Modelling Snowmelt-Induced Processes (Proceedings of the Budapest Symposium, July 1986). IAHS Publ. no. 155,1986. Simulation of snowmelt runoff in lowland and lower Alpine regions of Switzerland LUDWIG N. BRAUN & HERBERT LANG Department of Geography, Hydrology Section, Swiss Federal Institute of Technology, Winterthurerstr. 190, CH-8057 Zurich, Switzerland ABSTRACT This study investigates the influence of snowmelt model structure on the overall performance of runoff modelling in basins ranging from 3.2 to 1696 km 2 . For a given basin, melt rates as calculated by various snowmelt models of different complexity are used as input to the same runoff model, and the performance is assessed by linear scale plots of measured and simulated discharge and by a numerical efficiency criterion. In small to medium basins (<1000 km 2 ) there is a noticeable improvement in model performance when moving from a temperature index method to any other method investigated. During advection-melt conditions an energy balance method yields the best results, while during radiation-melt conditions index methods are sufficient. In larger basins (>1000 km ) , a noticeable change in model performance is observed only in individual years characterized by an above-normal snow pack. For operational purposes, the combination method according to Anderson (1973) seems to be the most suitable approach of the methods investigated. La simulation de l'écoulement des eaux de fonte dans les régions helvétiques basses et préalpines RESUME Cette étude étudie l'influence de la structure de modèles de fonte de neige sur la performance générale de modèles de prévision d'écoulement de basins versants d'une superficie de 3.2 à 1696 km 2 . Pour un bassin versant donné, des vitesses de fonte calculées avec des modèles de fonte de neige de différentes complexités sont utilisées comme données pour le même modèle de prevision d'écoulement. La performance est évaluée sur la base des courbes linéaires de débit calculées et mesurées ainsi qu'avec un critère d'efficacité numérique. Pour de petits basins versants (<1000 km 2 ) la performance du modèle d'écoulement augmente de manière significative si l'on passe d'un modèle de fonte de neige basé sur la température de l'air à tout autre modèle de fonte de neige. Lors de conditions de fonte par advection les meilleurs résultats sont obtenus avec un modèle basé sur le bilan énergétique alors qu'en périodes de fort rayonnement un modèle basé sur la température de l'air est suffisant. Pour de grands basins versants (>1000 km 2 ) 125 126 L.N.Braun & H.Lang la performance d'un modèle ne change de manière significative que pour certaines années avec une couche de neige supérieure à la moyenne. Pour les applications pratiques, la méthode combinée selon Anderson (1973) semble être l'approche la plus appropriée des méthodes analysées. INTRODUCTION This study evaluates the influence of snowmelt model structure on the overall performance of runoff modelling in various sized basins. At lower elevations, a great part of the snow cover is typically short-lived. Special attention is given to the fact that temporal resolution of data and steps of calculation need to be higher in small basins as compared to larger ones for adequately simulating runoff events. In the literature considerable attention is devoted to assessing the performance of point snowmelt models of different complexities. Significant contributions are made by Anderson (1976) and Obled & Rosse (1977), who compared melt rates calculated by different approaches with snowmelt measured using a snow pillow and snow lysimeters respectively. Compared with index methods, detailed energy balance approaches requiring additional data, such as radiation, generally yield better simulation of snowmelt in open area, as they can account for different meteorological conditions. For forested sites however, temperature index methods generally yielded acceptable results. Rosl (1976) investigated the performance of snowmelt models as used in various runoff models at sites located in the lowland and lower alpine regions (Mittelgebirge) of the Federal Republic of Germany (FDR). In his analysis, the snow accumulation and ablation model of the NWSRFS (Anderson, 1973) performed best. This approach employs a temperature index method (seasonally varied melt factor) during fair weather conditions, and calculations of the turbulent exchange of heat and water vapour using empirical wind functions, of longwave radiative exchange and of heat gained by precipitation during rainy periods. Assessing the performance of various snowmelt models over a basin in conjunction with a precipitation runoff model is a more difficult endeavour. Apart from the temporal variability, the spatial variability of input data needs to be considered. There is a WMO project for the intercomparison of conceptual models of snowmelt runoff near its completion (WMO, 1982), where some 10 different models are tested over six watersheds ranging from 8.7 to 2170 km . The results of the project are to be published soon. Charbonneau et al. (1981) tested different snowmelt runoff models in an alpine basin (Durance River, France, 548 km 2 ). They conclude that the choice of particular interpolation procedures for input data such as air temperature and precipitation is much more crucial than the level of sophistication of individual snowmelt models. Both the WMO project and Charbonneau et al. assess the overall performance of the different snowmelt runoff models. In this study the sole influence of the different structures of the snow Simulation of snowmelt runoff in Switzerland 127 accumulation and ablation model is investigated by using the same interpolation procedures for meteorological data and the same runoff model. Flemming & Gurtz (.1983) report first results of such an investigation in two lowland to lower alpine basins (Mittelgebirge, 4.9 and 363 km 2 ) situated in the German Democratic Republic (GDR). They found that temperature index methods performed as well as an energy balance method. Braun & Zuidema (.1982) have demonstrated that an energy balance method yields better results in snowmelt runoff modelling than simple temperature index methods in the Rietholzbach basin (3.2 km2) during advection-melt situations. In this study, published in more detail in Braun (1985), a wider variety of meteorological conditions and various other index methods are considered not only in this small basin, but in several other basins ranging from 79 km to 1696 km2. We try to show to what extent snowmelt model structure, including the choice of different meteorological input variables, influences the overall runoff model performance in the lowland to lower alpine environment in eastern Switzerland using one and the same runoff model. The results should also help to find the appropriate level of snowmelt model complexity for the operational forecast procedures for the the Rhine River system as used by the Hydrology Section of the Swiss Federal Institute of Technology (ETH) in Zurich (see for example Vischer, 1978, and Jensen, 1980). METHODS AND DATA The following snowmelt models of varying complexity are compared: (a) temperature index method (Bergstrom, 1976); (b) temperature and wind index method (T,u-index); (c) combination method (Anderson, 1973); (d) extended combination method (using also water vapour pressure as an input variable) (e) energy balance method (calculation of the turbulent fluxes of heat and water vapour based on Price & Dunne, 1976). In each case a water retention of the snow cover of 10% of its water equivalent is assumed. Refreezing of liquid water in the snow cover during periods with negative air temperatures is modelled according to the snow routine of the HBV runoff model as developed by the Swedish Meteorological and Hydrological Institute (Bergstrom, 1976). Melt rates as calculated by the various snowmelt models serve as input in a runoff model, and the overall model performance is assessed comparing linear scale plots of measured and simulated discharge and by the numerical efficiency criterion R2 (Nash & Sutcliffe, 1970) which is defined as follows: F 2 - F2 ™2 _ O where 2 F = the sum of squares of the differences between measured and 128 L.N.Braun S H.Lang and computed discharge; F2 = the sum of squares of the differences between measured ° discharge and mean discharge over the period investigated (also called initial variance or no model value of F ). The R2-criterion is a relative measure which facilitates comparisons between different snowmelt routines when applied to the same basin and the same period of time. It takes on values ranging from -°° to +1, whereby +1 represents a complete agreement between measured and computed hydrographs. R2-values are not directly comparable between different basins and different time periods as the initial variance F 2 may be quite different. The R2-criterion has been found to reflect fairly well the general conclusions of model performance based on visual inspection (Bergstrom, 1976)„ Ideally, other numerical and graphical criteria should be used to cover different aspects of model performance. In this study, however, the emphasis lay on visual inspection of linear scale plots of measured and simulated discharge of all years, basins and snowmelt models investigated. A more complete evaluation of the performances on this basis is given in Braun (1985). Optimization of selected model parameters is achieved by mapping R2-values as a function of these parameters (analysis of response surfaces). In all periods investigated these optimized "generally- valid" parameter values are applied with the exception of the correction factors for rainfall and snowfall, which are optimized for each period to yield a minimal value of accumulated differences between simulated and measured discharge. The basins The different snowmelt models are applied in the Rietholzbach basin (3.2 km ) and in four various-sized basins of the Thur River, all located in northeastern Switzerland (see Fig.l). The Thur basin above Andelfingen has an area of 1696 km2 and ranges from 356 m to 2500 m a.m.s.l. For calculation purposes it is subdivided into seven sub-basins. Sub-basins 3, 4, 5, 6 and 7 constitute the Thur basin above Halden with an area of 1085 km2. Sub-basins 4 and 5 constitute the Thur basin above Jonschwil with an area of 493 km2, and sub-basin 2 is identical with the Murg basin above Wangi with an area of 79 km . Mean yearly precipitation across the whole Thur basin ranges from 900 mm in the lowlands of the northern part to up to 2500 mm at elevations above 1500 m a.m.s.l. in the southern part. Mean annual runoff at Andelfingen is 1080 mm. Below about 700 m a.m.s.l. the mean annual temperature is around 8°C, the mean temperature in January is about -1°C and in July about 18°C. Coniferous and deciduous forests cover some 30% of the area. Based on measurements in western Switzerland by Maurer et al. (1975) it was established that a snow cover is formed and disappears again about 8 times during one winter at elevations between 400 m and 900 m„ The geographical location of the Rietholzbach basin within the Thur basin is given in Fig.l. It ranges from 680 m to 960 m a.m.s.l., and about 20% is forested. Mean annual precipitation is Simulation of snowmelt runoff in Switzerland 129 FiG.l Location of the Thur and the Rietholzbach basins. 1400 mm (Grebner & Goldi, 1983), and mean annual runoff is expected to be 800 mm. Meteorological and hydrological measurements in this basin have been taken since 1974/1975 by the Hydrology Section of the Swiss Federal Institute of Technology in Zurich, and the aim of this research project is to further our understanding of the water balance and the runoff processes in this lower alpine zone (Lang, 1978). More details about the hydrology of this basin can be found for instance in Germann et al. (1982). Runoff model and data used in the Rietholzbach basin Meteorological and hydrological data with a temporal resolution of 1 h are used for simulation in the Rietholzbach basin. Five specific periods totalling about 300 days of marked accumulation and ablation of snow in the winter months of the years 1976 to 1980 have been selected for simulation. No data after spring 1980 were available at the time of analysis due to a change in the data collection system. As a result no independent data set has been investigated in this basin. Precipitation is measured by a heated tipping bucket raingauge, and 1380 mm were recorded over the 300 days considered here. About 510 mm or a third of the total precipitation fell as snow, assuming a transition air temperature from snow to rain of 0.5°C which was found to be optimal. Total discharge over the investigated period amounts to 1330 mm. Meteorological data measured at one point in the Rietholzbach basin are considered representative for the whole basin in this analysis. A modified version of the approach used by Martinec (1970) has been chosen as a runoff model, using a time step of 1 h. 130 L.N.Braun & H.Lang Runoff model and data used in the Thur basin Meteorological data used for simulation of discharge in the Thur basins having a temporal resolution of 12 h are taken from 14 climatological stations of the Swiss Meteorological Institute. Distribution of these data across the watershed is achieved on the basis of a so-called "optimal" interpolation technique, where interpolated values are a linear function of the values measured at the stations, and where the coefficients of this function are determined using an arbitrarily chosen functional relationship between covariance and distance. Precipitation is determined at the centre of gravity of each sub-basin (see Fig.l) and the remaining meteorological variables are distributed to the various elevation belts of 200 m vertical extent between 400 and 2200 m a.m.s.l. Wind speed is taken as invariant across all basins and is represented by the arithmetic mean of about 10 stations. The water equivalent of the snow pack is simulated for each sub-basin and elevation belt, and calculated snowmelt and rain inputs are used with a distributed version of the HBV-3 runoff model to simulate daily discharge of the various Thur basins. This conceptual runoff model described by Bergstrom (1976) has been selected because it has a simple structure and because it is well documented. A total of 11 hydrological years (covering the months between October and June only) are used in this analysis, where the years 1976/1977 to 1980/1981 served as the calibration period, and the years 1971/1972 to 1975/1976 as well as 1981/1982 as the verification period. A comparison between simulated and measured water equivalent of the snow pack at one point can be achieved for all years investigated, where measurements are taken twice a month between November and April by the network of the Hydrology Section of the Federal Institute of Technology (Schwagalp station, 1290 m a.m.s.l., location see Fig.l). During the years 1980/1981 and 1981/1982 additional water equivalent measurements were taken along an easily accessible snow course ranging from 400 to 1200 m a.m.s.l. (Regelstein snow course). RESULTS FOR THE RIETHOLZBACH BASIN As mentioned in the previous section, the emphasis of the assessment of model performance lay on visual inspection of linear scale plots of measured and simulated discharge. It is beyond the scope of this paper to give due attention to these plots, and for further information the reader is referred to the more detailed report of this study given in Braun (1985). Table 1 summarizes the efficiencies of the various snowmelt models as applied in the Rietholzbach basin. Over the total 300 days of simulation using a temporal resolution of 1 h, an increase in model performance of about 4% can be demonstrated when moving from the temperature index to any other method. The energy balance method performed slightly less well than the combination method. The main reason may lie in the fact that slope and aspect are not considered when calculating the shortwave radiation balance Simulation of snowmelt runoff in Switzerland 131 2 TABLE 1 Performance R of different snowmelt models over 298 days of simulation and over a period of predominant advection-melt (10 December 1979-13 February 1980) Rietholzbach basin Performance R : F2 Comb. Energy O (mm h~l)z T-index T,u-index method balance Over 298 days 526.1 0.85 0.89 0.89 0.88 Period of 212.2 0.86 0.91 0.93 0.94 predominant advection-melt (66 days) . in this version of the energy balance method. On days with predominant advection-melt conditions, differences in exposition play an insignificant role, and the superiority of the energy precipitation (mm h"') -10 iii 10 f air temperature CC) i pA^/^^V-AAAAAfA/V JL- jrAJ^Af^r-^A ,1, \\\ . U .S\ ^ 200 16 18 20 22 24 26 28| 10 12 14 16 18 20 22 February 1978 March 1978 FIG.2 Performance of snowmelt routines during advection- and radiation-melt situations, Rietholzbach basin 1978. Radiation-melt situations identified by # . 132 L.N.Braun & H.Lang balance as compared to the index methods becomes evident (see Table 1). Figure 2 illustrates a period of snow accumulation and ablation in February and March 1978. On days with predominant radiation-melt conditions, index methods perform adequately, and the combination method using air temperature and wind speed only as input variables seems to be the most appropriate approach for operational purposes. RESULTS FOR THE THUR BASINS Influence of snowmelt model structure Figure 3 illustrates the performance of the various snowmelt extended . „ . . combination extended T,u- index . . ,. T-mdex T,u-index 1L J L. . combination method combination method method FIG. 3 Performance of different snowmelt models as a function of their sophistication, Thur basins (individual years 1971/1972 to 1981/1982, October-June). Simulation of snowmelt runoff in Switzerland 133 models as applied in the four Thur basins for every hydrological year (October to June only) from 1971/1972 to 1981/1982. There is a slight tendency to increased performance with increasing sophistication of the model used, particularly in the smaller basins and in years with an above-normal snow pack. Generally, the temperature and wind index approach performs less well than the temperature index method. It appears that a further input variable such as wind speed needs to be included through physically based functions and not as an index in order to increase model performance. This is in contrast with the findings from the Rietholzbach basin, where the temperature and wind index method increased performance considerably over the temperature index method. This may be due to the greater temporal resolution and the increased representativeness of the wind data in the Rietholzbach basin. The exceptionally low R2-values of the 1971/1972 simulations are due to the very low F -values as compared to other years. Winter 1971/1972 had by far the smallest snow pack of all years considered. Table 2 summarizes the results over the total calibration and verification periods as well as for the year 1981/1982. It can be stated that snowmelt model structure influences the overall performance over several years of runoff simulations only to an TABLE 2 Performance R of different snowmelt models, Thur basins F2 Extended Size o T- T,u- comb. comb. Basin (kmz) (mm day ,) index index method method Murg 79 C 6002 0.85 0.86 0.87 0.87 (Wangi ) V 3470 0.86 0.86 0.86 0.87 1981/82 2176 0.85 0.83 0.87 0.88 Thur 493 C 25566 0.85 0.85 0.86 0.86 (Jonschwil) V 14982 0.85 0.83 0.86 0.86 1981/82 5306 0.77 0.73 0.79 0.81 Thur 1085 C 15355 0.84 0.84 0.85 0.85 (Maiden) V 9950 0.85 0.83 0.85 0.84 1981/82 3094 0.78 0.78 0.81 0.82 Thur 1696 C 8959 0.82 0.81 0.82 0.82 (Andelfingen) V 5582 0.81 0.80 0.80 0.80 1981/82 2008 0.77 0.75 0.78 0.78 C = calibration period, 1976/1977-1980/1981 V = verification period, 1971/1972-1975/1976 Murg basin: October-April (212 days) all other basins: October-June (274 days) 1981/82: verification; maximal snow pack in all the years investigated 134 L.N.Braun S H.Lang insignificant degree. In other words, the temperature index approach using only precipitation and air temperature as input variables works almost as well as the extended combination method using precipitation, air temperature, wind speed and water vapour pressure as inputs. This conclusion applies for runoff simulations over extended periods of time (October-June and over several years) and using meteorological input data of a temporal resolution of 12 h, and for discharge data having a temporal resolution of one day. During individual years, snowmelt model structure may have a noticeable influence in the smaller Thur basins investigated, particularly during the years 1974/1975, 1980/1981 and 1981/1982, when the snowpack was above average. In these years an increase in model performance by about 5% can be demonstrated when moving from the temperature and wind index method to the extended combination method. Figure 4 shows part of the simulation of discharge of the Thur above Jonschwil in 1981/1982, when the snowpack was the greatest of all the 11 years investigated. The T,u-index method (It2 = 0.73) overestimates melt at the beginning of January 1982, whereas it underestimates melt in April and May 1982. The extended combination method (R2 = 0.81) gave the best results in this case here as well as in all other basins. precipitation ( m m / 1 2 h) sub-basin 5 (Nesslau) 20 + 0 j •• ** J l M n jili ..I, . .Mi ni. .,.1, 11 j. Ai\ N 0 J F M A M daily mean air temperature (°C) 20 T 500 m .1300 m level 10 0 -10 é 2100 m water equivalent SP (mm) — simulated (ext.comb method) simulated (T,u-index) measured • Schwàgalp 1290 m a.S-l. jn 1000 m Regelstein snow course 1000 discharge Q (mm d1) Thur/Jonschwil Q ( m J s1) 30 + measured T, u - index W0 extended combination method M 1981 ' 1982 FIG.4 Comparison of measured and simulated discharge and water equivalent of the snow cover, Thur basin above Jonschwil, 1981/1982. Simulated water equivalent values refer to the centre of gravity of sub-basin 5 (Nesslau). Simulation of snowmelt runoff in Switzerland 135 Measured and simulated water equivalent As an example, Fig.4 also compares measured and simulated water equivalent of the snow cover at different elevations in sub-basin 5 (Nesslau) for winter 1981/1982 (for locations see Fig.l). Simulated values are compared with Schwagalp data (1290 m a.m.s.l.) and data collected at the Regelstein snow course at different elevations. Generally speaking, the simulated water equivalents at different elevations correspond fairly well with the Regelstein data below the 1000 m level. However, simulated values above this level are significantly lower than the Regelstein and the Schwagalp data. This latter finding also applies to all other years investigated where Schwagalp data are available» This discrepancy may be due to the specific location of the Schwagalp station (northern exposure, shading effects). It seems, however, also connected to the interpolation procedure as used for precipitation. The annual precipitation gradient as suggested by the interpolated values is considerably lower than what can be expected for this region (Zeller & Gensler, 1980). On the other hand, areal precipitation and water equivalent values may not be directly compared with point values. Despite the discrepancy between measured and simulated water equivalent values above 1000 m, simulated discharge of the Thur at Jonschwil corresponds fairly well with the measured one. Influence of basin subdivision The influence of basin subdivision on model performance is assessed for the Thur basin above Halden. Simulations using a division into five sub-basins as given in Fig.l are compared to simulations treating the basin as one unit with the same vertical division into 200 m elevation belts (see Table 3)„ For both TABLE 3 Influence of basin subdivision on overall model performance, Thur basin above Halden, temperature index method, October-June o 5 sub-basins 1 sub-basin Period (mm day'1)2 R2 R2 Calibration period 15 355 0.84 0.83 Verification period 9 950 0.85 0.83 1974/1975 2 333 0.86 0.82 1978/1979 3 428 0.83 0.84 calibration and verification periods, a decrease of the efficiency R2 by 0.02 (about 2%) is found when using only one unit. In individual years, performance decreases by 4% in the year 1974/1975 (second highest maximal water equivalent at Schwagalp in all of the 11 years considered) and increases by 1% in 1978/1979 (below- 136 L.N.Braun Si H.Lang normal snowpack). It can be concluded that a more detailed subdivision of a basin may improve runoff simulations by the same order of magnitude as a more detailed snowmelt model. Influence of temporal resolution of meteorological data Here, an example of the influence of the temporal resolution of meteorological data is given. Between 16 and 20 February 1978 a cold polar air mass was stationary over northeastern Switzerland, while warm maritime air was moving from the southwest across Switzerland. This caused heavy precipitation falling as snow above about 2000 to 2500 m a.m.s.l., as rain below that elevation, and partly as freezing rain as it entered the cold bottom air layer in northeastern Switzerland. All snowmelt models as applied in the air temperature (°C) at 0700 and 1900 hours FIG.5 Simulation of discharge of the Thur River at Halden, January-March 1978. Failure of all snowmelt models to simulate the peaks on 18 and 20 February 1978 was due to insufficient resolution of meteorological data and inadequacy of a fixed air temperature divider. Simulation of snowmelt runoff in Switzerland 137 Thur basins recognized this situation as an accumulation period, increasing the simulated water equivalent by about 80 mm (Fig.5). At an elevation of 700 m a.m.s.l. a maximal water equivalent of the snow pack of about 130 mm resulted in sub-basin 4 (Wasserfluh, location see Fig.l) on February 20, which corresponds well with the Rietholzbach basin using data of the Buel station located at about 750 m a.m.s.l. (see Fig.2). However, the snow depth data as given in Fig.5 indicate a much smaller increase of the snow cover. Two distinct peaks of discharge of the Rietholzbach. and of the Thur river are observed on 17 (18) and 20 February. These are simulated fairly well by the energy balance method in the Rietholzbach basin, but are not simulated at all by any of the methods applied in the Thur basins. As a result of the overestimation of accumulation, simulated discharge is generally too high in early March. This failure can be partly ascribed to the use of the readings of air temperature, wind speed and vapour pressure at 0700 and 1900 h as mean values for the first and second half of the day in this analysis in the Thur basins, while in the Rietholzbach basin hourly values of meteorological data are available. As a result, the rise of air temperature above 0°C for a few hours around noon on February 17 and 20 is recognized in the Rietholzbach simulations, but not in the Thur simulations. Another reason for the poor performance of all snowmelt models in this case may also be the use of a fixed transition air temperature as the sole criterion to determine the precipitation type. In exceptional situations such as those described above, the temperature distribution in the free atmosphere may provide better information to determine whether precipitation falls as snow or rain, as suggested by Grebner (1978) for example. CONCLUSIONS The aim of this study is to investigate the influence of snowmelt model structure on the overall performance of a runoff model for different-size basins in the lower alpine to lowland environment of Switzerland. The following conclusions can be drawn: (a) Major snowmelt flood events usually occur during advection- melt situations associated with heavy rainfall. Sensible and latent heat fluxes are the primary sources for melt in these cases. In small-scale to medium-scale basins (up to about 1000 km2) the combination method according to Anderson (1973) brings an improvement of about 5% over index methods in years with an above- normal snow pack. A further slight improvement can be achieved by including measured water vapour pressure (extended combination method) or by using an energy balance method. No assessment of the statistical significance of these improvements has been attempted, s however, recent results of Cavadias 8 Morin (1985) indicate that differences in R2-values need to be larger than 5% in order to claim that they are significantly different. (b) In basins well over 1000 km2 (such as the Thur basin above Andelfingen) the influence of the snowmelt model structure on runoff simulations over several months cannot be demonstrated, 138 L.N.Braun & H.Lang Further investigations of individual melt events using a higher temporal resolution of hydrometeorological data are needed because snowmelt model structure must play a more significant role on a shorter time scale. (c) Preliminary results of the 1M0 project for the intercomparison of conceptual models of snowmelt runoff seem to indicate that differences in the oyerall performance of various snowmelt runoff models are larger than differences in performance using the same runoff model in connection with different point snowmelt models as investigated here. In other words: the choice of a particular runoff model may influence the results more than the choice of a particular snowmelt model. (d) Simulated areal values and measured point values of the water equivalent of the snow pack compare fairly well at elevations below 1000 m a.m.s.l., but at higher elevations there is a considerable discrepancy between simulated and measured values. Despite this discrepancy the overall model performance of snowmelt runoff simulations can be considered satisfactory in most cases. Further investigations should lead to a better understanding of the areal distribution of precipitation and other meteorological variables in mountainous regions. Ce) A more detailed subdivision of a basin may improve runoff simulations to the same extent as a more detailed snowmelt model. (f) A fixed air temperature divider to determine the state of aggregation of precipitation is generally adequate in medium-scale basins. However, under certain meteorological conditions considerable errors in runoff simulations may occur, and in these cases data from upper air soundings should be incorporated into snowmelt models. (g) More research should be aimed at the link between large- scale air mass characteristics and snowmelt. Moore & Owens (1984) have demonstrated the utility of large-scale indices in a maritime alpine environment for forecasting purposes. Large-scale factors are closely connected with the turbulent exchange of heat and water vapour over snow and are more predictable than surface air characteristics. ACKNOWLEDGEMENTS D.Grebner made valuable comments on the manuscript. REFERENCES Anderson, E.A. (1973) National river forecast system - snow accumulation and ablation model. NOAA Tech. Memo. NWS HYDRO-17, US Dept of Commerce, Silver Spring, Maryland. Anderson, E.A. (1976) A point energy and mass balance model of a snowcover. NOAA Tech. Rep. 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