tatstcal Evaluaton of WATFLD By: Angela MacLean, Dept. of Cvl & Envronmental Engneerng, Unversty of Waterloo, n. ctober, 005 The statstcs program assocated wth WATFLD uses spl.csv fle that s produced wth the WATFLD output. For each staton the relablty of the model s assessed usng eght dfferent crtera. The crtera used nclude devaton of runoff volumes (D v, the absolute percent bas (APB, the root mean squared error (RME, the mean absolute error (MAE, the bas (b, the ash-utclffe coeffcent ( r, the correlaton coeffcent (r, and the modfed Garrck coeffcent (G r. The frst sx crtera test the dfferences between models and the last three evaluate how well the smulated tme seres fts the observed data. Each of the crtera s brefly descrbed below. Devaton of runoff volumes (D v The devaton of runoff volumes D v, also known as the percentage bas, s perhaps the smplest goodness-ft crteron. Its value s calculated usng equaton : ( D v (% 00 ( where s the smulated dscharge for each tme step and s the observed value. s the total number of values wthn the perod of analyss. For a perfect model, D v s equal to zero. The smaller the D v value, the better the performance of the model.
Absolute Percent bas (APB The absolute percent bas s a measure of the tmng dfference between the streamflow observatons and the model smulatons. It s usually used n conjuncton wth the D v crteron. Gven an observed and smulated seres where the D v value s small and the APB s large, one could conclude that both seres share smlar volumes but that ther tmng s not as close. Thus, a good agreement n tmng and volume requres D v and APB to be small. APB s always greater than D v, and ts value s determned usng equaton : APB (% 00 ( where all values have the same meanng as n equaton Root mean square error (RME, mean absolute error (MAE, and bas (b These three ndcators provde a quanttatve estmate of the dfferences between models n unts of dscharge (m 3 /s. The values of these three crtera are used n ths study to establsh a relatve comparson of the three WAT models. RME, MAE, and b are calculated usng equatons 3 to 5: / RME ( (3
MAE (4 ( b (5 where all the terms have the same meanng as above. ash-utclffe Coeffcent ( r Along wth the coeffcent of correlaton, the ash-utclffe coeffcent ( r s a measure of statstcal assocaton, whch ndcates the percentage of the observed varance that s explaned by the predcted data. The ash-utclffe coeffcent, also known as the effcency crteron, s perhaps the most common measurement mentoned n the hydrologcal lterature for evaluatng the performance of a model. Intally proposed by ash and utclffe (970, r s estmated usng equaton 6: r ( (6 ( where s the average measured dscharge and all the other varables have the same meanng as above. The second term n equaton 6 represents the rato between the mean square error (ME and the varance of the observed data. Thus, a value of r equal to
zero ndcates that the model output s not better than that obtaned usng the smple averaged observed streamflow for the entre perod of analyss. A shortcomng of the ash-utclffe statstc s that, because of ts defnton, t puts more emphass on extreme events than on average flows. Addtonally, the tmng of the predcted seres greatly nfluences the value of the coeffcent. Garrck Coeffcent (Gr The Garrck coeffcent s a modfed form of the ash-utclffe coeffcent. The Garrck coeffcent uses daly averages as apposed to one overall average for the whole tme step. Ths n turn emphaszes the average flows and not extreme flows or the seasonal varaton. The Garrck coeffcent was ntally purposed by Garrck, Cunnane and ash (978. Gr s estmated usng equaton 7. r ( (7 ( d where d s the average flow measured on date d and all the other varables have the same meanng as above. Correlaton Coeffcent (R The R statstc descrbes the degree of colnearty between the observed and predcted tme seres. R s determned as ndcated n equaton 8. A perfect model has a correlaton coeffcent equal to.0. Hgh values of the R coeffcent ndcate better agreement between observatons and smulatons.
( ( ( ( R (8 where all symbols have the same meanngs as above. As wth the ash-utclffe statstc, the correlaton coeffcent s more senstve to outlers than to values near the observed mean.