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Calibrating a spatially distributed conceptual hydrological model using runoff, annual mass balance and winter mass balance Elisabeth Mayr a,⇑, Wilfried Hagg a, Christoph Mayer b, Ludwig Braun b a b

University of Munich, Department for Geography, Luisenstraße 37, D-80333 Munch, Germany Bavarian Academy of Sciences and Humanities, Commission for Geodesy and Glaciology, Alfons-Goppel-Straße 11, D-80539 Munich, Germany

a r t i c l e

i n f o

Article history: Received 31 January 2012 Received in revised form 29 September 2012 Accepted 18 November 2012 Available online 28 November 2012 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Emmanouil N. Anagnostou, Associate Editor Keywords: Conceptual hydrological models Multi-objective calibration Glacier mass balance

s u m m a r y We modiﬁed the well-known HBV-ETH model to develop a partially distributed hydrological model that was able to simulate runoff in a highly glacierised basin. By introducing additional calibration criteria (annual and winter glacier mass balance) we reduced the goodness-of-ﬁt for runoff, but improved the description of the accumulation and ablation processes involved. Final adjustment of the model parameters, after choosing the best out of 10,000 random parameter sets, allowed us to ﬁnd a parameter calibration with acceptable errors for all criteria, which was then conﬁrmed by good model performance during the validation period. The glacier-wide winter mass balance and the annual mass balance in the ablation area were simulated well, while the annual mass balance in the accumulation area showed inaccuracies. Good simulation of the processes during the 2003 heat wave in Europe proved that the model also delivers reliable results for meteorological conditions different from those used during calibration. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction In many mountain watersheds snow- and ice-melt provide an important contribution to runoff during summer months. Agriculture and hydroelectric power plants both depend on runoff from mountain regions, especially on the contribution to this from melt processes (Huss, 2011; Jost et al., 2012; Kaser et al., 2010; Koboltschnig and Schoner, 2011; Schaeﬂi et al., 2007). Hydrological models are needed to determine the share of total runoff provided by the different processes involved and to draw conclusions, based on this information, about future water availability. A great variety of melt models have been developed. Because of the limited availability of hydrometeorological data in high mountain regions, the temperature-index method, which only requires temperature and precipitation meteorological input, is widely used to calculate melt in these areas (Akhtar et al., 2008; Braun et al., 1993; Hagg et al., 2006; Konz and Seibert, 2010; Yong et al., 2006). Although this melt calculation is much simpler than using energy balance approaches, it actually gives results that are comparable with or better than such approaches when runoff is calculated at the catchment scale (Ohmura, 2001; WMO, 1986). ⇑ Corresponding author. Tel.: +49 89 21806663. E-mail addresses: [email protected] (E. Mayr), [email protected] (W. Hagg), [email protected] (C. Mayer), Ludwig. [email protected] (L. Braun). 0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.11.035

Conceptual temperature-index models need to be calibrated. Manual calibration by iterative parameter adaption (e.g., Braun and Aellen, 1990; Zappa and Kan, 2007) is time consuming and subjective, especially if more than one objective function is used (Seibert et al., 2000). A range of calibration procedures have been developed, including, for example, an automatic iterative procedure that follows a deﬁned sequence to help avoid subjective decisions (Huss et al., 2010; Stahl et al., 2008), a genetic algorithm to ﬁnd the best parameter by imitating evolution (Seibert et al., 2000), and testing numerous random parameter sets to ﬁnd the most appropriate, then reﬁning them manually (Konz and Seibert, 2010; Schaeﬂi et al., 2005). The differences between simulated and measured variables must be tested using a speciﬁc parameter set to assess model quality. This difference is expressed as the ‘objective function’. One type of objective function is the Nash–Sutcliffe coefﬁcient (Nash and Sutcliffe, 1970), which is frequently used to assess the quality of the runoff simulation. In glacierised catchments ice-melt is an additional source of runoff that can lead to error compensation between basin precipitation and glacier melt when calibrating using runoff only. Mass balance data can serve to avoid over- or underestimating melt rates. The value of a multi-criteria calibration approach, including runoff and other data, has been shown in several studies. Braun and Renner (1992) used measured mass balance data as an additional calibration quality check, but they did not introduce

E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

numerical values for the goodness of ﬁt. Stahl et al. (2008) reconstructed a mass balance from data from glaciers surrounding a catchment and divided it into summer and winter mass balance. Koboltschnig et al. (2008) used the snow-covered area and a glacier mass balance for their calibration, but did not consider snow depth. Parajka et al. (2007) worked with snow water equivalents calculated from snow depth measurements. Huss et al. (2008a) used point measurements of annual and winter mass balance to calibrate their model. These studies illustrate the importance of performing the calibration using different types of measurements, because both seasonal mass balance and spatial variation in mass balance could be calculated incorrectly if these are calibrated based on volume changes alone. Schaeﬂi and Huss (2011) stated that the seasonal mass balance is very helpful in performing reliable calibrations. Above all, the choice of objective function chosen depends on the availability of data. Using more calibration criteria leads to slightly poorer runoff simulations but signiﬁcantly better simulations of the additional water balance terms, such as snow storage or mass balance (Madsen, 2003; Parajka et al., 2007; Schaeﬂi and Huss, 2011; Seibert, 2000). Several methods, such as weighted sums, fuzzy logic and pareto optima, have been developed to choose the best parameter set using a multi-objective calibration approach (Parajka et al., 2007). The reliability of these model calibrations is commonly tested using a split sample test, in which the model is validated using years outside the calibration period (Seibert, 2003). The advantage of this test is that it is easy to do, providing that sufﬁcient data are available. However, it cannot guarantee that good simulation results will be produced for all possible future climatologies. The 2003 summer heat wave in Europe affords us the opportunity to validate models using data that differ completely from the calibration conditions (Beniston and Diaz, 2004; Schar and Jendritzky, 2004; Zappa and Kan, 2007). Konz and Seibert (2010) assessed the usefulness of limited runoff and mass balance data at the Vernagtferner glacier. In the present study we investigate the opposite case by assessing the model performance when the full set of additional calibration criteria is used. We modiﬁed the HBV-ETH precipitation and runoff model (Braun and Aellen, 1990) to allow a spatially distributed simulation of the mass changes. We used annual and winter mass balance point measurements as calibration and validation criteria, in addition to runoff, and analysed their impact on the results. The key questions addressed by this study are: (1) How accurate is the simultaneous modelling of runoff, ablation and accumulation? (2) How helpful is the use of additional information for the calibration procedure? (3) Using the proposed approach, is there any real improvement to the prediction of ablation and snow accumulation, compared to less sophisticated methods?

2. Study site and ﬁeld data The Vernagtferner glacier (46°520 N/10°490 E) is located in the eastern Alps, north of the main alpine chain, in Tyrol, Austria (Fig. 1). Its runoff feeds the Vernagt stream, which ﬂows through the Vernagt Valley and contributes to the Rofenache and Oetztaler Ache rivers, and ﬁnally to the River Inn. The glacier covers an area of 7.9 km2 (2010, orthoimage), and has a maximum ice thickness of 90 m and a mean thickness of approximately 25 m, measured by georadar in spring 2007 (Hoyer, 2007). The glacier altitude ranges from 2792 to 3582 m a.s.l., and approximately 59% of it is situated between 3100 and 3300 m a.s.l. (measured in 2006) because of its plateau character. The Commission of Geodesy and Glaciology of the Bavarian Academy of Sciences has been studying this glacier in detail since

41

the beginning of the 1960s, and the runoff from the Vernagtferner has been recorded continuously at a gauging station (Pegelstation Vernagtbach) since 1973 (e.g. Mayr et al., 2011). The catchment area is 11.4 km2, 69% of which is covered by the glacier. Meteorological data have also been collected next to the gauging station since 1973. The annual mass balance has been determined since 1964 using the glaciological method (Reinwarth and Escher-Vetter, 1999), and winter and summer mass balances are observed separately using the ’ﬁxed date’ system. Approximately 40 ablation stakes are distributed over the whole glacier surface to measure the summer balance (Braun et al., 2006). Winter accumulation is determined at several snow pits and snow depth is measured across the glacier. Snow accumulation and annual mass balance for the whole glacier are calculated using these data (Escher-Vetter et al., 2009). The topographic input for our hydrological model is derived from a digital elevation model with a cell size of 20 m, which was generated in 2006 using airborne laser scanning (operated by the Tyrol Province). The data available for the calibration and validation years are shown in Table 1. For the present study, it was originally intended that the model calibration be run using data from the years 2004/2005 to 2008/ 2009. However, the ﬁrst calibration runs showed that the parameter sets that produce good snow cover simulations for all other years simulated the year 2008/2009 very badly in that it overpredicted the snow accumulation. Closer inspection of the observation data revealed some days in April 2009 with unusually high precipitation. A digital camera was used to take pictures of the automatic weather station on a daily basis, showing that the rain gauge was completely covered with snow during that period, which caused measurement errors. Therefore, measurements from nearby weather stations were substituted for the erroneous data from these days. The year 2008/2009 was, therefore, omitted from the calibration period to avoid introducing inconsistencies resulting from the substituted data. 3. Methods 3.1. Model description The model used in the present study is based on the HBV-ETH precipitation and runoff model (Bergström, 1976; Braun and Aellen, 1990; Braun and Renner, 1992). This is a lumped temperature-index model with a semi-distributed snow and glacier module, and uses seasonally varying degree-day factors and discretization into elevation bands with three exposition classes. Glacierised and unglacierised areas are treated separately. We modiﬁed the HBV-ETH model to allow spatially distributed calculations, and added extensions to account for radiation differences and snow redistribution. The new model is raster-based and calculates accumulation and ablation in a fully distributed way. It works on a daily time step and consists of four storages which that the hydrological input, formed by precipitation and melt, pass through (see Fig. 2). Snowand ice-melt are calculated using the temperature-index method. The model output is the simulated hydrograph at the basin outlet. The detailed model structure and the parameters regulating the different simulation steps are described below, and the changes we made to the original HBV-ETH model are highlighted. The meteorological input data are the daily precipitation sums and the daily air temperature means, measured at the meteorological station near the glacier. Systematic precipitation gauge undercatch and its representativeness of the entire basin are revised using correction factors for rain (RCF) and snow (SCF). The meteorological data are extrapolated using lapse rates for temperature (TGRAD) and precipitation (PGRAD). A threshold temperature (T0) divides precipitation into liquid and solid fractions so that

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E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

Fig. 1. Vernagtferner in the Austrian Alps. PV: gauging station ‘‘Pegelstation Vernagtbach‘‘.

Table 1 Data used in the study.

Runoff Glacier-wide annual mass balance Glacier-wide winter mass balance Point data of annual mass balance Point data of winter mass balance Glacier area

Calibration period 2004/2005–2007/2008

Validation period 1 2001/2002–2003/2004

Validation period 2 2008/2009–2009/2010

Yes Yes Yes Yes Yes Yes

Yes Yes Yes No No Only 2003/2004

Yes Yes Yes Yes Yes Yes

Fig. 2. Model structure.

the accumulation of snow cover and the snow- and ice-melt can be calculated. The HBV-ETH model calculates accumulation based

only on elevation. However, because solid precipitation is strongly redistributed by wind and avalanches, we modiﬁed the model to account for these effects (in a similar way to Huss et al., 2008a) using curvature and slope, with accumulation being reduced from 100% to 0% between selected minimum and maximum slope angles (SMIN, SMAX). The catchment’s curvature is determined within a range of 120 m around each grid cell (20 20 m), with concave structures leading to increased accumulation and convex structures leading to decreased accumulation. This is driven by two parameters, namely the range of the curvature grid and the CURV parameter, which is a threshold value. Accumulation is set to a maximum value (SPREAD) if the concave curvature exceeds CURV, and accumulation in convex areas is set to a minimum (SPREAD) if the curvature falls below CURV. Accumulation is linearly modiﬁed between the minimum and maximum, so in ﬂat areas accumulation remains unchanged. Our approach is not mass conserving, and the parameters mentioned also change the total amount of snow, but that can be corrected via the snow correction factor SCF. To account for the transition of snow to ice, the model sets the snow storage at the beginning of each glaciological year at zero. There is no differentiation between ﬁrn and ice. The original HBV-ETH model calculates melt on the basis of elevation bands and exposition classes. Spatially distributed melt, M (mm), is calculated in the modiﬁed model by considering potential clear-sky solar radiation in the degree-day approach, using the methodology published by Hock (1999):

M¼

ðMF þ RSnow=Ice IÞðT T0Þ; T T0 > 0 0;

T T0 0

ð1Þ

E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

in which the melt factor, MF (mm d1 °C1), is added to the potential clear-sky solar radiation, I (W m2), which is governed by the radiation coefﬁcients for ice (RIce) and snow (RSnow). The result is then multiplied by the difference between the air temperature, T (°C), and the threshold temperature, T0 (°C). MF varies in the HBV-ETH model over the course of a year, to account for changes in the insolation angle. This is not necessary in our approach because seasonal variations in incoming solar radiation are already included in the potential clear-sky solar radiation I, which is updated every day. Snowmelt can inﬁltrate the snow cover and be stored there. The maximum storage capacity is calculated using the snow water equivalent (mm w.e.) and a parameter for the water-holding capacity of the snow (CWH). The amount of refreezing meltwater is determined by the air temperature and a refreezing coefﬁcient (CRFR), and added to the snow cover (Braun and Aellen, 1990). The sum of liquid precipitation and meltwater forms the input into the soil moisture routine. From there, water losses are controlled using a potential evapotranspiration parameter, ETpot, which changes in a sinusoidal way in the course of the year, and the soil moisture storage (SSM) ﬁll level. ETpot is adjusted to the maximum evapotranspiration on 1st August each year, and reaches a minimum of zero mm d1 on 1st February. The full potential evaporation (ETpot) value is assumed if the SSM ﬁll level exceeds a threshold (LP), but actual evaporation is calculated below LP as a function of potential evaporation and the relationship between the SSM ﬁll level and the threshold LP. The remaining water is transferred to the runoff routine, where inﬁltration is governed by the SSM ﬁll level, a parameter that limits the maximum soil storage capacity (FC) and a coefﬁcient (BETA). The runoff routine consists of upper and lower storage compartments. The upper storage compartment has two outlets, fast drainage that simulates surface runoff (Q0) and a slower outlet that describes the interﬂow (Q1). The outﬂow is controlled by the maximum ﬁll level of the storage compartment (SUZ) and two parameters, k0 and k1. Surface runoff takes place if the upper storage ﬁll level exceeds a threshold value (LUZ). A constant water depth per day (CPERC) inﬁltrates from the upper to the lower storage compartment, which then drains linearly like a groundwater body (Q2), controlled by parameter k2 and the storage level SLZ. The outﬂow of each cell is the sum of surface runoff (k0), interﬂow (k1)

43

and groundwater outﬂow (k2). For small alpine catchments, such as the Vernagtferner catchment, it can be assumed that all water provided by the three runoffs leaves the catchment within the same day (Hagg, 2003). For that reason, this model approach does not use a transformation function to route the discharge, and simply sums the total outﬂow of all pixels and releases them as discharge on the same day. 3.2. Model calibration Model calibration consisted of the following steps: (1) pre-calibration of the accumulation parameters; (2) testing 10,000 random parameter sets and the selection of the best of these by considering one or more objective functions; and (3) ﬁnal adjustment of the selected parameters. In step (1) the parameters controlling the accumulation distribution were determined in a pre-calibration procedure (Table 2). We used the pre-calibration procedure to allow better simulation results because using fewer parameters increased the probability of good simulation results in step (2). To achieve this, the relative inﬂuences of the slope, curvature and elevation were tested, using all possible values of the relevant parameters, to ﬁnd the combination most capable of reproducing the ﬁeld observations. We used standardised values for the winter accumulation, considering the relative spatial distribution of snow, rather than the measured amount. The values selected were used as input to the subsequent model calibration. In step (2) we generated 10,000 random parameter sets of the most sensitive parameters (Schaeﬂi et al., 2005), estimating the possible ranges from previously published data (Hagg, 2003; Schulz, 1999) and from our own experience (Table 2). The advantages of this calibration method are its easy application and the possibility to split the procedure to different computers to save computing time, which is not possible when for example a genetic algorithm is used, where each calibration step depends on the previous one. But using random parameter sets without any knowledge about the models parametric uncertainty leads to a large number of parameter sets far away from reasonable simulation results and decreases the number of good parameter sets. Additionally, the chosen limits of the different parameters are crucial for the modelling results – allowing unrealistic parameter values decreases the probability of ﬁnding a good parameter set,

Table 2 Model parameters. Not highlighted: parameters not considered during step two of the calibration; light grey: parameters used for step two of the calibration; dark grey: precalibrated parameters controlling snow accumulation.

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E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

but thresholds that are too tight could exclude good parameter values. We tested the sensitivity of the model to the different parameters by changing them in catchments that had already been calibrated. Estimates were used for parameters that had relatively little inﬂuence on the results. In step (3) the selected parameters were calibrated by manual adjustment. We simulated the calibration period using each of the 10,000 sets and chose the best of these using one or more objective functions as described below. The existence of a comprehensive set of observational data allowed us to calibrate the model using several objective functions. We calculated the R2 criterion for runoff for the entire basin using a method published by Nash and Sutcliffe (1970), and also calculated the total runoff volume error (VER). The equations used were: n X ðQ m Q s Þ2

R2 ¼ 1

i¼1

ð2Þ

n X ðQ m Q m Þ2 i¼1

VER ¼

y n n X X X abs Qs Qm i¼1

i¼1

! ð3Þ

i¼1

where Qm (mm d1) is the observed discharge, Qs (mm d1) is the simulated discharge, n is the total number of calculated time steps and y is the total number of calculated years. To include mass balance information in the calibration, we calculated the cumulative annual mass balance error (CEMB) and the cumulative winter mass balance error (CEWB). CEMB is calculated using Eq. (4), and the use of winter mass balance values rather than annual values allows the calculation of CEWB.

CEMB ¼

y X

absðMBs MBm Þ

ð4Þ

i¼1

where MBs (mm a1) is the simulated annual mass balance and MBm (mm a1) is the measured annual mass balance (WBs and WBm, respectively, for the winter mass balance). If only glacier-wide annual and winter mass balance sums are used, the overestimated accumulation or ablation in certain parts of the glacier could be offset by underestimates made in other parts, and vice versa. To avoid this, we used accumulation and ablation point measurements to calculate spatially distributed cumulative annual and winter mass balance errors, SDCEMB and SDCEWB, respectively:

SDCEMB

1 0 p X absðPs Pm ÞC y B X C B i¼1 C B ¼ C B p A i¼1 @

ð5Þ

where Pm is an annual mass balance point measurement (mm a1), Ps (mm a1) is the simulated annual mass balance in the associated cell on the simulation grid and p is the total number of measurement points. SDCEWB was calculated in the same way using winter mass balance point measurements. Fuzzy measures (M), calculated as the difference between each result and the best possible result for each function, were used to compare the results of each objective function, and were calculated using the following equation (Cheng, 1999):

M ij ¼

ðxij xiworst Þ xibest xiworst

ð6Þ

where xij is the ith value (i = 1, 2, . . . , n), and ximax is the maximum and ximin the minimum of the jth objective function. The best and worst values of each objective function are selected from all param-

eter sets with R2 of 0.5 or higher while the other objective functions are within their best 20%. The fuzzy measures are strongly dependent on these boundaries. We tested several boundaries, and compared the chosen parameter sets and their simulation results when one or more objective functions were considered for the combined measure calculation. We found that the values we had chosen provided the most reasonable selection. The combined measure (CM), by which the best parameter set is selected, was calculated as the geometric mean of two or more (n) fuzzy measures (Seibert, 2000):

CM ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ p n M1 M2 . . . Mn

ð7Þ

Our six objective functions can be divided into two runoff functions (R2 and VER) and four mass balance functions (CEMB, CEWB, SDCEMB and SDCEWE). We avoided overestimating the inﬂuence of the mass balance using an equal weighting of runoff and mass balance fuzzy measures. The choice of parameter set is highly dependent on the fuzzy measure calculation. For example, a lower Nash–Sutcliffe boundary increases the inﬂuence of R2 on the selection, and, therefore, boundaries must be chosen carefully to control their impact on the ﬁnal choice. Parajka et al. (2007) reached the same conclusions for the calculation of pareto optima. In step (3) the selected set was manually reﬁned using an iterative procedure. First, all parameters inﬂuencing the winter mass balance were adjusted. Here, the objective winter mass balance (CEWB and SDCEWB) functions were used to estimate the simulation quality. Afterwards, the remaining parameters were calibrated. Here, the objective winter mass balance, annual mass balance and runoff functions were considered.

4. Results After the three calibration steps, we found R2 values of 0.88 for the calibration period and 0.83 for the validation period. The ﬁnal adjustments for runoff, annual mass balance and winter mass balance for all simulated years are presented in Table 3. As expected, the error ranges were higher in the validation period. The year 2009/2010 was simulated worst in all respects; this was the only year with R2 below 0.8, and the yearly runoff sum and the winter mass balance showed higher percentage errors than the other years. The simulated annual mass balances were too negative for 6 years, but the percentage error ranges were less consistent than for runoff sum and winter mass balance. The year 2002/2003, which included a summer heat wave, was simulated quite well, although it was not considered in the calibration period. R2 reached 0.90 (one of the highest) in this year, and the winter and annual mass balance simulation proved to be good (Table 3). Plots of measured and simulated daily runoff sums show that inter-annual runoff variation was simulated well, although some runoff peaks were over- or underestimated (Fig. 3). In addition to the annual and winter mass balance, point measurements of each were also used to assess the spatial distribution of the variables. The quality of the simulation is shown in Fig. 4a and b. While the winter mass balance simulation was of consistent quality in the calibration period, it was notably different in the two validation years. The annual mass balance was more consistent, but the trend over time showed a similar pattern. The annual mass balance spatial distribution for the year 2004/ 2005 is shown in Fig. 5. Different melt rates were calculated for areas with different orientations. For example, the north-east oriented area of the south-western part of the Vernagtfener shows smaller mass losses than the southerly oriented areas in the central parts.

E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

45

Table 3 Results of ﬁnal adjustment: Nash–Sutcliffe coefﬁcient; measured and simulated runoff sums and measured and simulated annual mass balances and winter mass balances in (mm/yr) and their absolute and percental differences. Calibration period highlighted grey.

Fig. 3. Measured and simulated mean daily runoff for 2 years of the validation period (2002/2003, 2003/2004) and 2 years of the calibration period (2004/2005, 2005/2006).

Fig. 4. Comparison of simulated and measured winter mass balance (a) and annual mass balance (b) at individual measurement points.

5. Discussion 5.1. How accurately can runoff, ablation and accumulation be if they are modelled simultaneously? The runoff simulation shows good overall performance compared to other studies (Table 5). Seibert (2000) stated that using additional objective functions diminishes the quality of the runoff simulation. In view of the fact that runoff, annual mass balance and seasonal mass balance were all used in our study, the R2 values of 0.84–0.90 for the calibration and 0.67–0.90 for the validation period (Table 3) should be considered as highly skillfull. The quality of the mass balance simulation was tested for the entire glacier and for individual ablation stakes. With a mean absolute error of 120 mm for all years, the glacier-wide winter mass balance was simulated fairly well (Table 3), with only the years

2008/2009 and 2009/2010 showing larger errors. If these years are excluded, the mean absolute error is reduced to 52 mm. The quality of the spatially distributed annual and winter mass balance point measurements can be compared with results published by Huss et al. (2008a), in which a standard deviation of 0.72 m for the annual mass balance and 0.46 m for the winter mass balance was achieved. Our results are of comparable quality, considering the smaller absolute values at Vernagtferner, with standard deviations of 0.48 m for the annual mass balance and 0.28 m for the winter mass balance, respectively (Fig. 4). The simulated spatially distributed accumulation values for the years 2008/2009 and 2009/2010 were signiﬁcantly higher than in the calibration period (Fig. 4a), which inﬂuences the spatially distributed annual mass balance simulations (Fig. 4b), in which the ablation amounts were slightly less negative than in the calibration years. The 2008/2009 deviation was possibly caused by the

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E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

Fig. 5. Simulated surface changes in 2004/2005.

Table 4 Simulation results of parameter set choosen based on runoff data (R2 and VER): Nash–Sutcliffe coefﬁcient; measured and simulated runoff sums and measured and simulated annual mass balances and winter mass balances in (mm/yr) and their absolute and percental differences. Calibration period highlighted grey.

incorrect measurements of precipitation in April 2009, despite our application of the data corrections described above. The unusually low snow accumulation and very low spatial variability measured in 2009/2010 altered the correlation of snow cover with elevation and topography, which could not be simulated by the model. In addition, comparing the winter precipitation sums for different years indicates that the observed precipitation amount in 2009/ 2010 should have led to higher snow water equivalents than were actually measured on the glacier. However, it was not possible to correct the precipitation values because no evidence for measurement errors was found and precipitation measurements from the nearest alternative station (Vent, 1900 m a.s.l., 6.5 km away) were too different for the errors to be identiﬁed. The glacier-wide annual mass balances show an interesting pattern, with signiﬁcant deviation between the ﬁrst 2 years and the last 2 years of the calibration period. We have not been able to identify a reason for this deviation, which was present even when the parameter set with the smallest CEMB was used, and it seems that this error cannot be avoided. We chose the parameter set with the smallest CEMB and a good SDCEMB for the calibration period. In most validation period years the simulated annual mass losses were too small – the measured annual mass balance was more negative than the simulated one. Further analysis showed that this error was not caused by the incorrect simulation of the

ablation (which was avoided by using SDCEMB), but by the overestimation of snow accumulation in the accumulation area. This effect could not be avoided by using SDCEMB because of the small number of stake measurements in the upper parts of the glacier. Further analysis of the simulation results showed the continuing increase in snow cover in the accumulation area during the ablation period, whereas the measured data showed a clear decrease. This problem was probably caused because the simulated accumulation and ablation values in these areas were too high and too low, respectively. The model uses a single threshold value to differentiate between melting and freezing, and between precipitation as rain and snow, but separate thresholds were used in other studies (e.g. Koboltschnig et al., 2008; Parajka et al., 2007). A model test run including different thresholds for melting/freezing and rain/ snow showed that this could help to reduce the simulated snow in the accumulation area. There are two possible reasons why the simulated ablation is too small in these areas. The ﬁrst is the use of the degree-day approach. Closer inspection of the glacier melt data shows that the use of daily, rather than hourly mean temperature, leads to the underestimation of ablation at temperatures around the melt threshold. In our example, using hourly temperature data can increase melt in the upper glacier by 150 mm/year. The second reason is the possibility that snow reduction by sublimation is absent

Table 5 Summary of runoff simulation results from different studies. Model

Timestep

Investigation Area

Catchment size (km2)

Glacierized area (%)

Objective functions

R2 calibration period

R2 validation period

R2 year 2002/2003

(Akhtar et al., 2008)

HBV-Met

Daily

Hunza river basin

13925

34

Discharge

0.86

0.91

–

Gilgit river basin Astore river basin Hunza river basin Gilgit river basin Astore river basin Bridge River basin

12800 3750 13925 12800 3750 152.4

7 16 34 7 16 61.8

0.83 0.67 0.74 0.82 0.79 0.91

0.77 0.71 0.72 0.72 0.58 0.93

– – – – – –

98 8.7 28 31 463 58 3.34 –

41 78 25 36 42.5 51 56.9 3.1 km2

0.89 0.93 0.81 0.88 0.89 0.85 0.76 0.76–0.77 0.78–0.80 0.60–0.74 0.90

0.86 0.88 – – – 0.83 – – – – –

– – – – – – – – – – –

0.84 0.94

0.80 0.92

– –

HBV-PRECIS

Daily

Discharge

(Stahl et al., 2008)

HBV-EC

Daily

(Hagg, 2003)

HBV-ETH

Daily

(Hagg et al., 2004) (Hagg et al., 2006)

HBV-ETH HBV-ETH

Daily Daily

(Hock, 1999)

–

Hourly

Rofenache Vernagtbach Tuyuksu basin Ala Archa basin Oigaing basin Abramov glacier Glacier No. 1 Storglaciären

(Huss et al., 2008)

GERM

Daily

Zinal, Valais

20.1

60.9

(Moore, 1993) (Schaeﬂi et al., 2005)

– GSM-SOCONT

Daily Daily

Lillooet River basin Lonza at Blatten

2160 38.9

17 52.2

Discharge, reconstructed annual and winter mass balance Discharge, annual mass balance Discharge, annual mass balance Discharge, annual mass balance Discharge, geodetic mass balance Discharge Discharge, annual mass balance Discharge, annual mass balance Discharge, ablation Discharge, ablation Discharge, ablation Decadal ice volume changes, equilibrium line altitude, monthly runoff volumes Discharge, equilibrium line altitude Discharge, annual mass balance

Rhone at Aletsch Drace at inﬂow into the dam Mauvoisin Rhone, Gletsch

77.8 169.3

36.5 41.4

Discharge Discharge

0.92 0.90

0.91 0.84

– –

38.9

46.1

Discharge, winter and annual mass balance

0.92

–

0.91 – 0.74

(Schaeﬂi and Huss, 2011) (Zappa and Kan, 2007)

GSM-SOCONT, modiﬁed PREVAH

Hourly

Lütschine, Gstein

379

17.4

Discharge

0.92

0.90 (all years) 0.91

(Konz et al., 2007) (Koboltschnig et al., 2008)

TACD PREVAH

Daily Hourly

Rhone, Gletsch Langtan Khola basin Upper Salzach basin

38.9 360 593

52.2 46.1 5.5

Discharge Discharge, annual mass balance Discharge, snow cover distribution

0.93 0.87 0.83–0.86

0.91 0.81 0.74–0.89

E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

Citation

0.93

47

48

E. Mayr et al. / Journal of Hydrology 478 (2013) 40–49

from our model. Strasser et al. (2008) measured winter sublimation of about 100 mm in the Berchtesgaden Alps. On very wind-exposed mountain ridges sublimation can reach extreme values of more than 1000 mm. These values are smaller in the summer, but are still important for the Vernagtferner glacier because it is located in the Central Eastern Alps, where the relatively dry climate could theoretically lead to both evaporation and sublimation. 5.2. How useful is additional information for the calibration result? The importance of annual mass balance in model calibration has been stated by several authors (e.g., Braun and Renner, 1992; Huss et al., 2008a; Koboltschnig et al., 2008; Konz and Seibert, 2010; Stahl et al., 2008). In our study, annual and winter mass balance helped us ﬁnd a parameter set that was able to simulate both runoff and the mass evolution of the glacier (Table 3). While the glacier-wide annual mass balance showed a systematic error because of the model limitations, the ice loss in the ablation area was simulated well (Fig. 4). We compared the results using a parameter set chosen when only the objective functions for runoff (R2, VER) were derived using fuzzy measures (Table 4), in order to assess the robustness of the model calibration. This showed that incorrectly simulated winter and annual mass balance values did not necessarily affect the quality of the runoff simulation. In this example, the model accumulates insufﬁcient snow in the winter but that is offset by higher summer ice-melt rates, and produces good total runoff performance. Using winter and annual mass balance point measurements allowed us to calibrate the spatially distributed approach for accumulation and ablation. Additionally, it avoided the compensation of wrong accumulation values by altered ablation values, and vice versa, which would be possible if only glacier wide mass balances were used for calibration. This helped us to identify a systematic error in the model and ensured good and reliable simulation results, conﬁrming the beneﬁt of using the additional spatial distribution data in the model calibration. The reliability of the hydrological model beyond the calibration conditions could be estimated using the exceptional data from the year 2002/2003 (Koboltschnig et al., 2009, 2008; Seibert, 2003; Zappa and Kan, 2007). Zappa and Kan (2007) reported low R2 values for this year (results shown in Table 5), but we found one of the highest R2 values using our simulation, and we also found that the winter and annual mass balances were simulated well. This conﬁrms that our model calibration for the ablation area was robust, even though point measurements are not available for 2002/ 2003. The reason for the good annual mass balance simulation results was the complete disappearance of snow in summer 2003. The daily mean temperatures in the accumulation area were mainly above the threshold value, T0, and all precipitation was, therefore, considered to be rain. That meant that the inappropriate description of snow accumulation was avoided. However, the 2002/2003 mass balance simulation based on runoff (Table 4) was much too high, with the second highest difference between measured and simulated mass balance of all simulated years. The error caused by simulating too much ice-melt using this calibration was augmented by the heavy melt in summer 2003. 5.3. Is there a real improvement in the modelling of ablation and snow accumulation compared to less sophisticated methods? Including curvature and slope angle in our model allows the calculation of spatially distributed accumulation. Snow- and ice-melt was calculated using potential clear-sky solar radiation in addition to the temperature-index method. All these variables can be derived from a digital elevation model, and our aim was to calculate

accumulation and ablation in as much detail as possible. Nevertheless, it is important to assess how useful the additional data are for reproducing the spatial pattern of the snowpack. Snow accumulation and elevation depend on each other with a correlation coefﬁcient between 0.16 and 0.80, depending on the year (Mayr and Hagg, in press). To calculate the correlation between snow accumulation and slope or curvature and between melt and solar radiation it is necessary to divide the catchment into elevation bands (in our model we used 14 bands of 50 m each) to reduce the inﬂuence of elevation. We normalised the data from all the years available to values between 0 and 1, so that we could correlate all of the available data for each elevation band. Redistribution based on slope and curvature produced positive correlations for most of the 14 elevation bands, four of them with correlation coefﬁcients greater than 0.3. Two bands gave slightly negative correlations. This suggests that the spatial distribution of the snow pack is described slightly better if local topography is taken into account, although the differences are superimposed on the elevation effect. Spatially distributed melt was strongly correlated with elevation (correlation coefﬁcients of 0.95–0.98 for the different years). Although the Vernagtferner glacier has a relatively uniform orientation and ﬂat topography, variation in insolation does have an effect on local melt rates. Of the eight elevation bands for which measurements are available, ﬁve showed positive correlations, and three of those had correlation coefﬁcients greater than 0.3. The correlation between melt and radiation was more pronounced than the correlation between exposition classiﬁcation and melt, proving the value of using the approach of Hock (1999). This correlation can be seen in Fig. 5, which shows that the south oriented (major) part of the glacier had higher melt rates than the easterly and northeasterly oriented southern part of the glacier.

6. Conclusions The model developed in the present study shows good overall performance for all simulated attributes. The additional use of the annual and winter mass balances in the calibration had no noticeably negative effects on the runoff simulation. Comparing the simulated results with a parameter set calibrated only on runoff showed that the use of winter and annual mass balance data avoids systematic simulation errors. Using spatially distributed data prevented mass compensation within the glacier area and led to more reliable parameter calibrations. It also helped to detect the inaccurate simulation of the processes in the accumulation area and revealed limitations in the model structure. Tests still need to be conducted to determine whether changing the model structure would help to simulate accumulation and sublimation in the accumulation area more precisely. Statistical analysis of the distribution of ablation and accumulation proved that a simple approach to the calculation of spatially distributed accumulation and ablation can help to improve the quality of the model. Konz and Seibert (2010) demonstrated that the use of a single year glacier mass balance, or a geodetic mass balance derived from digital elevation models, can help the selection of better parameter sets. The validity of this assumption for the winter mass balance and spatially distributed data still needs to be tested. The identiﬁcation of measurement errors obtained by testing the model used in this study revealed another potential ﬁeld of application for conceptual hydrological models. Applying tested parameter sets to climate data from other (i.e., untested) years could help to reveal measurement errors. In our case there was a data error in the accumulation period that could not be recalculated from the runoff values because the precipitation fell as snow and was not immediately added to the runoff. However, data gaps

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