Hydrological Modeling of Snow Accumulation and ... - Springer Link

Water Resour Manage (2009) 23:2271–2287 DOI 10.1007/s11269-008-9381-2

Hydrological Modeling of Snow Accumulation and Melting on River Basin Scale H. Zeinivand · F. De Smedt

Received: 1 February 2008 / Accepted: 20 November 2008 / Published online: 9 December 2008 © Springer Science + Business Media B.V. 2008

Abstract Snowmelt is of importance for many aspects of hydrology, including water supply, erosion and flood control. In this study, snow accumulation and melt are modeled using a distributed hydrological model with two different snowmelt simulation modules. The model is applied for simulating river discharge in the Latyan dam watershed, in the southern part of central Alborz mountain range, Iran. The data consists of 3 years of observed daily precipitation, air temperature, potential evaporation, windspeed and discharge. The discharge data is used for model calibration. When using the temperature index method for snowmelt three parameters need to be calibrated, while for the energy balance approach all parameters are preset and not optimized. The model performance is satisfactory for both methods with efficiencies of more than 80%. In order to show the performance of the model, two interesting snow accumulation and melt periods are discussed in detail. This study shows that the model has great potentiality to simulate the impact of snow accumulation and melt on the hydrological behavior of a river basin. Keywords Snow melt · Degree day method · Snow energy balance · WetSpa model

H. Zeinivand (B) · F. De Smedt Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium e-mail: [email protected] F. De Smedt e-mail: [email protected] H. Zeinivand Lorestan University, P.O. Box 465, Khorram Abad, Lorestan, Iran

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1 Introduction Snow plays an important role in the hydrologic cycle, through its effects on water storage and the land surface energy balance. Snowmelt is a significant surface water input of importance to many aspects of hydrology including water supply, erosion and flood control (Tarboton et al. 1995). The processes involved in snowmelt have been widely described (U.S. Army Corps of Engineers 1998; Gray and Male 1981; Dingman 1994; Tarboton et al. 1995; You et al. 2004). The most reasonable approach to obtain information about the energy fluxes in mountainous areas with complex terrain is therefore a modelling approach that is verified by selected measurements at selected locations. Motivated by the interest in snowmelt runoff at the scale of catchments, the main effort towards the modelling of the spatial distribution of the energy fluxes over snow covered surfaces was undertaken in snow hydrology (Fierz et al. 2003). Snowmelt processes have been modeled with different approaches of variable complexity ranging from simple regression equations and other blackbox approaches based only on temperature measurements to physics-based models containing equations for all the processes involved (Ferguson 1999) or complete multilayer models based on an energy balance (Marks et al. 1999). The only way to correctly compute the amount of snowmelt is through an energy budget (Anderson 1968). But in most watersheds, all required data as air temperature, solar radiation, surface albedo, soil temperature, atmospheric vapor pressure, snow density, windspeed, etc. may not be available. Thus, practical operational procedures for snowmelt predictions generally rely on air temperature as the index of the energy available for melt (Gray and Male 1981; Watt et al. 1989; Westerström 1990). Although simple temperature-index models have proven to predict catchment runoff accurately (e.g. Zappa et al. 2003; Ohmura 2001), local snow-water-equivalent simulations yield much better results when using process-based models (e.g. Walter et al. 2005). Therefore, physical process models must be built in order to understand the diverse and non-linear interactions in the hydrological behavior of mountain catchments (Lehning et al. 2006). Modeling snowmelt in a hydrological model is especially problematic because an incorrectly simulated melt event not only incorrectly predicts flow on that day, but also on the day when the real melt occurs. So, an incorrectly predicted snowmelt event results in at least two periods of incorrect stream flow simulation rather than just one period, which is not the case with an incorrectly simulated stream flow from a rainfall event. Thus it is not surprising that snowmelt-modeling problems are commonly acknowledged weaknesses in hydrological models (Fontaine et al. 2002; Frankenberger et al. 1999). The WetSpa model (Wang et al. 1997; De Smedt et al. 2000; Liu 2004) includes a physically based and fully distributed description of the hydrological processes of runoff production. This model originally calculates snowmelt using the conceptual temperature index or degree-day method, used in previous studies such as for the Hornad catchment in Slovakia (Bahremand et al. 2007). In this study, we present snowmelt module for the WetSpa model, by simulating snowmelt according to the energy balance method. The results of these two different snowmelt simulation modules are compared to each other and to measured data. First a detailed description of the model is given, then the data set used to test the model and the results of the two approaches are discussed.

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2 WetSpa Model 2.1 General The WetSpa model was originally developed by Wang et al. (1997) and adapted for flood prediction by De Smedt et al. (2000) and Liu (2004). The hydrological processes considered in the model are precipitation, interception, depression storage, surface runoff, infiltration, evapotranspiration, percolation, interflow, ground water flow, and water balance in each layer. The model predicts river flows in any location of a channel network and the spatial distribution of the hydrological characteristics. The model equations have been published on several occasions (De Smedt et al. 2000; Liu et al. 2003; Liu 2004; Liu and De Smedt 2005; Bahremand and De Smedt 2008; Bahremand et al. 2007) and are not repeated here. In this study, we concentrate on the generation of runoff by snowmelt. The surface runoff is calculated using a moisture-related modified rational method with a potential runoff coefficient depending on land cover, soil type, slope, the magnitude of rainfall, and antecedent soil moisture (Liu 2004): α S = C (P − I + M) θ n

(1)

where S [meters per day] is the surface runoff resulting from snowmelt and rainfall, C [–] is the potential runoff coefficient. The values of C are taken from a lookup table, linking values to slope, soil type and land use classes. P [meters per day] is the rainfall intensity, I [meters per day] is the initial loss due to interception and depression storage, M [meters per day] is snowmelt, θ [cubic meters per cubic meter] is the soil water content in the root zone, and n [cubic meters per cubic meter] is the soil porosity. The exponent α [–] in the formula is a parameter reflecting the effect of rainfall intensity on the surface runoff (Liu 2004). The value is higher for low rainfall intensities resulting in less surface runoff, and approaches one for high rainfall intensities (Bahremand et al. 2007). The runoff is routed from each grid cell to the main channel, and then this is routed to the basin outlet by the channel response function and joined with groundwater flow at the subcatchment outlet (Liu et al. 2003). An advantage of this approach is that it allows spatially distributed runoff and hydrological parameters in the basin to be used as inputs to the model. Inputs to the model include digital elevation data, soil type, land use data, and climatological data. Stream discharge data is optional for model calibration and validation. All hydrological processes are simulated within a GIS framework (Bahremand et al. 2007). The WetSpa distributed model potentially involves a large number of model parameters to be specified during the model setup (Liu et al. 2004). Most of these parameters can be assessed from the field data, e.g. hydrometeorological observations, maps of topography, soil types, and land use, etc. However, comprehensive field data are seldom available to fully support specification of all model parameters. In addition, some model parameters are of a more conceptual nature and cannot be directly assessed. In the process of WetSpa model parameterization, the spatial patterns of the parameter values are defined using the available filed data to describe the most significant variations. This is done by using a data base and defining appropriate parameter classes of topography, soil type, land use, etc. For each class,

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all parameters are assessed directly from the data base. This approach enables to apply the model with information that is available in a catchment (Bahremand et al. 2007). The model has been applied in several studies, e.g. the Barebeek catchment in Belgium (De Smedt et al. 2000), the Alzette river basin in Luxembourg (Gebremeskel et al. 2002; Liu 2004), the Hornad watershed in Slovakia (Bahremand et al. 2007), and the Simiyu river and Speke gulf (Lake Victoria) in Tanzania (Rwetabula 2007). 2.2 Snowmelt Modules 2.2.1 Degree-Day Method A snow module is provided in the original WetSpa model based on the conceptual temperature index or degree-day method. The method is simple as it uses only daily air temperature data. This is physically sound in the absence of shortwave radiation when much of the energy supplied to the snowpack is atmospheric long wave radiation. The equation can be expressed as (Liu 2004): M = Max [0, (Ksnow + Krain P) (Ta − T0 )]

(2)

where Ta [◦ C] is the mean air temperature, T0 [◦ C] is a threshold melt temperature, Ksnow is a melt-rate factor [meters per day per degree Celsius], and Krain is a degreeday coefficient expressing the heat contribution from rainfall [per day per degree Celsius]. The critical melt temperature T0 is often intuitively set to 0◦ C. The meltrate factor Ksnow is an effective parameter and may vary with location and snow characteristics. However, Ksnow , T0 and Krain can be calibrated (Liu 2004). 2.2.2 Energy Balance Equation Physical processes within the snowpack and involved in snowmelt are very complex. These involve mass and energy balances as well as heat and mass transport (Fig. 1).

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Fig. 1 Energy (black arrows) and mass (gray arrows) fluxes involved in snowmelt: Sn net solar radiation, La atmospheric long wave radiation, Lt terrestrial long wave radiation, H sensible heat exchange, El latent heat of vaporization or condensation, Q p heat brought with precipitation, Qm amount of heat removed by snowmelt, G ground heat flux, U snowpack’s internal energy, P precipitation, Es sublimation, and M snowmelt intensity


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Formation of ice layers further complicates the evolution of a snowpack resulting in processes known from soil physics like fingering or lateral flow. Snowmelt is basically an energy driven process (Parajka et al. 2001). The energy balance of a snowpack is given by (Tarboton and Luce 1996; Walter et al. 2005): dU = Sn + La − Lt + H + El + G + Qp − Qm dt

(3)

where U is the internal energy of snowpack and the upper froze part of the soil (kilojoules per square meter), Sn is the net short wave solar radiation (kilojoules per square meter per day), La is the atmospheric long wave radiation (kilojoules per square meter per day), Lt is the terrestrial long wave radiation (kilojoules per square meter per day), H is the sensible heat exchange (kilojoules per square meter per day), El is the energy flux associated with the latent heat of vaporization and condensation at the snowpack surface (kilojoules per square meter per day), G is ground heat conduction to the snowpack (kilojoules per square meter per day), Qp is heat advected by precipitation (kilojoules per square meter per day), and Qm is the amount of heat removed by snowmelt (kilojoules per square meter per day). The water balance of a snowpack is given by (Tarboton and Luce 1996): dW = Pr + Ps − Es − M dt

(4)

where W is the snowpack’s water equivalence (meters), Pr is the precipitation as rainfall (meters per day), Ps is the precipitation as snowfall (meters per day), and Es is the sublimation from the snowpack (meters per day). All terms on the right hand side of Eqs. 3 and 4 can be evaluated using known physical laws as given by Dingman (1994), Tarboton and Luce (1996), Koivusalo and Kokkonen (2002), You et al. (2004), Debele et al. (2005), and Walter et al. (2005). Hence, the temporal evolution and spatial distribution of the snowpack water equivalent, W, and the energy of the snowpack, U, can be evaluated. As long as U remains negative all water remains frozen within the snow layer, but when the energy becomes positive snowmelt occurs, which can be calculated as: M=

1 dU λ dt

(5)

where λ (kilojoules per cubic meter) is the volumetric latent heat of fusion. The resulting snowmelt, M, is introduced in equation 1 and can contribute to surface runoff. Hence, the adaptation of the WetSpa model is only moderate, i.e. the degree day snowmelt procedure has to be replaced by the new snow energy and mass balance equations. All these parts of the WetSpa model, in particular the routing of the runoff, remain unchanged. The key point of this approach is that all calculations are physically based and as a consequence all parameters are inherently known so that no more calibration is necessary for the snow module part. The price to pay for this, is that more input is needed for the model. For the degree day method this was only mean daily air temperature, but for the energy balance method, this becomes minimum, mean, and maximum daily air temperature, and windspeed.

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3 Application 3.1 Study Area The Jajrood River basin is located in the southern part of central Alborz mountain range which almost entirely covers the northern part of Iran. The drainage area is 435.3 km2 up to Roodak hydrometric station at the entrance of the Latyan dam reservoir. The Latyan dam reservoir has several other tributary streams entering the reservoir, which are not evaluated in this study. Latyan dam is one of the main sources of water for the Tehran metropolitan area. A digital elevation model (DEM) of the basin was obtained from the topography map (1:50,000) provided by Iranian National Geographical Organization (1980, 1987, 1993) and converted to a 50 m grid size DEM. Figure 2 shows the location of the Latyan catchment in Iran and a detailed map of the basin upstream of Roodak, with topography and location of precipitation stations indicated. The basin is mountainous with elevations ranging from 1,700 to 4,212 m. The mean elevation is 2,830 m and the mean basin slope is about 45.6%. The maximum length of flow in the basin is 32.5 km. Figure 3 shows the spatial distribution of the slope angles in the study area. Land cover data were obtained from the Iranian Soil Conservation and Watershed Management Research Institute (SCWMRI) (2006) and Fatahi Ardakani et al. (2000). The final land use map for this study with 50 m grid size is composed of five different types of land cover: 91% of the basin is covered by deciduous shrubs, 6.2% by deciduous broad trees, 1.8% by short grass, and about 1.0% by agriculture and impervious areas, mainly villages, as shown in Fig. 4. There is no soil map available for this catchment, hence we derived a soil map using land capability and resources evaluation map (Iranian Agriculture and Natural Resources Ministry, Soil Sciences and Fertility Institute 1973) adjusted with data from the watershed management comprehensive project of Latyan dam (Iranian Agriculture Ministry 1975). There are three different soil textures in the catchment. The dominant soil texture is clay loam, which covers about 89.4% of the basin, and

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Fig. 2 Location of the Latyan dam watershed in Iran and detailed map of the subbasin upstream of Roodak station showing stream network, topography and location of precipitation stations

Hydrological modeling of snow accumulation and melting Fig. 3 Slope map of the Latyan dam watershed

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silt loam and sandy loam about 5.6% and 4.8% respectively. Hydrologic data for this study were obtained from Tehran Regional Water Organization and Iranian Water Resources Research Organization (TAMAB Co). The data set include, daily precipitation in eight stations, temperature (maximum, minimum and mean) and evapotranspiration in three stations, windspeed and daily discharge data at one gauging station. All data are available for a 3 year period from 2003 to 2006. The climate is more arid as the elevation decreases, the highest amount of precipitation occurs from January to March, and around 48% of the annual precipitation is snow. The mean annual precipitation of the watershed based on 3 years data of eight stations within the catchment is 758 mm, ranging from about 689 mm in the valley to more than 875 mm in the mountains. The spatial variation of the minimum and

Fig. 4 Land use map of the Latyan dam watershed

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maximum air temperature is largely due to irregular topography. The mean observed temperature of the three stations located on the lower parts of the catchment is about 10◦ C which is warmer than the upper parts of the catchment. The annual potential evapotranspiration based on 3 years observations by the Tehran Regional Water Organization is about 1,195 mm. The influence of elevation on input variables is accounted for in the model, as for instance temperature is corrected for altitude by using a linear correlation between elevation and average recorded temperature at each station. Similar procedures were applied for PET. Daily discharge data at the watershed outlet, Roodak station is used for model calibration. 3.2 Model Simulation Once the required data are collected and processed for use in the WetSpa model, identification of spatial model parameters is undertaken. All basic maps are in raster form with a resolution of 50 m. For the simulation of hydrographs at the basin outlet, the basin is divided into 193 subcatchments, corresponding to the threshold value of 1,000 raster cells when delineating the stream network based on topographic flow accumulation. The areas of the GIS derived subcatchments range from 0.005 to 11.47 km2 with an average subcatchment area of 2.25 km2 . In the WetSpa model, the grid of root depth is reclassified from the land use grid by means of an attribute lookup table, but in this study, the root depth was adjusted in parts of the catchment where the bed rock is very shallow and limits the soil thickness. The grids of potential runoff coefficient and depression storage capacity are also obtained by means of attribute tables combining the grids of elevation, soil and land use, for which the percentage of impervious area within an urban cell is set to 30%. The results are shown in Fig. 5. From this figure it follows that non-forested and steeper areas have a very high potential runoff coefficient (>50%), whereas the forested and gentle slopes generate less surface runoff. The grids for precipitation, temperature and PET are created based on the geographical coordinates of each measuring station and the catchment boundary using the Thiessen polygon extension of the ArcView Spatial

Fig. 5 Potential runoff coefficient map of the Latyan dam watershed

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Analyst. Finally, the grids of flow velocity, travel time to the basin outlet, as well as the standard deviation are generated, which enable to calculate the IUH from each grid cell to the basin outlet.

4 Results and Discussion The 3 years (2003–2006) measured daily discharge data are used for model calibration. The model calibration is performed manually for global WetSpa model parameters only, whereas the spatial model parameters are kept as they are. Initial global model parameters are specifically chosen according to the basin characteristics as discussed in the documentation and user manual of the model (Liu 2004), i.e. the initial groundwater flow recession coefficient is estimated by analyzing the base flow, which is separated from the observed hydrograph. Adjustment of this parameter is necessary in accordance with the fitting of base flow and the total flow volume. The interflow scaling factor is adjusted for the peak and recession part of the flood hydrograph, which is sensitive for both high and low flows. The additional two parameters controlling the amount of surface runoff, i.e. the surface runoff exponent for a near zero rainfall intensity and the rainfall intensity corresponding to a surface runoff exponent of 1, are adjusted mainly for small storms, for which the actual runoff coefficients are small due to the low rainfall intensity. The initial soil moisture and active groundwater storage are adjusted by comparison of the hydrographs and water balance at the initial phase of the simulation period. The maximum active groundwater storage controls the amount of vapor transpirated from the groundwater, and therefore can be adjusted by comparison of the flow volume during dry periods (Bahremand et al. 2007). The major model parameters (when using the temperature index method for snowmelt) that can be calibrated are listed in Table 1. Three parameters: the threshold melt temperature T0 , the meltrate factor Ksnow , and the rainfall melt-rate factor Krain are necessary for snowmelt calibration. Threshold melt temperature is typically a value near 0◦ C, particularly for short computation period using average temperature as input. Melt-rate factor is typically between 1.8 and 3.7 m d−1 ◦ C−1 for rain-free conditions (Gray and Male 1981; Liu 2004). This value can be determined by comparison between computed and observed spring flood hydrographs during calibration. Rainfall melt-rate factor Table 1 The model global parameters No.

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Energy balance approach

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Interflow scaling factor (–) Groundwater recession coefficient (day−1 ) Initial soil moisture (mm) Correction factor for PET (–) Initial active groundwater storage (mm) Maximum active groundwater storage (mm) Moisture or surface runoff exponent (–) Maximum rainfall intensity (m) Threshold melt temperature (◦ C) Melt-rate factor (m day−1 ◦ C−1 ) Rainfall melt-rate factor (day−1 ◦ C−1 )

0.309 5.E − 5 1.19 1.61 45.6 25.45 8.5 108 2.E − 6 3.0 7.57E − 2

0.309 5.E − 5 1.19 1.61 45.6 25.45 8.5 108 – – –

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is generally very small, typically around 0.01 d−1 ◦ C−1 , and can be determined during model calibration. If a zero value is given, the effect of rainfall on snowmelt is not considered. When we use the energy balance approach for snowmelt simulation these three parameters are not needed because all parameters related to snow accumulation and snowmelt are preset and not optimized or calibrated. The current physically based energy budget for snowmelt needs no more data than required for most temperature-index methods, i.e. maximum and minimum air temperature and catchment windspeed. Evaluation criteria for the model performance with two different methods for snowmelt are given in Table 2. Four evaluation criteria used by Hoffmann et al. (2004) are selected. The model bias for water balance criterion evaluates the ability of the model to reproduce the water balance. The accuracy of the model to simulate the discharge is evaluated through the Nash–Sutcliffe criterion, and two adapted Nash– Sutcliffe efficiencies are used to assess the model’s performance for low flows and high flows respectively. According to the results of the model evaluation criteria in Table 2, there is no significant difference between the two methods and the model performance is satisfactory for both methods. This indicates that the WetSpa model is able to simulate hydrologic processes in a spatially realistic manner including snowmelt based only on topography, land use and soil type, resulting in a fairly high accuracy for both high and low flows. It should be mentioned that we used windspeed data in only one station which is located in southern part of the basin and most probably if there were more windspeed stations in the basin, the result of energy balance method would be much better. Table 3 shows the estimated water balance components for the 3 year period (September 2003 to September 2006). According to this table there is no substantial difference between the results of the two models except for some small differences in the amount of rainfall and snowfall. In the degree day method precipitation is assumed to be snowfall when temperature drops below T0 . In the energy balance approach, the fraction of precipitation falling as snow is one when the air temperature is lower than −1◦ C, zero when the air temperature is higher than 3◦ C, and is linearly interpolated for temperatures in between. Hence, the amount of snowfall according to the degree day method is lightly less than in energy balance approach. Notice that for this catchment, the snowfall constitutes almost half of the total precipitation, and consequently snowmelt has a large impact on the hydrologic processes. Analysis of measured precipitation shows that the main period of precipitation occurs during late autumn till late winter, while river flow rises gradually in early spring to reach peak values in May. From the foregoing it can be concluded that in the study area precipitation falls from October to March, while runoff occurs mainly from March till June depending upon the air temperature, indicating that most of the runoff is generated by snowmelt. Table 2 Evaluation criteria for the assessment of model performance Criteria

Model with degree day method for snowmelt

Model with energy balance method for snowmelt

Model bias for water balance Nash–Sutcliffe efficiency Model efficiency for low flows Model efficiency for high flows

0.02 0.85 0.84 0.86

0.02 0.82 0.81 0.87

2,275

Total precipitation Rainfall Snowfall Snowmelt Interception Surface runoff Infiltration Evapotranspiration Interflow Groundwater recharge Groundwater discharge Total discharge Soil moisture storage Groundwater storage

DD degree day method, EB energy balance approach a Potential evapotranspiration

2,020

3,298a

Measured (mm)

Component 2,279 1,296 988 984 21 355 1,899 224 176 1,642 1,526 2,058 −60 44

2,279 1,179 1,100 1,097 12 345 1,918 225 240 1,585 1,485 2,071 −58 37

Calculated (mm) DD EB 100.1 56.8 43.3 43.3 0.9 15.6 83.3 9.9 7.8 72 66.9 90.3 −2.7 1.9

100.1 51.7 48.2 48.2 0.5 15.2 84.1 9.9 10.5 69.6 65.2 90.8 −2.6 1.6

Percentage (%) DD EB 2.08 1.18 0.90 0.90 0.02 0.32 1.73 0.20 0.16 1.5 1.4 1.87 – –

2.08 1.07 1.0 1.0 0.01 3.1 1.75 0.20 0.22 1.45 1.36 1.89 – –

Mean (mm/day) DD EB

Table 3 Estimated water balance components of the Latyan dam watershed for the 3-year period September 2003 to September 2006

66.7 62.5 32.7 14.6 0.7 26.9 42.1 1.5 1.3 20.8 4.1 29.3 – –

66.7 57.2 3.27 28.2 0.7 27.2 47.9 1.58 2.1 21 4.3 29.6 – –

Max (mm/day) DD EB

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Fig. 6 Daily average precipitation, mean air temperature, snow layer water equivalent, and snowmelt based on model using degree day method for snowmelt (a), same for model using energy balance approach for snowmelt (b), and graphical comparison between observed and simulated flow at Roodak station in the Latyan dam watershed between 28/11/2003 and 8/5/2004 (c)

For discussion we select two interesting periods with large snow accumulation and melt. The first period is from mid November 2003 to mid May 2004. All relevant information for this period is given in Fig. 6. The simulated snow accumulation and melt based on degree day method together with the basin average precipitation


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and mean air temperature is shown in Fig. 6a. The degree day method used in the WetSpa model, assumes that all precipitation falls as snow, when the mean temperature of the subcatchment is lower than T0 and as rain when the temperature is higher than T0 . The mean temperature in the catchment drops below zero from mid November 2003 till end February 2004, and accordingly only snowfall occurs and the snowpack gradually builds up to reach about 255 mm of water equivalent at the end of February while there is almost no snowmelt. From end of February till 13 March, the temperature becomes positive and around 160 mm of snow melts. From 13 March till 22 March, temperature again drops below zero and around 50 mm of snow is added to the old snow cover. From the last week of March onwards, the temperature sometimes alternates becoming positive resulting is some melt, or negative giving snow accumulation. However, at the end of April all snow has completely melted. The simulated snow accumulation and melt based on the energy balance approach together with basin average precipitation and mean air temperature is shown in Fig. 6b. In the energy balance approach applied in this study, the fraction of precipitation falling as snow is one when the air temperature is lower than −1◦ C, zero when the air temperature is higher than 3◦ C, and is linearly interpolated for temperatures in between. As the mean temperature in the catchment drops below zero from mid November 2003 till end February 2004, accordingly all precipitation falls down as snow and the snowpack gradually builds up to reach about 240 mm of water equivalent at the end of February. From end of February till 13 March, the temperature becomes positive and about 170 mm of snow melts. From 13 March till 22 March the temperature again drops below zero and around 50 mm of snow is added to the old snowpack. From the last week of March onwards snow melt and accumulation alternate depending upon the temperature variation. Figure 6c shows a graphical comparison between observed and calculated daily flow based on the degree day method and the energy balance approach at Roodak station. From mid November 2003 till end February 2004, there is no considerable direct runoff and river discharge is only maintained by groundwater drainage, except for some small snowmelt in mid February 2004 and a small amount of rainfall in January and February 2004. During this period the discharge is well simulated by the model. Next, the discharge increases from 27 February till 15 March, due to snowmelt. This discharge is somewhat overestimated by the two methods. The discharge further increases in March with at the end of March and beginning of April, there is considerable rainfall in combination with snowmelt, which leads to a huge flood in the basin with an observed peak of 87 m3 s−1 on 4 April. Although the two simulation methods are able to simulate this flood, there is again some overestimation with a simulated peak discharge of 123 m3 s−1 by the degree day, while for the energy balance method this is only 105 m3 s−1 . From then onwards, both simulations very well agree with the observations. The second period is from mid November 2004 to early May 2005. All relevant information for this period is given in Fig. 7. The simulated snow accumulation and melt based on the degree day method together with basin average precipitation and mean air temperature is shown in Fig. 7a. According to this figure the mean temperature in the catchment drops below zero from end of November 2004 till end February 2005, and accordingly only snowfall occurs and the snowpack gradually builds up to reach about 245 mm of water equivalent at the end of February. From end of February till 23 March, the temperature becomes positive and around 120 mm

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200

20

(b)

30

150

40 50

100

60

Precipitation Snowmelt Snow water equivalent Temperature

50

0 20/11/04

5/12/04 20/12/04

4/1/05

19/1/05

3/2/05

18/2/05

70

Precipitation P (mm/d) Air temperature Ta (ºC)


-10 250

80 90 5/3/05

20/3/05

4/4/05

19/4/05

5/3/05

20/3/05

4/4/05

19/4/05

135 120

Measured discharge

90

Simulated discharge (Degree day)

75

Simulated discharge (Energy balance)

3

Discharge Q (m /s)

105

(c)

60 45 30 15 0 20/11/04 5/12/04 20/12/04

4/1/05

19/1/05

3/2/05

18/2/05

Time (d)

Fig. 7 Daily average precipitation, mean air temperature, snow layer water equivalent, and snowmelt based on model using degree day method for snowmelt (a), same for model using energy balance approach for snowmelt (b), and graphical comparison between observed and simulated flow at Roodak station in Latyan dam watershed between 20/11/2004 and 3/5/2005 (c)

of snow melts. From 23 till 27 March temperature again drops below zero and around 12 mm of snow is added to the snow layer. From then onwards the temperature gradually increases and becomes positive so that all snow melts. The simulated snow accumulation and melt based on the energy balance approach together with basin


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average precipitation and mean air temperature is shown in Fig. 7b. According to this figure, from mid November 2004 till end February 2005, the snowpack gradually builds up to reach about 260 mm of water equivalent at the end of February. From end February till 23 March about 150 mm of snow melts, while from 23 to 27 March 12 mm of snow is added to the snow cover. From then onwards the temperature becomes positive and at the end of April all snow is melted. Figure 7c shows a graphical comparison between observed and simulated daily flows at Roodak station. From mid November 2004 till early March 2005 there is no direct runoff and river discharge is only maintained by groundwater drainage which is well simulated by the model. At the end of February and beginning of March, the temperature increases and together with snowmelt there is considerable rainfall, which leads to a huge flood in the basin with an observed peak of 120 m3 s−1 on 12 March. Both methods are able to simulate this flood, although the simulated peak discharges are a little bit higher, respectively 134 and 133 m3 s−1 for the degree day method and the energy balance approach. From then onwards, snowmelt and rainfall yield observed discharges varying between 20 to 40 m3 s−1 , which are well simulated by both methods.

5 Conclusions A physically based distributed hydrological model, WetSpa, was presented with two different approaches for simulating snow accumulation and runoff from snowmelt. The generation of runoff depends upon rain intensity, soil moisture status, and snowmelt. Snow accumulation and melt is simulated by a degree day method and an energy balance approach. The model performance was tested by simulating snow accumulation and melt in the 435 km2 Latyan dam watershed, upstream of Roodak station, in the southern part of central Alborz mountain range in the northern part of Iran. The model is applied and calibrated with 3 years (2003–2006) of observed daily rainfall, air temperature, windspeed, and daily potential evaporation. Daily discharge data at the gauging station of Roodak station were used for model calibration. The model calibration is performed manually for global parameters of the WetSpa model only, whereas spatial model parameters related to topography and soil and land-use types remain prefixed in a data base. Also, three parameters of the snow module are calibrated for the degree day method, while all parameters are preset and fixed in energy balance approach because these are physically based and known. The model efficiency turns out to be rather good for both methods. The resulting hydrographs compare favorably with measurements for both methods with model efficiencies of more than 80%. In order to show the performance of the model two interesting periods with snow accumulation and melt are discussed in detail. It is shown that once the air temperature drops below zero only snowfall occurs and the river discharge drops gradually as the snow accumulates on the soil surface and the discharge is only sustained by groundwater drainage. As soon as the temperature again rises above zero snowmelt occurs and river discharge increases. The degree day method for snowmelt with calibrated parameters gives good results, but the energy balance approach where all parameters are preset and fixed performs equally well. This study shows that the model has great potentiality to determine the impact of snow accumulation and melt on the hydrological behavior of the river basin. Hence, it can

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be concluded that accurate snowmelt prediction is possible with a physically based energy and mass budget approach with controlling parameters that do not need any calibration. It is evident that energy and temperature variations in a snowpack can be more complex than assumed in the present model. However, a more comprehensive approach would need very accurate temporal and spatial observations of snow depth, water content, temperature, and energy fluxes, which in practice are usually not available. Possibly such data can be obtained by remote sensing techniques. Hence, the methods presented in this study show to be useful tools for simulating snowpack processes and snowmelt, but should be verified in the field and improved provided more comprehensive datasets become available. Acknowledgements The authors like to thank Mr. Mohammad Ali Fatahi and Mr. Akbar Mobasher Nazemi from the Tehran Watershed Management Office for providing some of the maps, and Mrs. Behnam Azad from the Tehran Regional Water Organization for providing data.

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