SHYPFIT User's Manual
Contents
1. Br 1 E 1 1 for lt 1 e the unimodal model of van Genuchten 1980 1 m 155 2 mem e orthe model of Durner 1993 which is amultimodal form of van Genuchten s equation H 1 mi 27 PP p 3 gt cn 1 1 1 OVERVIEW 2 Equations 1 2 and 3 calculate the effective saturation as a function of the matric potential 4 L if expressed in pressure head units in the unsaturated range 0 0 The effective saturation is defined by 0 0 0 450 4 where 01 61 is the volumetric water content 0 is the saturated water content 0 is the residual water content In 1 Ya L is the matric potential at the air entry point and is a parameter related to the width of the pore size distribution Typical values for A range from 0 25 for sands to 0 1 for clays In 2 L is a scaling parameter for the matric potential and n and m are curve shape coefficients Equation 3 is a linear superposition of van Genuchten curves Its parameter indicates the modality of the pore size distribution Each subcurve is defined by its weight w subject to 0 lt w lt 1 and w 1 and the curve shape parameters gt 0 L n gt 1 and m gt 0 which can be interpreted analogous to the original van Genuchten parameters The properties of these models and the related pore size distributions are dis cussed by Durner 1991 19922. ar ot 1 4638 opt 3169 1 1 Number of data read 13 Average WC Deviation 00044 SEOB er Stagnation of fitting error E EXAMPLE OUTPUTFILE SHYP TAB E Example Outputfile SHYP TAB bsp DAT Bimodal Test model modal iun wgs wgr al 0 2 0 50 02 04992 pF WG pF Krel pF 3 00 500000 999501 400 2 90 500000 999408E 00 2 80 500000 999295E 00 2 70 500000 999159 00 2 60 500000 998994 00 2 50 500000 998794 00 2 40 500000 998551 00 2 30 500000 998257E 00 2 20 500000 997900 400 2 10 500000 997467E 00 2 00 500000 996941 00 1 90 500000 996302E 00 1 80 500000 995526E 00 1 70 500000 994582E 00 1 60 499999 993436E 00 1 50 499999 992042E 00 1 40 499999 990347 00 1 30 499998 988286E 00 1 20 499997 985781E 00 1 10 499995 982735E 00 1 00 499992 979033E 00 90 499988 974534E 00 80 499982 969067E 00 70 499972 962429 00 60 499957 954372E 00 290 499934 944601 00 40 499898 932761E 00 30 499844 918432E 00 20 499761 901119E 00 10 499634 880245E 00 00 499438 855145 00 10 499140 825072E 00 20 498683 789213E 00 30 497987 746731E 00 40 496927 696839E 00 50 495323 638944E 00 60 492908 572858E 00 70 489313 499118E 00 80 484036 419357E 00 90 476455 336653E 00 1 00 465884 255572E 00 1 10 451714 181596E 00 1 20 43
3. 15 15 15 15 15 16 16 20 20 21 22 23 Disclaimer The program SHYPFIT is a non commercial product for scien tific use The program can be used and copied for other users without restriction According to my knowledge the program is free of severe bugs However the actual program version 0 2 has not been thor oughly tested so far There is no warranty for it of any kind whether expressed or implied The SHYPFIT user is responsi ble for ascertaining the suitablility of the program for any use and consequently has all the responsibility and cost that may arise from using it It is not recommended to forward a copy of this version to new users Rather interested scientists should directly write to me so that they can get the latest program version SHYPFIT is available via anonymous ftp from server btgyx2 geo uni bayreuth de on directory pub msdos shypfit Users who fetch the software may want to send an information to me by e mail By this they can be put on the mailing list for notification of bug fixes and updates Bayreuth November 10 1998 Wolfgang Durner Dr W Durner Dept of Hydrology University of Bayreuth Phone 49 921 552147 D 95440 Bayreuth Fax 49 921 552263 Germany email durner uni bayreuth de iii Fast Start Follow the instructions below if you hate reading User Manuals but want to see immediately whether and how SHYPFIT works on your PG 1 2 Insert the SHYPFIT disk
4. 6 10 023049 961049E 15 446559 08 117225 02 910 6 20 022454 471362 15 320655 08 108413E 02 920 6 30 021916 231214 15 230263E 08 994473 01 930 6 40 021430 113428E 15 165362E 08 902428E 01 940 6 50 020990 556502 16 118760 08 806812E 01 950 6 60 020593 273056E 16 852956E 09 705852E 01 960 6 70 020233 133990 16 612635E 09 596614 01 970 E EXAMPLE OUTPUTFILE SHYP TAB 6 80 6 90 7 00 019908 019615 019349 657543 322704 17 17 158384 17 4400421 316084 09 09 2270521 09 4734471 321925 E 01 E 01 0000001 E 00 25 980 990 1 000
5. Al in appedix A At the upper left of the screen the values of the retention func tion parameters are shown They are updated at each iteration Those parametes which are allowed to vary are labelled by the sign lt The value of the param eter o is given in a unit which is inverse to the unit specified in SHYP INI for the matric potential measurements The last two lines in the parameter list indi cate the current number of iterations NIT and the root mean square fitting error RMSE 1 n 6 4 where 6 lt gt is the difference between fitted and measured water content at the th matric potential The axes of the plot of the water retention curve are scaled automatically ac cording to the range of values of the measured data Alternatively they can be prescribed in SHYP INI After the optimization has finished the information on RMSE and NIT can be erased from the screen by entering RET Pressing a second time will plot the estimated relative hydraulic conductivity function 0 on the same graphics window The ordinate for K is logarithmic and labelled on the right hand side of the plot Pressing a third time will finish the run and return to DOS 2 3 2 Outputfile SHYP ERG The file SHYP ERG containes the optimized parameters and a table of measured and fitted water contents and the residuals The file is self explaining If a file with that name exists on the current directory the output will be append
6. integral in Eq 9 numeri cally it is possible to restrict the largest pore sizes considered in the conductivity prediction to a reasonable value By this all pore space covered by pores with equivalent radii larger than the specified size is treated as if the pores had the al lowed maximum size Generally it appears reasonable to set this maximum pore size RMAX in the range 1 to 5 mm since for larger pores the Darcy law and hence the definition of K is probably no longer valid Soils with macropores should be treated by different approaches By default the pore sizes for the prediction are not truncated i e RMAX oo Note that for retention curves with large n the truncation has no effect For a more extensive discussion of the topic see Durner 1991 108 118 3 6 Technical Notes PC Settings The program SHYPFIT uses ANSI escape sequences to control the screen output For a correct interpretation of these sequences it is necessary that the ANSI device driver is loaded This is done by including the command REFERENCES 17 DEVICE C DOS ANSI SYS in the file CONFIG SYS The path description in the above command must be directed towards the directory that contains the file ANSI SYS Monitor A VGA monitor with appropriate graphics card is necessary to monitor the fitting progress in real time on the screen Hardcopy of Graphics The graphics on the monitor screen can be printed in a low resolution by pressing
7. into the disk drive assumed A From the hard disk run the archive extraction program by typ ing A SHYPINST by typing its name and pressing the key This will expand some files on a subdirectory SHYPFIT Verify that the ANSI SYS driver is installed on your system if you are unsure see chapter 3 6 Change to the subdirectory SHYPFIT and run the program executable SHYPFIT EXE by typing its name and pressing the key Communicate with the running program interactively by typing the answers to the questions followed by If you are not sure about an answer choose the default value by just pressing the key If you want to run SHYPFIT with your own data prepare an ASCII datafile lt name gt DAT with your measured retention data in a format according to the example file SHYP DAT The file must contain a title in line 1 the single character 1 in line 2 and datapairs for the measured matric pressures and the related water content data in the following lines for more de tails see chapter 2 2 3 iv 1 OVERVIEW 1 1 Overview SHYPFIT Soil Hydraulic Properties Fitting is a computer program designed to fit uni and multimodal retention functions to measured water retention data and to compute the related relative hydraulic conductivity function To run the program a data file with the measured water retention data is re quired as input Some control commands and parametes for model choice ini
8. line 5 Initial values WGS_INI ND_WGS WGS_MIN WGS_MAX DWGS_INI DWGS_MIN varname Index for getting during the fitting process a real time graphics on the PC monitor retention function and predicted conductivity function are plotted versus the matric potential The axis ranges are determined by the parameters PL PU WL WU Note This option is only valid on PC s 1 Linear axis for matric potential 0 No plot 1 pF axis for matric potential Scaling parameter for plot of the retention function matric po tential at origin of the abscissa Scaling parameter for plot of the retention function matric po tential at end of the abscissa Scaling parameter for plot of the retention function water con tent at origin of the ordinate Scaling parameter for plot of the retention function water con tent at end of the ordinate If SHYP INI was created by SHYPFIT line 4 containes the names of the variables in lines 5ff The names are explained in the context of line 5 bounds and variation parameters for the saturated water con tent 6 as follows Initial value of parameter WGS If this value is set to zero the highest water content in the current dataset is taken as WGS Index controlling optimization of parameter WGS 0 parameter is kept constant at initial value 1 parameter is optimized Lower bound for parameter WGS Upper bound for p
9. pF 00 0 40 where w is the matric pressure head in cm water column 2 RUNNING THE PROGRAM 8 in square brackets are optional 2 2 4 Inputfile SHYP INI If a file SHYP INI is used to specify the program parameters it is recommendable to create by an interactive dummy run the protocol file SHYP CTR This file then can be edited with a text editor and modified according to the needs Finally this file can be renamed and used as input file for subsequent runs The format of 5 is given by Table 2 the entries are explained in Table 3 Table 2 Format of inputfile SHYP INI Line Content 1 datafile 2 MODEL MODE NITMAX KAPPA BETA TAU KSPR RMAX IUNIT KPLOT PL P 3 0 1 12 1 2 50 0 41 435 0 1 0 5 1 0 58 4 ND MIN D INI d _MIN 5 00000 0 000000 1 0000 0100 0001 6 00025 1 000000 4000 0200 0001 7 00500 1 000001 10 0000 2 0000 1 0010 8 1 60000 1 1 000000 50 0000 2 0000 1 0010 9 37500 0 000000 100 0000 2 0000 1 0010 10 1 00000 0 010000 9900 1000 0100 Table 3 Variables of inputfile SHYP INI Line Variable Content 1 Dummy line The line is not interpreted by the program If SHYP INI was created by SHYPFIT the line containes the name of the related datafile 2 Dummy line The line is not interpreted by the program If SHYP INI was cre ated by SHYPFIT this line containes the names of the program parameters The names are explained in
10. respect to soils with heterogeneouos pore size distributions In general the relative hydraulic conductivity function K is esti mated from the water retention curve The relative conductivity is defined by K K K where K and K are the absolute and the saturated conductivity LT respectively To calculate absolute conductivities the relative conductiv ity function must be 7matched to a measured value Often the saturated conduc tivity is used for matching Due to estimation uncertainties near saturation this is however not recommended for structured soils In SHYPFIT one of the following predictive models can be chosen e the model of Burdine 1953 K 22 1 J 1 6 e the model of Mualem 1976 2 K 0 1 24 1 Q zav 7 1 OVERVIEW 4 e or the model of Alexander and Skaggs 1988 Ko 1 _ 1 5 a 8 The parameter 7 in 7 is an empirical tortuosity factor generally set to r 0 5 In SHYPFIT the relative conductivities are computed by numerical evaluation of K 1 abd 1 9 Equations 6 7 and 8 become special cases of Eq 9 dependent on values of the parameters 3 and The accuracy of the numerical approximation was verified for the unimodal cases by comparison with analytical solutions The relative conductivity function can be matched to any measured conduc tivity by K 0 0 where th
11. such cases an ASCH file named FILELIST DAT must be created which containes just the data filenames without extension one name on each line SHYPFIT automati cally searches for the existence of such a datafile on the current directory Contrary to the normal mode SHYPFIT will not inquire interactively on how to proceed if the convergence criteria are not met within the prescribed maximum number of iterations It is therefore recommended to set the value of NITMAX in the file SHYP INI see below to a reasonable high value e g 40 If the plot option is set on KPLOT Z 0 the fitted curves will be shown on the monitor and pressing is required to proceed to the next datafile If the plot option is set off no inquiry will occur during the run 2 2 3 Inputfile datafile The measured retention data must be written on a file with the name extension DAT Table 1 shows the required format of the data file 2 RUNNING THE PROGRAM 7 Table 1 Format of inputfile datafile column 2 j nPAR title NCOL h 1 WC 1 1 WC 1 2 WC 1 3 WC 1 nPAR h i WC 1 1 WC 1 2 WC 1 3 WC 1 nh WC nh 1 WC nh 2 WC nh j WC nh nPAR The variables in Tab 1 are specified as follows title Title line which helps to identify the data The lines must con tain less that 50 characters its text appears on the plot and in the output files NCOL Column number 7 for water content data to b
12. the Printscreen key if previously the DOS command GRAPH ICS device has been called See the DOS manual for more information Data Size Limits The maximum number of matric potential data is 1500 the maximum num ber of water retention measurements at one matric potential is 12 Chosing Default Values In the interactive menues the default values are indicated by the gt sym bol Pressing the key activates these defaults The default value for the name of the file with the measured retention data is 5 References 1 Brooks R H and A T Corey 1964 Hydraulic properties of porous media Hydrology Paper 3 Colorado State University Fort Collins CO 1 27 2 Burdine N T 1953 Relative permeability calculations from pore size dis tribution data Petroleum Transactions American Institute of Mining and Metallurgical Engineers 198 71 87 3 Durner W 1991 Vorhersage der hydraulischen Leitf higkeit strukturierter B den Bayreuther Bodenkundliche Berichte 20 1 180 Fakult t f r Bi ologie Chemie und Geowissenschaften der Universit t Bayreuth Postfach 101251 D 95447 Bayreuth Germany 4 Durner W 1992 Predicting the unsaturated hydraulic conductivity using multi porosity water retention curves in Proceedings of the International Workshop Indirect Methods for Estimating the Hydraulic Properties of Un saturated Soils edited by M Th van Genuchten F J Leij and L J Lund
13. the chosen model type This is an assumption which is not easy to verify and it is likely that a natural soil just does not posess its or in the sense of a unique property In practice small confidence regions mean that the model parameters are estimated for a given data set with high pre cision because they are not correlated Hence small confidence limits can result even in cases where the model is obviously wrong as an example see Fig 2 in Durner 1992 On the other hand for a multimodal retention curve the parame ters are often highly correlated even if it describes measured data very well Since retention curve parametes are not further interpreted in an isolated manner which is in contrast to parameters of solute transport models SHYPFIT does not print any confidence limits 3 5 RMAX Truncating Pore Sizes Truncating the pore sizes to some maximum value can be of Importance for wide pore size distributions as indicated by a value of the van Genuchten parameter n close to unity In such cases the asymptotic shype of the retention model close to saturation represents a very small but for hydraulic conductivity prediction purposes not negligible part of the pore space in the range of very large pores This can cause an unrelistic decrease in the hydraulic conductivity prediction near saturation such that at a matric potential of say 1 hPa K has already dropped by orders of magnitude Since SHYPFIT evaluates the
14. the context of line 3 3 Values of the program parameters R WL WR Name WGS WGR Al N1 M1 WEIGHT1 2 RUNNING THE PROGRAM MODE IUNI Ligne Type of basic retention function 0 Equation 3 m 1 1 n 1 Equation 3 m 1 2 Equation 3 m optimized 3 Equation 1 Modality of the retention function Possible values depend on the model choice as follows 1 Unimodal any retention model 2 Bimodal only for TYPE 0 1 or 2 3 Trimodal only for TYPE 0 1 Maximum number of iterations If the stop criteria are not reached after NITMAX iterations the programm inquires inter actively how to proceed see next section Coefficient of the conductivity prediction model Eq 9 Coefficient 3 of the conductivity prediction model Eq 9 Tortuosity coefficient r of the conductivity prediction model Eq 9 Index for writing the hydraulic functions in tabular form on a file SHYP TAB see section 2 3 3 0 Don t write on SHYP TAB 1 Write hydraulic functions on SHYP TAB Pore radius rar mm which limits the maximum pore size considered in the hydraulic conductivity prediction model See section 3 Pore Sizes for details Index for the matric potential units in the datafile 0 pF 1 hPa 2 kPa 3 cm water column 4 m water column 2 RUNNING THE PROGRAM 10 KP HOD ro 4 Dummy
15. 00 000100 WCR 0000 1 001000 Al 0000 1 001000 N1 0000 1 001000 M1 1000 010000 0000 1 001000 2 0000 1 001000 N2 0000 1 001000 M2 1000 010000 WEIGHT2 C HARDCOPY OF SCREEN FOR DATA EXAMPLE C Hardcopy of screen for data example 21 D EXAMPLE OUTPUTFILE SHYP ERG 22 D Example Outputfile SHYP ERG Bimodal Test Results of the 7 Parameter Optimization Comparison of measured vs calculated data matric pressure water contents cm measureq calculateq difference plot 1000E 00 5000 5000 0000 1000E 02 4643 4652 0009 2512 02 3871 3871 0000 3981 02 3366 3361 0005 6310E 02 2904 2900 0004 1000E 03 2530 2533 0002 3162E 03 21932 1942 0011 6310E 03 1670 1672 0002 1000E 04 1490 1484 0006 3162E 04 1025 2021 0004 1000E 05 0674 0680 0006 1000E 06 0348 0350 0003 1000E 07 0246 0239 0007 Retention 1 2 2 21 Van Genuchten m 1 1 n Prediction model was sea ass Mualem Sat Water Content 50 0 fixed Res Water Content 1 85 opt 6800 opt alphas 27 oe le ete tr s 04992 opt Thre seca teint Schelde aw re er Sema force Se a qua yes 1 8390 opt She ara nunay 4562 1 1 n WET Git z ee Mia 3200 opt 2 00121 opt
16. 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 23 m2 23427 w2 32 Se 000 010 020 030 040 050 060 070 080 090 100 110 120 13 0 140 150 160 42 70 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 2350 360 370 380 390 400 410 420 430 440 450 E EXAMPLE OUTPUTFILE SHYP TAB 24 1 60 336174 110576E 01 566475E 02 124486E 03 460 1 70 311947 541352 02 416706 02 115132E 03 470 1 80 289885 262212 02 296806 02 106859 03 480 1 90 270322 127957 02 207043E 02 995062E 02 490 2 00 253242 638820 03 142939 02 929379 02 500 2 10 238413 329998 03 986356 03 870421 02 510 2 20 225484 177482 03 686900 03 817254 02 520 2 30 214053 994142 04 487306 03 769095 02 530 2 40 203716 576814 04 355037 03 725290 02 540 2 9 0 194088 343220E 04 266934E 03 685285 02 550 2 60 184831 206823E 04 207007E 03 648610E 02 560 2 70 175675 124597E 04 164537E 03 614868E 02 570 2 80 166438 741982 05 132647 03 583718 02 580 2 90 157043 433122 05 107227 03 554867 02 590 3 00 147508 246610 05 860815 04 528064 02 600 3 10 2137992 136734 05 681962 04 503088 02 610 3 20 128456 738968E 06 531597 04 479752 02 620 3 30 119234 390327 06 407624 04 457887 02 630 3 40 110399 202221E 06 307897E 04 4
17. 1993 and specifically for Eq 2 by Nielsen and Luckner 1992 1 2 Parameter Optimization The model parameters of the retention functions are optimized by minimizing the objective function Z P Su db P 5 where Z P is the objective variable is the parameter vector 0 is the measured water content at matric potential 4 abi 15 the estimated value of 8 at b nd is the number of 0 data pairs and w are weighing factors which are set equal the present implementation of the program Note that the optimization procedure does not minimize the euclidic distance in the 6 4 plane The nonlinear optimization routine of SHYPFIT follows a modified golden search algorithm Press et al 1992 This algorithm is robust and strictly con verging A disadvantage lies in its slow convergence close to the minimum par ticularly if parameters are correlated Generally the search will converge towards the global minimum of the objective function if the number of simultaneously op timized parameters is low However if 2 modal or 3 modal curves are fitted the objective function may possess local minima which sometimes cause problems To overcome this difficulty the initial parameter estimates can be manipulated and the parameter space can be bound 1 OVERVIEW 3 The optimization process stops when at least one of the following criteria is met i the parameters estimates are sufficiently precise i e
18. 3653 119777E 00 1 30 411961 730624 01 1 40 387543 413374 01 1 50 361784 219131 01 nl m1 1 83 45 Cap pF 618206 747416 904291 109483 132633 160769 194974 236571 287167 348722 423627 514793 625767 760875 925388 112573 136973 166692 202895 246998 300728 366188 445942 543105 661471 805643 981202 119489 145480 177059 215363 261704 317540 384402 463699 556358 662161 778679 899788 101411 110442 114992 113283 104766 906827 736798 wl 6 68 E 05 E 05 E 05 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 03 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 02 E 01 E 01 E 01 E 01 E 01 E 02 E 02 a2 00121 1 p Se 100000 224110 459080 182047 945899 569804 376821 265716 196338 150314 118316 952214 780336 649106 546715 465322 399564 345674 300950 263411 2231582 204348 180853 160430 142560 126828 2112907 100531 894888 796100 707573 628213 557141 493653 437164 387166 343179 304722 211288 242352 217379 195847 177269 161203 147264 135119 n2 46 E 36 E 07 E 06 E 06 E 05 E 05 E 05 E 05 E 05 E 05 E 05 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 04 E 03 E 03 E 03 E 03 E 03 E
19. 37350E 02 640 3 50 102053 103142 06 229611 04 418012 02 650 3 60 094259 519705 07 169464 04 399759 02 660 3 70 087047 259467E 07 124065E 04 382491E 02 670 3 80 080421 128666E 07 902743E 05 366119E 02 680 3 90 074365 634938 08 653897 05 350563E 02 690 4 00 068853 312258 08 472092 05 335751 02 700 4 10 063849 153209 08 340040 05 321619 02 710 4 20 059315 750562E 09 244527 05 308108E 02 720 4 30 055213 367344E 09 175648 05 295165 02 730 4 40 051504 179688E 09 126080E 05 282743E 02 740 4 50 048154 878722E 10 904588 06 270796 02 750 4 60 045129 429689 10 648846 06 259284 02 760 4 70 042397 210128E 10 465347 06 248171 02 2770 4 80 039930 102773E 10 333732E 06 237420E 02 780 4 90 0371703 502763 11 239347 06 227000 02 790 5 00 035693 246007 11 171668 06 216879 02 800 5 10 033877 120403E 11 123137E 06 207028E 02 810 5 20 032237 589436 12 883349 07 197419 02 820 5 30 030756 288629 12 633761 07 188025 02 830 5 40 029419 141366 12 454744 07 178819 02 840 5 50 028210 692545E 13 326330E 07 169773E 02 850 5 60 027119 339345 13 234204 07 160861E 02 860 5 70 026132 166310 13 168102 07 152055 02 870 5 80 025241 815216E 14 120669E 07 143322E 02 880 5 90 024435 399668 14 866274 08 134633E 02 890 6 00 023707 195971 14 621943E 08 125948E 02 900
20. SHYPFIT Users Manual Wolfgang Durner Draft Version 0 24 November 10 1998 Durner W SHYPFIT 0 24 User s Manual Research Report 95 1 De partment of Hydrology University of Bayreuth D 95440 Bayreuth Germany 25pp 1995 Contents 1 Overview 11 Retention 1 2 Parameter Optimization aes e ss e 13 Conductivity Estimation 2 Running the Program 2 1 Program Elements 2 2 2 2 28 2 2 228 osos 2 2 Program Input a 325153 22 1 Interactive Runs 2 2 2 RUNS a eB i al hA ade il 22 3 Inputfile datafile 224 Inputfile SHYP INI va EEE 23 231 Sereen Output k uu dg Lai b a puya us ute SG 2 3 2 OutputfileSHYP ERG 2 3 3 Outputfile SHYP TAB 3 Miscellaneous 3 1 Optimizing WGS a 3 2 Choice of Modality 222228 ee SEE a 3 3 Plotting Retention Curves from Given Parameter 3 4 Confidence Limits 25 55 read 39 Truncating Pore Sizes oieee a S ee s 3 6 Technical Notes i papaq au ai ea A Example Inputfile SHYP DAT B Example Inputfile SHYP INI C Hardcopy of screen for data example D Example Outputfile SHYP ERG E Example OutputfileSHYP TAB 13 13 13 14
21. University of California Riverside 185 202 REFERENCES 18 5 6 7 8 ki 9 10 11 Durner W 1993 Hydraulic conductivity estimation for soils with heteroge neous pore structure Water Resources Research in press Mualem Y 1976 A new model for prediction of the hydraulic conductivity of unsaturated porous media Water Resources Research 12 513 522 Mualem Y 1986 Hydraulic conductivity of unsaturated soils prediction and formulas in Methods of Soil Analysis Part 1 Physical and Mineralog ical Methods 2nd Ed edited by A Klute pp 799 824 ASA and SSSA Madison Wisconsin Mualem Y 1992 Modeling the hydraulic conductivity of unsaturated porous media in Proceedings of the International Workshop Indirect Meth ods for Estimating the Hydraulic Properties of Unsaturated Soils edited by M Th van Genuchten F J Leij and L J Lund University of California Riverside 15 36 Nielsen D R and L Luckner 1992 Theoretical aspects to estimate reason able initial parameters and range limits in identification procedures for soil hydraulic properties in Proceedings of the International Workshop Indi rect Methods for Estimating the Hydraulic Properties of Unsaturated Soils edited by M Th van Genuchten F J Leij and L J Lund University of Cal ifornia Riverside 147 160 Press W H S A Teukolky W T Vetterling B P Flannery 1992 Numerical Recipes The Art of Scientific Comp
22. arameter WGS Initial value of absolute variation width DWGS see comments below Minimum absolute variation width DWGS see comments below Name of parameter This entry is not interpreted by SHYPFIT and may contain any information or be empty 2 RUNNING THE PROGRAM 11 6 WGR Initial values bounds and absolute variation parameters for the residual water content 6 Initial values bounds and relative variation parameters for if TYPE Z 3 or 1 2 if TYPE 3 asas Initial values bounds and relative variation parameters for n if TYPE 3 Dummy line else O ML aa ay Dummy line if TYPE 0 or 1 Initial values bounds and relative variation parameters for n if TYPE 2 or for of the Brooks and Corey model Eq 1 Gf TYPE 3 10 WEIGHT1 Initial values bounds and absolute variation parameters for w If MODE 1 this is a dummy line since then by definition w 1 Initial values bounds and variation parameters for o 722 M2 and we of the multimodal retention model Eq 3 cf lines 7 to 10 These entries are not read if MODE 1 5218125 2 Initial values bounds and variation parameters for ns 772 and of the multimodal retention model Eq 3 cf lines 7 to 10 These entries are not read if MODE lt 2 In the following some additional remarks with regard to the contents of Table 2 are
23. e indicates the measured conductivity at water content 0 f 10 2 RUNNING THE PROGRAM 5 2 Running the Program 2 1 Program Elements The following diagram shows the input and output files which are involved in an optimization run The files in square brackets are optional datafile SHYP CTR SHYPINI SHYPFIT lt gt SHYPERG SHYP TAB All input and output files are of ASCII format They are specified as follows datafile contains measured retention data SHYP INI controls the run specifications If a file SHYP INI is located on the current directory SHYPFIT tries to read the run spec ifications from it If a file of that name does not exist SH YP FIT requires interactive program input SHYP ERG isa file on which the results of optimization runs are written If the file exists already new data are appended Otherwise the file is newly created SHYP CTR isa file that containes a protocol of the run specifications Its format is identical to SHYP INI Therefore it can be used after a first run as input file for further runs The content of SHYP CTR is overwritten at each run SHYP TAB is a datafile which is optionally created by SHYPFIT and containes the hydraulic functions in tabular form If SHYP TAB exists already SHYPFIT appends the hydraulic properties table to the existing file Each table is written with a four line header which allows to identify the contents of the table The tables ca
24. e used in the opti mization Data from the j th column are used in the fitting pro cedure Note if NCOL 1 the data will be filtered very similar data will be lumped thereby reducing the total number of data To avoid the filtering set NCOL 1 NCOL lt the arithmetic mean of all water contents of column 1 to column 7 will be used in the fitting procedure h i Matric potentials W hPa or kPa or equivalently matric pressure heads in cm water column m water column or pF The unit of the matric potential is inquired interactively or read from the file 5 If no unit is specified 4 is assumed to be in pF or cm water column automatic recognition WC i 3 Volumetric water contents which are related to h i SHYPFIT recognizes the units by considering the magnitude of the values The water contents are considered absolut if 0 lt 06 0 lt 1 or in if 1 lt Amar lt 100 where fmax is the largest measured water content nh Number of different matric potential values 1 lt nh lt 1500 nPAR Number of water content data at each matric potential 1 lt nPAR lt 12 By using this data format this number has to be equal for each matric potential All entries in Tab 1 are free of format i e they can be written in integer or real format and the columns have not to be aligned at specific positions The values The pF is a logarithmic unit for the matric potential It is defined by
25. ed to the existing content SHYPERG will include a warning message if the predicted relative hydraulic conductivity function has dropped at a matric potential of 1 hPa by more than one order of magnitude see the discussion of parameter RMAX in section 3 5 2 RUNNING THE PROGRAM 14 2 3 3 Outputfile SHYP TAB The file SHYP TAB Tab 3 containes tables of the soil hydraulic relationships and some control information on the related model parameters The file is of the form Table 4 Format of outputfile SHYP TAB Line Content 1 title 2 TYPE MODAL IUN WGR WGS Al Wl 2 N2 W2 3 0 2 0 005 30h 23922 2254 23D 00020 1 34 269 4 pF WG pF Krel pF Cap pF p Se Se 51 3 0 499999 89852E 00 113721 02 100000E 36 000 6 2 9 499999 89149 00 122303 02 292477 08 010 104 6 9 005413 46070 16 230861 08 810502 00 990 105 7 0 005000 23869 16 169483 08 000000 00 1 000 106 The first line containes copy of the title line of datafile The second and third lines contain the names and values of the model parameters respectively as de scribed in section 2 2 4 The fourth line is the column header for the table below which reaches from line 5 to line 105 The bottom line 106 containes minus signs indicating the end of the table The six columns in lines 4 to 105 contain two independent tables The first four columns list pF pF K pF and d dz in t
26. given e The bracketing interval for a parameter P extends from P_INI DP to P_INI amp DP if the variation is absolute i e for WGS WGR and the weights whereas it extends from P_INI amp P_MIN DP to P_INI amp P_MIN DP if the variation is relative i e for a n and m The initial variation width is de termined by the entries tt DP_INI in SHYP INT If the objective function has its minimum at the center of the bracketing interval the size of DP will be diminished for the next iteration Otherwise it will be enlarged With continuing iterations DP converges towards zero for absolute variations and towards for relative variations If DP is smaller than DP_MIN then it is assumed that the parameter P is determined with sufficient precision e The default values the variables in SHYPFIT depend on model type and modality For the standard case of fitting a unimodal van Genuchten equa tion are they listed in Tab 2 RUNNING THE PROGRAM 12 e The type of prediction model is determined by the specific combination of the parameters KAPPA BETA and TAU e The entries in SHYP INI may be incomplete This is true with respect to the entries in one line or equivalently with respect to the number of lines required by the particular model choice In such cases SHYPFIT uses its internal default values for the missing values and prints out a warning mes sage e All entries SHYP INI are free of f
27. he pressure range from pF 0 amp 10 cm pressure head to pF 7 amp 10 cm pressure head The two columns Satur and Saturation list the inverted function in the saturation range from 0 to 1 Note If the Brooks and Corey retention model has been chosen columns five ans six are not printed since the inversion can be easily done analytically 3 MISCELLANEOUS 15 3 Miscellaneous 3 1 Optimizing WGS If the saturated and the residual water content are optimized simultaneously the convergence of the fitting algorithm can become quite slow requiring in cases hundreds of iterations to find the minimum Therefore it is recommendable to set the saturated water content to the greatest measured value this is achieved automatically if WCS_INI 0 If laboratory data are used this will generally lead to good results However if data from field measurements are used which scatter considerably near saturation 0 should also be optimized 3 2 Choice of Modality It is generally a good idea to describe a dataset as simply as possible The uni modal constrained or unconstrained van Genuchten model will in many cases be appropriate If a more flexible description is required the bimodal retention curve with m 1 amp 1 n TYPE 0 default and with flexible weights of the sub curves is in most cases a very good choice In exceptional cases e g if there is an equally high pore density over a considerable
28. n be used for plotting the hydraulic relationsships or for numerical simulation programs 2 2 Program Input 2 2 1 Interactive Runs SHYPFIT inquires at the beginning of each run the name datafile of the file with the measured retention data If a file SHYP INI exists all other run specifications will be read from it otherwise a minimum number of interactive inquiries will follow asking for the model type the modality and some other basic parameters 2 RUNNING THE PROGRAM 6 If the optimization does not match the stop criteria after NITMAX iterations the following menu will appear on the screen here for NITMAX 40 Stop criteria after 40 Iterations not met Should the program gt 0 go on 1 stop 2 restart with new initial parameter estimates NN continue with NN gt 2 additional interations Pressing will activate the default action 0 i e the program assumes the fit to be sufficiently accurate and proceeds with the hydraulic conductivity estimation Entering 1 will stop the run without further computations entering 2 will ask for new initial values of the model parameters Entering a number nn greater or equal to 3 will increase the parameter NITMAX by nn and the optimization continues until either the stop criteria are met or the same menu appears again on the screen 2 2 2 Batch Runs SHYPFIT can process consecutively a series of different data files In
29. ormat hence it is not necessary to write the parameter values at certain column positions However note that the en tries of each parameter line may have no missing value ahead of a specified parameter value e g if you want explicitly to set parameter bounds you must specify also the initial values and the variation index ND e Inconsistent entries are to some extent detected and automatically corrected Examples are i For unimodal model MODE 1 the parameter is set to 1 0 re gardles of the entries in line 10 more general the weight w with 2 MODE is always determined by the previous weights w with lt MODE 1 and the constraint gt w 1 0 1 If in a bimodal optimization one of the two weights 401 or 402 is allowed to vary the other one varies too regardless of its specific ND value 11 If the initial value of a parameter is larger than the specified maxi mum value or smaller than its minimum value SHYPFIT corrects it automatically e It is generally recommended to use the default values of SHYP CTR See section 3 1 for additional hints regarding the treatment of the parameter 6 2 RUNNING THE PROGRAM 13 2 3 Program Output 2 3 1 Screen Output If SHYPFIT is successful in activating the VGA graphics mode the measured data and the fitted retention function are plotted at each iteration as a real time graphics on the screen thus allowing to monitor the fitting progress See Fig
30. range of pore sizes application of the threemodal model can be necessary Since the required CPU time increases by a factor of three for each additional free parameter it is recommended to keep in such cases the three weights constant at values which can be a priory roughly estimated by viewing the data Further the residual water content can be set very often to zero without loss of fitting accuracy 3 3 Plotting Retention Curves from Given Parameter Values SHYPFIT can be used as a convenient tool for creating tables or plots of retention curves and conductivity curves if function parameters are given To achieve this set all ND s to zero and run SHYPFIT A dummy file datafile which containes just one pair of synthetic data can be used to scale the axes of the retention curve plot Otherwise the axis boundaries should be set by 5 as described in section 2 2 4 3 4 A Note on Confidence Limits According to our experience the interpretation of confidence regions for fitting parameters can very easily lead to misconclusions small confidence limits do not automatically mean that the chosen model describes the data in an optimal man ner Any interpretation of confidence regions depends on the assumption that the 3 MISCELLANEOUS 16 a priory chosen model type is correct i e that the measured data are a random sample from a statistically homogeneous dataset with a mean retention curve that can be precisely described by
31. the bracketing in tervalls for all optimized parameters are below their limiting values 11 the total fitting error is smaller than some prescribed value iii the fitting error does no longer improve from iteration to iteration The typical number of iterations re quired to meet one of these criteria is around 10 20 for 2 parameter fittings and becomes larger if more parameters are to be fitted since then the correlation be tween parameters becomes more important The CPU time requirements for a three parameter optimization are typically in the range of seconds 486 CPU but increase with each additional parameter by a factor of 3 Further the time increases linearly with the number of matric potential data 13 Conductivity Estimation Hydraulic properties of porous media can be estimated from pore size distribu tions considering microscopic conceptual models for pore connectivity and pore tortuosity Since pore size distributions can be deduced from water retention curves statistical models have been developed where the relative hydraulic con ductivity function is estimated from the water retention curve The theory of conductivity estimation models has been extensively reviewed by Mualem 1986 1992 For a discussion of the assumptions the problems and the reliability of conductivity estimations the SHYPFIT user is referred to this original literature Durner 1993 has discussed the conductivity estimation problem with specific
32. tial parameter values bounds for parameter values output control etc have to be en tered interactively or are read from a parameter file If required the user can tailor the parameter optimization procedure to his specific needs SHYPFIT s output consists of a protocol file a results file and optionally of a file which containes the optimized hydraulic functions in tabular form During an optimization run the current fitting progress is shown in real time graphics When fitting retention functions to measured data two important criteria are i the correct model choice and ii the precise estimation of the model parame ters The best and simplest method to judge on the reliability of the optimization result is to view a plot showing the measured data and the fitted retention curve and to view a plot of the deviations between them Slovenly expressed if the curve is fitted to the data in a way as the user would do it by hand the result is satisfying If the model choice was correct the deviations should be uncorrelated i e look more or less randomly scattered The aim when fitting retention func tions to data is generally not the precise determination of a fifth digit of any function parameter but a good description of measured data 1 1 Retention Functions In SHYPFIT one of the following functions can be selected for the description of the retention characteristic e The model of Brooks and Corey 1964
33. uting 2nd edition Cambridge Univer sity Press 1992 van Genuchten M Th 1980 A closed form equation for predicting the hy draulic conducitivity of unsaturated soils Soil Science Society of America Journal 44 892 898 Appendix A Example Inputfile SHYP DAT B Example Inputfile SHYP INI C Hardcopy of screen for data example D Example Outputfile SHYP ERG E Example Outputfile SHYP TAB A EXAMPLE INPUTFILE SHYP DAT A Example Inputfile SHYP DAT Bimodal Test 00 NV DD HH HH 00 40 60 80 00 590 80 00 50 00 00 00 55 464291 387130 336629 290358 253044 2193 52 166984 148982 102527 067396 034764 024612 It s no problem to include comments like this to the data file 20 Just enter it following the data columns B Example Inputfile SHYP INI Bimodal Test MODEL MODE N 0 2 40 1 2 ND xxx 00000 0 027073 02461 1 000000 50000 1 000001 00000 1 1 000000 3 1900 0 000100 50000 1 010000 01000 1 000001 00000 1 1 000000 37500 0 000100 50000 1 010000 KAPPA BETA TAU KSPR RMAX 50 1 1 436 N 1 0000 425295 10 0000 2 100 0000 2 100 0000 2 9900 10 0000 5 100 0000 2 100 0000 2 9900 IUNIT KPLOT PL PR WL WR 0 1 D gt 4 0 3 6 0100 000100 WCS 02
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