Degree-day factors are widely used to estimate snowmelt runoff in
operational hydrological models. Usually, they are calibrated on observed
runoff, and sometimes on satellite snow cover data. In this paper, we
propose a new method for estimating the snowmelt degree-day factor
(DDF

Mountain watersheds serve as important water sources by providing fresh water for downstream human activities (Viviroli et al., 2003; Langston et al., 2011). As a result of snow and glacier melt, the magnitude and timing of runoff from these watersheds tend to be very sensitive to changes in the climate (Immerzeel et al., 2009; Jeelani et al., 2012). Changes of melt runoff may even affect the sustainable development of downstream cities in the long run (Verbunt et al., 2003; Zhang et al., 2012). Modeling snow and glacier melt runoff processes is therefore quite important for local water supply, hydropower management and flood forecasting (Klok et al., 2001). However, melt runoff modeling in such regions faces two challenges: scarcity of meteorological data and uncertainty in parameter calibration due to limited understanding of the complex hydrological processes.

Melt runoff models generally fall into two categories: energy balance
models, and temperature-index models (Rango and Martinec, 1979; Howard,
1996; Kane et al., 1997; Singh et al., 2000; Fierz et al., 2003). Temperature-index models
operating on a basin wide scale are much more popular for operational
purposes due to the following four reasons (Hock, 2003): (1) wide
availability of air temperature data, (2) relatively easy interpolation and
forecasting possibilities of air temperature, (3) generally good model
performance and (4) computational simplicity. The temperature index model is
based on an assumed relationship between ablation and air temperature and
calculates the daily snowmelt depth,

Quite a few studies estimated the degree-day factor from observed snow water
equivalent (SWE) data. Martinec (1960) measured SWE with radioactive
cobalt and computed the DDF

Another method of estimating the DDF

In mountain watersheds, distributed hydrologic models are more widely
applied than lumped models due to the large spatial variability. Degree-day
factors estimated from point measurements or spatially uniform values from
calibration are not likely representative for the entire catchment. An
increasing need for spatially distributed estimation of DDF

The objective of this study is to propose a new method for estimating
spatial patterns of DDF

The remainder of this paper is organized in the following way: Sect. 2
details the estimation method of spatial snow density and the snowmelt
degree-day factor, as well as the stepwise calibration method for the model
parameters. Section 3 contains a description of the geographic and
hydrological characteristics of the study basin, including the main data
sources and data preprocessing. Section 4 presents the main simulation
results and comparisons between the hydrologic model performance using
DDF

The main idea of estimating the degree-day factor is as follows. The volume of snow for each subcatchment and each day is estimated using MODIS SCA data and ground-based snow depth time series. The snow volume time series are partitioned in time into three groups, based on the daily air temperatures: days with snow accumulation (when temperatures are below a threshold), days with ablation (when temperatures are above a different threshold) and days where both processes occur (when temperatures are between the thresholds). Snow density is estimated from the days with snow accumulation as the ratio between measured precipitation and changes in snow volume. The degree-day factor is estimated from the days with ablation as the ratio between measured changes in snow water equivalent (product of snow volume and density) and the difference between daily temperature and the threshold value.

For comparison, DDF

The estimated degree-day factors are tested by simulations of basin runoff and snow cover patterns. The study period for which the analyses are performed is 10 years, 2001–2010. 2001–2005 is the calibration period and 2006–2010 is the validation period.

The observed snow data used to estimate the degree-day factor, DDF

The snow density (

The snowmelt degree-day factor (DDF

The runoff generation processes simulated by the THREW model includes
subsurface baseflow, rainfall runoff, snowmelt and glacier melt. Rainfall
runoff is simulated by a Xin'anjiang module, which adopts a water storage
capacity curve to describe the non-uniform distribution of water storage
capacity in a subcatchment (Zhao, 1992). The storage capacity curve is
determined by two parameters (spatial averaged storage capacity WM and shape
coefficient

The parameter groups are calibrated on different partitions in a stepwise
way: The parameter group controlling subsurface baseflow is first calibrated
on the

The estimated values of DDF

Location of the study area in Austria. Three catchments are
analyzed, Lienz, Waier, and Innergschloess, with areas of 1190, 285, and 39 km

The methodology is evaluated in the Lienz catchment which is located in East
Tyrol, Austria, and covers an area of 1198 km

The MODIS snow covered area (SCA) data used in this study is the daily
product, i.e., MOD10A1 and MYD10A1 (V005) (Hall et al., 2006a, b). It has
been downloaded from the website of the National Snow and Ice Data Center
(NSIDC,

Snow depth data observed at 1091 stations in Austria (seven stations in the
study area) are spatially interpolated by external drift kriging based on
elevation. The resulting data product has a spatial resolution of 1 km. Snow
depth in each subcatchment is the average value of all the 1

Spatial distribution of the snow density and the snowmelt
degree-day factor (DDF

The daily precipitation data are spatially interpolated by external drift
kriging from 1091 stations in Austria (seven stations in the study area). The
temperature data are interpolated by the least-squares trend prediction
method from 221 stations in Austria (six stations in the study area). Both
methods using elevation as an auxiliary variable (see Parajka et al., 2005).
Daily streamflow data from three hydrological stations are used, Lienz,
Waier and Innergschloess, which drain areas of 1198, 285 and 39 km

Snow density and snowmelt degree-day factor (DDF

Based on Eq. (1a, c), we obtained the snow densities and snowmelt
degree-day factors (DDF

Comparison of the estimated degree-day factor for snowmelt
(DDF

Stepwise calibration results for the Lienz basin in the
calibration period.

The data set used in this study has been divided into two sub-periods:
calibration period from 1 January 2001 to 31 December 2005 and validation
period from 1 January 2006 to 31 December 2010. The average annual
precipitation is 1126 mm in the calibration period, and 1238 mm in the
validation period. The mean daily temperature is 2.28

Model parameters in the three basins are calibrated on the corresponding
hydrograph partitions separately (see He et al., 2014). After the calibration,
we combined the simulations of the four partitions and obtained the entire
simulation of daily discharge. As an example, the simulation in each step in
the largest basin, the Lienz basin, is shown in Fig. 5, using the calibrated
degree-day factors for snowmelt and glacier melt as 2.6 mm day

The calibrated DDF

Performance of discharge simulations in three basins. DDF

Simulation of daily discharge in the Lienz basin using the
snowmelt degree-day factor calibrated on runoff.

Same as Fig. 6 but using snowmelt degree-day factors estimated from snow data.

The runoff simulations in the medium basin (Waier) are the best with an
NSE value of 0.832 in the calibration period and 0.863 in the validation
period. Runoff simulations in the smallest basin (Innergschloess) exhibit a
slightly lower performance with an NSE value of 0.726 in the validation period.
This may be partly due to the remarkably low value of the calibrated
DDF

To evaluate the estimated DDF

Simulations of discharge segments generated by groundwater
baseflow (

Simulations of the snow covered area (SCA) time series for the
Lienz basin (1190 km

Same as Fig. 9 but for the Innergschloess basin (39 km

As the DDF

We also assess the suitability of the estimated DDF

Generally, the simulated snow covered areas by the two DDF

Simulations of snow patterns on 3 days within the calibration
period (29 April, 7 May and 10 June 2003). The top
row shows simulated snow water equivalent (SWE) using DDF

Same as Fig. 11 but for 3 days within the validation period (27 April, 7 and 27 May 2008).

Several days with available MODIS data (black dots in Fig. 9) were selected
to analyze the snow patterns in Figs. 11–12. The selected days include
29 April, 7 May and 10 June in 2003, and 27 April,
7 and 27 May in 2008. The snow patterns are expressed as
the spatial distribution of simulated SWE using calibrated DDF

This study proposes a method for estimating snowmelt degree-day factor
(DDF

The estimated values of snow density and DDF

It should be noted that the estimated values of snow density and DDF

This study was supported by the National Science Foundation of China (NSFC 51190092, U1202232, 51222901) and the foundation of the State Key Laboratory of Hydroscience and Engineering of Tsinghua University (2014-KY-01). We would like to thank the International Communication Fellowship of Tsinghua University for financial support. We also thank Thomas Nester and Jürgen Komma for their helpful suggestions on the hydrological modeling in Austria, and Magdalena Rogger for providing the hydrogeology data in the study area. Edited by: V. Andréassian