Results of an intercomparison of models of snowmelt runoff

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1 Mdelling Snwmelt-Induced Prcesses (Prceedings f the Budapest Sympsium, July 1986). IAHS Publ. n. 155,1986. Results f an intercmparisn f mdels f snwmelt runff WRLD METERLGICAL RGANIZATIN CP N.5, 1211 Geneva 2, Switzerland ABSTRACT Frm 1976 t 1983 the Wrld Meterlgical rganizatin cnducted an intercmparisn f mdels f snwmelt runff. The 11 mdels invlved were tested using data sets frm six river basins. The structures f the mdels and their abilities t simulate snwmelt runff under varius cnditins were cmpared. The results are presented in the frm f a reprt and a cmputer tape cntaining data used in the prject. Résultats d'une cmparaisn des mdèles d'éculement dû a la fnte des neiges RESUME De 1976 à 1983 l'rganisatin Métérlgiue Mndiale a entrepris une cmparaisn des mdèles d'éculement dû à la fnte des neiges. Les 11 mdèles utilisés nt été testes en utilisant les jeux de dnnées de six bassins de rivières. Les structures des mdèles nt été cmparées ainsi ue leurs capacités à simuler l'éculement dû à la fnte des neiges sus différentes cnditins. Les résultats snt présentés sus la frme d'un rapprt et d'une bande d'rdinateur cntenant les dnnées utilisées dans le prjet. n N Vci Vl y c ( z c> y Q (z > y (z ) y d ttal number f bservatins number f snwmelt seasns r years cmputed runff vlume during snwmelt seasn i r year i (m ) bserved runff vlume during snwmelt seasn i r year i (m ) 3 1 cmputed mean daily (mnthly) discharge (m s ) bserved mean daily (mnthly) discharge (m s~ ) the mean bserved daily (mnthly) discharge ver either the calibratin perid r the verificatin perid. mean bserved daily discharge fr each day f the year derived frm the calibratin perid (m s"~ ) INTRDUCTIN When a streamflw frecasting system calls fr a mdel t estimate dwnstream discharge frm measurements f precipitatin and/r snwmelt, it is necessary t select ne such mdel frm amng the many that are peratinally used fr the purpse. There is n single mdel t be recmmended under all circumstances and s the Wrld Meterlgical rganizatin (WM) has cncentrated n prviding infrmatin and guidance fr use by thse faced with the chice. 13

14 Wrld Meterlgical rganizatin Between 1968 and 1974 the rganizatin cnducted a prject n the intercmparisn f rainfall-runff mdels used fr hydrlgical frecasting.

2 14 Wrld Meterlgical rganizatin Between 1968 and 1974 the rganizatin cnducted a prject n the intercmparisn f rainfall-runff mdels used fr hydrlgical frecasting. The results (WM, 1975) prvide a cmprehensive set f infrmatin and data describing the mdels and their cmparative perfrmance under a variety f cnditins. Mdels invlving snwmelt were nt included in the first prject. ne reasn being that the data sets used fr the cmparisn f perfrmance were nt designed fr that purpse. A secnd prject, designed specifically t cmpare mdels f snwmelt runff, was therefre undertaken during the years 1976 t This prject is described in a paper submitted t the First Scientific General Assembly f IAHS (WM, 1982) and s is nly briefly intrduced here. The purpse f this paper is t present a summary f the results f the prject. DESCRIPTIN F THE PRJECT The aims f the prject were: (a) t btain infrmatin n mdels used fr frecasting snwmelt runff and t arrange fr an intercmparisn f such mdels; (b) t reprt n the results f the intercmparisn and thus ffer guidance n the use f the mdels in varius situatins; and (c) t disseminate t interested cuntries the material prepared in rder t encurage new appraches t frecasting snwmelt runff and t assist cuntries in which it is planned t use mdels fr such frecasting. The bject f the prject was nt t find the mdel which fits best in all circumstances but t give t users the pprtunity t examine the perfrmances f the tested mdels under varius cnditins. The prject invlved the intercmparisn f 11 peratinal mdels f snwmelt runff submitted by eight cuntries. The mdels were tested using data sets fr six river basins frm climatlgically and gegraphically varied areas in six cuntries. Each data set cnsisted f tw separate perids, a calibratin perid (six years) and a verificatin perid (fur years) fllwing immediately thereafter. The mdel wners were supplied with bserved input data (precipitatin, evapratin and ther meterlgical data) and bserved utput data (streamflw) fr the six-year calibratin perids, and nly bserved input data fr the fur-year verificatin perids. The bserved utput data fr the fur-year verificatin perids were retained by the WM Secretariat. Fr each data set the mdel wners used the cncurrent bserved input and utput data fr the six-year calibratin perid t establish the parameters f their mdels and emplyed the additinal fur years f bserved input data in the verificatin perid t prduce a simulated discharge (cmputed utput). The simulated discharges prduced by the mdels fr bth the calibratin and verificatin perids in each basin were then evaluated and cmpared by the WM Secretariat using graphical and numerical verificatin criteria previusly agreed upn by the mdel wners. A technical cnference was rganized by WM in Nrrkping, Sweden, in September It was attended by representatives f agencies participating in the prject plus several invited experts. The

3 Intercmparisn f mdels f snwmelt runff 15 cnference cnsidered the results f the prject and prepared a number f cnclusins and recmmendatins which are summarized here and presented in full in the reprt f the prject (WM, 1986). MDELS A large part f the reprt f the prject is devted t presenting detailed infrmatin n the structure f the mdels tested, their data and cmputing needs and their limitatins and areas f applicatin. Mst mdels f snwmelt runff cnsist f tw cmpnents: a snwmelt mdel, which simulates the prcess f snw accumulatin and melting, and a transfrmatin mdel, which takes the snwmelt r the rainfall as input data, and yields the basin runff as utput. At the start, the mdel wners prpsed a tentative classificatin f bth the snwmelt and transfrmatin parts f their mdels (WM, 1982). This classificatin was later refined and expanded and the final reprt (WM, 1985) presents and discusses it at sme length. A preliminary review was als made f the physical prcesses taken int accunt by each mdel. The final reprt cntains a descriptin f the varius algrithms and euatins used t simulate these prcesses, presented under the fllwing headings; (a) Handling f meterlgical data: (i) methd f subdividing catchment, (ii) distributin f temperature (lapse rates), (iii) determinatin f the frm f precipitatin, (iv) distributin f precipitatin (n a spatial r elevatin basis and methds f crrecting precipitatin measurements). (v) distributin f ther meterlgical inputs. (b) Structure f snwmelt mdels : (i) accumulatin (interceptin, depth and density f snw), (ii) areal snw distributin, (iii) surface energy exchange (including seasnal variatin), (iv) internal prcesses (the cld cntent f a snwpack, liuid water strage and perclatin), (v) snw-sil interactins. (c) Structure f transfrmatin mdels. Infrmatin has als been assembled and published n the data reuirements f the mdels and n the methds used t fit them during calibratin. DATA SETS The previus paper (WM, 1982) presented infrmatin n the data sets used in the prject. Table 1 indicates which data sets were used by each mdel. The mdel wners were reuested t send t the WM Secretariat the utput cmputed by their mdels fr bth the calibratin and verificatin perid f the data sets n which they had run their mdels. The cmputed utput was presented fr bth the streamflw

4 16 Wrld Meterlgical rganizatin C r-, Ql «T3 +J ) -i a 3 C * ^ e A; -H ^-H M U u i l-l In. > u c H i +J C u w U 11 w m +j 1! s w H «5 i 'r-1 3 Q M W m X). r7^ E A; >-i < S> M CD a, C M > «4) - «M c --H IH ) N U 'd S w ^ v ^* " *, N e A; <*\ i^i (7 s E A; 1 C ^r S S M S. H -^ 8 E A: c Is c! rx u fc> >H 1 3 H k. <M Q cc ) E B -s S n I t> h J3 d T3 ^- «B U & t l 63 W ^- Si s 1-1 ce H S a ce E ta 63 lvak. m -ç ) N U S J< 1s 1 E Q i S 5 *B K -i *~ ) ai 1 13 Qj ) i ï? îi c 3 as ) s: <n *-i ~i In M T3 ) 31 ' t) ) 4J E T3 tjl ) 1 c -i w -M i +J ib 1-i -v E t- ce ib M ce i i t H «C 4J C c ce E ce D i -u c 3i H CQ 4J 1 tn u M -H C^ M -N H -H W D «S i " ce (s CK û, S ^> C S. m M C M ) -H C u S: c -, c H t, H. S u C ce - ~ ' cas C KÇ -

5 Intercmparisn f mdels f snwmelt runff 17 runff at the utlet f the tested catchment and the ttal snwmelt ver the catchment. If, frm the cmputatinal prcedure, the cmputed snwmelt nrmally included rainfall, figures fr snwmelt and rainfall were presented separately where pssible. The data sets were fund t be generally satisfactry with respect t bth the develpment and peratinal needs f the mdels. Hwever, fr the benefit f ptential future users f the data, the mdel wners recrded their general and specific remarks n each set. The data that were exchanged in cmputer cmpatible frm have been cmpiled nt a single magnetic tape tgether with the utputs cmputed by the 11 mdels fr bth the calibratin and verificatin perids. This represents practically all the numerical data used in the prject and is all that were used fr the graphical and numerical verificatin prcedures described belw. The tape is written in EBCDIC cde with a density f 16 bpi and is available frm the WM Secretariat in Geneva fr a nminal fee t cver the expenses invlved in its cpying and pstage. CMPARATIVE VERIFICATIN Three graphical and nine numerical verificatin criteria were used in this prject t evaluate and cmpare the simulated discharges: Graphical verificatin criteria (a) Linear plts f simulated and bserved daily discharge fr each year f the calibratin and verificatin perids; (b) flw duratin curves (indicating the prprtin f time that runff/average runff was greater than any given value) fr simulated and bserved daily discharges. Separate curves were pltted fr the calibratin and verificatin perids. (c) Scatter diagrams f simulated vs. bserved mnthly maximum daily discharge (peak flws), separately fr the calibratin and verificatin perids. It was cnsidered that the linear scale plts f simulated and bserved daily discharge were the mst imprtant graphical verificatin criteria. Numerical verificatin criteria The verificatin frmulae used in the prject are listed belw: (a) The rati f the standard deviatins f cmputed t bserved discharges: E( * - y )2 (1) (b) ne minus the rati f the sum f suares f the daily residuals t the centred sum f suares f the daily bserved discharges:

6 18 Wrld Meterlgical rganizatin E( y c - y )2 NTD = 1 - (2) (c) Rati RN f the uantity (1 - NTD) fr the verificatin and calibratin perids: (1 - NTD) ver RN = ^=- (3) (1 - NTD) n cal (d) Rati f the sum f suares f the mnthly residuals t the centred sum f suares f the mnthly bserved discharges: (z - z ) 2 - z - z ) 2 C, AX NTM = (4) Z(z - 5 ) 2 (e) Rati f the standard deviatin f the residuals t the mean bserved discharges : s = {/[z<y c - y > 2 ]/ n >/y (5) (f) Rati f the mean errr t the mean bserved discharge:» E(y c " V R = (6) (g) Rati f abslute errr t the mean bserved discharge: S I y c - y 1 I A = (7) (h) Cefficient f gain frm daily means: Z( y - y H> 2 - E( y. - y«)2 NS = 2 d ç _ (g) Z ( y. - y H> 2 d (i) Rati f sum f abslute errrs t the ttal bserved runff vlume: PD - -^Lj-21 Si! (9) 1=1 l

7 Perids f cmputatin Intercmparisn f mdels f snwmelt runff 19 All the numerical criteria were cmputed separately fr the calibratin perid and the verificatin perid and, in additin, fr the snwmelt seasns during these perids. The criteria NTD, S, R and NS were als cmputed fr each individual year in the calibratin and verificatin perids. NTD, S, R and NS were further cmputed fr each individual snwmelt seasn in the calibratin and verificatin perids. In each case y Q was the mean bserved discharge cmputed fr the specific seasn, year and/r perid cncerned. Verificatin results Several examples demnstrated the variability f the numerical values f the criteria f fit. It is imprtant t realize that ne number can nly give a limited descriptin f verall perfrmance. In rder t btain sme infrmatin abut the variability f the numerical criteria, NTD, S, R and NS were als cmputed fr each individual year and individual snwmelt seasn in the calibratin and verificatin perids. The Nrrkping Cnference examined the graphical and numerical verificatin results and nted that values f the numerical criteria varied fr different years and different mdels. There was an verlap between the range f the annual values f the criteria fr different mdels. The Cnference cncluded that the difference between criterin values might thus be due t sampling variatins and, therefre, it wuld have been useful t cmpute cnfidence intervals. Hwever, it was cnsidered that fr the time being the state-f-the-art did nt permit the bjective cmputatin f cnfidence limits n the criteria; this was a field fr further research. The Cnference did nt attempt t make a ranking f mdels r classes f mdels n the basis f the prject intercmparisn results. INTERMEDIATE UTPUTS An upper limit f 5 km 2 was fixed n the size f the river basins used in the prject as ne means f reducing the effect f the transfrmatin mdel n the verall respnse. The Cnference felt that this decisin had been wise and that the verificatin results, including thse specifically fr the snwmelt seasns, had prvided a real indicatin f the extent t which the tested mdels reprduced snwmelt. As stated abve, the mdel wners were invited t submit cmputed utput fr ttal snwmelt in the basin. All but ne f the mdel wners submitted such intermediate utput and these utputs were seen as being f great ptential interest t thse wh wuld wish t study the detailed results f the prject. The intermediate utputs cmputed by the mdels have therefre been included in the final set

8 11 Wrld Meterlgical rganizatin f data assembled as an utcme f this prject. The Cnference examined the pssibility f using a standard transfrmatin mdel in cnjunctin with the intermediate utputs, but it was unanimusly recmmended that this shuld nt be dne, at least nt as part f the frmal WM prject. T much additinal infrmatin wuld be reuired (fr example evapratin and ther lss values) and it was felt that any results frm such a cmparisn wuld be f dubtful validity. VALIDITY F SELECTED MDEL PARAMETERS The cmparisn f snwmelt runff mdels ffers a gd pprtunity t cllect valuable infrmatin n the numerical values taken by certain mdel parameters. These values may be btained by calibratin using data frm the six-year calibratin perid, r by deriving a value externally. The mdel wners prvided infrmatin n the values taken by specific parameters and the manner in which these values were btained. This infrmatin has been included in the published reprt n the prject (WM, 1986). CNCLUSINS AND RECMMENDATINS The Nrrkping Cnference made several recmmendatins cncerning the develpment f mdels, ptimizatin techniues, the reuirements fr verificatin criteria and the preparatin and transfer f data sets fr use in similar prjects in the future. The Cnference als made specific recmmendatins, directed in particular t WM, fr future activities in this field: (a) The success f the prject resulted frm its careful and detailed preparatin and frm the excellent spirit f cperatin that had develped between the participants: (b) The mdels had perfrmed well and the detailed analysis bth f their structure and f their perfrmance characteristics prvided a wealth f valuable material fr use by thse interested in selecting a mdel fr a particular purpse r in furthering the develpment f snwmelt mdels: (c) There was cnsiderable variety in the structure f the mdels and in the manner in which they are calibrated, as well as in their updating ability and in the degree t which they had been r culd be used fr real-time frecasting. It was clear that the majr differences in the mdels derived frm the different purpses fr which they had been develped and the data and cmputing resurces which were available fr their use: (d) The temperature index apprach was applied by all f the tested mdels which were used fr peratinal frecasting. This was because the temperature index apprach generally prduced gd results and because there was a lack f real-time data fr the alternative energy budget apprach: (e) In mst mdels, an additinal sub-rutine was needed t suppress runff during the snw-ripening perid. Because f their interactins, the internal prcesses f heat flw (change in cld

9 Intercmparisn f mdels f snwmelt runff 111 cntent), liuid water strage and perclatin f free water culd be mdelled cllectively as a grup. (f) It wuld be valuable t cnduct sme further cmparisn f the sensitivity f predictins t the different methds used by the mdels t accunt fr internal prcesses. (g) Nne f the tested mdels cntained explicit euatins t mdel the effects f frzen sil. This was nt needed in this prject, but culd be very imprtant in sme ther applicatins. (h) The six data sets used in the prject were cnsidered t be generally satisfactry. They satisfied the needs f mst f the mdels tested in the prject. (i) The reuirements fr the preparatin and transfer f the data sets used in this prject can be recmmended fr the preparatin and exchange f meterlgical and hydrlgical data in future prjects f this type. (j) If at all pssible, data frm mre than ne precipitatin and temperature statin shuld be acuired fr a river basin. Nt nly d tw r mre statins prvide a measure f crss-checking, they als give the areal infrmatin reuired by mst meterlgical analyses. The same cnsideratins hld true fr ther variables such as wind speed and snw depth. (k) The subdivisin f river basins int elevatin znes was cnsidered desirable because f the strng elevatin dependent gradients f temperature and precipitatin in muntainus areas. (1) Further wrk n temperature lapse rates is t be recmmended because f their imprtance fr snwmelt calculatins and fr deciding n the frm f precipitatin. (m) A number f mdels used precipitatin adjustment factrs t accunt fr systematic measurement errr, lack f areal representativeness f pint measurements, and interceptin and sublimatin lsses. When pssible, crrectin shuld be made fr systematic measurement errr befre making further adjustments. (n) Areal snw cver distributin, a majr input variable fr ne f the mdels, is becming mre widely available as a result f advances in remte sensing. The use f such data shuld be encuraged in the interest f develping simple snwmelt-runff mdels. () It was imprtant that a range f verificatin criteria be evaluated in rder t cver different aspects f mdel perfrmance. Hwever, nt all the criteria prpsed fr use in the prject had supplied infrmatin that culd be usefully interpreted in terms f mdel perfrmance. The three graphical criteria and the nine numerical criteria finally adpted fr the prject might be used as a basic set in future prjects f this nature. (p) The perfrmance f the mdels n each criterin depended very much n the extent t which that r a similar criterin had been used during the calibratin perid. () The Cnference stressed that the graphical and numerical criteria used in this prject were fund useful fr snwmelt runff mdelling but fr ther purpses ther criteria may be eually r mre useful; fr example, a criterin based n a lgarithmic transfrmatin may be mre useful if lw flws were simulated. (r) WM shuld cnsider the pssibility f cnducting a simulated real-time intercmparisn f rainfall-runff and snwmelt-runff

10 112 Wrld Meterlgical rganizatin mdels designed t cmpare their perfrmance under streamflw frecasting cnditins with updating allwed. The final reprt f the intercmparisn prject (WM, 1986) cntains a large vlume f tabular, graphical and numerical data. It is nt pssible t present mre than a summary f these data in this paper and the reader is referred t the final reprt fr the full details and fr mre infrmatin cncerning the cnduct f the prject and interpretatin f the results. ACKNWLEDGEMENT The Wrld Meterlgical rganizatin is greatly indebted t the natinal agencies and the individual experts wh, in a spirit f internatinal cperatin, devted s much time and resurces t the cllectin and transfer f data, t the fitting and testing f the mdels and t the analysis f the results. REFERENCES WM (1975) Intercmparisn f Cnceptual Mdels Used in peratinal Hydrlgical Frecasting. WM peratinal Hydrlgy Reprt n.7; WM Publ. n.429; WM, Geneva. WM (1982) WM prject fr the intercmparisn f cnceptual mdels f snwmelt runff. In: Hydrlgical Aspects f Alpine and High-Muntain Areas (Prc. Exeter Symp., July 1982), IAHS Publ. n.138. WM (1986) Intercmparisn f Mdels f Snwmelt Runff. WM peratinal Hydrlgy Reprt n.23; WM Publ. n.646; WM, Geneva (in press).