FLOWNORM 1
Contents
1. Copy data to worksheets The concentration and precipitation data and sector data if necessary are copied to the worksheets Concentration by date and Precip and sector by date respectively Figure 1 shows how the input data shall be organised for the worksheet Concentration by date The date column shall be followed by an arbitrary number of columns containing the values of the monitored variables Strings found in the row immediately above the first observations row 2 in Figure 1 are interpreted as variable names Sampling site names are extracted from the cell two lines above the first date Missing values shall be entered as empty cells Less than values of the form lt 0 05 are permitted Figure 2 illustrates the Precip and sector by date worksheet The format of data inserted is the same as for concentration data but notice that precipitation data should be given in column 2 and sector in column 3 Sector data should be given as values 1 8 for classified sectors and 9 for remaining missing or unclassified Variable names f AE Aa wa gt BO w EEE O AT E 4 lt Hel 1987 01 07 987 01 08 0 18 DA 987 01 09 pa 987 01 10 Z 987 01 11 Pi 987 01 12 7 987 01 17 987 01 14 987 01 15 987 01 16 987 01 17 987 01 18 987 01 19 987 01 20 0 98 113 987 01 21 0 18 0 59 987 01 22 987 01 23 987 01 24 987 01 25 987 01 26 987 01 27 987 01 28 T ee at See z gt M Model selection2. Precip and sector by date Concentration by date Precipitation data summary 4 gt Ready Figure 1 The worksheet Concentration by date Insert you concentration data 1 5x 2 1 5x Ea 1 Te iis I w R a Kai FI Microsoft Excel Wetdepnorm_7_3 xls a x oe Type a question forhelp MEE Oshsn SRY t Be TESE Arial lio B CG Sy 48 808 O amp Arxe AE33 S Ta Ay B E Y D l F Soy H J K E A Birkene a date precip sector K 987 01 01 987 01 02 1987 01 03 987 01 04 28 987 01 05 987 01 06 4 1987 01 07 10 1987 01 08 1 11 1987 01 09 12 1987 01 10 13 1987 01 11 14 1987 01 12 7 15 1987 01 13 16 1987 01 17 1987 01 15 18 1987 01 16 19 1987 01 17 20 1987 01 18 21 1987 01 19 22 1987 01 20 23 1987 01 21 24 1987 01 22 25 1987 01 23 26 1987 01 24 27 1987 01 25 28 1987 01 26 29 1987 01 27 30 1987 01 28 ta M 4 gt i Model selection Precip and sector by date Concentration by date Precipitation data summary 4 gt Ready OO SO 1 Bw ra N oO Bm y DAWDWDADDINDWIADIAIWIDOOQOONOSBOWOODO Figure 2 The Precip and sector by date worksheet Insert precipitation and sector data here Sector data should be given in the third column and can be omitted if the analysis is done on seasonal data only Run macro Auditdailydata This macro checks that the data pasted on the worksheets Concentration
3. This list can then be edited prior to the load calculations Figure 4 shows the result of the matchprecipandconc macro on the Matched pairs worksheet In our dataset both series precipitation and concentration were labelled correctly with the site name Birkenes The macro matches the two series If the series were labelled using different site names but should be analysed together the combinations on the Matched Pairs worksheet can be edited now Ed Microsoft Excel Wetdepnorm_1_0 xls le x File Edit View Insert Format Tools Data Window Help Type a question for hep MAE X DERAS SBE Sna mwa R Arial 0 B Z U EFESBBES Wee el oA AE33 A f Pairs of sampling sites for flow and concentration Flow Concentration Birkenes Birkenes Site names are matched correctly M M 4 gt Mf Precipitation data summary Concentration data summary Matched pairs Annualtotals A Ready Figure 4 The matched pairs as result of the macro matchprecipandconc Select Analysis On the worksheet Model selection you have to choose if the computation of depositions and the normalisation of depositions should be done on annual summaries by sector or on seasonal summaries One of the methods has to chosen and it is not possible to choose both at the same time this implies that one of the cells must be empty while the other contains a yes or y When one of the classification methods is chosen for the computat
4. Run macro Compute_deposition This macro operates on the worksheets Model selection Precip and sector by date Concentration by date and Matched pairs The output worksheets are Annual totals and Monthly or sector totals Less than values are replaced by a fixed percentage of the detection limit The user is asked to enter the desired percentage when the macro is run In Figure 6 the computation of deposition is made by sector giving 9 outputs per year The response variables NH4 and NO3 concentrations and precipitation are used to compute annual deposition by sector The explanatory variable precipitation forms three new variables annual precipitation amount by sector number of precipitation days per sector number of precipitation periods 1 day of several consecutive precipitation days per sector Computation of depositions by seasons works in the same way then 12 values are given for each year the variables computed are the same File Edit View Insert Format Tools Data Window Help Type a question for help MER DERAN SRAY BBS o m Bxr 2 4 Mwy B Arial 7W BZU 8880 w EE LDA AE33 a f Birkenes Year Sector Precipitatii Raindays Rainperioc NH4 depo NO3 deposition 987 dl 81 8 6 18 31 20 013 987 2 35 1 7 0 462202 8 20699 987 3 1726 8 3 54 317 25 5225 987 4 96 3 12 2 123 774 99 859 987 5 223 8 8 2 87 17 79 926 987 6 240 6 20 4 86588 91 218 987 7 131 6 23 9 39 0853 40 9793 987 8 95 9 6 5 1
5. 1988 0 26 1989 0 17652 0 07245 0 38916 0 85964 1 26698 1 79445 0 75138 0 21446 3 18761 1989 0 25 1990 0 18703 0 07484 0 36848 0 82412 1 28344 1 79938 0 73115 0 22132 3 07334 1990 0 24 1991 0 19505 0 07667 0 35018 0 79 1 29315 1 79812 0 7094 0 22603 2 96279 1991 0 22 1992 0 20016 0 0778 0 33491 0 75535 1 29419 1 79099 0 68798 0 22849 2 85649 1992 0 21 1993 0 20158 0 07839 0 32273 0 72023 1 28585 1 77421 0 66818 0 22827 2 75365 1993 0 20 1994 0 19838 0 07852 0 31324 068358 1 26897 1 74518 0 64905 0 22548 2 65283 1994 0 18 1995 0 19138 0 07826 0 30618 0 64522 1 24361 1 70302 0 62883 0 22081 2 55153 1995 0 17 1996 0 18085 0 07755 0 30088 0 60541 1 21022 164826 0 60782 0 21504 2 44888 1996 0 15 1997 0 16696 0 07625 0 29559 0 56421 1 16824 1 58352 0 58604 0 20837 2 34367 1997 0 13 1998 0 15027 0 07449 0 28969 0 52311 1 11981 1 51192 0 56475 0 20137 2 23265 1998 0 12 1999 0 13177 0 07246 0 2822 048192 1 06717 143426 054526 0 19448 2 11725 1999 01 2000 0 11227 0 07049 0 27376 04415 1 01151 1 35342 0 52762 0 18783 2 00046 2000 0 0 2001 0 09259 0 0688 0 26475 040194 0 95592 1 271 0 51112 0 18118 1 88436 2001 0 06 2002 0 07285 0 06721 0 25555 0 36266 0 90035 1 18807 0495 0 17451 1 76825 2002 0 04 mereen at de a a SY e a Figure 12 On the worksheet Intercept the estimated time varying intercept for each class is given 14 Theoretical background Estimat
6. EA yim B Arial 10 BZU E886 wo EE LDA P2 z f AE c D E F G H J K E MZ 1 x x y y 3 Birkenes 4 Year Sector PrecipiatitRaindays Rainperioc NH4 depsNO3 deposition 5 987 1 81 8 6 1831 SQoN 6 987 i 5 1 7 0 462202 8 200 7 987 p 1726 8 3 54 317 25 5225 Beil 987 A 96 3 12 2 9 987 5 2238 2 y indicates that NH4 deposition aise i aet s and NO3 deposition are chosen me 1987 o 959 6 5 as response variables 13 987 9 4993 63 29 4 988 1 4 i r oe A 0 x indicates that precipitation 48 0059 and raindays are chosen as 338 25 explanatory variables 275 751 50 9356 2 7 825 6 298 22 1988 9 844 9 64 24 430 12 446 951 23 1989 1 35 1 9 i 21 065 18 0315 24 1989 2 9 4 4 2 1 21308 1 87919 25 1989 3 19 2 4 2 19 649 18 78 26 1989 4 12 6 2 0 7 542 8 127 ih 1989 5 T2 if 4 258519 42 6103 28 1989 6 4429 48 13 316 135 384 685 29 1989 T 1222 35 9 39 8464 56 8068 30 1989 8 29 8 4 762146 7 4103 i 8 ian M 4 gt vif Concentration data summary Z Matched pairs Annualtotals Seasonal or sectoral totals N 4 Ready Figure 7 Indicate explanatory variables by x and response variables by y Run macro definenormalisationmodels After indicating explanatory and response variables run the macro definenormalisationmodels which combines the variables in all possible ways See Figure 8 shows the output of this macro on the worksheet Normalisation models Also thi
7. Normalisation Models after editing 11 Run macro wet_dep_normalise This macro aims to remove or suppress the natural variation in deposition data either monthly or annual by sector The different normalisation models to be computed are read from the worksheet Normalisation models Input data are read from the worksheet Seasonal and sectoral totals and the outputs of the macro are printed on the worksheets Normalised annual totals see Figure 11 and Normalised seasonal totals Figure 10 When running the macro wet_dep_normalise there are two possibilities use cross validation to determine smoothing parameters recommended insert smoothing parameters manually After you start the program you will see a message box asking if cross validation should be used Insert yes for cross validation and no for manual input If you choose cross validation the macro will start running if you choose manual you get a new message box asking for the first smoothing parameter determining the smoothness between years and after that a last message box asking for the second smoothing parameter determining the smoothness between classes i e sectors or seasons E Microsoft Excel Wetdepnorm_1_0 xls Beles File Edit View Insert Format Tools Data Window Help Type a ionforhelp MTE X DSHS ARAY t Be Jinas eao BLE Arial H S w H aA M Model 1 Model 2 Model 3 Model NH4 depo SP no
8. by date and Precip and sector by date are of correct type and properly organised When Auditdailydata is run the macro first identifies the name of active worksheet Concentration by date or Precip and sector by date and then the first cell containing date values RI Microsoft Excel Wetdepnorm_7_3 xls le x i File Edit View Insert Format Tools Data Window Help Type a question for hep EEE X OSE AR GRY t Bea S anA E o h y im an gt Arial 70 B 7z UES Ses x WEEE DA Birkenes date NH4 NO3 987 01 01 987 01 02 987 01 03 987 01 04 0 26 0 27 1987 01 05 987 01 06 0 1 0 39 987 01 07 987 01 08 0 18 0 3 987 01 09 987 01 10 987 01 11 987 01 12 987 01 13 1987 01 14 987 01 15 987 01 16 987 01 17 987 01 18 987 01 19 987 01 20 0 98 1 13 987 01 21 0 18 0 59 987 01 22 1987 01 23 987 01 24 987 01 25 987 01 26 Ta gt M Concentration by date Precipitation data summary 4 Matched pairs Concentration data summ 4 gt l Ready Figure 3 Concentration by date worksheet after the macro Auditdailydata was run The first data row is moved to row five Run macro matchprecipandconc This macro facilitates the matching of precipitation sector values and concentration data for deposition calculations Based on the identified names of the sampling sites for flow and concentration the macro prints a preliminary list of matched pairs on the worksheet Matched pairs
9. 3 3473 10 8623 987 9 499 3 63 29 301 293 313 444 988 1 42 1 7 4 115609 8 0871 988 2 0 0 0 0 0 988 3 49 1 4 2 71 1753 48 0059 988 4 30 6 5 1 45 273 32 606 988 5 365 18 3 383 248 298 152 988 6 451 3 36 7 217 174 275 751 988 7 163 9 20 9 48 9024 50 9356 988 8 39 2 7 5 7 825 6 298 988 9 844 9 64 24 43012 446 951 989 l 351 9 T 21 065 18 0315 989 2 94 4 2 1 21308 1 87919 989 3 19 2 4 2 19 649 18 78 989 4 12 6 2 0 7 542 8 127 989 5 72 2 7 4 25 8519 42 6103 989 6 442 9 48 13 316 135 384 685 989 7 1222 35 9 39 8464 56 8068 989 8 29 8 8 4 762146 17 4103 M 4 gt MI Concentration data summary 4 Matched pairs_ _ Annual totals _ Seasonal or sectoral totals N 4 gt Ready Figure 6 Annual deposition by sector Besides NH4 and NO3 deposition and precipitation amount by sector two new variables are added raindays number of precipitation days per sector and rainperiods number of 1 days of longer precipitation periods per sector Define normalisation models and compute normalised values Indicate response and explanatory variables In this step the user must indicate which variables should be interpreted as explanatory and response variables respectively This is done by writing x for explanatory variables and y for response variables in the second row just above the data columns that are chosen File Edit View Insert Format Tools Data Window Help Type a question for help fila ig oe DEHAN SRAY Bae Snara
10. 6 989 1989 83 0 07621 0 23198 0 22817 0 07621 0 25246 0 25947 0 174 0 3292 0 31678 0 1m M 4 gt pif Normalisation models f Normalised annual totals Normalised seasonal totals Intercept f Si 4 gt Ready Figure 10 Output on the worksheet Normalised seasonal totals For each model defined on the worksheet Normalisation models three outputs are given deposition values SP normalised and Reg normalised values The same output can be found on the worksheet Normalised annual totals but there aggregated for each year Reg normalised ANNO nhwn oOo oanhwon 12 On the worksheet Normalisation Models Figure 11 some information on the fitted models can be found In the first columns after the chosen explanatory variables the number of observations is given Then the smoothing parameters are listed as Lambdal and Lambda2 Furthermore Mean squared prediction error MSPE and mean squared residuals MSRes are given for all combinations of explanatory and response variables and for both the semi parametric and the regression approach EI Microsoft Excel Wetdepnorm_1_0 xls 8 x File Edit View Insert Format Tools Data Window Help Type a question forhelp Fl gl X DSH AR GRY Be Snan A E ei g Arial 710 FB 7 ole S t EEA E G H MSPE Mean Square Prediction Error Semiparametric regression Ordinary regression Sampling Response Explanatory variable 1 Explanator
11. WETDEPNORM 1 0 a Visual Basic program for computing wet deposition of substances and extracting anthropogenic signals from time series of deposition data User s Manual 2005 04 14 Claudia Libiseller Department of Mathematics Link ping University Introduction en sammanfattning kanske fran artikeln The Visual Basic programme WETDEPNORM has been developed to facilitate calculation of substance deposition extraction of anthropogenic signals from time series of deposition data WETDEPNORM Version 1 0 consists of five Visual Basic macros having the names and functions listed below Two Excel worksheets containing concentration and precipitation data for the sampling site form the starting point for an analysis It is also possible to include sector information on these worksheets The final result consists of time series of normalised loads i e deposition values that have been adjusted to remove natural fluctuations and clarify anthropogenic impacts Theoretical details can be found in the end of this description Macro Function auditdailydata Identify illegal entries in raw data matchprecipandconc Define pairs of precipitation sector and concentration data for load calculations compute_deposition Compute monthly and annual deposition from precipitation and concentration data ordered by date definenormalisationmodels Define response variables and normalisation models wet_dep_normalise Select n
12. anges in the intercept are controlled by so called roughness penalty factors A and 2 and the intercept and slope parameters are estimated by minimising the expressions for seasonal data Qi FOA 2 i l j i l 2 S B E O Buytig Bp Xp ty H i j ij C4 FO oa A gt a a Lj where Qio E Qim VE 2D Qima o Tahaan to ensure that smoothness between december one year and january the next year for data by sector 15 2 r n l Gizi a j 5 Sla p X oy aj Ai 71 4 Bp jXpi A gt gt i aj 5 i j j li 2 n r l Qir 29 Qi j 1 Qi j 1 2 Qi r 1 t amp il 2 42 ie gt aj 5 i j 2 n l Qil r 1 t Qi 1 r 1 2 4 airy 5 i 2 Detailed information about algorithms for parameter estimation of the seasonal model has been published by Stalnacke and Grimvall 2001 Details for the model using sectoral data can be found in Libiseller et al 2005 The parametric normalisation model is an ordinary multiple regression model of the general form Vy At BP Xy tet Bpi Xpy tE i l on j l m where yj Xrip and amp have the same meaning as above The slope parameters kj k 1 p are permitted to vary with the class j under consideration whereas the intercept is assumed to be constant Selection of roughness penalty factors and assessment of the predictive ability of the tested normalisation models If the penalty factors A and A are determined by cross validation the ent
13. ion of deposition also the normalisation of deposition must be conducted using the same classification E Microsoft Excel Wetdepnorm_1_0 xls lej x fs File Edit View Insert Format Tools Data Window Help Type a question for help MEE OSGHSH 6QY B SF o oo xr 4k MH ix L Arial 10 BLUES SH S W EE LAr C5 fe Select season of sector by writing yes or y in Season the adjacent cell Analyse by Sector r information must be included on the v heet Precip and sec 11 Insert yes or y in the empty cell to choose either seasonal of sectral normalisation 16 This program is designed for normalisation of wet depostion Precipitation data per day must be given on the work 17 sheet Precip and sector by date Loads are computed as 18 Monthly data choose season above or 19 Annual data by sector choose sector above 20 21 If analysis by sectors is chosen wind sector information must be given on the worksheet Precip and sector by site 22 using the following form 23 24 precip sector 25 1995 01 01 0 4 where sectors are given as values from 1 8 and all 26 1995 01 02 0 9 unclassified sectors is given the value 9 ei 1995 01 03 0 9 28 1995 01 04 0 9 n o oa a o M aD 1 stan m AMETE E Microsoft Excel We Biv iO B Re 11 15AM Figure 5 Select which class to use season or sector for computation of deposition and normalisation of deposition Computation of depositions
14. ion of monthly and annual deposition and annual deposition by sector Monthly and annual deposition data are calculated by first replacing all missing precipitation data by zeros Missing sector values are replaced by sector value 9 and missing concentrations are imputed by a simple regression model using precipitation amount as explanatory variable Subsequently daily concentration is multiplied with daily precipitation values and then summed up to form monthly or annual data by sector Normalisation of deposition data Deposition data is normalised by employing parametric and semiparametric regression models to remove or suppress the temporal variation that can be attributed to fluctuations in precipitation The normalisation can be conducted on two different kinds of input data either monthly deposition or annual deposition by sector We therefore use the term class with means either month or sector The semiparametric normalisation model has then the general form Yj A PiX Fart Paron i 1 2 j 1 m where yj is the observed response for the jth class of the ith year x j k 1 p represent precipitation values number of precipitation days and or number or precipitation periods and amp is a random error term with mean zero The slope parameters jj k l p are permitted to vary with the class j under consideration and the intercept aj is permitted to vary with both class j and year i However rapid ch
15. ire data set is separated into an estimation set or training set and a test set The model is first fitted to the estimation set and is subsequently used to predict the observations in the test set that is the values that have been left out of the estimation step If the observation period covers m years we define m estimation sets Mj i 1 m by leaving out one year long blocks of observations and then we compute a so called PRESS value i e a sum of squared prediction errors SaF Yo Oy Bij Bo Xp i jem Finally the factors 2 and A are selected in such a way that S A1 42 is minimised and the corresponding Root Mean PRESS value minl 5 S04 gt 0 gt o is used as a measure of the predictive ability of the normalisation model under consideration Literature references Libiseller C Grimvall A and Hallberg L 2005 Meteorological normalisation of time series of wet deposition manuscript 16 St lnacke P and Grimvall A 2001 Semiparametric approaches to flow normalisation and source apportionment of substance transport in rivers Environmetrics 12 233 250 17
16. obs Lambda1 Lambda2 MSPE MSRes MSPE MSRes Birkenes NH4 depo Precipitation amount 5279 56 3656 96 Birkenes NH4 depo Precipitation amount Raindays X 6762 64 3492 01 Birkenes NO3 depo Precipitation amount Aae 36 320 0 078 1 34 6334 27 4472 33 j E 136 10240 0 03 7 66 7317 92 4167 08 3 Birkenes NO3 depo Precipitatloner ant Raindays Smoothing parameters are listed for all models Mean squared prediction errors are listed for model comparison X gt Ml Normalisation models Normalised annual totals Normalised seasonaltotals Intercept Si 4 i Ready Figure 11 The output on the worksheet Normalisation models The estimated intercepts of the semi parametric models are given on the worksheet Intercept Figure 12 In this case nine columns are given for each pre specified model providing a time varying intercept for each sector Normalised values from a simple regression model only using annual deposition and annual precipitation amount is also provided This can be found on the worksheet Simple Regression Model No picture is given here 13 Type a question for help 5 ae 120 Arial o Q1 Sector 5 Sector 1 Sector2 Sector3 Sector4 Sector5 Sector Sector Sector8 Sector 9 Secto 1987 0 15101 0 06694 04318 0 93617 1 21769 1 76535 0 78937 0 1966 3 41469 1987 0 27 1988 0 16416 0 06976 041083 089728 1 24497 1 78171 0 77053 0 20597 3 30141
17. ormalisation models by cross validation and compute monthly and annual normalised deposition Each macro operates on predefined worksheets for inputs and outputs The table below shows which worksheets that are used for the different macros Further details are given in the documentation of each macro Macro Input worksheets Output worksheets auditdailydata Concentration by date The same as input and or Precip and sector by Concentration data summary date or Precipitation data summary matchflowandcons Concentration by date Matched pairs and Precip and sector by date compute_deposition Matched pairs Precip Annual totals and Seasonal or and sector by date and sector totals Concentration by date definenormalisationmodels Seasonal or sector Normalisation models totals wet_dep_normalise Normalisation models Normalisation models Normalised seasonal totals and Normalised annual totals Running the WETDEPNORM programme Copy data to worksheets l Run macro Auditdailydata Input and Jl data checking Select analysis on Model selection worksheet Run macro C f Compute_depostion see utation s deposition Indicate response and explanatory variables for the normalisation model Run macro Define models definenormalisationmodels and compute normalised values Run macro wet_dep_normalise Input and data checking
18. rmalReg norm NH4 depo SP normal Reg norm NO3 depo SP normal Reg norm NO3 d j 0 1831 0 15318 0 10832 0 20013 0 08546 0 10069 0 20 8 04622 0 02021 0 02065 0 08207 0 00191 0 00792 0 08 0 40564 0 35043 0 25522 0 04541 0 0908 0 25 0 93528 0 95334 0 99 Year Season Time 0 32378 0 36332 0 79 Normalised values using EES TIECEE a regression model 0 77775 0 79071 0 40 0 00405 0 01242 0 10 3 52116 3 47398 3 13 0 12604 0 12004 0 08 0 0845 0 09487 Normalised values using 0 82861 0 76964 048006 055354 053764 0 48 0 93519 0 79281 032606 069875 059245 032 a semi parametric model 2 0021 207121 298152 147082 159645 298 SP normalised 1 96786 1 98137 2 75751 2 26479 2 28386 2 75 0 48096 0 42868 0 50936 067949 0 68548 0 50 0 07825 0 19693 0 19403 0 07825 0 25287 0 26705 0 06298 0 18115 0 17168 0 06 1988 94 43012 3 39255 361287 43012 3 50002 3 02712 446951 3 36644 3 50102 4 46 1989 06 0 21065 0 28523 0 28008 0 21065 0 31375 0 29395 0 18031 0 25425 0 24443 0 18 1989 17 0 01213 0 0276 0 03017 0 01213 0 02517 0 0249 0 01879 0 0592 0 06416 0 01 989 28 0 19649 034858 0 31734 0 19649 0 36727 0 31528 01878 0 32987 0 29913 0 1 1989 39 0 07542 0 61856 04424 0 07542 0 77788 0 59806 0 08127 057341 0 43304 0 08 1989 5 0 25852 1 04423 0 99185 0 25852 1 12529 1 03707 04261 1 0621 1 00921 04 1989 61 3 16135 286418 28738 3 16135 2 25054 2 20201 3 84685 340139 341863 3 84 989 72 039846 072441 072124 0 39846 0 76085 0 76942 0 56807 0 99359 1 00858 05
19. s sheet can be edited prior to further analysis Figure 9 10 Type a question for help a2 120 Arial 10 AE32 Sampling Response Explanator Explanatory variable 2 Birkenes NH4 depo Precipitation amount Birkenes NH4 depo Raindays j Birkenes NH4 depo Precipitatii Raindays F For each response variable Birkenes NO3 depo Precipitation amount S different models are given Birkenes NO3 depo Raindays ini i Birkenes NO3 depo Precipitatii Raindays combining all explanatory variables In various ways Normalisation models ot Figure 8 Output of the macro definenormalisationmodels on the worksheet Normalisation Models Type a question for help 3 gt 120 Arial o X25 Sampling Response Explanatory variable 1 Explanatory variable 2 Birkenes NH4 depo Precipitation amount Birkenes NH4 depo Precipitation amount Raindays Birkenes NO3 depo Precipitation amount iai i Birkenes NO3 depo Precipitation amount Raindays The models containing only Raindays as explanatory variables are removed The four remaining models are given on the worksheet left ji Normalisation models m EEEE T A A E A TG BE a E Figure 9 The worksheet
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