Home

Hydromad Tutorial

1. lt I width 90 Q P extendrange as Date c 1980 01 01 1990 01 01 Rolling cross correlation between rainfall and streamflow rises lagQ lt CS x e E s e lt L S s La w d K C S va e E e m lt S Fs 2 gt C a CEN ee o ae L E C n K r K S C e S a L v L LLZ S E s e gt SS S e E SS SJ C lL K e a G 4 fj E S F S T C Ss S e 2S 4 MODEL SPECIFICATION gt x lt rollccf Cotter gt xyplot x xlim T T EEE T T 80 90 v0 20 00 8s09070c0 z0 Sz UZ SLOL S O DUL OS 1982 1984 1986 1988 1990 1980 Figure 3 Cross correlation between rainfall and streamflow rises in two rolling windows of width 90 days and 365 days 4 MODEL SPECIFICATION 6 A nice simple starting point is the classic IHACRES model of Jakeman and Hornberger 1993 which is a Soil Moisture Accounting model referred to here as cwi Catchment Wetness Index The routing component typically used in IHACRES is a Unit Hydrograph composed of exponential components a structure referred to here as ex puh Up to three time constants can be specified referred to as tau_s slow component Ts tau_q quick component 7 7 and tau_3 The parti tioning of flow between the stores is set by v_s fractional volume in the slow component vs and by default the quick flow component
2. SMA and armax routing Start 1990 01 01 End 1999 12 31 SMA Parameters tw f scale 1 D t_ref 29 2377 1 8969 0 0017 0 0000 1 0000 20 0000 Routing Parameters a_l a_2 b_0O b_1 delay 1 5382 0 546 0 156 0 141 0 000 TF Structure S Q two stores in parallel Poles 0 5655 0 9661 Fit fit result fitByOptim MODEL cotterMod method PORT samples 100 216 function evaluations in 85 8 seconds Routing fit info list converged TRUE iteration 5 Message false convergence 8 Figure 5 Printing a model to view its parameter values Note one can get hold of the parameter values using coef cotterFit or coef cotterFit which routing for the unit hydrograph only 7 MODEL AND CALIBRATION OPTIONS 11 To display basic performance statistics for a model gt summary cotterFit Call hydromad DATA ts90s tau_s c 5 100 tau_q c O 5 v_s K c 0 1 sma cwi routing armax rfit list sriv order c n 2 m 1 tw 29 2377 f 1 89694 scale 0 00170432 Time steps 3552 33 missing Runoff ratio Q P 0 818 3 21 0 255 rel bias 0 0314 r squared 0 773 r sq sqrt 0 836 r sq log 0 852 For definitions see hydromad stats Figure 6 Calculating basic performance statistics for a model The sum mary function actually returns a list containing the values of various per formance statistics 7 Model and Calibration Options There are several extension
3. a specification can be given for fitting the routing component rfit If given this is applied automatically to fit the routing component after the SMA parameters have been specified Let us define some data periods We will fit a model to one the calibra tion period and then simulate it on the other periods to cross check model performance gt ts70s lt window Cotter start 1970 01 01 end 1979 12 31 gt ts80s lt window Cotter start 1980 01 01 end 1989 12 31 gt ts90s lt window Cotter start 1990 01 01 end 1999 12 31 When we first set up the model most of the parameters are not uniquely specified but rather have a range of possible values These defaults are taken from hydromad options and they can be over ridden by arguments to the hydromad function lag 1 width 365 lagi e SS L _ 1 ee T LLS e SSS SS Sys e Z e e T ELZ An p r E E S P S E a S E sy S e E ES e K n se S CT l e SSS a r a C SSS lt lt z E a 7 gt gt Baa w a P SSS _ A S2 SS s p a Er SS e SS S u Z n T E A a D a E CA 2 lt EE d a E S d C E C s K d lt a E Ss gt Cs S lt _ lt _ a S Z e _
4. is assigned the remainder When a model structure is specified default parameter ranges for the given SMA model are applied and others can be specified gt cotterMod lt hydromad ts90s sma cwi routing expuh tau_s c 5 100 tau_q c 0 5 v_s c 0 177 gt print cotterMod Hydromad model with cwi SMA and expuh routing Start 1990 01 01 End 1999 12 31 SMA Parameters lower upper tw 0 100 f 0 8 scale NA NA 1 0 0 p 1 1 t_ref 20 20 Routing Parameters lower upper tau_s 5 100 tau_q 0 5 V_s 0 1 With this model specification we can choose to calibrate the model in various ways or to simulate from the specified parameter space or to run sensitivity or uncertainty analysis 4 1 Calibration Currently implemented calibration methods include simple sampling schemes fitBySampling general optimisation methods with multistart or presam 3for more complex structures v_3 and or v_q may be specified See the help page for details 5 MODEL OUTPUT 7 pling fitByOptim and the more sophisticated Shuffled Complex Evolution fitBySCE and Differential Evolution fitByDE methods All attempt to maximise a given objective function The objective function can be specified as the objective argument to these functions or by setting hydromad options objective It is given as an R function which may refer to the values Q and X represent ing observed and modelled flow respect
5. is usually a linear transfer function which can be as simple as a single exponential recession i e constant decay rate although variants with non linearities are also available rainfall temp PET Soil Moisture Accounting SMA __ other inputs model effective rainfall unit hydrograph streamflow oe routing model Figure 1 The modelling framework in the hydromad package The hydromad package is intended for 2 INPUT DATA 2 e defining and fitting spatially lumped hydrological models to observed data e simulating these models including model state variables and compo nent flow separation e evaluating and comparing these models summarising performance by different measures and over time using graphical displays hydro graph flow duration curve residuals etc and statistics e integration with other types of data analysis and model analysis in R including sensitivity and uncertainty analyis This tutorial describes how to get started with the hydromad R package It covers the basics of reading data in from files converting it into the appropriate format and fitting and analysing a simple model Once you have R running and have installed the hydromad package you can load it gt library hydromad 2 Input data The example we will look at is the Cotter River catchment at Gingera gauge 410730 in the Australian Capital Territory Australia This i
6. Hydromad Tutorial Felix Andrews June 17 2011 1 Introduction The hydromad package is designed for hydrological modelling and associ ated data analysis It is focussed on a top down spatially lumped empir ical approach to environmental hydrology In practice the emphasis is on models of rainfall runoff in catchments watersheds Such models predict streamflow from time series of areal rainfall and temperature or potential evapo transpiration They can be calibrated to time series of observed data As spatially lumped models they do not explicitly represent spatial vari ation over the catchment area In particular the standard formulations do not attempt to model effects of changes in land cover These models are usually calibrated to a period of observed streamflow and the parameters defining the modelled relationship between rainfall evaporation and flow are assumed to be stationary in this period The modelling framework in the hydromad package is based on a two component structure 1 a soil moisture accounting SMA module and 2 a routing or unit hydrograph module Figure 1 The SMA model converts rainfall and temperature into effective rainfall the amount of rainfall which eventually reaches the catchment outlet as streamflow i e that which is not lost as evaporation etc The routing module converts effective rainfall into streamflow which amounts to defining the peak response and shape of the recession curve It
7. a cwi 1 c 0 200 e 0 166 7 2 Optimisation settings Each of the fitting functions has several options and the help pages should be consulted for details An important option is the choice of objective function see the discussion above about how to specify it In the simple cases of using fitBySampling or fitByOptim the argu ment samples specifies how many random parameter sets will be sampled from the predefined parameter ranges and argument sampletype chooses Uniform Random Latin Hypercube or all combinations a regular grid of values The one model with best objective function value is chosen In the case of fitByOptim this is then improved locally with an optimisation algorithm 7 3 Unit Hydrograph Transfer Functions A typical unit hydrograph model at least in IHACRES models is a linear transfer function i e an ARMAX like Autoregressive Moving Average with eXogenous inputs This can often but not always be formulated mathematically as a set of exponentially receding stores which may be in a parallel and or series configuration ARMAX type models are specified by the number of auto regressive terms n and the number of moving average terms m For example a model with one store is n 1 m 0 two stores in parallel is n 2 m 1 two stores and an instantaneous store in parallel is n 2 m 2 Three stores in parallel is n 3 m 2 When using armax or expuh routing specialised methods are ava
8. d POSTXct but this represents time zones which can sometimes lead to complications so objects are a generalisation of ts objects and in many cases can be used in the same way see vignette zoo This avoids name conflicts since in R T is a shorthand for TRUE A READING IN DATA 21 P Q E 1964 01 03 NA 0 337 28 8 1964 01 04 NA 0 328 29 4 1964 01 05 NA 0 313 32 8 1964 01 06 NA 0 301 35 7 1964 01 07 NA 0 283 37 2 1964 01 08 NA 0 291 22 9 gt range time Cotter 1 1964 01 03 2005 12 31 This shows that the rainfall data has missing values at the beginning At the other end of the series Streamflow data is missing This will not cause a problem but let us tidy it up anyway gt Cotter lt na trim Cotter The final dataset extends from 1966 05 01 to 2003 06 12 and is shown in Figure 2 and Table 3 gt summary Cotter P Q E Min 0 00 0 01 2 80 Ist Qu 0 00 0 23 14 00 Median 0 00 0 48 19 20 Mean 2 97 0 83 19 69 3rd Qu 1 65 1 04 24 60 Max 141 39 28 50 42 20 NA s 0 00 33 00 0 00 Table 3 Data summary P precipitation mm day E temperature deg C Q streamflow mm day Computational details The results in this paper were obtained using R 2 13 0 with the pack ages hydromad 0 9 8 zoo 1 6 5 and latticeExtra 0 6 17 R itself and all packages used are or will be available from CRAN at http CRAN R project org
9. gt A at Q 4 N 2 1970 1980 1990 2000 Figure 2 Input data averaged over months 4 MODEL SPECIFICATION 4 of the rainfall which flows out of the catchment In a simple case this is just sum Q sum P but as we have missing values we should only compare the common observations gt ok lt complete cases Cotter 1 2 gt with Cotter sum Q ok sum P ok 1 0 279 This figure is within the range we would expect so is looks like we probably have the right data series and units To estimate the delay time between rainfall and a consequent streamflow response we can look at the cross correlation function The hydromad func tion estimateDelay picks out the lag time corresponding to the maximum correlation between rainfall and rises in streamflow In the Cotter this is 0 days For more detail there is a function rollccf which calculates the cross correlation in a moving window through the data shown in Figure 3 When the cross correlation value drops down towards zero there is little connection between rainfall and streamflow and you should start to worry about the data If the lag 1 value jumps above the lag 0 value this indicates that the delay time has changed 4 Model Specification A hydromad object encapsulates the chosen model form parameter values or ranges of values as well as results The model form is divided into two components SMA Soil Moisture Accounting and routing Additionally
10. ilable to estimate for calibration such as the SRIV Simple Refined Instrumental Variable algorithm These are specified using the rfit argument The order of the transfer function may be varied as well as the delay time If there is any ambiguity in choosing the best delay time each possi bility should be tried To test different model structures systematically a convenience function tryModelOrders is provided An example is given in Table 2 In this case a simple SMA is used with fixed parameters For more information on these issues see for example Jakeman et al 1990 and Young 2003 7 4 Unit Hydrograph Inverse Fitting Methods Unit Hydrograph routing models are typically fitted using least squares or SRIV algorithms but this depends on the modelled effective rainfall and 7 MODEL AND CALIBRATION OPTIONS 17 gt ihSpec lt hydromad ts90s sma cwi tw 10 f 1 routing armax gt osumm lt tryModelOrders update ihSpec rfit sriv n 0 3 m 0 3 delay 0 gt summary osumm ARPE r squared r sq log n 0 m 0 d 0 0 000 5 432 2 421 n 1 m 0 d 0 0 000 0 545 0 705 n 1 m 1 d 0 0 000 0 671 0 774 n 2 m 0 d 0 0 014 0 346 0 554 n 2 m 1 d 0 0 001 0 694 0 782 n 2 m 2 d 0 0 005 0 698 0 782 n 3 m 0 d 0 98 529 0 605 0 720 n 3 m 1 d 0 0 023 0 697 0 782 n 3 m 2 d 0 54 085 0 698 0 782 n 3 m 3 d 0 0 005 0 699 0 785 Table 2 Fit and information statistics fro
11. ively For more advanced use it may also refer to U modelled effective rainfall or the full input DATA matrix The nseStat function implements a generalisation of the familiar R coefficient of efficiency Nash and Sutcliffe 1970 nseStat Q X DIQ Xa 1 where Q and X are the observed and modelled values Z is the result from a reference model which is the baseline for comparison Z defaults to the mean of observed data E Q corresponding to the typical R statistic Subscript x denotes transformed data and the transform can be specified See nseStat and hydromad stats for examples Here we use the default which is a weighted sum of the R of square root transformed data and with less weight the R of monthly aggregated data For this simple example the model will be calibrated using the fitBy Optim function which performs parameter sampling over the pre specified ranges selecting the best of these and then runs an optimisation algorithm from that starting point gt cotterMod lt update cotterMod routing armax rfit list sriv order c n 2 m 1 gt cotterFit lt fitByOptim cotterMod samples 100 method PORT See the help pages help hydromad and help fitByOptim for de tails of some of the options available 5 Model Output Now that we have an object representing a calibrated model what can we do with it There are many standard R functions which have methods for hydromad ob
12. jects which allow one to s view model info using print summary and objFunVal e extract parameter values using coef 6 MODEL SIMULATION 8 e access data with fitted residuals and observed These exclude the warm up period by default e run with new data using update or predict e simulate from parameter ranges using simulate e generate plots using xyplot qqmath etc For details see the examples below the user manual and the help page of each function The help pages are also available from the web site http hydromad catchment org Most basically one can extract the modelled streamflow time series with the function fitted and this can of course be used with any of R s library of analysis functions A quick way to view the modelled and observed streamflow time series together is to call xyplot on the model object as in Figure 4 Figures 5 and 6 also show the output from calling the functions print and summary on the model object 6 Model Simulation We can simulate this model on the other periods using the update function gt sim70s lt update cotterFit newdata ts70s gt sim80s lt update cotterFit newdata ts80s gt simAll lt update cotterFit newdata Cotter For verification purposes we would like to calculate performance statis tics for the whole dataset but excluding the calibration period The easiest way to do this is to set the observed streamflo
13. lt NA gt pqdat Q pqdat Q lt 0 lt NA gt tdat lt subset tdat is na Date The hydromad model fitting functions require that rainfall and stream flow are given in the same units typically mm day The streamflow data in our input file is measured in ML day so we need to convert it supplying the catchment area of 148 km gt pqdat Q lt convertFlow pqdat Q from ML area km2 148 For simple applications when the data series are already synchronised this data frame or matrix format may be enough However there are benefits in working with actual time series objects because they handle observation times they allow powerful merging treatment of missing values rolling averages and other functions While R has a built in structure for regular time series ts these do not handle specific dates or times only index numbers It is recommended to work with zoo objects using the zoo package gt library zoo gt tsPQ lt zoo pqdat 1 2 pqdat Date frequency 1 gt tsT lt zoo tdat 1 tdat Date frequency 1 We can now merge the time series together into a final dataset Note that the hydromad package expects temperature or evapo transpiration data to be called E not T gt Cotter lt merge tsPQ E tsT all FALSE Print the first few rows the head of the time series to check that everything looks OK gt head Cotter 6 There is a time class built into R calle
14. m fitting different unit hydrograph transfer functions with SRIV algorithm ARPE is the Average Relative Pa rameter Error estimated by SRIV The effective rainfall input was generated by an IHACRES CWI model with fixed parameters 8 WHAT NEXT 18 so must be continuously re fitted while calibrating the SMA model One alternative is to fit the unit hydrograph to the observed streamflow data directly though usually constrained by rainfall and then use that as a fixed component while calibrating the SMA model This can be done using an inverse filtering method with rfit list inverse There are many options here also Other such inverse fitting methods are possible e g average event unit hydrograph estimation but are not currently implemented in this package 7 5 Other Options If model calibration is failing you can set hydromad options trace TRUE and or hydromad options catch errors FALSE to track down what is happening It is sometimes useful to look at the model state variables available as predict mod return_state TRUE for the SMA model or pre dict mod return_components TRUE for the routing model to see if they look sensible Some other things to try are e using different calibration periods e changing the warmup period length e changing the optimisation method and or settings 8 What Next This document has described only a basic model fitting process Help pages are available for
15. most functions and these are also available online at http hydromad catchment org There is also a set of demos see demo package hydromad for a list Please discuss any problems or suggestions with the package maintainer A Reading in data The required input data files for this tutorial are included with the hydromad package in the doc directory Note that the processed data is available directly in R just type data Cotter but this section shows how to read it in from text files as an exercise A few simple steps are required to import and convert the data into a usable form extracting dates from the files converting streamflow from ML day to mm day handling missing data values and aligning the three time series in a common time period A READING IN DATA 19 Let s first view the content of one of the input files Set the working directory to where the data file is gt setwd system file doc package hydromad gt file show pq_cotter csv 99 49 8405 3 01 1964 99 48 5998 4 01 1964 99 46 3199 5 01 1964 99 44 5028 6 01 1964 99 41 9241 7 01 1964 There is no header in the file but we know that the columns represent rainfall P streamflow Q and date of observation The temperature file is similar Knowing the format and columns we can use read table to import the data gt pqdat lt read table pq_cotter csv sep col names c P Q Date as is TRUE gt tda
16. observed simAl1 layout c 1 5 x same TRUE layer_ panel refline h F O v time statSeries r squared 0 5 0 6 0 7 0 80 9 r sq sart rel bias runoff 0 3 0 5 07 09 0 0 0 2 statistic 0 15 0 25 0 35 0 45 0 4 observed streamflow 1970 1980 1990 2000 0 5 10152025 Figure 9 Performance statistics plotted over time in regular 2 year blocks The runoff coefficient and observed streamflow data are also shown 7 MODEL AND CALIBRATION OPTIONS 15 To plot the flow duration curve for modelled vs observed data in the calibration period gt qqmath cotterFit scales list y list log TRUE type c 1 g To plot a flow duration curve for each of the simulated models gt qqmath allMods type c 1 g scales list y list log TRUE xlab Standard normal variate ylab Flow mm day f value ppoints 100 tails n 50 as table TRUE observed modelled 9 calibration sim70s 10 4 L 10 0 4 L 10 1 4 L 10 2 L Ss ia L I1 Ir NAAT z 2 0 2 2 0 2 sim80s simVerif o EL L 10 J 10 0 4 K 10 1 4 K 104 2 2 0 2 4 2 0 2 4 Standard normal variate Figure 10 Log normal Daily Flow Duration Curve for models in simula tion 7 MODEL AND CALIBRATION OPTIONS 16 evapo transpiration coefficient e defaults to the range 0 01 1 5 to fix it to a given value just specify it gt hydromad ts90s sm
17. ow in validation periods 7 MODEL AND CALIBRATION OPTIONS 13 gt summary simAll breaks 1966 08 09 1971 01 01 1976 01 01 1981 01 01 1986 01 01 1991 01 01 1996 01 01 2001 01 01 2003 06 12 1966 08 09 1971 01 01 1976 01 01 1981 01 01 1986 01 01 1991 01 01 1996 01 01 2001 01 01 2003 06 12 timesteps missing mean P mean Q runoff rel 2 17 67 91 15 36 04 47 5 years 1606 0 1826 0 1827 0 1826 0 1826 33 1826 0 1827 0 893 0 893 0 r squared r sq sqrt 0 533 0 632 0 719 0 701 0 663 0 716 0 775 0 842 0 695 0 804 0 775 0 842 0 756 0 812 0 517 0 668 0 517 0 668 H KM K G G G KM KM G 67 u A N O OO OO C9 C9 630 0 GO OOO OO LA 853 164 719 790 956 915 627 395 395 log 681 621 682 861 854 855 838 694 694 0 367 269 271 303 273 206 160 160 O O O OO OO 319 bias 3172 3318 2259 1119 1579 0909 1466 1685 1685 Figure 8 Viewing a break down the performance of a model over 5 year blocks 7 MODEL AND CALIBRATION OPTIONS 14 To plot performance statistics over time gt twoYrStats lt summary simAll breaks 2 years gt statSeries lt twoYrStats c r squared r sq sqrt rel bias runoff gt statSeries 1 2 lt pmax statSeries 1 2 0 gt c xyplot statSeries type s lwd 2 ylab statistic xlab NULL observed streamflow xyplot
18. s a 148 km catchment managed for urban water supply Areal rainfall was estimated from several rain gauges operated by the Bureau of Meteorology and Eco Wise The temperature records come from Canberra Airport The Cotter data is built in to the hydromad package and can be loaded into the workspace with gt data Cotter See Appendix A for a demonstration of reading in the time series data from files 3 Data checking In a real data analysis problem data checking is a central issue However as this document aims to introduce the core modelling functions only a simple check will be demonstrated here The most obvious thing to do is to plot the time series as shown in Figure 2 Table 3 shows the mean and quartiles of each input data series One measure that is of key interest in hydrology is the runoff ratio the proportion See http www r project org See http hydromad catchment org 3 DATA CHECKING 3 To plot the raw daily time series gt xyplot Cotter To plot a section of the time series gt xyplot window Cotter start 1974 01 01 end 1975 01 01 And to plot the time series aggregated to a monthly time step gt monthlyPQE lt aggregate Cotter as yearmon mean gt xyplot monthlyPQE screens c Streamflow mm day Areal rain mm day Temperature deg C xlab NULL Streamflow mm day 2 ie oO Areal rain mm da wo s a a g Temperature deg C
19. s to the basic model used so far With different types of data such as very dry or wet catchments sub daily time steps poor areal rainfall estimates cases of baseflow loss to groundwater etc different models or calibration methods will need to be used 7 1 Model Structure and Parameter Ranges We have used an IHACRES CWI model in this tutorial which is a simple metric type model Other SMA models are included in the package or one can define a new model See the user manual for details Ranges of parameters to search when calibrating the effective rainfall model can be specified as arguments to the hydromad or update functions Alternatively parameters can be fixed to a given value by specifying a single number The default ranges can be seen and set using the function hydro mad options The example in the CWI model the threshold parameter 1 used for intermittent or ephemeral rivers defaults to a fixed value of 0 To al low calibration of this parameter specify a numerical range Similarly the 7 MODEL AND CALIBRATION OPTIONS 12 gt xyplot allMods 2 3 scales list y list log TRUE observed modelled 9 sim70s 10 1010 IU i i VID NAIA i Ia WY l l l M S Hy U 10 1 l ik 104 2 T T T T T T 1970 1972 1974 1976 1978 1980 sim80s 1982 1984 1986 Time 1988 1990 101 100 10 1 10 2 Figure 7 Observed vs modelled streamfl
20. t lt read table t_cotter csv sep col names c T Date as is TRUE and view the structure of the resulting data frames gt str pqdat data frame 15339 obs of 3 variables P num 99 99 99 99 99 99 99 99 99 99 U num 49 8 48 6 46 3 44 5 41 9 Date chr 3 01 1964 4 01 1964 5 01 1964 6 01 1964 gt str tdat data frame 15467 obs of 2 variables T num 28 8 29 4 32 8 35 7 37 2 22 9 25 5 23 8 23 7 24 9 Date chr 3 01 1964 4 01 1964 5 01 1964 6 01 1964 So far the Date columns are only text R does not know they are dates We need to specify the date format where d is day m is month number b is month name Y is four digit year and y is two digit year see strptime gt pqdat Date lt as Date pqdat Date d m Y gt tdat Date lt as Date tdat Date d m Y If the day month and year were in separate columns of the file with names day mon and yr then you could do something like A READING IN DATA 20 gt pqdat Date lt with pqdat as Date ISOdate yr mon day If you have sub daily time steps a good choice is to use the chron function from the chron package to represent the time index Negative values 99 in the pq input file represent missing data in R they should be set to the special value NA Also some dates in the temperature file are blank and need to be removed gt pqdat P pqdat P lt 0
21. w data in the calibration period to NA missing and then run the simulation gt tsVerif lt Cotter gt tsVerif Q time ts90s lt NA gt simVerif lt update cotterFit newdata tsVerif It is convenient to group these models together into a runlist which is just a list of fitted models gt allMods lt runlist calibration cotterFit sim70s sim80s simVerif The predicted time series hydrograph and cumulative distribution flow duration curve can be generated as in Figures 7 and 10 Note that to get help for generic functions it is necessary to specify the method for hydromad objects e g predict hydromad or xyplot hydromad 6 MODEL SIMULATION 9 gt xyplot cotterFit with P TRUE xlim as Date c 1994 01 01 1997 01 01 observed modelled streamflow S l lt N oO rainfall S oy GO G ca LO So al lt oy N oO T T T T T 1994 07 1995 01 1995 07 1996 01 1996 07 Time Figure 4 Observed vs modelled streamflow in part of the calibration pe riod gt summary al1Mods rel bias r squared r sq sqrt r sq log calibration 0 03 0 77 0 84 0 85 sim70s 0 32 0 68 0 68 0 61 sim80s 0 12 0 73 0 83 0 86 sim Verif 0 18 0 70 0 75 0 75 Table 1 Performance statistics for a set of models 6 MODEL SIMULATION 10 To display information and parameters of a model gt print cotterFit Hydromad model with cwi

Hydromad Tutorial

Contents

Download Pdf Manuals

Related Search

Related Contents