Evaluation of modelled snow depth and snow water equivalent at three contrasting sites in Switzerland using SNOWPACK simulations driven by different meteorological data input

Cold Regions Science and Technology 99 (2014) 27–37

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Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions

Evaluation of modelled snow depth and snow water equivalent at three contrasting sites in Switzerland using SNOWPACK simulations driven by different meteorological data input Edgar Schmucki a,b,c,⁎, Christoph Marty a, Charles Fierz a, Michael Lehning a,d a

WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos Switzerland Institute of Geography, University of Bern, Switzerland c Oeschger Centre for Climate Change Research, University of Bern, Switzerland d CRYOS, School of Architecture, Civil and Environmental Engineering, EPFL, Lausanne, Switzerland b

a r t i c l e

i n f o

Article history: Received 30 October 2012 Accepted 5 December 2013 Keywords: SNOWPACK Radiation parameterization Precipitation correction Snow modelling Model uncertainty Snow water equivalent

a b s t r a c t The knowledge of certain snow indices such as the number of snow days, maximum snow depth and snow water equivalent or the date of snow disappearance is important for many economical and ecological applications. However, snow data are frequently not available at the required locations and therefore have to be modelled. In this study we analyse the performance of the physically based snow model SNOWPACK to calculate the snow cover evolution with input data commonly available from automatic weather stations. We validated the model over several years at three very diverse stations in Switzerland: Weissfluhjoch (2540 m a.s.l.), Davos (1590 m a.s.l.) and Payerne (490 m a.s.l.), where snow depth and the full radiation balance are measured in order to assess the uncertainties induced by the parameterizations of radiation fluxes and by the use of uncorrected precipitation measurements. In addition, we analysed the snow water equivalent at the high-alpine station Weissfluhjoch. The results demonstrate that the radiation balance, which is often measured incompletely, can successfully be parameterized and has an unexpectedly small impact on the modelled snow depth. A detailed analysis demonstrates that an adequate precipitation correction decreases the mean absolute percentage error by 14% for snow depth at the alpine and high-alpine stations and by 19% for snow water equivalent at Weissfluhjoch. The low altitude station Payerne (ephemeral snow conditions) revealed a high sensitivity with regard to the temperature threshold to distinguish solid from liquid precipitation. The analysis further suggested a high sensitivity to ground heat fluxes for ephemeral snow covers. Overall, the daily snow depth could be modelled with a mean bias error of less than − 8 cm at all sites, whereas the mean bias error for the snow water equivalent was less than −55 mm w.e. at Weissfluhjoch. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The snow depth HS, the snow water equivalent SWE, the snow load on a roof or the duration of snow on the ground are all important parameters for services and regulations such as road maintenance, avalanche warning, water management, hydro power, flood prevention or building codes. The measurement of these snow parameters is not always possible or too expensive. Moreover, even if there are snow measurements available for recent times, these series are often not long enough for a sound trend analysis (e.g. Marty, 2008) or the calculation of return periods of extreme snow events (e.g. Blanchet and

⁎ Corresponding author at: WSL Institute for Snow and Avalanche Research SLF, Flüelastrasse 11, 7260 Davos Dorf, Switzerland. Tel.: + 41 81 4170 368; fax: + 41 81 4170 110. E-mail address: [email protected] (E. Schmucki). 0165-232X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.coldregions.2013.12.004

Lehning, 2010). To overcome the problem of short time series, snow models driven by meteorological variables can be used. However, models have uncertainties, which need to be quantified. Typical uncertainties of snow models in mid-latitude climates may range from 50 to 200 mm w.e. for SWE in terms of root mean square error, and show a mean bias error between − 40 to 20 days concerning the number of snow days (Etchevers et al., 2002). Modelling the snowpack is a complex task, since the accumulation and ablation of snow is highly dependent on the different fluxes of the energy budget. These fluxes are highly variable in space and time and often not easily determined from weather parameters observed at one height. The successful modelling of these fluxes hence depends on representative and high quality meteorological input data. Furthermore, previous snow model inter-comparisons (Etchevers et al., 2004; Feng et al., 2008; Rutter et al., 2009) have demonstrated that models with higher complexity often do a better job in reproducing the energy budget of a snowpack and therefore are more reliable for extrapolation to future climate scenarios.

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One of these higher complexity snow-cover models, which was successfully used in the above-mentioned inter-comparisons, is the widely used model SNOWPACK (Lehning et al., 2002a,b). SNOWPACK requires air temperature, relative humidity, wind speed and direction, incoming or reflected short-wave radiation and precipitation intensity or measured snow depth as input data. Earlier validation studies mainly assessed the performance of the model in reproducing the stratigraphy of the snowpack. These studies used automatic snow depth and snow surface temperature measurements (Hirashima et al., 2004; Lehning et al., 1999, 2001; Lundy et al., 2001) or long-wave incoming radiation (Etchevers et al., 2004; Rutter et al., 2009; Yamaguchi et al., 2004) as input data, which are usually not available from Automatic Weather Stations (AWS). The sensitivity of the energy and mass exchange over snow was investigated in Dadic et al. (2013), whereas we quantify model sensitivity to meteorological input data options in general. The study by Rasmus et al. (2007), which validated SNOWPACK at 5 stations in Finland, is the only one which used standard meteorological data as input. It is also the only study which included a location with an ephemeral snow cover regime. The input data for this study were mostly only available at 3- or 6-hour time resolutions and the largest contribution to the energy balance, the global radiation, had to be estimated from cloudiness observations and theoretical calculations. The goal of this paper is to explore how accurately SNOWPACK, as a typical detailed snow energy and mass balance model, can reproduce the snow depth and snow water equivalent under different input conditions: (1) We investigate the model accuracy for situations when a maximum set of meteorological input data from one measurement height above the ground is available, i.e. all four components of the radiation balance are measured. (2) We examine the effect of the parameterization of the incoming long-wave radiation, since this parameter is usually not measured at automatic weather stations. (3) We analyse whether a precipitation correction for under-catch can improve the model performance. (4) We explore if the model performance in an ephemeral snow cover regime is different from that in an alpine snow cover regime. We assess the performance of SNOWPACK, driven with standard meteorological input data (see parameters with an asterisk in Table 1), to model important parameters such as the number of snow days, the maximum snow depth and SWE or the date of complete snow melt for three stations in Switzerland (Weissfluhjoch (2540 m a.s.l), Davos (1590 m a.s.l.) and Payerne (490 m a.s.l.), see Fig. 1 and Table 2). The snow water equivalent could only be analysed at the high-alpine station Weissfluhjoch because the other two stations do not have SWE data. 2. SNOWPACK model SNOWPACK is a one-dimensional snow-cover model, which was originally developed for avalanche warning purposes (e.g. Lehning et al., 1999; Schirmer et al, 2009). The model provides information on

the state of the snowpack at one point in space, including new snow depth (Lehning and Fierz, 2008) and possible surface hoar formation (Stössel et al., 2010). It is operationally used for avalanche forecasting purposes in Switzerland, Italy (Monti et al., 2012), Canada (Bellaire et al., 2011) and Japan (Hirashima et al., 2004). SNOWPACK uses finite elements to solve the partial differential equations governing the mass, energy and momentum transport within the snowpack. The model is physically based and calculations of the energy balance, mass balance, phase changes, water movement and wind transportation are included. Most of the process representations take a parameterized snow microstructure into account. Finite elements can be added by the advent of new snow and subtracted by erosion, melt water runoff, water evaporation, or sublimation (Lehning et al., 2002a). The density of new snow is an important parameter that controls the amount of snow water equivalent. We use a power function to calculate new snow density ρHN: ρHN ¼ 10

c

ð1Þ

where an empirical relation between air temperature TA and wind speed VW yields c: pffiffiffiffiffiffiffi c ¼ 3:28 þ 0:03  TA−0:36−0:75  arcsin RH þ 0:3  log10 ðVW Þ ð2Þ c ¼ 3:28 þ 0:03  TA−0:75  arcsin

pffiffiffiffiffiffiffi RH þ 0:3  log10 ðVW Þ

ð3Þ

where Eq. (2) is used for TA ≥ − 14 °C and Eq. (3) for TA b − 14 °C. Relative humidity RH is set constant to 0.8 (80%) during snowfall and the lower boundary for the wind speed is set to 2 m s−1. The performance of the SNOWPACK model depends on the choice and availability of input quantities, as well as the quality of the (surface) energy and mass exchange models (Lehning et al., 2002b). Avalanche warning services usually use SNOWPACK with input data from Alpine automatic snow and weather stations (e.g. stations from the Intercantonal Measurement and Information System (IMIS) in Switzerland) or meteorological models, which measure or model wind, air temperature, relative humidity, snow depth or precipitation, snow surface temperature, ground surface temperature and reflected short wave radiation. IMIS stations are located between 2000 and 3000 m a.s.l in the vicinity of avalanche starting zones. Note that the reliability of measurements obtained from IMIS stations is lower compared to those obtained from the stations of the Federal Office of Meteorology and Climatology MeteoSwiss, which comply with the international WMO guidelines. The IMIS instruments are of a lower quality and not ventilated—partly because only solar power is available and so the instruments can ice up. Time resolution of the measurements is 30 min, which is also an ideal time resolution for running the SNOWPACK model (Lehning et al., 1999). When the data from synoptic weather stations are considered as input data, it is clear that not all of the required parameters are always available. There are several ways

Table 1 Parameters and the corresponding instruments used as input for the SNOWPACK model. Parameters with an asterisk are defined as standard meteorological input data. Note that all measurements from the different sources are carried out at the same location. Parameter

Abbreviation

Unit

Source

Instrument

Air temperature* Relative humidity* Wind speed* Wind direction* Incoming short-wave radiation* Reflected short-wave radiation Incoming long-wave radiation Outgoing long-wave radiation Precipitation intensity* Snow depth

TA RH VW DW ISWR RSWR ILWR OLWR Pmeas HS

°C % m s−1 ° W m−2 W m−2 W m−2 W m−2

ASRB/BSRN ASRB/BSRN MeteoSwiss MeteoSwiss ASRB/BSRN ASRB/BSRN ASRB/BSRN ASRB/BSRN MeteoSwiss SLF

Meteolabor Thygan Meteolabor Thygan Lambrecht L14512 .ambrecht L14512 Kipp&Zonen CM21 Kipp&Zonen CM21 Eppley PIR Eppley PIR Lambrecht (Joss-Tognini) Manual observation

−1 mm h

cm

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

29

© swisstopo

Fig. 1. Map showing the location of the meteorological stations Weissfluhjoch, Davos and Payerne in Switzerland.

to overcome the input data problems, which will be discussed below. SNOWPACK determines the energy exchange at the snowpack surface by imposing either the measured snow surface temperature as a Dirichlet boundary condition or using long-wave radiation, latent and sensible heat, and advected (rain) fluxes as Neumann boundary conditions (Lehning et al., 1999). Net short wave radiation penetrates the snowpack and is then treated as an internal heat source comparable to the refreezing of liquid water. If soil layers are not modelled, ground surface temperature is prescribed as a Dirichlet boundary condition at the bottom of the snowpack. Operational applications usually use Dirichlet boundary conditions at the snow surface as long as no melt/refreeze phase changes occur there. For melting snow (surfaces) or if a measured surface temperature is not available, all surface energy fluxes need to be either modelled or measured. Incoming longwave radiation (ILWR) is often not measured and can be replaced by a modelled quantity based on air temperature, humidity and – if available – cloudiness. Ground surface temperature can, at least in central Europe, in the absence of permafrost and if a significant snow cover exists, be assumed to be close to 0 °C (Lehning et al., 1999). To determine the densification rate, snow is treated as a viscous material (Domine et al., 2008). Snow surface albedo is calculated by a statistical model that includes the time elapsed since the last snowfall and many other parameters such as snow grain size and liquid water

Table 2 Meteorological stations used in this study. Station

ID

Coordinates (lat/lon)

Elevation (m a.s.l.)

Measurement Period (month/year)

Snow cover regime

Weissfluhjoch Davos Payerne

WFJ DAV PAY

46.83/9.81 46.82/9.85 46.82/6.95

2540 1590 490

09/1996–08/2010 09/2003–08/2006 09/1994–08/2009

High Alpine Alpine Ephemeral

content (Lehning et al., 2002b). The importance of a time-varying albedo for the improvement of model simulations has been shown in several other studies (Livneh et al., 2010; Wang and Zeng, 2010; Wiscombe and Warren, 1980). SNOWPACK calculates density and temperature profiles and simulates metamorphic processes. It also allows melt and re-freezing within individual layers and a simple bucket water transport scheme (Lehning et al., 2002a) has been chosen for this study. 3. Data and methods 3.1. Input data We used data from Switzerland for this sensitivity study because three representative stations from the MeteoSwiss and the SLF networks offer a good opportunity to validate model results in ephemeral, alpine and high alpine environments. SNOWPACK is validated at three stations at different elevations (500, 1500 and 2500 m a.s.l.), representing different characteristics of the snow season in three contrasting snow cover regimes. The number of stations and the available time period were limited as all four components of the radiation balance and snow depth were required from the same measurement field for the sensitivity analysis. The three stations which fulfilled these requirements are shown in Fig. 1 and Table 2, with their coordinates, elevations, measurement periods and snow cover regimes. The short measurement period in Davos is due to several relocations of snow and/or radiation measurements. Standard meteorological input data were available from the MeteoSwiss and SLF stations, the radiation data were provided by the Alpine Surface Radiation Budget (ASRB) network (Marty et al., 2002) for Davos and Weissfluhjoch and the Baseline Surface Radiation Budget (BSRN) network (Ohmura et al., 1998) for Payerne.

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The parameters used are listed in Table 1 and have a temporal resolution of 30 min, except snow depth and snow water equivalent, which respectively have a daily and bi-weekly temporal resolution. The precipitation intensity is measured with a heated Lambrecht Joss-Tognini rain gauge. The output data from SNOWPACK has been set to a temporal resolution of three hours. All output is averaged over this period except modelled snow depth and snow water equivalent, which are the instantaneous values at the corresponding time step. The daily snow depth and bi-weekly SWE measurements are used for evaluation purposes. We compare the simulated values of these parameters at the closest point in time for each measurement. Extensive preparatory work has been carried out in order to have a complete time series of the parameters described in Table 1. For Weissfluhjoch, the few data gaps for all parameters except precipitation intensity could be replaced using redundant measurements from this site (Marty and Meister, 2012). For the missing values of precipitation intensity, values from the nearby station Davos have been used. However, these replaced values account for less than 4‰ of the whole dataset. Since data gaps in Davos were very rare and also lasted less than 1 day, no replacement was necessary. In Payerne, missing BSRN data were replaced by ASRB data, and remaining data gaps could be filled by redundant sensors on local MeteoSwiss stations. Some shorter data gaps of less than 2 days could not be replaced with data from other sensors in the vicinity. These gaps were filled with linearly interpolated values. 3.2. Precipitation correction and calibration Due to wind-induced under-catch, it is not recommendable to use the snow precipitation data provided by MeteoSwiss as a direct input to SNOWPACK. These measurements are not corrected for gauge under-catch. Various studies have dealt with the concept of precipitation correction and found an empirical relationship where the catch ratio is a function of wind speed and – for mixed precipitation – temperature (e.g. Goodison et al., 1998; Hamon, 1973; Sevruk, 2004). After testing many precipitation correction procedures, the one developed by Hamon (1973) yielded the best results, because the other precipitation corrections overestimated the solid precipitation to a large extent. The precipitation correction by Hamon (1973) is applicable to a wide range of different wind speeds and includes a temperature dependent factor b: Pcor ¼ Pmeas  expðbðTAÞ  VW Þ

ð4Þ

Where Pcor is the corrected precipitation in mm, Pmeas is the measured precipitation in mm, VW is the wind speed in m s−1 and b(TA) is the temperature dependent coefficient which amounts to 0.0294, 0.0527 or 0.0889 for 1.2 ≥ TA N 0 °C, 0 ≥ TA N −5 °C or − 5 °C ≥ TA, respectively. The correction factor, determined from (4) for each input data time step based on instantaneous temperature and wind data, has been averaged over one day. This was due to the fact that unrealistically high corrections are obtained at individual time steps, which are thus smoothed out without introducing an arbitrary upper limit for the correction factor. The mean daily correction factor was then applied to Pmeas at each time step for the corresponding day. Note that we do not apply a correction scheme for liquid precipitation as this would introduce another source of uncertainty due to the lack of a true validation value. The maximum (mean) precipitation corrections applied amount to 96 (17) %, 82 (9) % and 79 (5) % for Weissfluhjoch, Davos and Payerne respectively. Furthermore, the temperature threshold distinguishing solid/liquid precipitation was set to 1.2 °C for Weissfluhjoch and Davos, and to 0.25 °C for Payerne which then gave the best match between the modelled and observed snow depth data. The reason for the lower temperature threshold in Payerne is the simple observation that – with a higher threshold – the model would build-up snow during times when no snow cover was observed. Note that we have no

possibility to quantify in how far heat from the soil also contributes to the observation of a reduced and delayed build-up of a snow cover. The lower temperature threshold for rain may therefore partly compensate for an undetermined geothermal heat flux. This must be investigated in a further study using detailed soil heat balance data. To assess the performance of the precipitation correction, we used two different ways of running SNOWPACK relying a) on measured precipitation (Mode A) and b) on measured snow depth (Mode B) as input data. In Mode A, SNOWPACK models the snow depth directly from the provided precipitation measurements. In Mode B SNOWPACK models the snow depth and precipitation with the observed snow depth as input, i.e. snow depth is enforced. Mode B is used for operational avalanche forecasting, where the structure and layering of the snowpack are most important. We used both modes to calculate a monthly calibration factor fi, X fi ¼ X

PsolidðModeBÞi PsolidðModeAÞi

ð5Þ

where Psolid(ModeB)i is the total modelled solid precipitation at month i and Psolid(ModeA)i is the total measured solid precipitation at month i for each station. Finally, Pmeas is then multiplied by the climatological calibration factor fi in the corresponding month i at each time step to obtain the calibrated precipitation Pcalib. No such intra-model calibration has been performed in Payerne, because the calculation of a reasonable calibration factor is not possible in the ephemeral snow cover with large short term variations and high inter-annual variability. Note that all the following simulations have been conducted with precipitation intensity as input, i.e. Mode A. However, simulations with calibrated precipitation as input are strongly influenced by the snow depth measurements and therefore by Mode B. 3.3. Importance of long-wave parameterization Since weather stations do not usually provide ILWR data, this flux needs to be parameterized. This is done using a parameterization based on air temperature, relative humidity, and incoming short-wave radiation ISWR. In our case, ILWR was estimated using a combination of the Dilley and O'Brien (1998) clear-sky algorithm and the Unsworth and Monteith (1975) cloud correction algorithm. This method was found to be robust for various sites at different elevations (Flerchinger et al., 2009; Juszak and Pellicciotti, 2013). The clear sky emissivity εclr (Dilley and O'Brien, 1998) was calculated as follows:   pffiffiffiffiffiffiffiffiffiffiffiffi TA þ 273:16 6 Lclr ¼ 59:38 þ 113:7 þ 96:96 w=25 273:16   4 ε clr ¼ Lclr = σ ðTA þ 273:16Þ

ð6Þ ð7Þ

Where Lclr [W m−2] is the clear sky long-wave radiation and w [cm] is the precipitable water given by w = 4650e0/(TA + 273.16), where e0 [kPa] is the vapour pressure. The effective atmospheric emissivity εa is calculated using the cloud correction algorithm suggested by Unsworth and Monteith (1975): εa ¼ ð1−0:84cÞεclr þ 0:84c

ð8Þ

where c is the fraction of cloud cover estimated from a clearness index k, which is defined as the ratio of measured incoming short-wave radiation at the earth's surface to the short-wave radiation at the top of atmosphere (TOA) given by STOA = 1360sin(α), where α is the solar elevation angle and 1360 is the solar constant in W m−2. c can be linearly interpolated between c = 1.0 at a clearness index k of 0.25 to c = 0.0 at a clearness index k of 0.8. Note that Campbell (1985) used

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37 Table 3 Different model setups used for this study. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input. RadMeas

RadPar

Parameter/setup

Pmeas

Pcor

Pcalib

Pmeas

Pcor

Pcalib

Air temperature Relative humidity Wind (speed and direction) Incoming short-wave radiation Reflected short-wave radiation Incoming long-wave radiation Outgoing long-wave radiation Measured precipitation Corrected precipitation Calibrated precipitation

x x x x x x x x

x x x x x x x

x x x x x x x

x x x x

x x x x

x x x x

3.4. Different model setups

x

x x

x

We used 6 different model setups (Table 3) to investigate the sensitivity on the input data options. We distinguish between the optimal but unusual case, in which all radiation fluxes are measured (RadMeas) and the common case, in which only ISWR is measured and the albedo as well as ILWR are parameterized (RadPar). For both cases, we use either the measured (Pmeas), the corrected (Pcor) or the calibrated (Pcalib) precipitation as input. In our analysis, we therefore concentrate on a) results for simulated snow depth and SWE obtained with all four radiation fluxes available against results obtained with parameterized ILWR and parameterized albedo, and b) the effect of precipitation correction and calibration. To assess the performance of the different setups we use MAE and MBE as introduced above. In addition the mean absolute percentage error MAPE and the mean percentage error MPE are used to describe the absolute and the mean deviations in percent, since the differences in snow depth are large between the three snow cover regimes.

(1) WFJ RadMeas

250

snow depth [cm]

use the MAE because it is a natural measure of the average error, whereas the MBE is used to indicate average model bias (Willmott and Matsuura, 2005). Note that we use these measures in the following to compare the different setups. Although the all-sky algorithm is not able to reproduce the high frequency variation of measured ILWR correctly, it can be seen as a running mean and models approximately the correct long-wave energy input over a period of about 1–2 days. This is especially important in spring, where a clear-sky parameterization would underestimate energy input and therefore lead to far too small settlement and melt rates of the snowpack (not shown).

x

clearness indices of 0.4 and 0.7 for c = 1.0 and c = 0.0, respectively, whereas the above mentioned clearness indices are proposed by Flerchinger et al. (2009). Finally, the incoming long-wave radiation is estimated using the effective atmospheric emissivity εa and the Stefan–Boltzmann law. Since our time window for the algorithm is chosen to be 24 h, nocturnal values for the clearness index and thus the estimated cloud cover are linearly interpolated between the diurnal values, which have a time resolution of 30 min. As an example, mean absolute error MAE and mean bias error MBE for the parameterized all-sky ILWR are 25.6 W m − 2 and −4.2 W m−2, respectively. MAE and MBE describe the mean absolute and the mean deviation between simulations and observations. We

200

31

a

HS obs HS mod (Pmeas) HS mod (Pcor) HS mod (Pcalib)

150

100

50

0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

snow depth [cm]

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

(2) WFJ RadPar

250

200

02 Mar 2005

b

HS obs HS mod (Pmeas) HS mod (Pcor) HS mod (Pcalib)

150

100

50

0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

Fig. 2. Observed (black) and modelled (colours) snow depth at Weissfluhjoch (WFJ) for the year 2004/2005 with different treatment of precipitation measurements. (a) RadMeas, (b): RadPar. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input.

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In the analysis, we refer to beginning and end of season, which are defined in the following way: If the observed or modelled snow depth was higher than 10 cm over the 60 subsequent days, then the beginning of the season (onset) was set to this date. The end of the season (disappearance) was defined when the observed or modelled snow depth was below 10 cm for the first time. We have chosen the 10 cm threshold because it is a common lower boundary for the snow depth (Baker et al., 1992; Beniston, 1997; Marty, 2008).

4. Results and discussion 4.1. Simulated and observed snow depth during 2004/2005 We first show the performance of SNOWPACK for the year 2004/ 2005, because snow depth evolution was rather average for all three locations and therefore is used as an example season. The simulated and observed snow depth for Weissfluhjoch, where a high-alpine continuous snow cover exists throughout the winter, is shown in Fig. 2. In addition, Fig. 3 shows simulated and observed SWE (Weissfluhjoch only). Figs. 2a and 3a correspond to the RadMeas case, i.e. the albedo as well as outgoing and incoming long-wave radiation are measured. Figs. 2b and 3b show the RadPar case, where only incoming short-wave radiation is measured and the albedo as well as the incoming long-wave radiation are parameterized. The blue line in Fig. 2 corresponds to the modelled snow depth for measured precipitation. An apparent under-catch of precipitation can be clearly seen. The red line presents the simulated snow depth with the calibrated precipitation as input as discussed above. Finally, the green line shows the modelled snow depth obtained with the precipitation correction of

SWE [mm]

800

4.2. Performance of the simulations over the entire period 4.2.1. Onset and disappearance at Weissfluhjoch and Davos and the effect of albedo parameterization In order to show the performance of SNOWPACK for several years, we present here the errors of some important snow indices over the entire measurement period in Table 5. The onset of the snow cover is reasonably well captured in all model setups at Weissfluhjoch and Davos. It is noteworthy that the modelled snow depth does not melt

(1) WFJ RadMeas

1200 1000

Hamon (1973). Concerning SWE shown in Fig. 3, the same colours apply for the different precipitation inputs, whereas the black dots represent the bi-weekly SWE measurements. The top panel of Table 4 shows the specific dates of onset, disappearance, and maximum HS, as well as the maximum depth and the duration of the season at Weissfluhjoch. Fig. 4 shows the evolution of the observed and modelled snow depth at Davos. At first glance, Davos is quite similar to Weissfluhjoch, but with a shorter snow season (104 days shorter) and less snow in general (76 cm less at maximum HS, cf. middle panel Table 4). Payerne is an example of how well SNOWPACK can model an ephemeral snow cover. From Fig. 5 it is obvious that SNOWPACK has some problems in modelling the exact snow depth, but in general, yields reasonable results concerning the timing of different short-time snow events. Problems exist mainly in the disappearance of the snowpack after short-term snow events, especially in the RadPar case. Since the snow cover is ephemeral and not continuous (in time and space) at this elevation, we only compare the number of snow days SD with a threshold of 1 cm (Beniston, 1997), as well as the date of maximum HS, and maximum HS (cf. bottom panel Table 4).

a SWE obs SWE mod (Pmeas) SWE mod (Pcalib) SWE mod (Pcor)

600 400 200 0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

SWE [mm]

800

07 Apr 2005 14 May 2005 19 Jun 2005

26 Jul 2005

31 Aug 2005

(2) WFJ RadPar

1200 1000

02 Mar 2005

b SWE obs SWE mod (Pmeas) SWE mod (Pcalib) SWE mod (Pcor)

600 400 200 0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005 14 May 2005 19 Jun 2005

26 Jul 2005

31 Aug 2005

Fig. 3. Observed (black dots) and modelled (colours) snow water equivalent at Weissfluhjoch (WFJ) for the year 2004/2005 with different treatment of precipitation measurements. (a): RadMeas, (b): RadPar. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming longwave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input.

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

33

Table 4 Observed and simulated snow cover evolution at Weissfluhjoch (top) and Davos (middle) for the year 2004/2005, as well as the date of maximum snow depth, maximum snow depth, and the number of snow days for Payerne (bottom). In addition, the date of maximum SWE and maximum SWE at Weissfluhjoch are shown in the top panel. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input. 2004/2005

Observed

Simulated RadMeas

RadPar

Pmeas

Pcor

Pcalib

Pmeas

Pcor

Pcalib

Weissfluhjoch Onset Disappearance Max date Max depth (cm) Duration (days) Max Date SWE Max SWE (mm)

20 Nov (2004) 20 Jun (2005) 15 Feb (2005) 182 212 17 May (2005) 606

20 Nov (2004) 3 Jun (2005) 13 Feb (2005) 137 195 10 May (2005) 387

19 Nov (2004) 15 Jun (2005) 13 Feb (2005) 176 208 18 May (2005) 536

20 Nov (2004) 20 Jun (2005) 13 Feb (2005) 183 213 19 May (2005) 679

19 Nov (2004) 14 Jun (2005) 13 Feb (2005) 143 206 18 May (2005) 442

19 Nov (2004) 19 Jun (2005) 13 Feb (2005) 180 212 18 May (2005) 588

20 Nov (2004) 21 Jun (2005) 13 Feb (2005) 182 214 18 May (2005) 659

Davos Onset Disappearance Max date Max depth (cm) Duration (days)

18 Dec (2004) 5 Apr (2005) 14 Feb (2005) 106 108

20 Dec (2004) 25 Mar (2005) 15 Feb (2005) 62 95

19 Dec (2004) 28 Mar (2005) 15 Feb (2005) 76 99

19 Dec (2004) 1 Apr (2005) 15 Feb (2005) 102 103

19 Dec (2004) 2 Apr (2005) 15 Feb (2005) 80 104

18 Dec (2004) 5 Apr (2005) 15 Feb (2005) 95 108

18 Dec (2004) 6 Apr (2005) 15 Feb (2005) 102 109

Payerne Max date Max depth (cm) # of snow days

23 Jan (2005) 10 24

23 Jan (2005) 6 20

23 Jan (2005) 7 20

N/A N/A N/A

23 Jan (2005) 6 29

23 Jan (2005) 7 29

N/A N/A N/A

out or fall below the threshold of 10 cm after early season snow events compared to the observed onset of the snow season, thus causing high MAE's. For Weissfluhjoch, the MAE's range from 5.2 to 9.9 days in onset, and from 1.3 to 19.9 days in disappearance. Note that MAE's

and MBE's are very similar in magnitude but not in sign, which means that the modelled onset as well as the disappearance of the snowpack are both too early compared to the observations. For Davos, the MAE's range from 0.7 to 12.3 days in onset, and from 2.7 to 12.3 days in

(1) DAV RadMeas 140

snow depth [cm]

120 100

HS obs HS mod (Pmeas) HS mod (Pcor) HS mod (Pcalib)

a

80 60 40 20

0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

(2) DAV RadPar 140

snow depth [cm]

120 100

HS obs HS mod (Pmeas) HS mod (Pcor) HS mod (Pcalib)

b

80 60 40 20

0 01 Sep 2004

07 Oct 2004

12 Nov 2004 19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

Fig. 4. Observed (black) and modelled (colours) snow depth at Davos (DAV) for the year 2004/2005 with different treatment of precipitation measurements. (a): RadMeas, (b): RadPar. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input.

34

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

disappearance of the snowpack. Again, errors in onset stem mainly from the choice of the definition of the snow season. Interestingly, in the RadPar setups at Davos the disappearance of the snowpack is too late compared to the observations as can be seen in the positive MBE. In general, errors in onset are lower in the RadMeas case, whereas errors in disappearance are lower in the RadPar case at Weissfluhjoch and Davos. A reason for these lower MAE's in the RadPar case could be explained by a modelled albedo, which is slightly too high, with a MAE of 0.057 and a MBE of 0.046 or a MAPE of 7% and a MPE of 6.2% at Weissfluhjoch, calculated over 14 years, if the snow depth was higher than 10 cm (see Fig. 6 as an example). A higher modelled albedo reduces the energy input into the snowpack, and therefore produces less settlement and melt—especially (but not only) at the end of the season. For this reason, the disappearance of the modelled snowpack is delayed in time and therefore closer to the observed disappearance of the snowpack at Weissfluhjoch. This also explains the unusual case in Davos, where the modelled disappearance of the snow cover is too late compared to the observations. 4.2.2. Maximum snow depth and duration at Weissfluhjoch and Davos Maximum snow depth at Weissfluhjoch is reasonably well captured, if the precipitation is calibrated or, in the RadPar case, corrected or calibrated. In RadPar_Pcor, the MAE and MAPE in maximum HS is only slightly higher than in RadPar_Pcalib and amounts to 16.8 cm or 6.9% for Weissfluhjoch and to 14.5 cm or 12.4% for Davos. Maximum snow depth is better reproduced in the RadPar case because in these setups modelled snow depths are higher throughout the season. Concerning the duration of the snow season at Weissfluhjoch and Davos, the MAE's between calibrated and corrected precipitation are very similar

in the RadMeas and RadPar cases at Weissfluhjoch. The modelled onset and disappearance of the snowpack are both too early compared to the observations, which yield good results for the duration of the snow season. In contrast, in the RadPar case at Davos, the modelled onset is too early and the modelled disappearance is too late compared to the observations, which results in high errors for the duration of the snow season. 4.2.3. Simulations in the ephemeral snow cover regime at Payerne At Payerne, the MAE in the date of maximum HS between the different model setups is quite similar and ranges from 6.3 days (RadMeas_Pcor) to 7.5 days (RadMeas_Pmeas). Note that errors get substantially smaller in terms of MBE, i.e. on average the date of maximum HS can be reproduced quite well. The deviations to the mean observed number of snow days SD (14.1 days) is high and MBE's are between − 1.6 days (RadPar_Pcor) and − 4.6 days (RadMeas_Pmeas). Interestingly, errors in terms of MAPE are significantly higher in RadPar_Pcor compared to RadMeas_Pcor (62.1% and 36.5%, respectively) because the snowpack persists longer after short-term snow events in the RadPar case and hence the errors become larger. Errors for maximum HS are very similar between the different model setups in terms of MAE and MAPE and lowest in the RadPar_Pcor setup (5.2 cm and 46.1%, respectively) and highest in the RadMeas_Pmeas setup (5.7 cm and 49.9%, respectively). In the ephemeral snow cover regime of Payerne, SNOWPACK is able to reproduce the snow depth and especially the timing of the onset of snow. However, the model has some problems in melting the snow away at the correct time (see Fig. 5 as an example). A reason for this model failure at this elevation could be the inaccurate representation of ground temperatures, which are set constantly to 0.0 °C

(1) PAY RadMeas

14

snow depth [cm]

12 10

a HS obs HS mod (Pmeas) HS mod (Pcor)

8 6 4 2 0

01 Sep 2004

07 Oct 2004

12 Nov 2004

19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

(2) PAY RadPar 14

snow depth [cm]

12 10

b HS obs HS mod (Pmeas) HS mod (Pcor)

8 6 4 2

0 01 Sep 2004

07 Oct 2004

12 Nov 2004

19 Dec 2004

24 Jan 2005

02 Mar 2005

07 Apr 2005

14 May 2005

19 Jun 2005

26 Jul 2005

31 Aug 2005

Fig. 5. Observed (black) and modelled (colours) snow depth at Payerne (PAY) for the year 2004/2005 with different treatment of precipitation measurements. (a): RadMeas, (b): RadPar. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas and Pcor correspond to model runs with measured and corrected precipitation as input.

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

35

Table 5 Errors for different indices over the entire measurement period at Weissfluhjoch, Davos, and Payerne. In addition, errors for the date of maximum SWE and maximum SWE at Weissfluhjoch are shown in the top panel. Positive (negative) values for the MBE correspond to model results which are too late (early) compared to the observations. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation is parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input. At Weissfluhjoch and Davos, the onset is defined if HS is higher than 10 cm for 60 subsequent days and disappearance is defined when HS is below 10 cm for the first time. In Payerne, a snow day is defined if HS is higher than 1 cm. ERRORS

Observed

Simulated RadMeas

RadPar

Pmeas

Pcor

Pcalib

Pmeas

Pcor

Pcalib

845.1

5.2/−4.9 19.9/−19.9 8.1/−6.7 174.1/74.2/30.0 229.6/18.6/7.6 5.0/1.7 560.4/284.8/33.6

5.2/−5.2 9.9/−9.9 11.5/−2.8 219.6/28.7/11.8 239.9/10.3/4.2 5.3/3.1 740.1/106.7/12.6

5.7/−5.7 2.6/−2.5 8.5/4.8 238.2/13.6/5.6 247.8/7.1/3.0 9.0/7.1 845.6/65.0/7.9

8.8/−8.8 12.6/−12.6 15.1/4.9 189.3/59.0/23.9 240.7/14.3/5.9 8.4/7.6 608.4/236.7/27.8

9.9/−9.9 4.1/−4.1 8.2/0.6 231.5/16.8/6.9 250.4/9.4/4.0 10.1/9.4 778.9/72.8/8.5

9.8/−9.8 1.3/−0.4 15.6/12.1 236.2/13.6/5.5 253.9/10.1/4.3 11.6/10.6 827.1/63.1/7.3

Davos (09/2003–08/2006) MAE/MBE onset (days) MAE/MBE disappearance (days) MAE/MBE max date (days) Mean max depth/MAE (cm)/MAPE (%) Mean duration/MAE (days)/MAPE (%)

116.3 123.3

3.0/3.0 12.3/−12.3 0.7/0.7 73.3/43.0/37.1 108.0/15.3/12.5

0.7/0.0 8.3/−8.3 0.3/0.3 87.2/29.2/25.2 115.0/8.3/6.9

1.0/−0.3 2.7/−2.7 0.3/0.3 111.3/5.1/4.3 121.0/2.3/2.0

1.0/−0.3 3.7/1.7 0.7/0.7 87.3/29.0/25.0 125.3/4.0/3.2

10.0/−9.3 3.7/3.7 0.7/0.7 101.8/14.5/12.4 136.3/13.0/11.4

12.3/−11.7 5.3/5.3 0.7/0.7 110.6/5.7/4.8 140.3/17.0/14.4

Payerne (09/1994–08/2009) MAE/MBE max date (days) Mean max depth/MAE (cm)/MAPE (%) Mean # of snow days/MAE (days)/MAPE (%)

12.5 14.1

7.5/−0.2 6.8/5.7/49.9 9.5/5.7/40.2

6.3/1.8 7.2/5.3/46.8 9.7/5.4/36.5

N/A N/A N/A

6.5/2.1 6.9/5.6/49.2 12.1/7.7/62.9

6.6/2.1 7.3/5.2/46.1 12.5/7.6/62.1

N/A N/A N/A

Weissfluhjoch (09/1996–08/2010) MAE/MBE onset (days) MAE/MBE disappearance (days) MAE/MBE max date (days) Mean max depth/MAE (cm)/MAPE (%) Mean duration/MAE (days)/MAPE (%) MAE/MBE max Date SWE (days) Mean max SWE/MAE (mm)/MAPE (%)

248.3 244.6

in our simulations if HS is larger than 0 cm, as well as the lack of a soil representation in our simulations, which fully neglects ground heat flux contributions. In addition, modelled snow depth at Payerne revealed a high sensitivity to the temperature threshold distinguishing solid from liquid precipitation. As can also be seen in Fig. 5, the model underestimates the number of snow days in some cases. This problem stems from the fact that winter precipitation in this climate often falls around the temperature threshold. These findings are in accordance with an international model inter-comparison (Rutter et al., 2009), which also included maritime and taiga snowpacks and concluded that frequent mixed precipitation events were the dominant influence on model divergence. Furthermore, Essery et al. (2013) stated that the simulation of snow depth is much more difficult at warmer sites with mid-winter melt events, even if the snow cover is continuous.

and Davos, errors have been calculated if the observed and simulated snow depth was above 10 cm. In Payerne, the threshold of observed and simulated snow depth was set to 1 cm. At Weissfluhjoch and Davos, MAE's and MBE's are in general smaller in the RadPar case. Besides the influence of the modelled albedo discussed above, there are other reasons, which may explain the higher errors in the RadMeas case: - Parameterized radiation leads to a slightly smaller energy input into the snowpack and therefore to less settlement and melt. - Corrected solid precipitation is too small in both radiation cases, which introduces a bias that probably compensates for the radiation error. - Biases could be introduced by measurement errors. For example, Dadic et al. (2013) stated that after a fresh snowfall in spring, an overestimation in wind speed (or measurement error) results in overestimation of melt, due to an increase of the turbulent heat fluxes. Of course, this overestimation would be valid for both radiation cases, but since the modelled snow depth in the RadMeas case is generally lower, the error between observed and modelled snow depth gets higher, thus increasing the bias.

4.2.4. Statistical measures of snow depth over the entire period and source of errors Table 6 reveals MAE's and MAPE's, as well as MBE's and MPE's in snow depth for Weissfluhjoch, Davos, and Payerne. For Weissfluhjoch WFJ

1.0 0.9

Albedo [-]

0.8 0.7 0.6 0.5

Albedo obs Albedo mod

0.4 01 May 2005 04 May 2005 08 May 2005 12 May 2005 16 May 2005 20 May 2005 24 May 2005 28 May 2005

01 Jun 2005

Fig. 6. Example of observed (black) and modelled (red) albedo at Weissfluhjoch (WFJ) for 40 days in spring 2005.

05 Jun 2005

09 Jun 2005

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E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

Table 6 MAE's, MAPE's, MBE's, and MPE's in snow depth for the entire period at Weissfluhjoch, Davos, and Payerne and for the different model setups. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming short-wave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input. No precipitation calibration has been carried out for Payerne (see text for details). Errors have been calculated if the observed and the modelled snow depth was above 10 cm (Weissfluhjoch and Davos) or above 1 cm (Payerne). Station

WFJ (09/1996–08/2010)

DAV (09/2003–08/2006)

Model setup/Errors

MAE [cm]

MAPE [%]

MBE [cm]

MPE [%]

MAE [cm]

MAPE [%]

MBE [cm]

MPE [%]

MAE [cm]

MAPE [%]

MBE [cm]

MPE [%]

RadMeas Pmeas RadMeas Pcor RadMeas Pcalib RadPar Pmeas RadPar Pcor RadPar Pcalib

44.2 19.1 8.7 33.5 11.3 8.3

30.8 16.9 8.7 25.7 13.4 9.6

−43.7 −17.5 −4.7 −32.3 −6.9 −1.4

−28.2 −10.7 −2.5 −19.7 −1.6 2.0

27.4 17.8 5.0 15.2 8.0 6.2

40.6 27.3 9.6 24.6 14.8 13.7

−27.4 −17.8 −3.7 −14.9 −5.7 1.3

−40.6 −27.3 −7.6 −22.5 −6.3 5.6

3.3 3.1 N/A 3.2 3.1 N/A

39.6 39.8 N/A 41.5 42.0 N/A

−2.4 −2.0 N/A −1.6 −1.3 N/A

−21.1 −17.2 N/A −11.8 −6.9 N/A

- Finally, model structural errors could be another source of the decreased skill in the RadMeas case. Model structural errors are defined as deficiencies in the model structure and associated with the models equations, including simplifications such as parameterisations or the use of approximate numerical solutions or finite time steps (Beven and Binley, 1992; Ewen et al., 2006). For example, model structural errors can be introduced by the parameterisation of albedo discussed above or the parameterisation of snow settlement. We additionally investigated separately the effect of the albedo parameterization as well as the effect of long-wave parameterization on the performance of the snow cover evolution for a reduced subset. These setups indicated that the parameterized albedo has a stronger effect than the parameterized long-wave radiation and thus is mainly responsible for the effect of error compensation. Not surprisingly, errors are smallest when precipitation is calibrated. Concerning MBE's at all stations, it is noteworthy that in all model setups (except in the RadPar_Pcalib setup at Davos), a negative bias is inherent, which gets considerably smaller, if measured precipitation is corrected for gauge under-catch. This is in accordance to the study by Barlage et al. (2010), where small differences in precipitation input made quite substantial differences in the accumulation and ablation of snow. MAPEs at Weissfluhjoch and Davos show that observed snow depth is reasonably well captured by the Pcor and Pcalib model setups, ranging from 8.7% (RadMeas_Pcalib) to 16.9% (RadMeas_Pcor) at Weissfluhjoch and from 9.6% (RadMeas_Pcalib) to 27.3% (RadMeas_Pcor) at Davos. Again, errors are generally lower in the RadPar model setups and differences between corrected and calibrated precipitation in these setups are quite small. In Payerne, MAE's and MBE's in HS are very low and range from 3.1 cm to 3.3 cm and −1.3 cm to −2.4 cm, respectively. This is due to the fact that the maximum snow depth in the period considered is quite low, 20 cm, which results in small mean errors. However, percentage errors are highest in Payerne compared to the two other stations and range between 39.6% to 42% in MAPE and from −6.9% to −21.1% in MPE. Table 7 MAE's, MAPE's, MBE's, and MPE's in SWE for the entire period at Weissfluhjoch. In RadMeas, all radiation fluxes are measured, whereas in RadPar only incoming shortwave radiation is measured and the albedo as well as incoming long-wave radiation are parameterized. Pmeas, Pcor and Pcalib correspond to model runs with measured, corrected and calibrated precipitation as input. Errors in SWE at WFJ (1996–2010) Model setup/errors

MAE [mm]

MAPE [%]

MBE [mm]

MPE [%]

RadMeas_Porig RadMeas_Pcor RadMeas_Pcalib RadPar_Pmeas RadPar_Pcor RadPar Pcalib

193.9 89.6 42.7 161.4 61.9 43.8

44.1 25.4 13.5 38.5 20.3 14.1

−193.2 −85.9 −24.7 −159.3 −53.2 −27.6

−39.3 −17.2 −4.0 −31.0 −7.5 −1.8

PAY (09/1994–08/2009)

4.2.5. Comparison of observed and modelled snow water equivalent at Weissfluhjoch The date of maximum SWE in 2004/05 (cf. Table 4) is reproduced well by all setups (except in the RadMeas_Pmeas setup), with errors of 2 days at most. Errors are higher when concerning the entire period (cf. Table 5), with MAE's ranging from 5 days to 11.6 days. Note that the SWE observations are carried out bi-weekly, which means that some errors could be explained by this low temporal resolution (see Fig. 3 as an example). In 2004/2005, the lowest deviation to observed maximum SWE is obtained by the RadPar_Pcor setup, with an underestimation of only 18 mm (cf. Table 4). For the entire period (cf. Table 5), best results are obtained with the Pcalib setups, whereas reasonable results are also achieved by the Pcor setups, with an MAPE between 8.5% (RadPar_Pcor) and 12.6% (RadMeas_Pcor). Note that all model setups, except the RadMeas_Pcalib setup, underestimate the maximum SWE. Table 7 shows the SWE errors for the whole period. Again, reasonable results are obtained when precipitation is either calibrated or corrected, while the results are considerably better in the RadPar_Pcor setup compared to the RadMeas_Pcor setup. For example, MAPE and MPE for the RadMeas_Pcor setups are 25.4% and −17.2%, respectively, and drop to 20.3% and − 7.5%, respectively, in the RadPar_Pcor setup. Besides the effect of the albedo parameterisation, this can be explained by the various sources of errors discussed above. In general, the applied precipitation correction yields to an underestimation of SWE. It is not surprising that the errors are lowest in the Pcalib setups, since the calibration factor relies strongly on the new snow density and thus the snow water equivalent (see Eqs. (1)–(3) and (5)). 5. Conclusions In summary, the analyses showed that SNOWPACK successfully reproduces short-term variations of the observed snow depth for a high alpine and alpine snow cover regime (Weissfluhjoch and Davos, respectively) over the course of a winter season, even with standard meteorological input data. This implies that with input data consisting of air temperature, relative humidity, wind speed, incoming short-wave radiation and precipitation intensity, good results can be obtained. It is noteworthy that besides a successful parameterization of incoming long-wave radiation, an adequate treatment of the precipitation measurements is crucial for obtaining good results, especially for correctly modelling maximum HS and SWE. This means that precipitation measurements either need to be corrected or, if measured snow depth is available, calibrated. The approach of calibrated or corrected precipitation could be useful if snow depth needs to be modelled for past or future time periods, where measured snow depth is not available. For the task of generating a long-term homogeneous time series of snow depth from long-term weather observations but only part-time snow observations, a correctly modelled snow accumulation is extremely important. In this case, a calibration offers additional value over the more unstable correction. The same holds true

E. Schmucki et al. / Cold Regions Science and Technology 99 (2014) 27–37

for modelling SWE, where the lowest errors can be obtained with calibrated precipitation. Our results reveal that especially the onset and the duration of the snow season can be modelled quite well (at Weissfluhjoch and Davos), whereas MAE's are generally slightly higher for modelling the disappearance of the snowpack. This result is not surprising as errors will accumulate for much longer, affecting the prediction of the snow disappearance. The lower station Payerne (ephemeral snow conditions) otherwise revealed a high sensitivity to the temperature threshold distinguishing solid from liquid precipitation. The analysis further suggested a high sensitivity on ground heat fluxes for ephemeral snow covers. In the RadPar_Pcor model setup, MBE's and MPE's in snow depth do not exceed −8 cm or −7%, respectively, at all sites, and are comparable to the errors in the RadPar_Pcalib setup, especially in terms of MAE and MAPE. MBE and MPE in SWE are less than −55 mm or −8%, respectively, at Weissfluhjoch in the RadPar_Pcor setup but drop significantly to − 27.6 mm or − 1.8%, respectively, in the RadPar_Pcalib setup. It is clear, that the best results are almost always obtained when the precipitation is calibrated. However, similar good results can also be obtained by simply correcting the precipitation for under-catch. It is likely that our approach is also valid for other snow models of high complexity, if the albedo parameterization therein is similar to the one in SNOWPACK. In a future study, SNOWPACK will be validated in terms of representing the climatology of snow depth when driven with standard meteorological input data. Moreover, future trends of the snowpack in Switzerland will be assessed by perturbing the observed time series of temperature and precipitation through scenario data from ENSEMBLE RCM runs. Acknowledgments This study was funded by the Swiss National Science Foundation (Grant No. 200021_132200). We highly acknowledge MeteoSwiss for providing the meteorological data and the ASRB/BSRN community for allocating the radiation data. Special thanks are addressed to Marcia Phillips and Rolf Weingartner for their contributions. We would like to thank three anonymous reviewers and the editors for their valuable comments. References Baker, D.G., Ruschy, D.L., Skaggs, R.H., Wall, D.B., 1992. Air–temperature and radiation depressions associated with a snow cover. J. Appl. Meteorol. 31 (3), 247–254. Barlage, M., Chen, F., Tewari, M., Ikeda, K., Gochis, D., Dudhia, J., Rasmussen, R., Livneh, B., Ek, M., Mitchell, K., 2010. Noah land surface model modifications to improve snowpack prediction in the Colorado Rocky Mountains. J. Geophys. Res.-Atmos. 115. Bellaire, S., Jamieson, J.B., Fierz, C., 2011. Forcing the snow-cover model SNOWPACK with forecasted weather data. Cryosphere 5 (4), 1115–1125. Beniston, M., 1997. Variatons of snow depth and duration in the Swiss Alps over the last 50 years: links to changes in large-scale climatic forcings. Clim. Chang. 36, 281–300. Beven, K., Binley, A., 1992. The future of distributed models—model calibration and uncertainty prediction. Hydrol. Process. 6 (3), 279–298. Blanchet, J., Lehning, M., 2010. Mapping snow depth return levels: smooth spatial modeling versus station interpolation. Hydrol. Earth Syst. Sci. 14 (12), 2527–2544. Campbell, G.S., 1985. Soil physics with basic: transport models for soil–plant systems. Elsevier, New York. Dadic, R., Mott, R., Lehning, M., Carenzo, M., Anderson, B., Mackintosh, A., 2013. Sensitivity of turbulent fluxes to wind speed over snow surfaces in different climatic settings. Adv. Water Resour. 55, 178–189. Dilley, A.C., O'Brien, D.M., 1998. Estimating downward clear sky long-wave irradiance at the surface from screen temperature and precipitable water. Q. J. R. Meteorol. Soc. 124 (549), 1391–1401. Domine, F., Albert, M., Huthwelker, T., Jacobi, H.W., Kokhanovsky, A.A., Lehning, M., Picard, G., Simpson, W.R., 2008. Snow physics as relevant to snow photochemistry. Atmos. Chem. Phys. 8 (2), 171–208. Essery, R., Morin, S., Lejeune, Y., Ménard, C.B., 2013. A comparison of 1701 snow models using observations from an alpine site. Adv. Water Resour. 55 (0), 131–148. Etchevers, P., Martin, E., Brown, R., Fierz, C., Lejeune, Y., Bazile, E., Boone, A., Dai, Y.-J., Essery, R., Fernandez, A., Gusev, Y., Jordan, R., Koren, V., Kowalczyk, E., Pyles, R.D., Schlosser, A., Shmakin, A.B., Smirnova, T.G., Strasser, U., Verseghy, D., Yamazaki, T.,

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