New Approaches to Hydrologcal Predcton n Data-sparse Regons (Proc. of Symposum HS.2 at the Jont AHS & AH Conventon, Hyderabad, nda, September 29). AHS Publ. 333, 29. 11 A unversal approach to runoff processes modellng: copng wth hydrologcal predctons n data-scarce regons O. M. SEMENOA 1 & T. A. NOGRADOA 2 1 Department of Expermental Hydrology and Mathematcal Modellng of Hydrologcal Processes, State Hydrologcal nsttute, 23 2-ya lnya O, 19953 St Petersburg, Russa omakareva@gmal.com 2 Department of Geography and Geoecology, St Petersburg State Unversty, 31/33 1-ya lnya O, 199178 St Petersburg, Russa Abstract Ths paper dscusses the features whch a hydrologcal model should possess to be successfully appled n the task of hydrologcal predctons n poorly gauged regons. The Determnstc Modellng Hydrologcal System developed on the bass of the prncple of unversalty s descrbed as an example of such a model. The results of the smulatons conducted across the data scarce basns of eastern Sbera are presented. Key words prncple of unversalty; Determnstc Modellng Hydrologcal System, DMHS; data scarce regons; eastern Sbera NTRODUCTON Physcally-based dstrbuted modellng can be consdered to be a core component of modern hydrologcal scence. The ablty of the hydrologcal communty to dentfy and master the prncpal problems of hydrologcal modellng s crucal for progress to be made n the appled task of hydrologcal predcton; the ssue of ts further development s currently under ntense consderaton by many authors, for example, Beven (26). Data scarce regons present a partcular challenge for hydrologcal modellng. Models developed for specfc rver basns and/or for descrbng specfc groups of runoff formaton processes become useless n the absence of long-term or detaled observatons. The reason s that they have ncomplete physcal valdty and therefore requre ntensve parameter calbraton for any new applcaton. What are the approaches to whch the hydrologcal modellng has to move from calbratonbased ones? The essental fundamentals of physcs suggest that the process of runoff formaton must be the same n any pont of space, mplyng the possblty of smulatng runoff formaton processes n any basn wthn the framework of a sngle (or unversal) methodologcal approach, ts mathematcal realzaton and unfed nformatonal support. The prncple of unversalty s the base of the Determnstc Hydrologcal Modellng System (DHMS) (often called Hydrograph ). Ths model s beng developed at the State Hydrologcal nsttute (St Petersburg, Russa) by Prof. Yu. B. nogradov. ts successful applcaton to basns of dfferent scales n a varety of geographcal zones wthout change of model structure, algorthms and based on a unfed set of model parameters, has suggested the possblty of a general approach n hydrologcal modellng (nogradov, 1988; nogradov & nogradova, 29). Ths paper brefly presents the man propertes and basc concepts of the DHMS. Several basns of eastern Sbera are used to test the model under condtons of consderable lack of any knd of data. THE DMHS The prncple of unversalty What can be the measure of model unversalty? And how does t relate to the adequate presentaton of the natural processes? We clam that only the successful results of multfold testng of a model over basns of any type, regardless of ther scale and landscape/clmate characterstcs, can lead us n the rght drecton to answer these questons. Copyrght 29 AHS Press
12 O. M. Semenova & T. A. nogradova The dea of unversalty requres the fulflment of several mportant concepts whch are strongly related to the approach of model parsmony. The unversal model should use only exstng and commonly avalable meteorologcal forcng data, whch should be avalable for any terrtory, even f they are very lmted. The approprate characterstcs descrbng runoff condtons (n other words, parameters of the model) should be general for any basn and at the same tme take nto account ther unque propertes. Reflectng the objectve propertes of watersheds they obvously would have very clear physcal meanng. The possblty for a pror estmaton of the model parameters on the bass of some general dea about the features of the basn, and wth the use of any ndrect nformaton or expert evaluaton, s essental. The model s valuable f the parameters can be systematzed, generalzed and normalzed n relaton to calbrated parameters of models of other types. General descrpton of the DMHS The DHMS s a dstrbuted model of runoff formaton processes. t descrbes all components of the land hydrologcal cycle, ncludng: precptaton and ts ntercepton; snow accumulaton and melt; evaporaton from snow, sol and vegetaton cover; surface flow and nfltraton; sol water dynamcs and flow; heat dynamcs and phase change n sol layers; underground flow formaton, slope and channel flow transformaton; and flow dscharge. t s desgned to be appled n any geographcal area of the Earth. The model forcng data consst of the standard and most smple meteorologcal nformaton from observatonal networks that can be obtaned even for data scarce regons; these nclude daly values of ar temperature, mosture defct, and precptaton. The performance of the model s mproved by some approaches whch are used for estmaton of the effectve characterstcs of the nput data. For example, effectve temperature dffers from ts common analogue by an addtve constant that s computed as a functon of gven lattude, elevaton, terran slope and orentaton toward drect solar radaton. The specfc defnton accounts for clmatc thermal gradents for temperature and for precptaton nterpolaton from the precptaton rato to ts annual total that s ndependently estmated. The varous outputs of the model are the contnuous runoff hydrographs at the outlet, from any part of the basn or a specfed landscape; the dstrbuted state varables, reflectng water and heat dynamcs n sol layers and snow cover; spatal and temporal dstrbuton of water balance elements ncludng precptaton; evaporaton from snow, sol and vegetaton cover; surface, subsurface and underground runoff. The parameters and characterstcs of the model are horzontally dstrbuted as a system of representatve ponts and runoff formaton complexes n space, and vertcally, deep nto the sol column and layers of underground runoff. Most parameters have strong physcal meanng and are assessed a pror. The set of parameters descrbng one landscape can be used both for small and large basns wthout change of values. The spatal-computatonal schematzaton of the basn n the framework of the DMHS, the basn s represented by a system of ordered ponts whch are stuated wthn the basn terrtory. A regular hexagonal mesh s used (the dstance between neghbourng ponts s equal). Each calculaton pont, or so-called representatve pont (RP) corresponds to ts own area, whch s consdered to be homogenous n all characterstcs such as absolute alttude, orentaton, nclnaton and others. The RP quantty depends nonlnearly on basn area, ts orographc structure, densty and evenness of meteorologcal staton locatons. The regular system of RPs s combned wth the scheme of runoff formaton complexes (RFC). The RFC can be dentfed wth any knd of landscape; t s the part of a rver basn where the process of runoff formaton s assumed to be unform. Whle allocatng RFCs, the prncples of homogenety of sol, vegetable and landscape characterstcs of the basn surface are followed. By means of these crtera, the areas wth consderably dfferent relef and elevaton are separated nto dfferent RFCs. The nformaton about most of the model parameters s related and systematzed to the RFC; ther values reman fxed wthn ts range and change step-wse at ts borders.
A unversal approach to runoff processes modellng 13 The dstrbuton of the RFCs wthn each RP area s defned. The exact locaton of the specfc RFC n an RP s not mportant. Runoff varables are calculated for each RFC and summed up accordng to the relatve fractons of area wthn the RP hexagon; then they are summed up for the whole basn accordng to the RP s lag tme. The weather forcng data s nterpolated from meteorologcal statons nto RPs, and all RFCs wthn one RP get the same nput data. Further, the forcng data (for example, precptaton) are modfed accordng to the landscape qualtes. The example of basn schematzaton for one of the studed basns s shown n Fg. 1. ostochnaya Suntar Lower Base Runoff formaton complexes "golets" area mountan tundra sparse mountan larsh forest Suntar- Khayata meteorologcal staton representatve pont Fg. 1 The spatal-computatonal schematzaton. The Suntar Rver basn at the Sakharynya mouth (basn area: 768 km 2 ). The concept of runoff elements The approach used for descrbng water dynamcs wthn the rver basn greatly determnes the structure of runoff formaton model. The use of partal dfferental equatons, such as equatons of St enant or knematc wave for surface and channel flow, and the Boussnesq equaton for underground waters s prevalent n modern determnstc hydrologcal models. For the numercal soluton of the dfferental equatons of movement and contnuty, t s requred to approxmate the basn surface structure by a set of fnte elements, usually takng nto consderaton relef and landscape type. The assumpton of the presentaton of water movement as a thn contnuous water layer s very approxmate and not n correspondence wth natural process of water moton over the real surface and underground slopes. The ncomplete physcal valdty of these models s aggravated by the lack of relable nformaton about the real condtons of water movement, requrement of large amount of nformaton about nclnatons, morphology, roughness coeffcents for solvng these equatons. Here the calbraton procedure s necessary n whch the parameters are optmzed to ft the observatons. Because the parameters are evaluated not ndvdually, but n complexes, they often lose any physcal meanng and can not be relably transferred to the data scarce basns. The DMHS uses an ntegral approach for descrbng water movement wthn the basn the concept of runoff elements (nogradov, 1988, 23b). A runoff element s a part of surface or underground elementary slope or watershed lmted by mcro-dvdes whch s orented wth ts open part towards the slope non-channel or underground dranage system. The basn s consttuted by a set of elementary slopes or watersheds, whch, n turn, conssts of a system of runoff elements whch can be surface, subsurface and underground ones. The sze of a runoff element depends on nclnaton; the underground runoff elements are larger than the surface ones.
14 O. M. Semenova & T. A. nogradova The types and features of runoff elements determne the transformaton character of runoff formaton hydrographs at the pont of orgn of water flux nto the channel system. Accordng to nogradov (1988, 23b), the equaton for water flux, Q, from all runoff elements of the gven level to the channel system s: S + b Q = b (1) + [( S Q ) ( Q + b)]exp[ aδt( S + b)] 1 Here, Q s the ntal value of runoff Q, and S s the runoff formaton ntensty (m 3 s -1 ); Δt s the computaton tme nterval (s) durng whch S s constant; a = a* F -1 and b = b* F, where a* and b* are normalzed hydraulc coeffcents wth unts m -1 and m s -1 ; and F s the basn area (m 2 ). The total water flux to the channel system s descrbed by an equaton system such as equaton (1) when values S, Q, a and b are dfferent for the multtude of surface, sol and underground runoff elements of dfferent levels that form a rver basn. The dervaton of equaton (1), the herarchcal system of runoff elements and related descrpton of flow types, the ranges of а* and b* parameters values are worked out n nogradov (1988, 23b). He marks out surface, subsurface types of runoff and 15 underground layers correspondng to rapd ground, ground, upper, deep and hstorcal underground types of runoff. Each runoff type (and layer of runoff elements) s characterzed by the specfc values of resdence tme τ * = 1/( a * b*), outflow q and water storage Н. t s assumed that the outflow rate decreases and water storage ncreases wth depth n groundwater aqufers. The concept of runoff elements allows carryng out smulatons for basns of any sze; snce the value of basn area s ntroduced nto the calculaton scheme. The parameters of the DMHS The parameters of the DMHS can be dvded nto fve groups accordng to landscape components: sol column (unsaturated zone), vegetaton cover, slope surface, underground runoff and clmate parameters. The problem of heterogenety of earth surface characterstcs (and thus of model parameters) s consdered to be one of the fundamental challenges of hydrologcal scence. n partcular, t refers to the physcal propertes of sols. However, consderaton must be gven to the fact that the varaton of sol propertes depends on the areal extent used for estmatng or measurng ther values. The DMHS parameters of the sol (unsaturated zone) for dfferent sol depths are densty; porosty; maxmum water holdng capacty; nfltraton coeffcent; specfc heat capacty and conductvty; the ndex of ce content nfluence at nfltraton; the contrbuton rato to evaporaton; hydraulc parameter of sol runoff elements. They should represent the values of the sol strata typcal (or representatve) for the specfc RFC. For Russan basns such values are obtaned from publshed agrcultural-hydrometeorologcal surveys, or estmated on the bass of observatons at water-balance statons (a hghly nstrumented small watershed ntended for long-term collecton of observatons) or expermental watersheds. Our experence of runoff process smulatons ndcates that such data can be systematzed for dfferent landscapes and are stable enough. n seekng the approprate range of values that do not have much varaton, t s not necessary to search for the exact values of these parameters. n contrast to calbrated and optmzed parameters they can be extrapolated to ungauged basns for any forecastng and research task. Parameters of the vegetaton cover nclude: four phenologcal dates; maxmum and mnmum values of seasonal shadow fracton by vegetaton cover; ntercepton water capactes; landscape albedos; the coeffcents of potental evaporaton; and the coeffcent of evaporaton from the ntercepton storage durng the maxmum development of vegetaton cover. Ths nformaton can be found n specal lterature related to geobotancal, agrcultural and clmate research. The parameters of the slope surface are: maxmum and mnmum values of the snow redstrbuton coeffcent; spatal varaton coeffcent of SWE n snow cover; spatal varaton of nfltraton capacty of upper sol layer; maxmum pondng fracton; maxmum surface depresson
A unversal approach to runoff processes modellng 15 storage; and hydraulc parameter of surface runoff elements. The parameters descrbng snow characterstcs are assessed aganst snow survey data. The spatal varaton of the nfltraton capacty of the upper sol layer can be calbrated aganst runoff observatons on small watersheds or water-balance statons. The propertes descrbng the surface storage process are obtaned from the lterature. The parameters of the underground system of runoff elements are: the hydraulc parameter and redstrbuton values. The hydraulc parameter s usually assumed to be constant; the values of redstrbuton of water volume among modellng groundwater layers are assgned on the bass of observed hydrograph analyss wthn the concept of runoff elements. For runoff hydrographs of smlar type these values are closely related. Clmate parameters, f not obtanable, are estmated usng the forcng meteorologcal data. Here the serous problem of nterpolaton of precptaton n data poor regons (manly mountanous areas) s to be mentoned. Whle mplementng the DHMS, we use the approach of normalzng daly precptaton layer by ts mean annual value. The assessment of mean annual values for each representatve pont dependng on ts alttude and locaton s a specal problem to be solved. THE STUDY OBJECTS To llustrate the descrbed prncples, four basns wthn the terrtory of eastern Sbera have been chosen for the smulaton of runoff formaton processes. The basns are of dfferent szes and represent dfferent landscape characterstcs. The basn selecton s summarzed n Table 1. All study basns are stuated n the zone of contnuous permafrost; they have mountanous relef, and the clmate s characterzed as severe contnental. The man landscape type s taga domnated by larch. The rvers have mxed snow meltng and ranfall supply. Well-defned maxmum dscharge n June, due to snowmelt, s typcal only for the Nzhnaya Tunguska; the other basns are subject to ntensve summer rans causng flows comparable to and greater than sprng snowmelt. Table 1 Descrpton of watersheds used n the study. No. Rver; outlet Basn Average Mean area elevaton annual (km 2 ) (m) runoff (mm) / dscharge (m 3 s -1 ) 1 Nzhnaya Tunguska; Bolshoy Porog 2 Yana; Dgangky 3 Uchur; Chul bu 4 Suntar; Sakharynya Rver Mouth 5 Detrn; akhanka Rver Mouth Number of RP Number of meteorologcal statons (ncludng those stuated nsde the basn) Locaton 418 5 245 / 34 51 19 (8) The rght trbutary of the Yensey Rver 216 83 12 / 965 45 15 (8) The rver of the Laptev Sea basn 18 11 38 / 13 48 9(3) The trbutary of the Aldan Rver (Lena Rver basn) 7 68 15 176 / 43 16 3 (1) The Headstream Of The ndgrka Rver 5 63 92 324 / 58 15 6 (2) The headstream of the Kolyma Rver
16 Q [m 3 sec -1] 4 3 2 1 O. M. Semenova & T. A. nogradova 198 1981 4 3 2 1 4 3 2 1982 4 1983 3 2 1 1 (a) Q [m 3 sec -1] 9 6 3 197 1971 6 4 2 6 4 1972 1973 6 4 (b) 2 2 Q [m 3 sec -1 ] 15 1 5 1981 1982 15 1 5 1 5 1983 1984 15 1 5 (c) smulated observed Т Fg. 2 Smulated and observed hydrographs for: (a) the Nzhnaya Tunguska Rver at Bolshoy Porog (basn area: 418 km 2 ), 198 1983; (b) the Yana Rver at Dgangky (basn area: 216 km 2 ), 197 1973; and (c) the Uchur Rver at Chul bu (basn area: 18 km 2 ), 1981 1984.
A unversal approach to runoff processes modellng 17 Q [m 3 sec -1] 1 1959 196 1 5 5 (d) 4 3 1961 15 1 1962 2 1 5 Q [m 3 sec -1] 6 4 2 1977 1978 12 9 6 3 8 6 4 1979 8 198 6 4 (e) 2 2 smulated observed T Fg. 2 contnued Smulated and observed hydrographs for: (d) the Suntar Rver at the Sakharynya Rver mouth (basn area: 768 km 2 ), 1959 1962; and (e) the Detrn Rver at the akhanka Rver mouth (basn area: 563 km 2 ), 1977 198. RESULTS The study nvolved runoff modellng for four watersheds wth 24-hour calculaton nterval for the dfferent perods (from 7 to 19 years). The comparson of observed and smulated hydrographs s shown n Fg. 2(a) (e). n general, the model smulatons capture the shape and depleton curves of observed hydrographs durng both the snowmelt and rany perods; the dscrepancy between observed and smulated volumes of flood peaks can be related to the uncertantes of precptaton data. Table 2 presents the statstcal characterstcs evaluatng the model performance of runoff smulatons. They nclude: mean annual observed runoff, H obs, and calculated runoff, H calc (mm); the Nash-Sutclffe effcency, Ef, descrbng the qualty of smulated runoff compared to observed data for daly and annual values; and the relatve error, Er, between smulated and observed daly and mean annual runoff. The Ef and Er are calculated as:
18 O. M. Semenova & T. A. nogradova n = 1 calc calc obs obs 2 ( Q Q ) = 1 Ef = 1 (2) n 2 ( Q Q ) n Q calc Q = 1 Qcalc obs Er(%) = 1 (3) n where and are the calculated and observed runoff at day (or year) for daly (or annual) Q calc Q obs values; Qobs s ether: the observed annual average n the case of daly flows, or the long-term average n a case of annual flow values; and n s the number of the days n the year (or the number of years). Table 2 Statstcal characterstcs of flow smulatons. Basn Perod H obs H calc Ef Er, % Daly Annual Daly Annual Hgh flow Low flow Average Nzhnyaa Tunguska Rver at Bolshoy Porog 1978 1984 242 234.91.98 28 35 32 4 Yana Rver at Dgangky 1966 1984 12 13.81.8 4 88 72 1 Uchut at Chul bu 1977 1984 38 38.81.95 32 36 35 8 Suntar Rver at the Saharynya Rver mouth 1957 1964 176 181.71.91 38 76 63 1 Detrn Rver at the akhanka Rver mouth 1977 1984 324 354.75.94 4 79 66 12 The relatve error, Er, for daly values s presented n three varants: for the perods of hgh and low flow and the average for the year. Ths follows the seasonal cycle of runoff whch ndcates low flows durng October Aprl and hgh flows durng May September. Therefore, by the hgh-flow perod we mply the warm part of the year wth 9 98% of annual runoff; dependng on the basn t starts n dfferent 1-day perods of May and fnshes n September or October. For perods of rver freeze-up (observed value equals zero), Er was not calculated. For all basns, the calculated Nash-Sutclffe effcency, Ef, exceeds.7 and for three of them t exceeds.8 for daly values; for annual values t exceeds.8. Such values of Ef are usually consdered to be rather hgh and ndcate good model performance. But the man weakness of ths crteron s the overestmaton of smulaton effcency for the perods of hgh flow and small contrbuton of low flow perods to ts estmaton; t s nsenstve to systematc under- or overestmatons of smulated flow. The annual Er vares wthn the range 4 12%, showng maxmum values for smaller basns. Ths may be due n part to the hgher dependence of small basns on precptaton nput from very few, or even a sngle, meteorologcal staton(s). For the basns of Nzhnyaa Tunguska and Uchur rvers, the average Er for daly values s around 35%, wth lttle varaton through the year. The average Er for the other three basns (nos 2, 4 and 5 n Table 1) exceeds 6% (even amountng to 72% for the Yana Rver). Ths s caused by hgh values of Er (76 88%) durng the low-flow perod; t can hardly be seen from Fg. 2, but for these specfc basns the model systematcally overestmates the baseflow. The reason for such hgh dscrepances s that whle the rvers 2, 4 and 5 are subject to complete freezng durng the cold perod when the observed runoff values equal zero, the
A unversal approach to runoff processes modellng 19 calculaton algorthm for runoff elements does not reflect these processes. Some modfcaton of the calculaton scheme should be done for the condtons of very low wnter temperatures when the outflow from the deep groundwater reservors s hampered by ce. DSCUSSON Estmaton of the credblty and acceptablty of the smulaton results s the natural stage of any model applcaton. t s clear that the greater the quantty and varety of verfed smulatons, the more lkely t s that the concepts underlyng the model are not defectve. The possblty of gettng smlar results, complyng wth the observatonal data, by the use of dfferent models (the problems of non-unqueness and equfnalty: Beven, 21) relates to the actve use of parameter calbraton and gnorng of the prncple of unversalty n the methodology of model development. Numerous calculatons for the basns stuated n dfferent clmate and landscape zones can mpressvely mprove the models value. The task of choosng of approprate evaluaton crtera s mportant. Accordng to (nogradov, 23a), the relatve error at every tme step of the calculatons, ts annual dstrbuton and ts varaton over the smulaton perod, can objectvely affect the model effcency. t s sgnfcant that the value of the relatve error f averaged should be taken n ts absolute value wthout mutual compensaton of negatve and postve devatons. REFERENCES Beven, K. (21) How far can we go n dstrbuted hydrologcal modellng? Hydrol. Earth System Sc. 5(1), 1 12. Beven, K. (26) Searchng for the Holy Gral of scentfc hydrology: Qt=H(S,R,Δt)A as closure. Hydrol. Earth System Sc. 1, 69 618. nogradov, Yu. B. (1988) Mathematcal Modellng of Runoff Formaton. A Crtcal Analyss. Gdrometeozdat, Lenngrad (n Russan). nogradov, Yu. B. (23a) Rver runoff modellng. n: Hydrologcal Cycle (ed. by. A. Shklomanov), Encyclopeda of Lfe Support Systems (EOLSS). Developed under the auspces of UNESCO. EOLSS Publshers, Oxford, UK (http://www.eolss.net). nogradov, Yu. B. (23b) Runoff generaton and storage n watershed. n: Hydrologcal Cycle (ed. by. A. Shklomanov), Encyclopeda of Lfe Support Systems (EOLSS). Developed under the auspces of UNESCO, EOLSS Publshers, Oxford, UK (http://www.eolss.net). nogradov, Yu. B. & nogradova, T. A. (28) Current Problems n Hydrology. Academa Publshers, Moscow, Russa (n Russan). nogradov, Yu. B. & nogradova, T. A. (29) Mathematcal Modellng n Hydrology. Academa Publshers, Moscow, Russa (n Russan) (n press).