of chlorophyll a and phaeophytin a The default spectra provided with WASI are shown in Fig 2 1 They are based on measure ments at Lake Constance The five spectra a A as A represent the lake
32. 0 constant 0 30 0 30 0 20 0 20 o oO 0 10 0 10 0 0 0 00 200 500 600 700 800 400 500 600 700 800 Wavelength nm Wavelength nm FIG24A 4 6 2005 FIG24B 4 6 2005 0 40 0 40 Chara aspera 0 30 0 30 0 20 0 20 o o 0 10 0 10 0 500 600 700 800 0 500 600 700 800 Wavelength nm Wavelength nm FIG24C 4 6 2005 FIG24D 4 6 2005 0 40 0 40 Potamogeton perfoliatus Potamogeton pectinatus 0 30 0 30 2 e 0 20 0 20 d o 0 10 0 10 0 0950 500 600 700 800 0 000 500 600 700 800 Wavelength nm Wavelength nm FIG24F 4 6 2005 FIG24E 4 6 2005 Fig 2 4 Albedo spectra of 6 bottom types WASI manual version 3 21 2 8 Downwelling irradiance 2 8 1 Above water surface An analytic model of the downwelling irradiance spectrum E A with only few parameters was developed by Gege 1994 1995 It fits to measured spectra with a high degree of accu racy average rms error of 0 1 The radiation illuminating the water surface is parameter ized as the sum of four spectrally different components 1 the direct solar radiation 2 the blue sky Rayleigh scattering 3 radiation scattered by aerosols Mie scattering and 4 clouds Each component is expressed in terms of a wavelength dependent fraction of the ex traterrestrial solar irradiance Eo A Ea a ta B AAR y gt A A 8 to Eo 2 23 The four functions t A ta A AR A Am tc 1 are transmission spectra which spectrally charac
33. 000 00500 00020 05460 31800 31800 31800 31800 31800 31800 000000kr000o0oo Model parameters forward default 10 0 T_WO nW Lambda_0 Lambda_L Lambda_S bbW500 bbL_A bbL_B bbL_norm bbs_norm sigma_Eu sigma_Ed sigma_Lu dynamics noise KO BRDF 0 BRDF 1 BRDF 2 BRDF 3 BRDF 4 BRDF 5 ooooo 0 500 0 0 500 0 0140 1 00 18 0 5 00 0 0200 200 200 200 200 0 200 200 200 200 330 0 100 30 0 ae ES ooooo start 2303 39 oJoooo 0 393 0 0140 0 18 0 5 00 0 0201 0 200 0 100 0 100 0 0 200 100 100 0 0 330 0 3 00 47 0 ooo fit of Ed fit of R and Rrs in IR region fit of R and Rrs in UV region fit of R and Rrs fit of a shallow water fit of R and Rrs in IR region shallow water fit of R and Rrs in UV region shallow water fit of R and Rrs shallow water LambdaLf wavelengths for C_L and f initialisation dLambdaLf wavelength intervals of LambdaLf LambdaLsh wavelengths for C_L initialisation shallow water dLambdaLsh wavelength interval of LambdaLsh shallow water LambdaCY wavelengths for C 0 and C_Y initialisation dLambdaCY wavelength intervals of LambdaCY LambdazB wavelength for zB initialisation shallow water dLambdazB wavelength interval of LambdazB shallow water shallow water shallow water shallow water zB_inimin CL_inimin cO_inimin CY_inimin zB minimum during initial value determinat
34. 470 nm e 2 should be chosen below 500 nm e 3 should be chosen below 550 nm In each case preference should be given to shorter wavelengths A good choice is Az Ao since S errors don t affect Gelbstoff absorption at Ao For no separate wavelength must be chosen it can be set A2 Consequently selection of only two wavelengths is implemented in WASI Their defaults are A 413 nm A2 440 nm Steps 3 and 4 These steps were suggested by Gege 2002 The newly developed steps 1 and 2 make them now unnecessary in most cases but they are useful under certain conditions for instance if no suitable infrared channel is available for accurate determination of Cr or Cs or if S is fit parameter Steps 3 and 4 improve the estimates for Co Cr Cs and Y by including additional spectral information and a start value of S can be determined Wavelength range data interval and maximum number of iterations for the fits of steps 3 and 4 are specified in the Pre fit frames of the register card Irradiance reflectance of Fig 4 9 If max Itera tions is set to 0 or 1 the respective fit is not performed Step 5 Wavelength range data interval and maximum number of iterations for the fit of step 5 are specified in the Final fit register card of the Fit tuning pop up window see Fig 4 7 The maximum number of iterations forces the fit routine to stop the number should be set high enough that a forced stop is exceptional 4 4 2 Irradiance
35. 7 nm Quickenden amp Irvin 1980 228 390 nm Interpolation between Quickenden amp Irvin 1980 and Buiteveld et al 1994 391 787 nm Buiteveld et al 1994 788 874 nm own unpublished measurements on UV treated pure water of 20 C 875 2000 nm Palmer amp Williams 1974 27 C For daw A dT a spectrum is provided which was measured by Gege unpublished data 10 WASI manual version 3 2 2 Backscattering Backscattering by of a water body is the sum of backscattering by pure water index W and suspended matter For the latter a distinction between large 25 um index L and small lt 5 um index S particles is made Thus the following parameterization is chosen by 2 br w 2 CL bp1 bL A Cg bo s A As 2 4 2 2 1 Pure water For pure water the empirical relation of Morel 1974 is used bvw A bi A A1 7 The specific backscattering coefficient b depends on salinity It is b 0 00111 m for fresh water and b 0 00144 m for oceanic water with a salinity of 35 38 o when A 500 nm is chosen as reference wavelength 2 2 2 Large particles Backscattering by large particles is calculated as the product of concentration Cr specific backscattering coefficient bp1 and normalized scattering function br A The user has se veral options for calculation e C can be treated either as an independent parameter or Cr Co can be set where Co is the concentration of phytoplankton c
36. C O and C_Y afans 4f50 nm andfss0o f50 nm Pre fit of C_LL C_Y from 760 to 300 nm steps fio nm max Iterations 100 Pre fit of C O C_Y from 380 to 450 nm steps fio nm max Iterations 100 Fig 4 8 The pop up window Fit tuning with the opened register cards Initial values and Irradi ance reflectance of deep water WASI manual version 3 43 4 4 Optimisation of inversion 4 4 1 Irradiance reflectance of deep water The most important parameters that can be determined from irradiance reflectance spectra of deep water are the concentrations of phytoplankton Gelbstoff and suspended matter A study has been performed which investigated their retrieval sensitivity to errors Gege 2002 It re sulted a very small sensitivity for suspended matter some sensitivity for Gelbstoff but very high sensitivity for phytoplankton The study suggested a procedure for initial values deter mination which has been optimised by further simulations Finally the 5 steps procedure summarised in Table 4 2 was implemented in WASI The user can fine tune the procedure in the Fit tuning pop up window which is shown in Fig 4 8 It is accessed from the menu bar via Options Invers calculation Fit tuning Step determine algorithm Procedure 1 CL Cs analytical Determine a first estimate of C and Cs from an analytic equation at a wavelength in the Infrared 2 Y Co analytical Determine a first estimate o
37. CL hi cs jo CX jf Parameter Value er 0 250 cto Ho g jooo ci o n jo Cr2 o TW iso CR IN Foo C 4 jo sigma_L fo CI jo A oso Cul hi ARE fo 100 ESS jo gamma fo 100 cx fo Nes fo cy jozs0 me Iradiance reflectance KEJ sE Dos n jo beta jo100 sun fazio delta jo IV shallow water E 7 00 i o Fig 6 2 Settings of the spectrum type Irradiance reflectance in the main window Left Drop down list with Irradiance reflectance selected as spectrum type Center Parameter list of the deep water model Right Parameter list of the shallow water model Irradiance reflectance spectra R A are calculated using the Gordon algorithm see eq 2 14a or the Prieur algorithm see eq 2 14b Both algorithms parameterize R A as a function of absorption and backscattering and thus require as parameters the concentrations of the differ WASI manual version 3 59 RIE ce Surface Bottom R_rs irradiance Absorption Backscattering R Algorithm R f bb a bb Gordon et al 1975 R f bb a Prieur 1976 f factor f constant Gordon et al 1975 f 0 975 0 629 cos sun_w Kirk 1984 f 0 6279 0 2227n 0 0513n 2 0 3119 0 2465n cos sun Morel amp Gentili 1991 f 0 5 0 5 cos sun_w Sathyendranath amp Platt 1997 f p1 1 p2 x p3 x 2 p4 x 3 1 p5 cos sun_w Albert amp Mobley 2003 sun sun zenith angle above wa
38. The Water Colour Simulator WASI User manual for version 3 Peter Gege 2 WASI manual version 3 This document can be cited as follows Gege P 2005 The Water Colour Simulator WASI User manual for version 3 DLR Internal Report IB 564 01 05 83 pp The actual version of the program and of this manual can be downloaded from the following ftp site Server ftp dfd dlr de User anonymous Directory pub WASI Copyright The software was developed by Peter Gege DLR Remote Sensing Technology Institute Oberpfaffenhofen D 82234 Wessling Germany He owns all copyrights WASI version 3 is a public domain software and can be used free of charge There is no warranty in case of errors There is no user support Commercial distribution is not allowed Commercial use is not allowed unless an agreement with the author is made Publication of results obtained from using the software requires to quote the use of WASI in the text cite a recent publication about WASI inform Peter Gege via email send Peter Gege a copy of the paper as file or paper hardcopy VVVV WASI version 3 Date 26 August 2005 Author Peter Gege Contact peter gege dlr de WASI manual version 3 3 Table of contents DTCC ON A O O ite 5 2 Models i ON 7 PN ADITO AEE AAE i 7 Dl Ae Water COMSUTUCTIES toa tl 7 2 12 Natutal Water canile awed 9 2 2 O eee 10 224 URS WAT O 10 233 Large PAS agile 10 223 5mall partici isa iio da 11 2 3 A O
39. The downwelling irradiance above the water surface Eq A is calculated according to eq 2 1 as a weighted sum of 4 spectra Since the curve forms of these spectra are quite differ ent it is not possible to obtain similar sum curves by using rather different sets of weights In other words the solution of the inversion is unequivocal Consequently no fine tunig of the inversion scheme is necessary The downwelling irradiance below the water surface Eg A is calculated according to eq 2 4 using the above water spectrum E A For Ea A either the parameterization of eq 2 1 can be chosen or a measured spectrum can be taken The selection is done in the register card Irradiance of the pop up window Fit tuning which is shown in Fig 4 12 It is accessed from the menu bar via Options Invers calculation Fit tuning Settings for individual spectrum types Subsurface downwelling irradiance TT use Ed measurement no fit of Ed only of A File wasi data demo E_down R2A C1 Header lines 0 Column fi Y Column 2 Fig 4 12 The register card Irradiance of the pop up window Fit tuning Downwelling irradiance spectra below the water surface are not very different from those above the surface i e the curve form of Eg A depends much more on the parameters of Ea A than on those of R A Hence small errors of Eg A cause large errors of the retrieved parameters of R A Thus the option of using Eq A measurem
40. ance Parameter Fit Value bet 0 0500 Start V invert spectra eta l V batch mode I read from file delta V above water KULCE v gamma Sv 0 200 nue Fig 5 1 Example of a parameter list Top values of forward modeling bottom start values of inversion By clicking the invert spectra check box the user can quickly switch between the forward and inverse values Fig 5 1 shows as an example the parameter list of the downwelling irradi ance model above the water surface On top the forward values are shown on bottom the start values of the inverse mode The forward and inverse values are chosen identical for two pa rameters alpha delta and differently for three other parameters beta gamma nue Fig 5 1 is an example how to study propagation of model errors A different value of the pa rameter nue is chosen for forward and inverse calculation and nue is not fitted This is an efficient way to introduce a well defined model error the error of the inverse model is attrib uted to the parameter nue and the error is given quantitatively as nue nue 0 1 54 WASI manual version 3 Due to the wrong nue value the fit cannot find the correct values of the fit parameters alpha beta gamma The errors of these parameters depend only on the nue error In this way the sensitivity of alpha beta gamma on nue errors can be studied Systematic investigations of such error propagation are the basis of sen
41. ater colour simulator WASI INI version 25 August 2005 WASI EXE Version 3 Latest update 11 June 2005 Spectrum of x values d wasi data ch_meris prn 3 Header lines Column with x values E0 Spectrum of solar constant d wasi data E0_sun prn 1 Header lines Column with x values Column with y values N Il tA Spectrum of transmission of atmosphere d wasi data ta t 7 Header lines Column with x values Column with y values 2 tc Spectrum of transmission of clouds d wasi data tc t 7 Header lines Column with x values 2 Column with y values aW Absorption of water d wasi data water a 0 Header lines Column with x values 2 Column with y values dadT Temperature dependence of water absorption d wasi data dawdt prn 0 Header lines Column with x values 2 Column with y values aP 0 Specific absorption spectrum of phytoplankton class no 0 d wasi data phyto a 2 Header lines Column with x values 2 Column with y values aP 1 Specific absorption spectrum of phytoplankton class no 1 d wasi data cry lo a 0 Header lines Column with x values 2 Column with y values aP 2 Specific absorption spectrum of phytoplankton class no 2 d wasi data cry hi a 1 Header lines Column with x values Column with y values N Il aP 3 Specific absorption spectrum of phytoplankton class no 3 d wasi data dia a 0 Header lines Column with x values 2 Col
42. ce reflectance For deep water For shallow water Remote sensing reflectance Below surface for deep water Below surface for shallow water Above surface for deep water Above surface for shallow water Bottom reflectance For irradiance sensors For radiance sensors Downwelling irradiance Below surface Upwelling radiance Below surface Above surface Table 1 1 Spectrum types and major model options Basis of all calculations are analytical models with experimentally easily accessible parame ters Most of them are well established among ocean colour modelers and experimentally and theoretically validated They are described in detail in chapter 2 the corresponding refer ences are cited in chapter 8 The program consists of an executable file WASI EXE an initialisation file WASLINI and 28 input spectra WASI INI is an ASCII file that comprises all paths and file names of the data files parameter values constants and user settings An example listening is given in Ap pendix 2 Much effort was spent to make the user interface as clear as possible Since most 6 WASI manual version 3 settings in the different pop up windows are self explanatory not every detail is described in this manual Alternatively to the usual interactive mode of operation WASI can also be started from an other program through the command WASI INI_File In this case the file INI_File is read instead of WASI INI then calculation is started automatically
43. ck box is marked the remote sensing reflectance will be cal culated for a sensor above the water surface when the hook is removed calculation is per formed for below the surface 2 Wavelength dependent surface reflections Since the check box is unmarked the surface reflections will be treated as constant RA 01 r according to chapter 2 5 3 Calculate sigma L from viewing angle Since the check box is unmarked the reflectance factor for sky radiance cr is treated as a parameter that can be defined by the user Oth erwise OL would be calculated from the viewing angle using eq 2 18 3 2 3 Parameter selection AIl model parameters are read during program start from the WASI INI file The parameters which are relevant for the actual spectrum type are listed at the left side of the main window in Fig 3 1 This list can be edited 3 2 4 Calculation options Several calculation settings are made in the pop up window Forward calculation settings This pop up window is accessed from the menu bar via Options Forward calculation see Fig 7 1 and displayed in Fig 3 2 Forward calculation settings mr d wasi data ch_meris prn Fig 3 2 The pop up window Forward calculation settings 28 WASI manual version 3 Wavelength interval The wavelength range and the data interval of the calculated spectra can be selected in two ways e For non equidistant intervals e g if calculations should be per
44. cy an inherent optical property which can be related to absorption a A and backscattering by A The correction factor is the ratio of downwelling vector irradiance to downwelling scalar irradiance E E 4 Hais also called the average cosine of the downwelling light field since it were cos O m if there were no atmosphere with O n the sun zenith angle in water Gordon showed by Monte Carlo simulations that for sun zenith angles below 60 the difference between HU and cos6 is usually below 3 near the water surface Thus the following parameterization of K4 is adapted from Gordon 1989 a b A LOS cos 0 2 5 a A is calculated according to eq 2 3 by A using eq 2 4 The coefficient K depends on the scattering phase function Gordon 1989 determined a value of xo 1 0395 from Monte Carlo simulations in Case 1 waters Albert and Mobley 2003 found a value of ko 1 0546 from simulations in Case 2 waters using the radiative transfer program Hydrolight Mobley et al 1993 Some authors use eq 2 5 with xo 1 Sathyendranath and Platt 1988 1997 Gordon et al 1975 In WASI io is read from the WASI INI file the default value is 1 0546 2 3 2 Diffuse attenuation for upwelling irradiance For upwelling irradiance two attenuation coefficients are used Kyw for the radiation backscat tered in the water and Kus for the radiation reflected from the bottom The following parame terization is adopted from Alb
45. ding input field is not displayed Save spectra Automatic saving of calculated spectra is activated by a hook in the check box save all spectra The directory is selected in the Directories window see section 7 1 Fig 7 2 The calculated spectrum is stored in ASCII format as file B1 FWD Note If a file with the name B1 FWD already exists it will be overwritten without warning Two additional files are created automatically in the same directory as the spectrum First a copy of the initialisa tion file WASI INI containing the actual parameter settings It documents the data and pa rameters used for calculation Second a file CHANGES TXT which can be ignored it is relevant only if a series of spectra is calculated The check box if N lt 22 save all spectra in a single table is not relevant for calculating a single spectrum 3 2 5 Start calculation Calculation is started by pressing the Start button O in Fig 3 1 After calculation the resulting curve is plotted in the main window 8 in Fig 3 1 and stored automatically if spectra saving is activated in the pop up window Forward calculation set tings see section 7 1 Fig 7 2 3 Spectral weighting using sensor specific response functions is not supported WASI manual version 3 29 3 2 6 Example An example of a spectrum calculated in the forward mode is given in Fig 3 3 The spectrum type is irradiance reflectance in deep water The values of the model pa
46. e Load INI file Save INI file Exit Load spectrum EN x Suchen in amp LOE e ex FI Verlaut a Desktop A Eigene Dateien Arbeitsplatz Netzwerkumg Dateiname BI v Dateityp fwd X Abbrechen Ls Fig 4 2 Loading a single spectrum for inversion Top Menu bar and pull down menu File Bottom Pop up window for selecting the file After the spectrum is loaded it is automatically displayed in the plot window of Fig 4 1 and the program mode is automatically set to single spectrum mode 1 e the check boxes of Fig 4 1 are set as shown in Fig 4 3 No user action is required 38 WASI manual version 3 invert spectra batch mode JV read from file Fig 4 3 Check box settings of the single spectrum mode 4 2 2 Definition of initial values Initial values of each fit parameter are read from the WASI INI file The user can change them either in the parameter list of Fig 4 1 or in the Fit parameters pop up window which is shown in Fig 4 4 FI Fit parameters E 10 x Parameter Units Symbol Fit Start Hin Max Water temperature E TW n 18 0 0 35 0 Q factor sr Q 5 00 0 500 fi 0 0 reflection factor 1 sigma L IT 0 0201 o 0 500 Default values Fig 4 4 The pop up window Fit parameters with the register card Miscellaneous Only the parameters relevant for the selected spectrum type are displayed in the main window in the parameter
47. e method from the SeaWiFS protocols Mueller and Austin 1995 which is widely used in optical oceanography leads to rms errors of the corrected water leaving radiance as large as 90 under typical field condi tions Toole et al 2000 Thus WASI offers different methods The radiance reflected from the surface L A is a fraction or of sky radiance L A LA oL L 2 11 L A is the average radiance of that area of the sky that is specularly reflected into the sensor It can be imported from file or calculated using eq 2 26 or is the Fresnel reflectance and depends on the angle of reflection The value can either be specified by the user or it can be calculated from the viewing angle 6 using the Fresnel equation for unpolarized light Jerlov 1976 o L sin 0 0 tan 0 0 2 12 E 2 sin2 0 0 tan 0 0 0 is the angle of refraction which is related to Oy by Snell s law nw sin0 sin0y where nw 1 33 is the refractive index of water For viewing angles near nadir o 0 02 The ratio of the radiance reflected from the water surface to the downwelling irradiance Re A Le GL aUL 2 13a E A E A is called specular reflectance Eq A and L A can either be imported from file or one or both can be calculated using eq 2 23 or 2 26 If the wavelength independent model of surface reflection is chosen it is Rw OL 2 13b rs T Toole et al 2000 showed that R
48. ears when the thematic area Display is selected in the Options menu see Fig 7 1 8 Display options ojx xmin 380 xmax 805 ymin E ymar fi 38 MW autoscale RW display filename MW display grid TT display path TT display subgrid Background Color a sa cr Fig 7 3 The popup window Display options Range of x and y values The range of the displayed x values is defined by the values in the fields xmin and xmax The range of the displayed y values is either defined by the values in the fields ymin and ymax or adjusted automatically to the actual spectrum if the check box autoscale is marked with a hook In the latter case the input fields for ymin and ymax are deactivated By default the autoscale option is activated Spectrum information On top right of the plot window the file name of the actual spectrum can be displayed either excluding or including the path The selection is made using the check boxes display filename and display path Layout The spectra can be plotted either on a blank background or on a coarse or fine grid The selection is made using the check boxes display grid and display subgrid The back ground colour can be changed by pressing the button and selecting the desired colour in the upcoming popup window not shown 7 3 General options The pop up window for some general settings is shown in Fig 7 4 It appears when the the matic area General is selected in
49. ed at the interface by Fresnel reflection factor 1 o71 0 and refraction flux dilution by widen ing of the solid angle factor 1 ny The second term are specular reflections of downwelling radiance at the surface Eq 2 28 is valid for a flat surface i e without waves Integration of eq 2 28 over the upper hemisphere yields eq 2 24 Omitting for simplicity the symbol 6 and using the more general model 2 11 for the radi ance reflected from the surface the following equation is obtained ei 2 29 n WwW L A This equation is used in WASI for calculating L A Lu A is calculated using eq 2 27 The sky radiance L A can either be calculated using eq 2 26 or a measured spectrum can be imported from file The reflection factor for upwelling radiance is set to or 0 02 by default This value which is valid for a nadir looking sensor can be changed in the WASI INI file The reflection factor for downwelling radiance o can either be calculated using the Fresnel equation 2 12 or it can be set constant The default o 0 02 is valid for a nadir looking sensor By setting o 0 the water leaving radiance can be calculated Furtheron nw 1 33 is set as default WASI manual version 3 25 3 Forward mode The forward mode allows to calculate a single spectrum or a series of spectra according to user specified parameter settings The supported spectrum types are listed in Table 1 1 3 1 Graphical user
50. elow water surface for shallow E 2 2 25 26 Co Cs X Y S T CL Cs n water Osun fo fs ZB a B y v Below water surface for deep Ly A 2 27 20 Co C5 X Y S T CL Cs n Osun water or f 9 or Q a B y 5 v Below water surface for shallow LAO 2 27 27 Co C5 X Y S T CL Cs n Osun water By orQ fo o ZB Q B Y v Above water surface for deep L A 2 29 26 Co C5 X Y S T CL Cs n Osun water and wavelength dependent or f amp or Q a B y v oL surface reflections a Bx yx 6 OL Above water surface for deep L A 2 29 Co Cs5 X Y S T CL Cs n Osun water and constant surface re or f 0 or Q a B y v OL OL flections Above water surface for shallow LO 2 29 33 Co C5 X Y S T CL Cs n Osun water and wavelength dependent 0 or Q fo fs ZB a B y 5 v OL surface reflections 0 Bx ya OL Above water surface for shallow LAO 2 29 29 Co C5 X Y S T CL Cs n Osun water and constant surface re Ov or Q fo fs ZB a B y 5 v OL flections OL
51. ents for fitting Eg A must be applied with care in general it should not be used The option has been included for consistency reasons Es A measurements are useful for inversion of upwell ing radiance and specular reflectance spectra WASI manual version 3 53 5 Reconstruction mode The reconstruction mode is a combination of forward and inverse mode A spectrum is calcu lated in the forward mode and subsequently this spectrum is fitted in the inverse mode The model parameters of the forward calculation are stored together with the fit parameters of the inversion in one file the spectrum may be saved or not Analogously to the forward mode up to three parameters can be iterated simultaneously Parameters of the forward mode and of the inverse mode can be chosen differently The mode is called reconstruction mode because in version reconstructs model parameters of the forward mode at altered conditions It is useful for sensitivity studies 5 1 Definition of parameter values Initial values of each fit parameter are read from the WASI INI file The user can change them most conveniently in the parameter list at the left side of the main window or alterna tively in the Fit parameters pop up window see Fig 4 4 An example is shown in Fig 5 1 Downwelling irradiance Parameter Value alpha 0 200 bet 0 100 Start TT invert spectra eta gamma 0 100 delta o V above water nue fi Downwelling irradi
52. ependent parameter no hook or if Cr Co is set with Co C 0 denoting phytoplankton concentration hook In case 1 water types suspended matter is highly corre WASI manual version 3 61 lated with phytoplankton hence it is suggested to mark the box for case 1 waters but not for case 2 waters The boxes scattering function from file and scattering function calculated from phyto plankton absorption are exclusive i e exact one of both is marked with a hook They deter mine how the function by A of eq 2 15 is selected it is either read from file scattering function from file is marked or it is calculated from the specific absorption spectrum of phytoplankton the other box is marked Calculation is useful when suspended matter and phytoplankton are highly correlated i e for case 1 waters otherwise a spectrum independent from phytoplankton should be taken If no information about the spectral dependency of backscattering by large particles is available it is a good idea to use a constant function br A 1 This provides good results for instance in Lake Constance Heege 2000 By default bL A 1 is read from the file eins prn For reading another file the WASLINI file must be changed accordingly The box nonlinear with concentration determines whether the specific backscattering coef ficient bi of eq 2 15 is treated as constant no hook or if it is calculated as A C1 hook B is the value in the input fie
53. ert and Mobley 2003 Kw 20 b 0 1 0 0 DI uae 2 6 cos Kn a b 0 1 0 0 1 pa e 2 7 cos O an The function depends on absorption a and backscattering by A of the water body 0 0 24 46 0 Sa WASI manual version 3 13 Egs 2 6 and 2 7 are used implicitely in the model of irradiance reflectance in shallow wa ters see eq 2 16 The spectra Kyw A and Kyp A cannot be calculated explicitely using WASI 2 3 3 Attenuation for upwelling radiance For upwelling radiance two attenuation coefficients are used kyw for the radiation backscat tered in the water and kug for the radiation reflected from the bottom The following parame terization is adopted from Albert and Mobley 2003 a A b 4 3 5421 fy 0 2786 kw 0 E l 0 A oar 2 9 kep RATOU hoop re LU 2 10 cosB cos O an These equations are used implicitely in the model of remote sensing reflectance in shallow waters see eq 2 19 The spectra kyw A and kug cannot be calculated explicitely using WASI 14 WASI manual version 3 2 4 Specular reflectance An above water radiance sensor looking down to the water surface measures the sum of two radiance components one from the water body one from the surface The first comprises the desired information about the water constituents the second is an unwanted add on which has to be corrected However correction is difficult For example th
54. ery close to pure water absorption aw Air except for high Gelbstoff concentration The calculation of f depends on the selected f model cf chapter 6 2 If f is parameterised solely as a function of the sun zenith angle eqs 6 1 6 3 the f value resulting from the given sun zenith angle is taken If f is parameterised additionally as a function of backscattering eqs 6 2 6 4 f is calculated in two steps First the values from the parameter list are taken to calculate backscattering at wavelength r using eq 2 4 with that result a first estimate of f is calculated In the second step eq 4 2a or 4 2b is applied to calculate Bo using the f value from the first step Then fis calculated again using eq 6 2 or 6 4 A special algorithm has been implemented for the f model f constant Obviously a constant f value needs no further consideration for applying eq 4 2a or 4 2b However if that f model is selected f can be treated as a fit parameter If fitting of f is activated an initial value for f can be calculated in addition to Bo as described in the following WASI manual version 3 45 Special case Initial values for f and By Calculation is based on reflectance values at two wavelengths Ar and Agra Oir 2 gt Aur It re quires that R A1r 1 ROuz 2 if that is not the case f is kept constant at the value from the parame ter list and Bo is calculated as described above Initial values determination makes use
55. f Y and Co from analytic equations at two wavelengths for C and Cs the values from step 1 are taken 3 C Cs Y fit Determine initial values of C_ Cs and Y by fit Co is kept constant at the value from step 2 C Cs and Y are initialized using the values from steps 1 and 2 respectively 4 Co Y S fit Determine initial values of Co Y and S by fit C is kept constant at the value from step 3 Y is initialized using the value from step 3 S is initialized by the user setting from the parameter list 5 All parame fit All parameters are fitted starting with initial values for CL Cs Co ters Y and S from steps 3 and 4 Table 4 2 Procedure for inversion of irradiance reflectance spectra of deep water Fine tuning of steps 1 to 4 is done in the Irradiance reflectance register card of the Fit tun ing pop up window It is shown in Fig 4 9 Steps 1 and 2 are performed if the check boxes Analytic estimate of are marked with a hook Otherwise the initial values from the pa rameter list or from the previous fit are taken as described in section 4 2 2 Steps 3 and 4 are tuned in the Pre fit frames The pre fits are performed if max iterations is set to a value larger than 1 At step 5 the user can define the wavelength range to be fitted the intervals be tween data points and the maximum number of iterations The relevant user interface is shown in Fig 4 7 Step 1 Suspended matter backscattering Bo can be calculated analy
56. f albedo a A are viewed simultaneously the measured albedo is the following sum R A y f a A 2 21 fa is the areal fraction of surface number n within the sensor s field of view it is 2 fa 1 This equation is implemented in WASI for N 6 bottom types The spectra an A provided with WASI are shown in Fig 2 4 They were measured by Pinnel 2005 using a submersible RAMSES spectroradiometer Three of them represent bare bottom the other green makro phytes 0 constant an artificial spectrum with constant albedo of 10 1 sand sandy bottom in a coastal shallow area in Bolivar South Australia 2 silt fine grained sediment in 50 cm water depth close to the shoreline of Starnberger See Germany 3 Chara aspera green makrophyte from Bodensee Lake Constance Germany 4 Potamogeton perfoliatus green makrophyte from Starnberger See Germany 5 Potamogeton pectinatus green makrophyte from Starnberger See Germany 2 7 2 For radiance sensors When the upwelling radiation is measured by a radiance sensor the corresponding remote sensing reflectance can be expressed as follows R A Y f B a A 2 22 n B is the proportion of radiation which is reflected towards the sensor In WASI the B s of all surfaces are assumed to be angle independent The default values are set to Bn 1 1 0 318 sr which represents isotropic reflection Lambertian surfaces 20 WASI manual version 3 0 40 0 4
57. flectance spectra by inverse modelling Gege 1994 1995 Measured at the University of Constance by Beese Richter and Kenter gt Measured by Tilzer Hartig and Heege Tilzer et al 1995 Heege 2000 8 WASI manual version 3 0 04 phytoplankton i cryptophyta type L o E a E 0 02 o o 0 01 0 00 400 500 600 700 800 400 500 600 700 800 Wavelength nm Wavelength nm AP 4 6 2005 0 04 cryptophyta type H 0 03 o E a E 0 02 k a o 0 01 0 00 5 400 500 600 700 800 400 500 600 700 800 Wavelength nm Wavelength nm ACH 4 6 2005 AD 4 6 2005 0 04 dinoflagellates 0 05 green algae 0 04 0 03 2 0 03 a a E 002 E E o 0 02 0 01 0 01 0 00 0 00 400 500 600 700 800 400 500 600 700 800 Wavelength nm Wavelength nm ADF 4 6 2005 AG 4 6 2005 Fig 2 1 Specific absorption spectra of 6 phytoplankton classes Gelbstoff absorption is calculated in WASI by default using the exponential approximation of eq 2 2 However Gege 2000 showed that this approximation provides model errors below 10 only for the wavelength interval of 10 60 nm Ao 60 nm and a better approximation is a sum of 3 Gaussian distributions the x axis must be transformed from the wavelength scale nm to the engergy scale cm The Gaussian model is physically more reasonable than the exponential model and offers a deeper understanding of the chemical interactions affecting CDOM molecular structure Schwarz et al 2002 T
58. formed for channels of a specific sensor the wavelengths are read from an ASCII table In this case the box x values from file must be marked with a hook and the corresponding file must be se lected The pre selected file can be changed by pressing the button e which causes the opening of a file selection window The number of lines in the ASCII file that are skipped are specified in the header lines input field the column with the wavelengths is speci fied in the column with x values field e Ifthe spectra shall be calculated at equidistant wavelengths the check box x values from file has to be deselected The first wavelength is specified in the xmin field the last wavelength in the xmax field and the intervals in the dx field Add noise Two types of sensor characterics deterioriating data quality can be simulated noise and dynamics e Ifthe check box add statistical noise is marked with a hook Gaussian distributed noise is added to each calculated value Its standard deviation is specified in the input field StdDev If no noise is added the StdDev input field is not displayed e If the check box reduce radiometric resolution is marked with a hook the numerical accuracy is limited to the value shown in the corresponding input field For example 0 001 rounds original real numbers such that values of 0 000 0 001 0 002 0 003 etc re sult If reduce radiometric resolution is not selected the correspon
59. he selection is done in the box Adjust bottom albedo If none is selected the weights are not automatically ad Justed In the example of Fig 6 8 the weight for surface no 3 is automatically adjusted This is visible in the main window by an inactive input box for fa 3 in the parameter list i e the calculated value is displayed in gray instead of black see Fig 6 7 right For a radiance sensor the bottom reflectance spectra are weighted additionally to f with re flection factors B which are the ratio of radiance reflected in the direction of the sensor rela tive to the downwelling irradiance For an isotropic Lambertian reflecting surface it is Ba 1 1 0 318 sr thus 0 318 sr are the default values for all B s The reflection factors can be set for each surface type individually in the register card Bottom of the pop up window Model options see Fig 6 8 WASI manual version 3 i Hodel options Fig 6 8 The register card Bottom of the pop up window Model options 65 66 WASI manual version 3 7 Program options The Options item of the menu bar on top of the WASI window is the entry point to all pro gram settings Fig 7 1 shows the main menu bar of WASI and the structure of the Options item The various program settings are grouped in 7 thematic areas one of these Invers cal culation is further divided into 3 themes When one of the themes is selected a pop up win dow shows up which allo
60. hus a spectrum Y A is pro vided with WASI which was calculated using the Gaussian model eq 3 in Gege 2000 and the average model parameters determined for Lake Constance Table 1 in Gege 2000 It is shown in Fig 2 2 right on a logarithmic scale WASI manual version 3 9 Non chlorophyllous particles 100 ay A 900 500 600 700 800 Ya 200 300 400 500 600 700 800 Wavelength nm Wavelength nm AX 4 6 2005 AY 4 6 2005 Fig 2 2 Normalised absorption spectra of non chlorophyllous particles ax A and Gelbstoff ay A 4 T T 0 02 T T T T T 0 00 Absorption m Absorption gradient m7 C L L L L a L L 400 500 600 700 800 900 Oe 400 500 600 700 800 900 Wavelength nm Wavelength nm AW 5 11 2001 DAWDT 5 11 2001 Fig 2 3 Pure water absorption aw A and temperature gradient of water absorption daw A dT 2 1 2 Natural water The bulk absorption of a natural water body is the sum of absorption of pure water and of the water constituents a A aw T_T Sul al 2 3 Absorption of pure water is split up into a temperature independent term aw which is valid at a reference temperature To and a temperature gradient daw dT with T being the actual water temperature The spectra aw A and daw A dT are shown in Fig 2 3 The spectrum ay A provided with WASI is a combination from different sources for a tem perature of To 20 C 196 22
61. iE 35 4 1 Graphical user interface AAA shaceoseteaden peteanere ss 35 4 2 Inversion of a single spectrum sci iew ech adv urla 37 4 21 Spectrum selection arreca 37 4 2 2 Definition of Mittal vales dad 38 ADO HAUSER Ae A A lodi ia 39 4 2 4 Definition of fit region and number of iterations 40 4 3 Inversion of a series of spectra arios 41 4 3 1 Seleetion ofspectrasiastia dere abia 41 4 3 2 Definition of initial values A cias 41 4 4 Optimisation of A elle alli 43 4 4 1 Irradiance reflectance of deep water av 43 4 4 2 Irradiance reflectance of shallow water i 47 4 4 3 Remote sensing reflectance of deep water 50 4 4 4 Remote sensing reflectance of shallow water 51 AAS Downwelling irradiance sacca leleine 32 gt Reconistugnoniniode atalanta 53 5 1 Definition of parameter valles o 53 5 2 Definition of output information guarita 54 6 Model options messire e e e e a e E o eg 57 6 1 Downwellins adiacenti 57 6 2Irradiance Tefieetancei oriali e iaia 58 6 3 ADS A A abeadeeecusaeeausagncdee 62 0 A Bottom reflectance oleole 64 TPrastam opliofit ninnan a a a ADA a 66 TI Directories siliconata Risa 66 2 Display elle ia 67 E II deh sae egeuaa ec eee 67 8 ROI aaa e ae eee aa A a T aN ae a ATA i 69 Appendix 1 Installation ea 13 Appendix 2 WASTING passeri taa 74 Appendix 3 Parameters salle allena 79 Appendix 4 CONOR lc aio la
62. ion C_L minimum during initial value determination C 0 minimum during initial value determination C_Y minimum during initial value determination shallow water a_ini start value of absorption for nested intervals shallow water da_ini initial absorption interval for a_ini shallow water delta_min threshold of spectrum change for nested intervals shallow water res_mode type of residuum 0 least squares Temperature of water absorption spectrum C refractive index of water Reference wavelength for Gelbstoff absorption nm Reference wavelength for scattering of large particles nm Reference wavelength for scattering of small particles nm Backscattering coefficient of pure water 1 m Multiplicative factor of C_L in scattering by large particles Power of C_L in scattering by large particles Specific backscattering coeff of large particles m 2 g Specific backscattering coeff of small particles m 2 g reflection factor for upwelling irradiance reflection factor for downwelling irradiance reflection factor for upwelling radiance radiometric resolution noise level coefficient of Kd BRDF of bottom type 0 BRDF of bottom type 1 BRDF of bottom type 2 BRDF of bottom type 3 BRDF of bottom type 4 BRDF of bottom type 5 min max fit sv 0 100 100 t g c 0 Concentration of phytoplankton class 0 0 60 0 0 0 C 1 Concentration of phytoplankton class 1 0 60 0 ud C 2 Concentration of
63. iterated has to be selected from one of the three Parameter drop down lists of the selection panel 4 of Fig 3 1 it is irrelevant which of the 3 lists the selection in the two other drop down lists must be none The range of variation of the iterated parameter is specified by a minimum and a maximum value from to and the number of calculated spectra by the number of steps steps If the check box log is marked with a hook the parameter intervals are equidistant on a logarith mic scale otherwise they are equidistant on a linear scale WASI manual version 3 31 Parameter from to steps log Eg 0 100 10 0 z none y fi 10 0 fro rT none foroo fi fo fr xI Fig 3 5 Iteration over 1 parameter In the example of Fig 3 5 the phytoplankton concentration C 0 is iterated from 0 100 to 10 ug l in 7 steps which are equidistant on a logarithmic scale i e 7 spectra with concentrations of 0 100 0 215 0 464 1 0 2 15 4 64 and 10 ug l are calculated 3 3 2 2 Iteration over 2 parameters When 2 parameters should be iterated these parameters their range of variation and the num ber of steps must be specified analogously to iterating 1 parameter This is illustrated in Fig 3 6 Parameter from to steps log feo y 0 100 10 0 FR ey foro fi mis none y 0 100 fi fio fi Fig 3 6 Iteration over 2 parameters In the example of Fig 3 6 the phytoplankton concentration C 0 is iterated as in Fig 3 5 from
64. kton set C_L C_P useful in case 1 water types T scattering function from file Kenane Reader lines COMIT SVI VAES SUMM SVI y valles V scattering function calculated from phytoplankton absorption Y nonlinear with concentration Power of C_L o 370 Specific backscattering coefficient o 00060 m 2 g 1 at 550 nm Small particles Specific backscattering coefficient 0 00420 m2 g 1 at 500 nm cora Fig 6 4 The register card Backscattering of the pop up window Model options The settings are not the default settings of WASI they correspond to the model of Sathyendranath et al 1989 f 0 1034 1 3 3586 x 6 5358 x 4 6638 x4 6 4 COS Equation 6 1 is taken from Kirk 1984 6 2 from Morel and Gentili 1991 6 3 from Sathyendranath and Platt 1997 and 6 4 from Albert and Mobley 2003 Osun is the sun zenith angle above the water surface O sun below the surface The factor np in eq 6 2 is the ratio bp w bp The factor x in eq 6 4 is bp a by for the Gordon algorithm and by a for the Prieur algorithm The options for calculating absorption are described in section 6 3 Those for calculating backscattering are set in the register card Backscattering of the pop up window Model op tions see Fig 6 4 Backscattering by large particles In Fig 6 4 the box correlate with phytoplankton determines whether Cr of eq 2 15 is treated as an ind
65. labeled error and headed by parameter names list the relative errors of user selected parameters The selection which parameters to tabulate is done in the pop up window Re construction mode settings which is shown in Fig 5 4 This window is accessed from the menu bar via Options Reconstruction mode see Fig 7 1 The relative errors are calculated as 100 inv fwd 1 where inv is the fit result of inverse modeling and fwd is the pa rameter value used during forward calculation Hence the relative errors are the fit parame ter s deviations from the true values in percent 56 WASI manual version 3 Reconstruction mode settings Lo o quo omo o omo e on js L oo ALICI m m om N N Js ls l LI LI LI LI LI LI LI LI LI n Fig 5 4 The pop up window Reconstruction mode settings WASI manual version 3 6 Model options 6 1 Downwelling irradiance The spectrum type Downwelling irradiance is activated by selecting in the main window Downwelling irradiance from the drop down list above the Start button see Fig 6 1 left After the spectrum type is selected the check box above water is displayed and the accord ing parameter list If above water is selected the parameter list shown in the center of Fig 6 1 is displayed otherwise the right one The above water calculation is done using eq 2 1 which requires the parameters a alpha B beta y gamma 6 delta v nue
66. lass no 0 see eq 1 The latter is useful for Case 1 water types where the concentrations of particles and phytoplankton are highly correlated e bp can be treated either as constant with a default value of 0 0086 m g Heege 2000 or as bp A Cr Such a non linear dependency of scattering on concentration was observed for phytoplankton Morel 1980 It may be used for Case 1 water types while bpL constant is appropriate for Case 2 waters with significant sources of non phytoplankton suspended matter Typical values of the empirical constants are A 0 0006 m g and B 0 37 Sathyendranath et al 1989 which are set as defaults in WASI e b A can either be read from file or it can be calculated as bi ao L ao A where ao A is the specific absorption spectrum of phytoplankton class no 0 see eq 1 and Ar denotes a reference wavelength A 550 nm by default This method assumes that back scattering by large particles originates mainly from phytoplankton cells and couples ab sorption and scattering according to the Case 1 waters model of Sathyendranath et al 1989 However such coupling may be used in exceptional cases only since living algae have a negligible influence on the backscattering process by oceanic waters Ahn et al 1992 and in Case 2 waters particle scattering is weakly related to phytoplankton absorp tion in general In WASI br A 1 is set as default WASI manual version 3 11 2
67. ld Power of C_L which is visible only in the nonlinear case The value in the input field Specific backscattering coefficient corresponds to by in the linear case and to A in the nonlinear case The at nm input field of Fig 6 4 specifies the wavelength where the specific backscattering coefficient is valid After a scattering func tion is read from file or calculated from phytoplankton absorption it is normalized at that wavelength Backscattering by small particles The value in the input field Specific backscattering coefficient of the Small particles sec tion of Fig 6 4 corresponds to bps of eq 2 15 The at nm input field specifies the wavelength As of eq 2 15 62 WASI manual version 3 6 3 Absorption The spectrum type Absorption is activated by selecting in the main window Absorption from the drop down list above the Start button see Fig 6 5 left After the spectrum type is set to Absorption the check box include pure water Fig 6 5 left and the parameter list shown in Fig 6 5 right are displayed Parameter Value cyo po co DE ct o cal o cia e box jo CY E 5 ama TT include pure water T_W iso Fig 6 5 Settings of the spectrum type Absorption in the main window Left Drop down list with Absorption selected as spectrum type and include pure water check box Right Parameter list The spectrum type Absorption supports two options include or exclude pure water
68. list for selecting the spectrum type 2 Check box for switching between forward and inverse mode 3 Parameter list model spe cific 4 Selection panel for specifying the parameter iterations 5 Check boxes for selecting model options model specific 6 Menu bar 7 Start button 8 Plot window 26 WASI manual version 3 3 Parameter list This list tabulates the parameters which are relevant for the selected spec trum type It displays the parameters symbols in WASI notation see Appendix 3 and their actual values Default values are read from the WASL INI file actual values are set by the user by editing the corresponding Value fields Depending on the model options not all parameters may be relevant Irrelevant parameters are disabled i e the correspond ing symbol and value is displayed in gray colour and the value cannot be edited 4 Selection panel for specifying the iterations Up to 3 parameters can be iterated simultane ously during one run thus the panel has 3 rows one for each parameter The iterated pa rameters are selected in the Parameter drop down lists their minimum and maximum values in the from and to fields and their numbers of values in the steps fields The log check boxes specify whether the intervals are equidistant on a linear scale no hook or on a logarithmic scale hook 5 Check boxes for selecting model options Several spectrum types support options which further specify the
69. meters in the two Pre fit frames of Fig 4 10 Step 8 Wavelength range data interval and maximum number of iterations are specified in the Final fit register card of the Fit tuning pop up window see Fig 4 7 The maximum number of iterations forces the fit routine to stop the number should be set high enough that a forced stop is exceptional 4 4 3 Remote sensing reflectance of deep water The remote sensing reflectance of deep water above the surface R s A is calculated using eq 2 20a 2 20b or 2 20c that below the surface Rss A according to eq 2 17a or 2 17b R s A has 25 parameters which may be fitted R A has 15 This high number of fit parame ters makes fit tuning necessary In particular it is important to find suitable start values of the parameters i e to start with initial values which are not too different from the final results The user interface for controlling fit tuning is shown in Fig 4 11 It is accessed from the menu bar via Options Invers calculation Fit tuning WASI manual version 3 51 Settings for individual spectrum types Iradiance Inadiance reflectance Remote sensing reflectance TT use Ed measurement for wavelength dependent surface reflections deep water File di Wwasi data demo E_down FR2R C1 Header lines 0 olumn fi Y Eolumn 2 automatic determination of initial values TPre Fit Ed measurement from 400 ta e00 nm steps E Am may Iterations 400
70. model cf Table 1 1 Each option is either switched on or off 6 Menu bar Further details concerning the model data storage and visualisation can be specified in various pop up windows which are accessed via the menu bar 7 Start button Calculation is started by pressing this button 8 Plot window Each spectrum is plotted in this window after calculation All curves are plotted together in order to visualize the spectral changes for the chosen iterations A counter in the upper right corner is updated after each plot 3 2 Calculation of a single spectrum 3 2 1 Mode selection For calculating a single spectrum in the forward mode the following settings must be made e Set forward mode the invert spectra box 2 in Fig 3 1 is unchecked e No parameter iteration select none in each parameter drop down list O in Fig 3 1 3 2 2 Spectrum type selection WASI allows to calculate 8 different types of spectra see Table 1 1 The desired type is se lected in the main window from the drop down list of Fig 3 1 Several types of spectra support further options see Table 1 1 If that is the case for the se lected type the options are displayed at the bottom of the main window in Fig 3 1 Each option is either switched on or off The selection is done by marking the corresponding check box with a hook In the example of Fig 3 1 three options are available WASI manual version 3 27 1 Above water Since the che
71. n shallow waters 0 flag_Fresnel calculate Fresnel reflectance flag_bL_file large particle scattering spectrum from file flag_bL_linear large particle scattering linear with C_L 0 flag_CLisC0 set C_L C 0 flag_norm_X normalize SPM absorption spectrum from file at Lambda_0 flag_norm_Y normalize Gelbstoff spectrum from file at Lambda_0 Settings for batch mode 0 iter_type parameter that is iterated 2 0 rangeMin first value of successive calculation 4 0 rangeMax last value of successive calculation rangeDelta interval of successive calculation Parl_Type Parameter 1 0 Par2_Type Parameter 2 0 Par3_Type Parameter 3 WASI manual version 3 2 00 0 100 0 0 8 00 from 400 760 380 400 400 700 400 400 870 5 760 2 413 5 625 25 0 10 10 10 010 0 0 010 o0oruoooo to 800 900 450 900 800 800 500 800 900 0 440 5 Parl_Min Par2_Min Par3_Min Parl_Max Par2_Max Par3_Max Parl_N Par2_N Par3_N Minimum of Parameter Minimum of Parameter Minimum of Parameter Maximum of Parameter Maximum of Parameter Maximum of Parameter Steps of Parameter 1 Steps of Parameter 2 Steps of Parameter 3 WNFWNHW Settings for inverse mode step MaxIter 5 10 10 KA 5 5 5 1 440 870 400 a 100 100 1000 100 100 100 2000 Model constants 20 0 1 33000 440 550 500 0 00111 0 00060 0 3700 0 00860 00420 54000 03000 02
72. nate models of f are also included in WASI and can be used if desired namely those of Kirk 1984 Morel and Gentili 1991 and Sathyendranath and Platt 1997 The equations are given in chapter 6 2 Independently from Gordon Prieur 1976 found the relation R A f by A a It is also included in WASI However the Gordon algorithm 2 14 is favoured and set as default be cause it restricts the values to the physically reasonable range from 0 to 1 which is not the case for the Prieur equation 2 5 2 Shallow water For shallow water the parameterization found by Albert and Mobley 2003 is used R RQ 1 A exp K AK wy A Ze 2 16 ARO expt Ky A K s 1 24 The first term on the right hand side is the reflectance of a water layer of thickness zg the second term the contribution of the bottom Bottom reflectance R A is calculated using eq 2 21 The K s account for attenuation within the water layer and are calculated using eqs 2 5 2 6 and 2 7 The empirical constants are set to A 1 0546 and A 0 9755 accord ing to Albert and Mobley 2003 and cannot be changed by the user 16 WASI manual version 3 2 6 Remote sensing reflectance The ratio of upwelling radiance to downwelling irradiance R s A Lu A Ea A is called remote sensing reflectance Mobley 1994 It is an apparent optical property AOP i e it depends on the geometric distribution of the incoming light 2 6 1 Dee
73. ng to eq 2 3 WASI manual version 3 63 EZ Model options OF x Backscattering Reflectance Bottom Gelbstoff 7 Y Exponential function FT Specific absorption from file Filename 1 wrasiidataly a Header lines fi Golum svittt vas i alumn vit y vaes E Mormalize absorption spectrum at 440 nm Particles Specific absorption from file 1 wrasiidataidaten sat Filename Header lines fi 3 Column with x values fi Column with y values V Normalize absorption spectrum at 440 nm coca Fig 6 6 The register card Absorption of the pop up window Model options The input spectrum ax A may be normalized after it is read from file or not The selection is done in the check box Normalize absorption spectrum of the Particles section of Fig 6 6 If normalization is selected the corresponding wavelength o must be specified in the at nm input field When ax A is normalized the concentration of large suspended particles is given in units of absorption at the reference wavelength Ao otherwise it is given in units re lated to the units of the input file By default ax A is normalized The 10 input spectra aw A daw dT A ay A ax A ai A with 1 0 5 are read from files which are specified in the initialisation file WASLINI If these spectra should be replaced by other spectra the WASI INI file must be changed accordingly 64 WASI manual version 3 6 4 Bo
74. ntration of large suspended particles C_L was changed from 2 to 8 mg l in 3 steps i e concentrations of 2 5 and 8 mg l were taken The values of the other parameters are shown in the parameter list at the left side The list values of the iterated parameters C 0 and C_L are invalid When save all spectra is activated in the Forward calculation settings popup window see Fig 3 2 all 15 spectra are saved in ASCII format as separate files in the specified directory an example listening of such a file was given above in Fig 3 4 The file names are B01 fwd B02 fwd B15 f wd If the number of calculated spectra is less than 22 and if the check box if N lt 22 save all spectra in a single table of the Batch mode options menu is marked with a hook a single table with the file name spEC FWD is created instead of separate files An example of that ta ble is shown in Fig 3 9 This file was generated by the program WASI Version 3 Latest update 29 May 2005 Parameter values in files WASI INI CHANGES TXT Irradiance reflectanc 1 2 3 4 5 6 380 00 381 00 382 00 383 00 384 00 385 00 386 00 387 00 388 00 389 00 390 00 002158 002186 002214 002243 002272 002301 002331 002362 002393 002424 002456 005170 005244 005320 005397 005476 005555 005636 005718 005801 005886 005972 008426 008552 008679 008808 008939 009072 009208 009345 009484 009625 009768
75. o a el 12 2 3 1 Diffuse attenuation for downwelling irradiance 12 2 3 2 Diffuse attenuation for upwelling irradiance 12 2 3 3 Attenuation for upwelling radiance 13 2 4 Specular r flectante A a Ra ai E e iE a A 14 Dd dd 15 2 Sil Deep WI A shock caer 15 Di O eis riale 15 2 6 Remot sensing id a el 16 DA DEE A iena 16 20 2 Shallow Wales ii ls 16 2 6 3 Above The SUMACE x25 so 17 A A A a a a a ahae 19 27A Forirradi nce SENSOrS e dd e da a aE 19 2 7 2 For radiance sensors A A A AA R S 19 2 8 Downwelling rada dl dades 21 DS ACABOVE water UTC ile elisa 21 2 8 2 Below water surface liti 22 DoD Sky TAGIANCE O A tals cchsiel pct AA 23 2 10 WUpwellins radian e ae leale lie rea 24 2 10 1 Below the water surface arte lla lana 24 2 10 2 Above the watersuttate scleri ale Be 24 3 Forward MOS A ii 25 3 Grapiical User It bile 25 3 2 Calculation of a sino PE CUM see creaveain evs se areallatacvauee ammuaretanevicatastoctaae 26 Ded Mode selection sso ele LAN oa 26 32 2 Spectrum type Selectiva li ds 26 3 2 3 Parameter slo Lorca a 27 E ricada 27 3 2 5 Start calculation a allo iii 28 32 0 Examplo artioli 29 3 3 Calculation of a series OF spectra mirra 30 JIA General coinn RR RO E IR PNE OA o 30 3 3 2 Specification of the iteration i 30 353 Datastorage REO GEES 32 A lr aa RRO 32 4 WASI manual version 3 A O A eben saaamio ads sede a Aa
76. of eq 4 1a no corresponding algorithm for eq 4 1b is implemented First the factor f is eliminated by taking the ratio of eq 4 1a for two wavelengths Ag and Ag 2 RQ r aries byw uri By Dow Aur B 4 3 RAR a yz gt ale Dow in2 By Dow Ouro B Eq 4 3 assumes that Bo is the same at r and Ag 2 Multiplication of eq 4 3 with the product of both denominators leads to a quadratic expression in Bo of the form a B B B y 0 4 4 with a R A1 RA 0 G09 B RQ ip 80181 tbr w Ar brw Aina 4 5b RQiro amo T Dow Ari Dow Ga Y RO A yz 1 b wr Dow Aino gt 4 5c Ripa aa R2 T bow A rR2 Dow Ar It has two solutions gie PP Ae 4 6 2a The positive solution gives the correct value of Bo This is the algorithm for calculating Bo The al gorithm for calculating f is obtained directly from eq 4 1a a A p3 b w Arz B Dow A r2 Bo 4 7 f R p gt It has been investigated how the accuracy of the retrieved C values depends on the choice of the wave lengths Aja and Ar and on the errors of the initial Y and CL values The more Ag and Mg are shifted towards longer wavelengths the better are the results For Gelbstoff concentrations below 1 m the rela tive error of Cr is always below 20 if both wavelengths are above 820 nm For the MERIS channels Aur 870 nm and 2 2 900 nm the relative errors are always below 5 for Y lt
77. of start minimum and maximum value The complete set of start values of a displayed regis ter card can be overwritten by default values from the WASI INI file by pressing the Default values button These default values are stored separately from the start values in the WASI INI file and can be changed only by editing the WASLINI file 4 2 3 Fit strategy The values of the model parameters are determined iteratively In the first iteration a fit curve is calculated using the initial values as parameters and as a measure of correspondence be tween measured and fitted curve the residual is calculated In all further iterations the fit pa rameters are altered and the new residual is compared with the previous one If the new resid ual is smaller the correspondence between measurement and fit is better hence the new pa rameter set is the better one The calculation is stopped when the difference between the re siduals of two subsequent steps is smaller than some threshold or if the number of iterations is above some threshold The parameter values of the step with the smallest residuum are the fit results The residuum is a measure of the correspondence between the measured spectrum and a fit curve WASI supports two calculation options e wavelength dependent weighting e 6 different minimisation methods The residuum is calculated by averaging the weighted differences between measured and fit curve over all wavelengths The weighting func
78. ormation WASI INI CHANGES TXT and indicates the spectrum type y It follows the calculated spectrum 30 WASI manual version 3 This file was generated by the program WASI Version 3 Latest update 29 May 2005 Parameter values in files WASI INI CHANGES TXT y Irradiance reflectance 0 0 0 0 0 0 0 0 0 0 0 Fig 3 4 Listening of the first lines of the spectrum from Fig 3 3 3 3 Calculation of a series of spectra 3 3 1 General Calculating a series of spectra in the forward mode is very similar to calculating a single spec trum The only difference is that the parameter iterations have to be specified Hence the set tings are as follows e Define the spectrum type select the type from the drop down list A in Fig 3 1 e Set forward mode the invert spectra box 2 in Fig 3 1 is unchecked e Specify the parameter values set the values of all model parameters in the parameter list in Fig 3 1 Up to three model parameters can be iterated simultaneously as described below For these the parameter list entries are irrelevant since the values are set during iteration 3 3 2 Specification of the iteration 3 3 2 1 Iteration over 1 parameter For studying the dependence of a spectrum on a certain parameter the values of that parame ter can be iterated over its typical range of variation WASI allows to iterate the parameters of Appendix 3 As shown in Fig 3 5 the parameter to be
79. ottom type 2 10 0 0 0 fA 3 fraction of bottom type 3 10 0 0 0 fA 4 fraction of bottom type 4 10 0 0 0 fA 5 fraction of bottom type 5 100 0 0 C_X Concentration non chlorophyllous particles 1000 0 0 test test parameter WASI manual version 3 79 Appendix 3 Parameters The following table summarizes the 36 model parameters of all 8 spectrum types The No s are used program internally as parameter indices The parameters z and db are included for future developments and are so far not used Forward mode Each parameter can be set by the user When a series of spectra is calculated iteration can be performed over each of the parameters Invers mode The user defines for each parameter if it should be treated as a constant or as variable to be fitted during inversion 80 WASI manual version 3 Appendix 4 Constants The following table summarizes the model constants of all 8 spectrum types They can be changed by editing the WASI INI file ASI symbol Unis Beraun vive pesci oi Lamas is am 500 Refrnce wavlongh o satin fal pais vo n re 29 remo eratrsteeunan6 Refractive index of water ECON O EGONT_ eci confini iu rom BLA A 0 006 Nutpicane scri scatena tere prices bee 8_ gt 037 _ FesorotnonIneaniynscetemg tre peices ia bbS_norm Specific backscattering coefficient of small particles Romei o gt _ PSE CEIC somes o gt 098 Retedionfeorofdownveinginadance Somali
80. p water The remote sensing reflectance below the water surface is for deep water proportional to R A RQ RA A 2 17a This follows from the definitions Rs Ly Eq Q Ey Ly andR E E4 R A is ei ther calculated using eq 2 14 or imported from file The factor Q which is a measure of the anisotropy of the light field in water is treated in WASI as a wavelength independent pa rameter with a default value of 5 sr It depends on the geometric distribution of the upwelling and downwelling light and thus on the scattering and absorption properties of the water body Consequently Q depends on wavelength However this is not accounted for in WASI since no convenient parameterization of Q is known Yet an alternative to eq 2 17a with a con venient parameterization of the factor fis was found by Albert and Mobley 2003 Ris A frs i lA 2 17b The following parameterization of the factor f s is valid for both deep and shallow waters Al bert and Mobley 2003 f 0 0512 144 6659 7 8387 5 4571 0 1098 0 4021 2 18 1 1 cos O n cos O Parameters of f are p of eq 2 8 the sun zenith angle in water 0 sun and the viewing angle in water 0 Alternately fis can be calculated in WASI as fis f Q using the ill favoured parameter Q 2 6 2 Shallow water For shallow water the following parameterization is chosen Albert and Mobley 2003 RQ R 0 1 A expe
81. parameters which change from one spectrum to the next are listed in the file changes txt A copy of the wasi ini file is created for documenting completely all parameters and input files The directory where all the files are stored is se lected as described in section 7 1 If the number of calculated spectra is below 22 the spectra can alternately be stored in a sin gle file spec fwd This option is selected by marking the check box if N lt 22 save all spec tra in a single table in the Forward calculation settings pop up window see Fig 3 2 3 3 4 Example An example of a series of spectra calculated in the forward mode is given in Fig 3 8 E wasi Water color simulator a loj xj File Display Options Help Irradiance reflectance simulated spectra Parameter Value Cro 200 en o CR jo ca Eo c ooa OH o CE 4 00 400 500 600 700 800 cs io wavelength nm cx jo cy osoo E Parameter from to steps log TT invert spectra Cro hd fo so B E iu a RRS SER CL 1 200 8 00 E r E TT shallow water 0100 fio r _ Fig 3 8 A series of irradiance spectra calculated in the forward mode WASI manual version 3 33 The spectrum type of Fig 3 8 is irradiance reflectance N 15 spectra have been calculated by iterating two parameters phytoplankton concentration C 0 was changed from 0 to 8 ug l in 5 steps i e concentrations of 0 2 4 6 8 ug l were taken and the conce
82. phytoplankton class 2 0 60 0 0 0 Gral Concentration of phytoplankton class 3 0 60 0 0 0 C 4 Concentration of phytoplankton class 4 0 60 0 0 0 C 5 Concentration of phytoplankton class 5 0 100 200 1 0 C_L Concentration large particles 0 125 0 0 ES Concentration small particles 0 0500 10 0 1 0 GE Gelbstoff absorption 0 00400 0 0250 0 0 Gelbstoff exponent 2 00 2 00 0 0 n Angstr m exponent of SPM backscattering 0 350 0 0 T_W Water temperature C 0 500 10 0 0 0 Q Q factor of Lu 1 sr 0 0 500 0 0 sigma_L reflection factor of sky radiance 5 00 50 0 0 0 alpha fraction of Ls due to sun 5 00 50 0 0 0 beta fraction of Ls due to blue sky 5 00 50 0 0 0 gamma fraction of Ls due to aerosols 5 00 50 0 0 0 delta fraction of Ls due to clouds 2 00 2 00 0 0 nue Angstr m exponent of aerosols 0 500 5 00 0 0 alpha fraction of Ed due to sun 0 500 950 0 0 beta fraction of Ed due to blue sky 0 500 5 00 0 0 gamma fraction of Ed due to aerosols 0 500 5 00 0 0 delta fraction of Ed due to clouds 0 100 0 900 0 0 f factor of R 0 100 0 0 z depth m 0 100 o 1 zB bottom depth m 0 89 9 0 0 sun sun zenith angle TI 2 50 00 100000 DI PO000roooo DO ADO SO WASI manual version 3 89 9 0 0 view view zenith angle 180 0 0 dphi azimuth difference sun observer 10 0 0 0 fA O fraction of bottom type 0 10 0 O 0 fA 1 fraction of bottom type 1 10 0 90 fA 2 fraction of b
83. r 100 inv fwd 1 fwd Inversion inv inv nue Iterations Residuum alpha beta 1 000 105 0 166 0 8000 ILL 0 129 0 6000 112 0957 0 4000 114 0654 195 0895 0 2000 118 0383 197 0945 0 186 0741 0 0 0 0 5 551E 17 103 0147 0 199 0993 0 0 0 0 0 189 0794 192 0845 2000 99 0103 201 104 4000 110 0281 6000 111 0444 8000 142 0585 1 96 0703 203 109 206 207 118 123 oo o DDD 0 0 204 0 113 0 0 6 056E 17 111 0 06557 0 1981 0 09894 1 000 142 0 1663 0 2070 0 1230 Fig 5 3 Example of the output file FITPARS TXT WASI manual version 3 55 studies are generally based on a large number of spectra usually not all spectra are saved but only a few for illustration purposes Thus a study may be performed in two steps in the first step the parameters of interest are iterated over the interesting ranges with few steps and the resulting spectra are saved in the second step the calculations of step 1 are repeated but with much more steps and without saving the spectra How to save forward calculated spectra is described in sections 3 2 4 and 3 3 3 the corresponding pop up window is shown in Fig 3 2 How to save fit spectra is described in section 4 3 1 How the directories are selected is de scribed in section 7 1 the corresponding pop up window is shown in Fig 7 2 The second column of the data block lists the values of the parameter which is iterated during
84. rameters are listed in the parameter list at the left hand side phytoplankton concentration C 0 3 ug l concentra tion of large suspended particles C_L 1 mg l Gelbstoff absorption C_Y 0 3 m at 440 nm Gelbstoff exponent S 0 014 nm n is irrelevant since C_S 0 water temperature T_W 18 C sun zenith angle sun 47 0 the concentrations of all other substances are zero The factor Q is irrelevant for the chosen model which is indicated by gray text color The fact that the displayed spectrum is a model curve and not a measurement is indicated by simulated spectra at top right Ta WASI Water color simulator Dx File Display Options Help Irradiance reflectance simulated spectra 0 0060 0 0040 Parameter Value CIO 3 00 ch a 0 0020 CR 0 CI 0 C4 0 CIS z a CL 1 400 500 600 700 800 cs 0 wavelength nm cx fo irradiance reflectance y CY 0 300 Parameter from to steps log n o I invert spectra none y fi 6 00 ls n RE ai apse al eae rec none aa faoo 2 B F TT shallow water none y 0 100 i fio sun 47 0 g E 00 Fig 3 3 A single irradiance reflectance spectrum calculated in the forward mode A listening of the first lines of the calculated spectrum is shown in Fig 3 4 The header of the spectrum file contains the information that the spectrum has been created by the program WASI gives the software version latest update lists the files which contain additional inf
85. rome et al 1990 Mobley 1999 The defaults of the other constants are set to Q 5 sr and nw 1 33 Which of the equations is used depends on the application e Eq 20a is useful when R A shall be connected to R A for example if in situ meas urements of R A were performed as ground truth for a remote sensing instrument e Eq 20b links remote sensing reflectance in water to that in air Since the same spectrum type is used above and below the water surface it is the most convenient parameterisation This equation is used by default e Eq 20c avoids the use of the factor Q which is difficult to assess The equation is use ful for example for optical closure experiments which investigate the consistency of measurements above and below the water surface by measuring simultaneously the spec tra Ris A R A and Rs A Eq 2 20a 2 20b or 2 20c is also used to calculate the corresponding spectrum R A for shallow water R A is replaced by RYO and Rx A by Ri A in the case of shallow wa ter WASI manual version 3 19 2 7 Bottom reflectance The models of bottom reflectance are used to calculate reflectance and radiance spectra in shallow waters However they can be applied as well to land surfaces if the input spectra are replaced by suitable albedo spectra from terrestrial bottom types 2 7 1 For irradiance sensors The irradiance reflectance of a surface is called albedo When N different surfaces o
86. rption by coloured dissolved organic matter CDOM Oceanologia 44 2 209 241 M M Tilzer N Stambler C Lovengreen 1995 The role of phytoplankton in determining the underwater light climate in Lake Constance Hydrobiologia 316 161 171 D A Toole D A Siegel D W Menzies M J Neumann R C Smith 2000 Remote sensing reflectance determinations in the coastal ocean environment impact of instrumental characteristics and environmental variability Applied Optics 39 3 456 469 WASI manual version 3 73 Appendix 1 Installation WASI has no custom setup routine like most WINDOWS programs However installation is very easy Method 1 The simplest method is to install WASI in the directory D WASI The steps are e Create the directory D WASI e Copy WASI ZIP into D WASI Unzip WASLZIP Method 2 If you prefer to install WASI in another directory than D WASI then installation needs a little bit more effort The steps are e Create the desired directory e Copy WASI ZIP into that directory e Unzip WASI ZIP e Edit WASLINI Replace with a text editor all occurences of D WASI with your direc tory To start WASI execute the file WASLEXE 74 WASI manual version 3 Appendix 2 WASLINI WASI INI is the initialization file of WASI It is read automatically during program start All program settings are stored in this file The following is an example listening Initialization file for the program WASI w
87. sitivity studies Error propagation can be investigated systematically by iterating the erroneous model pa rameter during forward calculation The way to do this is explained in section 3 3 2 Fig 5 2 shows as example how to study systematically the errors caused by wrong values of the pa rameter nue nue is iterated from 1 to 1 in 11 steps Thus 11 spectra are calculated in the forward mode with nue values of 1 0 8 1 and these spectra are subsequently fitted If nue is fixed during inversion like in Fig 5 1 a series of inversion results is obtained for a sys tematically changing error of the parameter nue Parameter from to steps log SI CIN Fig 5 2 Iteration of the parameter nue HEK lt 5 2 Definition of output information The results of fitting a series of spectra are stored in a single file FITPARS TXT Fig 5 3 shows as an example a listening of this file for the settings of Figs 5 1 and 5 2 The first lines explain the file content and summarize relevant information The first column of the data block of the file FITPARS TxT headed File lists the file names of the calculated spectra Whether the spectra are saved or not decides the user As sensitivity This file was generated by the program WASI Version 2 4 Latest update 6 July 2004 List of fitted parameters which may differ from one spectrum to the next Common parameter set of all spectra in file WASI INI 2 Errors are given in erro
88. surface For deep water above water R A 2 20a 25 surface and wavelength depend ent surface reflections 2 20b 26 2 200 25 For deep water above water R s A 2 20a surface and constant surface reflections Rrs A 2 20b 17 Co Cs X Y S T CL Cs n Osun or f Ov Q oL 2 20c 16 Co Cs X Y S Y CL Cs n Osun or f Q or 6 OL Co C5 X Y S T Ci Cs n Osun fo fs ZB Q A B Y S a Bx y v OL Co C5 X Y S T CL Cs n Osun Ris A 2 2 A A 2 gt For shallow water above water Ra 2 20a 32 surface and wavelength depend ent surface reflections 2 20b 32 Ov fo fs ZB Q a B y ax px y V OL 2 20c 31 Co Cs X Y S T CL Cs n Osun Oy fo fs ZB Q B Yi a px Y V OL 2 20a 23 Co Cs X Y S T CL Cs n For shallow water above water Ra WASI manual version 3 83 surface and constant surface Osun fo fs ZB Q OL reflections 2 20b 23 Co C5 X Y S T CL Cs n Osun fo fs Zp Q OL 2 20c 22 Co C5 X Y S T CL Cs n Osun fo f5 ZB OL Bottom reflec For irradiance sensors R A 2 21 fo fs tance For radiance sensors 2 22 el fo fs Downwelling Above water surface Ea A 2 23 5 a B y 5 v irradiance Below water surface for deep Ey A 2 25 C5 X Y S T CL Cs n Osun water n a B y 6 v B
89. t_Ed multiply spectrum Ed with factor flag_mult_E0 multiply spectrum EO with factor 0 flag_mult_Rrs multiply spectrum R_rs with factor 0 flag_x_ file read x values from file 0 Parl_log Logarithmic steps of Parameter 1 0 Par2_log Logarithmic steps of Parameter 2 L Par3_log Logarithmic steps of Parameter 3 0 flag_b_SaveFwd save all spectra of forward mode 0 flag_b_SaveInv save all spectra of invers mode 0 flag_b_LoadAll load spectra from files 1 flag_b_Reset reset start values 0 flag_b_Invert invert spectra 0 flag_Res_log weight residuals logarithmically 1 flag_Y_exp exponential Gelbstoff absorption 0 flag_surf_inv wavelength dependent surface reflections inversion 0 flag_surf_fw wavelength dependent surface reflections forward mode 0 flag_use_Ed make use of Ed measurement 0 flag_use_Ls make use of Ls measurement 0 flag_use_R make use of R measurement 0 flag_radiom reduce radiometric resolution 0 flag_noise add noise 0 flag_aW include water absorption in bulk absorption flag_above above water 0 flag_shallow shallow water flag_autoiniR automatic determination of R start values flag_anX_R analytic determination X start value for R spectra flag_anX_Rsh analytic determination X start value for R spectra in shallow waters flag_anCY_R analytic determination C Y start values for R spectra flag_anzB analytic determination of zB start value i
90. ter surface and moreover gravity waves spread greatly the sky area that is reflected into the sensor and change the angle of reflection Consequently measurements of L A are frequently not reli able For these cases and if no L A measurement is available eq 2 26 can be applied If the user selects the wavelength independent model of surface reflections L A E A TT is set 24 WASI manual version 3 2 10 Upwelling radiance The upwelling radiance is that part of the downwelling irradiance which is reflected back from the water into a down looking radiance sensor Calculation is based on a model of R s and a model or a measurement of Ea 2 10 1 Below the water surface In water eq 2 25 is used for calculating Eg A and eq 2 17a 2 17b or 2 19 for R s A The upwelling radiance is then calculated as follows LA R A Ed 2 27 In shallow waters Rx A is used instead of Rxs A and Ea A instead of Eg A 2 10 2 Above the water surface The upwelling radiance after crossing the water air boundary is related to the upwelling radi ance in water Ly as follows L 4 0 al L 4 0 0 0 L A 0 2 28 W 0 is the zenith angle of the observer in air 0 in water These two angles are related to each others according to Snell s law via ny sin0 sin0 with nw refractive index of water The first term on the right hand side of eq 2 28 is the radiance upwelling in the water weaken
91. ter surface sun_w sun zenith angle below water surface n bb_wW b x bb a bb cana Fig 6 3 The register card Reflectance of the pop up window Model options ent phytoplankton classes Ci C i i 0 1 5 of large CL C_L and small Cs C_S suspended particles of non chlorophyllous particles X C_X and of Gelbstoff Y C_Y and the Angstr m exponent n water temperature T T_W proportionality factor f and eventually Gelbstoff exponent S f can either be treated as a parameter or it can be calcu lated as a function of absorption backscattering and the sun zenith angle R algorithm and f calculation method are selected in the Reflectance register card of the Model options pop up window which is shown in Fig 6 3 The pop up window is accessed from the menu bar via Options Models The factor of proportionality f depends on the scattering properties of the water and on the illumination geometry In WASI f can either be treated as a parameter or it can be calculated using one of the following algorithms f 0 975 0 629 cos O sun 6 1 f 0 6279 0 2227 ny 0 0513 mp7 0 3119 0 2465 mp COS Osun 6 2 0 5 63 0 5 cos Om 60 WASI manual version 3 EZ Model options Al x Absorption Backscattering Reflectance Bottom Pure water Backscattering coefficient fo 001 44 m 1at 500 nm Large particles IV correlate with phytoplan
92. terize the four light sources Their weights a B y may change from one measurement to the next but the t A themselves are assumed to be constant In order to make the weights a B y the relative intensities of the four light sources each t A is normalized as J t Eo A da Eo A dA the integration interval is set to 400 to 800 nm by default The functions WAR and A Am are calculated during run time Normali zation yields their scaling factors Ar 533 nm and Ay is typically between 563 nm v 1 and 583 nm v 1 The exponent v parameterizes the wavelength dependency of aerosol scat tering The two other functions ta A and tc A are read from file After import they are nor 2 5 2 5 F kc Q o 2 20 2 20 T E E o 3 g 15 e 15 c 2 iS B 10 B 10 E E 2 a 05 a 05 tei E E 0 0 0 0 400 500 600 700 800 400 500 600 700 800 Wavelength nm Wavelength nm 2 5 aerosols ie 3 3 2 2 20 T E E 3 e 15 c 9 2 a 3 10 E E 2 2 sl o 05 tei d i 0 0 N 400 500 700 800 400 500 7 800 600 Wavelength nm 600 Wavelength nm Fig 2 4 The four base spectra of the model of the downwelling irradiance 22 WASI manual version 3 malized The two spectra provided with WASI were determined from measurements at Lake Constance The four functions t A are shown in Fig 2 4 2 8 2 Below water surface The downwelling irradiance in water Eq is related to the downwelling
93. tically from the reflec tance at any wavelength for which phytoplankton and Gelbstoff absorption are either known or can be neglected The equation of determination is obtained from the irradiance reflectance model described in section 2 5 1 Two models are implemented RO f den Bo 4 1a SRG a A b w A Bo_ RO f bow 0 Bo 4 1b a A 44 WASI manual version 3 Settings for individual spectrum types Rossccssesasesesessesiasenisasiasessenccssenessosesenni deep water IV Analytic estimate of C_L h at 870 5 0 nm JV Analytic estimate of C O and C_Y at 413 2 150 nm and 440 5 0 nm Pre fit of C_L C_Y from 760 to 800 nm steps fio nm max Iterations 100 Pre fit of C O C_Y from 380 to 450 nm steps fio nm max Iterations 100 Fig 4 9 The register card Irradiance reflectance for deep water of the pop up window Fit tuning Eq 4 1a is the Gordon et al 1975 model eq 4 1b the Prieur 1976 model see section 2 5 1 If absorption of water and its constituents a is known at a certain wavelength Ar Bo is calculated as follows B nt Dow Ag oe a A ie RAR f B bw jp 4 2b These equations are obtained by solving eqs 4 1a and 4 1b for Bo respectively Which is used for calculating Bo depends on the selected R model a A r is calculated according to eq 2 3 using as inputs the values from the parameter list typically a Ajr is v
94. tion is specified in the Weights register card of the pop up window Fit tuning which is shown in Fig 4 5 and accessed from the menu bar via Options Invers calculation Fit tuning see Fig 7 1 Path and file name of that function are displayed in the File field the file can be exchanged by opening a file selection window by pressing the button The number of header lines and the columns of the x and y values have to be specified also If all wavelengths shall be weighted equally the file must contain a constant function at the best with 1 as y values Such a file EINS PRN is set as de fault in WASI Settings for all spectrum types Initial values Final Fit Residual Weights File d Header lines 2 Column with x values fi Column with y values 2 Fig 4 5 The register card Weights of the popup window Fit tuning 40 WASI manual version 3 Settings for all spectrum types Initial values Final Fit Residual Weights Minimize rare A TC y values logarithmic Least squares m f 2 Absolute differences m fl C Relative differences 1 f ml nessuna F HF Fig 4 6 The register card Residual of the popup window Fit tuning The minimization method is selected in the Residual register card of the pop up window Fit tuning which is shown in Fig 4 6 The equations of calculation are summarized in Ta ble 4 1 Cno method Jyvalues minimize sere 39 Jim nE
95. tiply automatically all remote sensing reflectance spectra R A those read from file as well as those forward calculated with a factor whose value is set in the adjacent input field This provides a fast way to convert R s A to irradiance reflectance R A using the model of Eq 2 13a Ris A R A Q The conversion factor is set to Q x 3 1416 by default which represents the idealized case of isotropic reflection WASI manual version 3 69 8 References E Aas 1987 Two stream irradiance model for deep waters Applied Optics 26 11 2095 2101 Y H Ahn A Bricaud A Morel 1992 Light backscattering efficiency and related proper ties of some phytoplankton Deep Sea Res 39 1835 1855 A Albert C D Mobley 2003 An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case 2 waters Optics Express 11 2873 2890 http www opticsexpress org abstract cfm URI OPEX 1 1 22 2873 A Albert 2004 Inversion technique for optical remote sensing in shallow water Ph D the sis University of Hamburg http www sub uni hamburg de opus volltexte 2005 2325 A Albert P Gege 2005 Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties Applied Op tics accepted A Bricaud A Morel L Prieur 1981 Absorption by dissolved organic matter of the sea yellow substance in the UV and visible
96. ttom reflectance The spectrum type Bottom reflectance is activated by selecting this type in the main win dow from the drop down list above the Start button see Fig 6 7 left After the spectrum type is set to Bottom reflectance the check box radiance sensor Fig 6 7 left and the parameter list shown in Fig 6 7 right are displayed Parameter Value falo 0 200 Bottom reflectance arty 0 fa 2 fo 300 Start fal3 0500 fa 4 fo Y radiance sensor fa 5 fo Fig 6 7 Settings of the spectrum type Bottom reflectance in the main window Left Drop down list with Bottom reflectance selected as spectrum type Right Parameter list of the forward mode If the check box radiance sensor is marked with a hook like in Fig 6 7 left the bottom reflectance is calculated for a radiance sensor using eq 2 22 Otherwise 1t is calculated for an irradiance sensor using eq 2 21 Bottom albedo irradiance reflectance is calculated as a weighted sum of 6 albedo spectra The weights fn fa n n 0 5 are the relative areas of the 6 bottom types within the sensor s field of view Consequently it is 2 fa 1 thus only 5 of the fi are independent parameters while one is calculated using 2 f 1 Which of the weights is adjusted in this manner is de fined in the register card Bottom of the pop up window Model options see Fig 6 8 It is accessed from the menu bar via Options Models see Fig 7 1 T
97. types The following table gives for all spectrum types an overwiew which equation is used for cal culation and which parameters can be used as fit parameters N maximum number of fit parameters Spectrum type Model options Symbol Absorption Exclude pure water awc A 2 1 Include pure water aw A 2 3 10 Co C5 X Y S T Attenuation For downwelling irradiance Kal 2 5 14 Co C5 X Y S T CL Cs n Osun Specular reflec Wavelength dependent Rea 2 13a tance N Fit parameters Co Cs X Y S o 10 a B y 5 a Bx y v OL 4 Co Cs X Y S Tr CL Cs n Osun or f Constant Reo 2 13b Irradiance reflec For deep water R A 2 14 tance For shallow water R 2 16 Osun fo fs ZB Remote sensing For deep water below water sur R s A 2 17a 15 Co Cs X Y S T CL Cs n Osun reflectance face or f Q Rrs A 2 17b 15 Co Cs X Y S T CL Cs n Osun Ov Co C5 X Y S T CL Cs n Osun 0 or Q fo f5 ZB Co C5 X Y S T CL Cs n Osun or f Q a B y ax Br yx Se Vy OL Co Cs X Y S T CL Cs n Osun or f Ov Q a B y ax Br yx 6 v OL Co C5 X Y S T CL Cs n Osun or f Q or Ov a B y ax Be yx 9 v OL 16 Co C5 X Y S T CL Cs n Osun or f Q oL 2 Co C5 X Y S T Ci Cs n BE For shallow water below water Ra 2 19 22 A
98. types Determine a second estimate of C Cs Y and Zz by fitting a wave length interval in the infrared Co Y S Zg All parameters Table 4 3 Procedure for inversion of irradiance reflectance spectra of shallow water Determine a first estimate of S a second of Co and a third of Y ae and Zp by fitting a wavelength interval in the blue All fit parameters are fitted Fine tuning of steps 1 2 4 6 and 7 is done in the Irradiance reflectance register card of the Fit tuning pop up window It is shown in Fig 4 10 Steps 1 and 2 are performed if the check boxes Analytic estimate of are marked with a hook Otherwise the initial values from the parameter list or from the previous fit are taken as described in section 4 2 2 Steps 4 6 and 7 are tuned in the Pre fit frames The pre fits are performed if max iterations is set to a value larger than 1 At step 8 the user can define the wavelength range to be fitted the inter vals between data points and the maximum number of iterations The relevant user interface is shown in Fig 4 7 Step 1 The equation 2 16 which parameterises irradiance reflectance of shallow water is simplified by setting Kuw A Kup A Ka A The resulting equation R A R A A R A exp 2K A z A R A expt 2K A z 4 14 is solved for Zp b pe 4 15 2K A R A R A Various simulations were performed to study the accuracy of this equation depending on
99. uction mode the panel of the forward mode for specifying the parameter iterations is displayed 5 Check boxes for selecting model options As in the forward mode 36 PI wast water color sim 13 ur File Display Options Help MY Parameter Fit Value CIO cn CP ca cia cs GL C CX CY 5 3 Iv C st III UT a sii ab BUG SIA ali GES sta sio ata ndo SEA W E 1 m 0 400 0 0140 8 0 330 FF calculate sigma_L from viewing angle Remote sensing reflectance sr 1 WASI manual version 3 210 x D WASI LOESB1 fwd 0 020 0 018 0018 0 014 0 012 0 010 0 0080 0 0060 measurement fit wei pity T T 400 500 Remote sensing eni y 7 shallow water above water E wavelenath dependent suf3de reflections T T T 600 700 800 wavelength nm resi A 57 Residuu 9 85E 6 im Y invert spectr O batch mle tead from file Fig 4 1 Graphical user interface of the inverse mode 1 Drop down list for selecting the spectrum type 2 Check boxes for specifying the operation mode 3 Parameter list model specific 4 Dis play elements depending on mode of operation 5 Check boxes for selecting model options model specific 6 Menu bar 7 Start button 8 Plot window 6 Menu bar As in the forward mode 7 Start button Inverse modeling is started by pressing this button 8 Plot window The inp
100. umn with y values aP 4 Specific absorption spectrum of phytoplankton class no 4 d wasi data dino a 0 Header lines Column with x values Column with y values N Il aP 5 Specific absorption spectrum of phytoplankton class no 5 d wasi data green a 0 Header lines Column with x values 2 Column with y values aX Absorption of non chlorophyllous particles d wasi data x a WASI manual version 3 large particles const sand silt green makrophyte Chara aspera green makrophyte Potamogeton perfoliatus green makrophyte Potamogeton pectinatus Sky radiance reflected at surface Ls Remote sensing reflectance R_rs 7 Header lines Column with x values 2 Column with y values aY Specific absorption of Gelbstoff d wasi data y a 2 Header lines Column with x values 2 Column with y values bL Scattering coefficient of d wasi data eins prn 2 Header lines Column with x values 2 Column with y values albedo 0 Bottom albedo 0 d wasi data bottom r 5 Header lines Column with x values 2 Column with y values albedo 1 Bottom albedo 1 d wasi data sand r 21 Header lines Column with x values 2 Column with y values albedo 2 Bottom albedo 2 d wasi data bottom r 5 Header lines Column with x values 3 Column with y values albedo 3 Bottom albedo 3 d wasi data bottom r 5 Header lines Column with x values 4 Column with
101. ut spectrum is displayed in blue the fit curve in red The window is refreshed before a new pair of spectra is plotted thus only the last pair remains on screen when a series of spectra is analyzed The file name of the imported spectrum is shown on top right In the example of Fig 4 1 a remote sensing reflectance spectrum above water imported from the file B1 fwd was inverted in the single spectrum mode The spectrum had been previously generated in the forward mode where noise with a standard deviation of 2 10 sr was added During inversion three parameters were fitted C 0 C_L sigma_L the other parame ters were kept constant Fit results are C 0 1 88 ug I C L 3 96 mg 1 and sigma L 0 201 The fit converged after 157 iterations at a residuum of 9 85 10 sr WASI manual version 3 37 4 2 Inversion of a single spectrum 4 2 1 Spectrum selection A single spectrum from file is selected as follows e Define the spectrum type select the type from the drop down list in Fig 4 1 e Load the spectrum Loading the spectrum is illustrated in Fig 4 2 The pull down menu File is opened from the menu bar and Load is selected top Then a pop up window for file selection opens where the desired file is selected bottom Note The layout of the file selection window depends on the operating system and the language here the version of Windows 2000 in German is shown File Display Options Help Load Sav
102. vity studies 4 1 Graphical user interface The appearance of WASI s graphical user interface GUI depends on the spectrum type and on the operation mode Fig 4 1 shows the GUI for the example of the spectrum type Remote sensing reflectance and the single spectrum mode The GUI consists of 8 elements 1 Drop down list for selecting the spectrum type As in the forward mode 2 Check boxes for specifying the operation mode In the inverse mode the box invert spec tra is checked A hook in the batch mode check box indicates that a series of spectra is analyzed Otherwise a single spectrum is inverted single spectrum mode The check box read from file selects whether the spectra are read from files hook or 1f previously forward calculated spectra are used reconstruction mode no hook 3 Parameter list The list tabulates the start values of the fit parameters Defaults are read from the WASI INI file the user can change them by editing the Value fields A hook in a Fit check box makes the corresponding parameter to a fit parameter otherwise the parameter is kept constant during inversion In the single spectrum mode the resulting fit values are displayed after inversion is finished 4 The appearance of this area depends on the mode of operation In the single spectrum mode the residuum and the number of iterations are shown here after calculation is fin ished In the batch mode this area is empty In the reconstr
103. wavelength and on errors of concentration and bottom type Albert 2004 The wavelength interval 600 650 nm was found to be best suited thus it is used by default in WASI By aver aging the zg values of that interval an accuracy of zg of typically 20 40 can be expected at moderate suspended matter concentration lt 10 mg l and zg lt 10 m Such accuracy is suffi cient to initialise zp WASI manual version 3 49 Settings for individual spectrum types Irradiance Itradiance reflectance Remote sensing reflectance JV Analytic estimate of 2B shallow water at 630 120 nm Y Analytic estimate of C_L at 760 20 nm M C O and C_Y by nested intervals and fit of absorption spectrum from 400 to e00 nm steps 5 nm max Iterations 100 m Pre Fit of C_L C_S and C_Y from 700 to 800 nm steps 5 nm max Iterations 100 m Pre Fit of C 0 C_Y and S from 400 to 500 nm steps 5 nm max Iterations 100 Fig 4 10 The register card Irradiance reflectance for shallow water of the pop up window Fit tun ing Step 2 Like in the deep water case an analytic approximation of the reflectance spectrum is solved for suspended matter backscattering Bo by A bp w A to obtain an analytic equation for Bo The analytic approximation of the reflectance spectrum is given by eq 4 14 in which R A is replaced by eq 4 1a Solving this equation for Bo yields RBN wb 100 B i 1 R A
104. way with different A values until one of the following stop criteria is reached 1 the ratio R RY 1 which is a measure of the deviation between calculated value R and measurement R is below a threshold Sin 2 the number of iterations exceeds a threshold imax The rule for cal culating Aj from A is as follows Ke if 8 lt 0 A 4 18 i he Adesso 1 The value of the last iteration A 1 is assigned to awc These iterations are performed wave length for wavelength The wavelength range 400 800 nm and a wavelength interval of 5 nm were found suitable thus these are used by default in WASI As a result an estimate of the spectrum awc A is obtained Ao 5 m A 1 m Smin 0 01 and imax 100 are set as de faults in WASI Wavelength range wavelength interval and imax can be changed in the frame labeled C 0 and C_Y by nested intervals and fit of absorption spectrum of Fig 4 10 Ao A and min can be changed by editing the WASLINI file Step 4 A first estimate of the two parameters Co and Y is determined by fitting the spectrum awc A from step 3 with the Simplex algorithm using eq 2 1 The parameters C Cz and X of eq 2 1 are set to zero in this step For wavelength range wavelength interval and imax the same values are taken as in step 3 Step 5 The areal fractions f of all those bottom types are set equal which are marked as fit parameters Steps 6 and 7 These steps can be tuned by the para
105. wind roughened sea surface J Phys Ocean 16 1293 1316 L Prieur 1976 Transfers radiatifs dans les eaux de mer Thesis Doctorat d Etat Univ Pierre et Marie Curie Paris 243 pp L Prieur S Sathyendranath 1981 An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments dissolved organic matter and other particulate materials Limnol Oceanogr 26 671 689 T Pyh lahti P Gege 2001 Retrieval of water quality parameters using different channel configurations Proc ISPRS symposium Physical measurements amp signatures in remote sensing Jan 8 12 2001 Aussous France T I Quickenden J A Irvin 1980 The ultraviolet absorption spectrum of liquid water J Chem Phys 72 8 4416 4428 72 WASI manual version 3 S Sathyendranath T Platt 1988 Oceanic Primary Production Estimation by Remote Sens ing at Local and Regional Scales Science 241 1613 1620 S Sathyendranath L Prieur A Morel 1989 A three component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters Int J Remote Sensing 10 1373 1394 S Sathyendranath T Platt 1997 Analytic model of ocean color Applied Optics 36 2620 2629 J N Schwarz P Kowalczuk S Kaczmarek G Cota B G Mitchell M Kahru F Chavez A Cunningham D McKee P Gege M Kishino D Phinney R Raine 2002 Two models for abso
106. ws to inspect and modify the settings di WASI Water color simulator File Display Options Help Models Forward calculation Invers calculation Data in out Reconstruction mode Fit tuning Directories Fit parameters Display General Fig 7 1 The structure of the Options menu The pop up menus of the first four thematic areas are described in the previous chapters Models in chapter 6 Figs 6 3 6 4 6 6 6 8 Forward calculation in chapter 3 Fig 3 2 Invers calculation in chapter 4 Figs 4 4 to 4 12 and Reconstruction mode in chapter 5 Fig 5 3 The pop up menus of the three remaining themes are described in the following 7 1 Directories The directories for saving calculated spectra and for reading import spectra are selected in the Directories pop up window It is accessed from the menu bar via Options Directories see Fig 7 1 and shown in Fig 7 2 The pre selected directories can be changed by entering a new directory name or by pressing the button and selecting a directory from the displayed directory tree not shown E Directories A ES Save results Forward calculations a Wasitsimul loe E Inversion d WASI simul loe le Read spectra Inversion D Wasi simul loe E Cancel Fig 7 2 The pop up window Directories WASI manual version 3 67 7 2 Display options The pop up window for settings concerning visualisation is shown in Fig 7 3 It app
107. y values albedo 4 Bottom albedo 4 d wasi data bottom r 5 Header lines Column with x values 5 Column with y values albedo 5 Bottom albedo 5 d wasi data bottom r 5 Header lines Column with x values 6 Column with y values Measurement d wasi data demo R fwd r 8 Header lines Column with x values Z Column with y values Measurement Irradiance reflectance R d wasi data demo R fwd r 8 Header lines Column with x values 2 Column with y values Measurement Downwelling irradiance Ed d wasi data demo E_down R2R C1 30 header lines column with x values 2 column with y values Measurement d wasi data demo L_sky Ls fwd 8 header lines column with x values 2 column with y values Measurement D WASI DATA DEMO R_rs s2am c o 27 Header lines Column with x values 2 Column with y values 5 Measurement Attenuation for downwelling irradiance Kd d Wasi data demo K_down K prn Header lines Column with x values Column with y values Weighting function for inversion d Wasi DATA EINS PRN 76 WASI manual version 3 2 Header lines Column with x values 2 Column with y values Spectra inverted in batch mode D WASI TEMP fwd 8 Header lines Column with x values 2 Column with y values Directories D WASI TEMP D WASI TEMP save FWD save INV General settings and parameters 380 xu lowest x coordinate displayed 805

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