Evaluation of North Eurasian snow-o ff dates in the ECHAM 5 . 4 atmospheric GCM

Evaluation of North Eurasian snow-off dates in the ECHAM5.4 atmospheric GCM P. Räisänen, A. Luomaranta, H. Järvinen, M. Takala, K. Jylhä, O. N. Bulygina, A. Riihelä, A. Laaksonen, J. Koskinen, and J. Pulliainen Finnish Meteorological Institute, Helsinki, Finland Department of Physics, University of Helsinki, Helsinki, Finland All-Russian Research Institute of Hydrometeorological Information, World Data Centre, Obninsk, Russian Federation (RIHMI-WDC), Russia Department of Physics, University of Eastern Finland, Kuopio, Finland Finnish Geodetic Institute, Masala, Finland

geographical pattern of snow-off dates, with earliest snow-off (in March) in the Baltic region and latest snow-off (in June) in the Taymyr Peninsula and in northeastern parts of the Russian Far East. The primary biases are (1) a delayed snow-off in southeastern Siberia (associated with too low springtime temperature and too high surface albedo, in part due to insufficient shielding by canopy); and (2) an early bias in the western and 10 northern parts of Northern Eurasia. Several sensitivity experiments were conducted, where biases in simulated atmospheric circulation were corrected through nudging and/or the treatment of surface albedo was modified. While this alleviated some of the model biases in snow-off dates, 2 m temperature and surface albedo, especially the early bias in snow-off in the western parts of the Northern Eurasia proved very 15 robust and was actually larger in the nudged runs.
A key issue underlying the snow-off biases in ECHAM5 is that snow melt occurs at too low temperatures. Very likely, this is related to the treatment of the surface energy budget. On one hand, the surface temperature T s is not computed separately for the snow-covered and snow-free parts of the grid cells, which prevents T s from rising above 20 0 • C before all snow has vanished. Consequently, too much (too little) of the surface net radiation is consumed in melting snow (heating the air). On the other hand, ECHAM5 does not include a canopy layer. Thus, while the albedo reduction due to canopy is accounted for, the shielding of snow on ground by the overlying canopy is not considered, which leaves too much solar radiation available for melting snow.

Introduction
Snow cover is one of the most important elements in the climate and hydrology of the Northern Hemisphere. Large areas of the Eurasian and North American continents are covered by seasonal snow. The varying snow cover affects directly the surface energy balance by interfering with the energy storage, net radiation and fluxes of sensible 5 and latent heat. A significant positive feedback mechanism of the snow, albedo and solar radiation amplifies the climatic effects related to the snow cover: decreasing snow cover reduces the surface albedo and increases the amount of absorbed solar radiation at the surface, leading to increased melting and further reduction in the snow cover. The snow-albedo feedback is largest when changes in snow cover area are linked 10 with substantial changes in regional albedo (Brown, 2000). This coincides with the maximum influence of snow cover on surface net radiation in spring, typically in April and May, when the strong solar radiation and snow cover co-exist (Groisman et al., 1994). Snow cover also serves as a fresh water reservoir, thus regulating run-off in winter and spring, and influencing soil moisture content. Typically, delayed snow melt 15 can increase spring and summer soil moisture content which can further contribute to cooler and wetter weather conditions even after the snow melt (Cohen, 1994), and conversely for early snow melt (Wetherald and Manabe, 1995;Rowell and Jones, 2006;Kendon et al., 2010).
The key climatic role of snow cover has prompted a wide range of observational and 20 modelling studies on the topic. These include several intercomparisons of snow conditions simulated by atmospheric and fully coupled general circulation models (GCMs) with observational data (Foster et al., 1996;Frei and Robinson, 1998;Frei et al., 2003Frei et al., , 2005Roesch, 2006;Brutel-Vuilmet et al., 2013). Most recently, Brutel-Vuilmet et al. (2013) evaluated the snow cover simulated by models participating in Phase 5 of the 1 (AMIP1) models. Second, the models underestimated considerably the observed negative trend in snow cover in spring (for years 1979-2005), which is similar to the findings of Roesch (2006) for CMIP3 models.
Regarding the reasons for biases in modeled snow conditions, the intercomparison studies have, in general, not been very conclusive. Most attention has been paid to 10 biases in simulated air temperature (Foster et al., 1996;Räisänen, 2008) and total precipitation or snowfall (Foster et al., 1996;Roesch, 2006;Brutel-Vuilmet et al., 2013). Frei et al. (2005) further suggested that the exclusion of subgrid-scale treatments for terrain and land cover contributed to overestimated ablation rate of snow in spring over North America in AMIP2 models. 15 The focus of the current work is narrower than in the multi-model intercomparisons discussed above, which, however, allows for more in-depth analysis. We look in detail at the performance of a single model, the ECHAM5 atmospheric GCM (Roeckner et al., 2003(Roeckner et al., , 2006 in simulating the timing of snow melt in spring in Northern Eurasia, north of latitude 55 • N. Specifically, we focus on the average timing of the end of the snow 20 melt season (i.e., the snow-off date; the day when all snow accumulated during the winter has vanished). Snow-off dates simulated by ECHAM5 are compared with snow-off dates derived from two observational datasets: first, a satellite dataset based on data from passive multichannel microwave radiometers (Takala et al., 2009), and second, Russian in-situ snow course measurements (Bulygina et al., 2011a). The geographical focus on Northern Eurasia is motivated by the vast area of the continent, which makes Eurasian snow conditions important for understanding the planetary climate as a whole.

3674
The performance of a slightly earlier version of ECHAM5 in simulating the Northern Hemisphere snow depth, snow-covered area and surface albedo was assessed by Roesch and Roeckner (2006). By using snow products based on visible and microwave remote sensing data, they found that ECHAM5 reproduces the amplitude and phase of the annual snow depth cycle quite precisely, however, with a slight overes-5 timation of the snow depth in late winter and spring over Eurasia. The present work builds on Roesch and Roeckner (2006) but goes deeper in analyzing the regional details and causes underlying the biases in modelled snow-off-dates. Thus, while it is shown that in ECHAM5 simulations, snow-off tends to occur too late in the eastern part of Northern Eurasia (especially southeastern Siberia) and too early in the western and northern parts, the most fundamental issue is that snow-off occurs at lower-thanobserved air temperatures. The likely main reason for this are simplifications inherent to the model's surface energy budget calculation in the presence of partial snow cover and in the treatment of forest canopy. This highlights the need to consider carefully the treatment of the surface energy budget in the models, in addition to the fidelity of 15 simulated temperature and precipitation fields.
The rest of this paper is organized as follows. First, in Sect. 2 we introduce the ECHAM5 model and the experiments conducted. In Sect. 3, the observational datasets used in this work are described. Section 4 addresses the non-trivial issue of the definition of snow-off dates. Results are reported in Sect. 5, both for the default version 2 Model and experiments

Model description
Version 5.4 of the ECHAM5 atmospheric general circulation model (Roeckner et al., 2003(Roeckner et al., , 2006 was used. The dynamical part of ECHAM5 is formulated in spherical harmonics, while physical parameterizations are computed in grid point space. The 5 simulations reported were conducted at horizontal resolution T63 (corresponding to a grid-spacing of 1.875 • ) with 31 layers in the vertical and model top at 10 hPa. A semiimplicit time integration scheme is used for model dynamics with a time step of 12 min. Model physical parameterizations (Roeckner et al., 2003) are invoked at every time step, except for radiation, which is computed once in two hours.

10
The snow scheme in ECHAM5 is relatively simple: the snow water equivalent (SWE; kg m −2 ) is a prognostic quantity, but changes in snow density or grain size are not considered. In the presence of snow, the top of the snow layer is treated as the top of the soil model. For snow-free and snow-covered land alike, the surface temperature is determined through the surface energy balance, while the thermal diffusion equation 15 is used to calculate the soil (or snow) temperature profile. Five layers within the topmost 10 m are considered, with thicknesses of 0.065 m, 0.254 m, 0.913 m, 2.902 m and 5.700 m, respectively. For snow-free land, spatially varying volumetric heat capacity and thermal diffusivity are prescribed for five soil types according to the FAO soil map (Gildea and Moore, 1985;Henderson-Sellers et al., 1986). For snow-covered land the 20 procedure is the same except that the thermal properties are modified. For example, if snow fills the top soil layer completely, and the second layer partially, the thermal properties of snow are used for the top layer while a mass-weighted mixture of soil and snow properties is used for the second layer. A constant snow density of 330 kg m −3 is assumed in this procedure. 25 The ECHAM5 snow scheme considers both SWE intercepted by the canopy and SWE on the ground, the latter being more interesting for this study. The budget equation for snow on the ground accounts for snowfall through the canopy, 3676 sublimation/deposition, melting, and unloading of snow from the canopy due to wind. The snow melt rate M is computed from the surface energy budget equation: where C L is the heat capacity of the surface layer, T s the surface temperature, R net the 5 surface net radiation, H the sensible heat flux, LE the latent heat flux, and G the ground heat flux (all defined positive when the surface layer gains energy). A preliminary estimate for T s at the next time step (T * ) is obtained by considering everything else but snow melt (M = 0). If T * exceeds the melting point (T * > T 0 = 0 • C), the snow melt rate is inferred from the condition that the heat consumed in melting snow restores T s to T 0 : where L f is the latent heat of fusion and ∆t the model time step. The parameterized grid-mean surface albedo depends on the specified background albedo, the fractional forest area of the grid cell, the snow cover on the canopy, the snow 15 cover on the ground (diagnosed based on SWE and subgrid-scale standard deviation of surface elevation), and a specified snow albedo. While a complete description of the parameterization can be found in Roeckner et al. (2003), two details are mentioned here to provide a background for the sensitivity tests in Sect. 2.2.3. First, the albedo of snow on land (α sn ) depends on the surface temperature T s according to 20 α sn = α sn, min + α sn, max − α sn, min f (T s ) where and α sn, min = 0.3, α sn, max = 0.8, T 0 = 0 • C and T d = −5 • C. Second, the albedo of snowcovered forests is parameterized according to where α g is the ground albedo (α g = α sn if the ground is completely snow-covered), 5 α can is the albedo of the canopy (0.2 for completely snow-covered canopy) and the sky view factor SVF depends on the leaf-area index (LAI):

10
A total of six ECHAM5 experiments were conducted at resolution T63L31. All experiments were run for years 1978-2006, and years 1979-2006 were used for analysis of the results. All simulations used observed sea surface temperatures (SST) and sea ice (AMIP Project Office, 1996), and some of them used nudging fields and/or observed albedo fields that likewise included "real" year-to-year variations (see below).

15
The concentrations of well-mixed greenhouse gases were held constant following AMIP II guidelines (AMIP Project Office, 1996), at 348 ppmv for CO 2 , 1650 ppbv for CH 4 , 306 ppbv for N 2 O, 280 pptv for CFC-11, and 484 pptv for CFC-12. For aerosols, a climatological distribution was assumed (Tanré et al., 1984). The distribution of ozone, vegetation area and LAI followed a presribed climatological seasonal cycle. 20 Three of the experiments (REF, ALB1 and ALB2) were run in an ordinary climate simulation mode. In the remaining three experiments (REF_NDG, ALB1_NDG and ALB2_NDG), four model fields were nudged towards ERA-Interim reanalysis data (Dee et al., 2011): vorticity (relaxation time scale 6 h), divergence (48 h), atmospheric temperature (24 h) and logarithm of surface pressure (24 h). Nudging acts to minimize the errors in simulated atmospheric circulation, which is one of the possible causes for differences between simulated and observed snow-off dates. 3678

REF and REF_NDG
The reference experiment (REF) and the corresponding nudged experiment (REF_NDG) used the default version of ECHAM5.4. To evaluate the impact of model internal variability on the results, three runs were conducted for the REF experiment. The runs were started from different initial dates (1, 2 and 3 January 1978, respec-5 tively), which is sufficient for ensuring that within a few weeks, the weather conditions in the three runs become essentially independent of each other. Where not otherwise stated, the mean value of these three runs is reported. REF_NDG, as well as ALB1, ALB1_NDG, ALB2 and ALB2_NDG consist of a single run for years 1978-2006.

ALB1 and ALB1_NDG
10 Surface albedo influences strongly the energy available for melting snow in spring. In an attempt to eliminate errors in surface albedo, in the experiments ALB1 and ALB1_NDG the model's albedo field over continents was replaced by prescribed surface albedos based on observations. Monthly-mean albedos in the CLARA-SAL dataset derived from AVHRR satellite data (Riihelä et al., 2013) were applied. Since this dataset starts 15 from year 1982, for years 1978-1981 the average annual cycle of CLARA-SAL albedo for years 1982-2006 was employed. While this approach is instructive for diagnostic purposes, it has the major weakness that the albedo is independent of simulated landsurface properties, including snow cover. 20 In an attempt to reduce biases in ECHAM5's surface albedo field while keeping it interactive, experiments ALB2 and ALB2_NDG were conducted. Two modifications were implemented in ECHAM5's surface albedo parameterization. First, for snow-covered forests, the sky-view factor in Eq. (6) was replaced by Here, the stem area index (SAI) assumes a constant value of 2 for all forest types, following the Biosphere-Atmosphere Transfer Scheme (Dickinson et al., 1993). This modification was motivated by Roesch and Roeckner (2006), who noted that ECHAM5 overestimates the total surface albedo in eastern Siberia in the dormancy season of deciduous needleleaf trees, and ascribed this problem to the fact that the shadowing of 5 the ground below the canopy by stems and branches is neglected. Second, the value of α sn, min in Eq. (3) was increased from 0.3 to 0.6. This was motivated by the findings of Pedersen and Winther (2005) and Mölders et al. (2008), who note that for ECHAM5's snow albedo parameterization, and also for ECHAM4 for which α sn, min = 0.4, snow albedo decreases too early and too fast during snowmelt.

Observational data
Five observational datasets were used in the present work. First, a snow-off date dataset based on remote sensing of snow with space-borne microwave radiometer measurements (Takala et al., 2009) was used for evaluating snow-off dates in the ECHAM5 simulations. The Eurasian region is well suited for remote sensing of snow 15 melt for two reasons. First, temperatures in much of the Eurasian region are very low in winter-time, which leads to the formation of a dry snow pack. Second, as tundra is the predominant surface type, the snow conditions are relatively homogeneous over extended areas in the absence of e.g. mountain regions with a complicated topography. These properties are profitable for microwave instruments that measure highly Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | algorithm based on the brightness temperature difference between vertically polarized radiances around 37 GHz and 19 GHz was used to determine the snow-off date for each year (see Takala et al., 2009 for details). The snow-off dates (given as day-ofyear from 1 to 180) are provided at a nominal resolution of 25 km × 25 km. The snow-off date estimates in the microwave dataset were calibrated against the 5 INTAS-SCCONE observations (Kitaev et al., 2002;Heino and Kitaev, 2003) of snow depth and snow melt flag at Eurasian, mostly Russian, weather stations. Specifically, for the calibration data, the snowmelt date was defined as the last event during spring when the station snow status flag changed from "snow depth is correct" to "temporary melting" or "continuous melting". Thus, in principle, the microwave dataset is targeted at presenting the final snow-off date at each station. This is discussed further in Sect. 4. Second, snow course measurements made in Russia (or the former Soviet Union) were used for evaluating both the simulated snow-off dates and the seasonal cycle of snow water equivalent (SWE). These data were acquired from the Russian Hydrometeorological Centre; http://meteo.ru/english/climate/snow1.php (Bulygina et al.,15 2011a). The "routine snow surveys" dataset contains data from 517 meteorological stations (288 within the region considered here), for which either field or forest snow course measurements (or both) have been performed. These are a subset of the 958 stations considered in Bulygina et al. (2011b). The snow water equivalent (SWE) was measured at 100 (200) meter intervals along a forest (field) snow course with a total 20 length of 1 (2) km. Typically, measurements are provided at 10 day intervals in winter and 5 day intervals in spring (starting from March or April). The data availability varies, however, and not all stations provide data throughout the period 1979-2006 considered here. To compare with ECHAM5, the SWE values were regridded to the T63 grid, by averaging the SWE values over the stations if several stations existed in a grid cell. 25 The procedure for estimating the snow-off date from the snow course data is described in the Appendix. We include in our analysis those grid cells for which the snow-off date could be determined for at least five years during 1979-2006. Third, for surface albedo, we employ the monthly mean version of the CLARA-SAL dataset (Riihelä et al., 2013), which is based on a homogenized AVHRR radiance timeseries. These data provide black-sky albedo values from January 1982 onwards. The data, originally given at a 0.25  15 Snow-off date is evaluated in ECHAM5 based on daily-mean SWE values. There are several possible methods for defining the snow-off date, the most obvious ones being (1) the first snow-off date (i.e., the first day with zero SWE after a winter's SWE maximum) and (2) the final snow-off date (i.e., the day following the last day with SWE > 0 in spring). In some cases, the first and final snow-off dates differ substantially. As an 20 example, Fig. 1  fast it melts in the spring. In contrast, when the final snow-off date differs from the first snow-off date, it is, in essence, determined by the last occurrence of solid or mixedphase precipitation in spring. This makes the final snow-off date much more sensitive to day-to-day weather patterns in spring than the first snow-off date. Even when setting aside potential issues related to spatial and temporal resolution, 5 the definition of snow-off date in ECHAM5 results is not fully compatible with how the snow-off date is derived from the microwave satellite data. As noted in Sect. 3, the satellite snow-off date represents, in principle, the final snow-off date rather than the first snow-off date; that is, it can be affected by secondary periods of snow after the first snow-off date. Nevertheless, the use of final snow-off date in ECHAM5 for comparison 10 with the satellite data would be problematic. The secondary periods of snow after the first snow-off date in ECHAM5 are often short and the values of SWE very low (e.g., SWE ∼ 0.1 kg m −2 for the last two periods of snow in Fig. 1) so it is unclear whether they would really be detected by the satellite algorithm. Thus, we opt to use the first snow-off date for ECHAM5, but acknowledge that this may contribute towards an early 15 bias in snow-off dates when compared with the satellite data. Finally, in the comparisons with the snow course data, the snow-off date in ECHAM5 is evaluated as the first snow-off date, but using SWE for only those days for which snow course measurements are available (i.e., every 5th or 10th day). This is fully consistent with how the snow-off date is derived from the snow course data (see the 20 Appendix).

Reference experiment REF
The geographical distribution of the mean snow-off date during the period 1979-2006 in the satellite retrievals is shown in Fig. 2a 2008; Pulvirenti et al., 2008), these features are expected on physical grounds: colder temperatures and orographically enhanced precipitation favour later snow melt. The REF experiment (Fig. 2b) reproduces well the general pattern of snow-off dates seen in the satellite data, the snow-off being latest in the Taymyr Peninsula (between days 150 and 160) and earliest in the Baltic Sea region (around day 80). However, in 15 most of Northern Eurasia, snow melts earlier in the model results than in the satellite retrievals (Fig. 2c). The difference to the satellite retrievals is mainly 5-20 days, but exceeds locally 20 days in Northern Europe. On the contrary, in eastern Siberia and in some far eastern parts of Russia, snow melts locally over 10 days later in REF than in the satellite data. The orographic effects seen in Fig. 2a are absent in the model 20 results, presumably because the model resolution (T63) is too coarse for describing them. Figure 2d displays the standard deviation in the 28 year mean  snowoff date among the three runs included in the REF experiment. For most of Northern Eurasia, the standard deviation is less than 2 days, with larger values mainly confined 25 to the southwestern part of the domain and the Scandinavian coastline. In general, the standard deviation is much smaller than the respective differences between REF and the satellite data. This provides a justification for including only a single model run in the sensitivity experiments.
3684 Figure 3a compares the snow-off dates in the REF experiment with those derived from the snow course data. The general tendency towards too early snow-off dates in the west (about 30-90 • E) and too late snow-off dates in the east in REF as compared with the snow course data is in qualitative agreement with the corresponding comparison with satellite data (Fig. 2c). However, the positive differences in the east, 5 indicating delayed snow-off in ECHAM5, are more widespread and more pronounced than those in Fig. 2c, exceeding 20 days at some locations. Figure 3b and c show a similar comparison as Fig. 3a, but separately for field and forest snow courses. It is seen that particularly in the west, the model snow-off dates are rather close to those derived from the field snow courses, the differences being only slightly negative, and 10 in some cases slightly positive. In contrast, a comparison with the forest snow courses west of 90 • E shows a persistent negative bias, indicating too early snow melt in the model. The differences are more negative for the forest courses than the field courses because -as conventional wisdom indicates -in spring snow tends to persist longer in forests than on open ground. For those grid cells (located mainly in western Rus-15 sia) that have both forest and field courses, the snow clearance occurs on average 10.5 days later for the forest courses. In ECHAM5, however, neither snow-off dates nor SWE values are defined separately for the forested and non-forested parts of a grid cell.
To set the stage for further discussion, 2 m air temperature (T 2 ), surface albedo and 20 SWE are considered. Figure 4 shows a comparison of T 2 in REF and in the CRU data for the extended spring season (March through June). A cold bias prevails through most of the spring and peaks at −7 K in southeastern Siberia in April. Positive temperature biases occur in the Taymyr region (throughout the spring) and in the Russian Far East (mainly in March and April). Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a negative albedo bias occurs in the northernmost parts of Northern Eurasia (especially in the Taymyr region) in May and June, and in northern Fennoscandia especially in April. Figure 6 shows the average annual cycle of SWE in the REF experiment and in the snow course measurements, for the entire Northern Eurasia and for two subregions 5 denoted as Western Russia (55-70 • N, 30-70 • E) and Eastern Siberia (55-70 • N, 100-140 • E). Note that grid cells without snow course data are not included in the averages, and therefore, for example, the average over the entire Northern Eurasia gives more weight to the western and southern parts of the region than its eastern and northern parts, especially when considering field snow courses. With this caveat in mind, we 10 note that the domain-mean annual cycle of SWE over the entire Northern Eurasia in REF agrees well with the snow course data, although the maximum is slightly higher and occurs 5-10 days earlier than observed (Fig. 6a). There are, however, regional differences. For Western Russia (Fig. 6b), the simulated maximum SWE is very close to that observed, but SWE starts to decrease earlier than observed in the spring, in 15 agreement with the too early snow-off days in Figs. 2c and 3a. In contrast, for Eastern Siberia, the REF experiment overestimates substantially the accumulation of snow during winter (Fig. 6c), and the timing of maximum SWE and snow melt is delayed, which is again consistent with Fig. 3a.
When considering the field snow courses only, the simulated SWE maximum is 20 higher than observed for all three regions ( Fig. 6d-f), and the overestimate is especially pronounced for Eastern Siberia. In contrast, when compared with the forest snow courses, the simulated maximum SWE is slightly too low for the entire Northern Eurasia (Fig. 6g) and for Western Russia (Fig. 6h) and only moderately overestimated for Eastern Siberia (Fig. 6i). Although the geographical distribution of forest and field courses 25 is not identical, this reflects the fact that in reality (but not in ECHAM5), more snow tends to accumulate in forests than on open ground. The delayed snow-off in the REF experiment in central and eastern Siberia is physically consistent with the low temperature bias and high albedo bias in spring. On Introduction

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Interactive Discussion
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | one hand, overestimated surface albedo keeps the absorbed solar radiation low, which favours cold temperatures and delays the onset of snow melt. On the other hand, delayed snow melt provides a positive feedback by keeping the albedo high. Furthermore, too large accumulation of snow in winter contributes to the delayed snow-off in Eastern Siberia (Fig. 6c). Similarly, underestimated albedo and overestimated T 2 in spring in the 5 Taymyr region are consistent with the snow vanishing too early. For Western Russia, however, the main reason for the earlier than observed snow-off dates (Figs. 2c and 3a) seems to be that at least in a domain-average sense, snow melt starts somewhat too early (Fig. 6b). Intriguingly, this occurs in spite of a slightly negative temperature bias in spring (Fig. 4).

Sensitivity experiments
The sensitivity experiments show that both nudging and changes in the treatment of surface albedo have substantial impacts on the snow-off date simulated by ECHAM5 (Fig. 7). Nudging makes snow-off to occur earlier in most of northern Eurasia, with largest effect (over 15 days) in southeastern Siberia and locally in western Finland. The 15 earlier snow-off in REF_NDG is both due to higher temperatures (as discussed below) and due to slightly reduced snowfall in eastern Siberia, as reflected in the seasonal cycle of SWE in Fig. 6c, f and i. However, in the Taymyr region, snow-off is delayed by more than 5 days in REF_NDG as compared with REF (Fig. 7a). Use of observed (CLARA-SAL) albedo in ALB1 likewise makes the snow melt earlier in southeastern 20 Siberia and later in the Taymyr region, with larger impact in the latter (ALB1-REF differences of ≈ −5 days and ≈ 15 days, respectively; Fig. 7b). In general, snow-off is delayed somewhat in the northern parts of Northern Eurasia, and also in central Russia.
For the ALB2 experiment with changed albedo parameterization, snow-off occurs up to 5 days earlier in southeastern Siberia than in REF (Fig. 7c). This is very similar to the 25 ALB1 experiment, and results from the modification of the sky-view factor in the calculation of surface albedo in forested regions. However, due to the increase of the albedo of "warm" snow (T s ≥ 0 • C) from 0.3 to 0.6, snow-off is delayed in the northeastern parts Introduction of the Russian Far East and particularly in the Taymyr region, locally by 5-10 days. This response is qualitatively similar but somewhat weaker than that in ALB1. Finally, when nudging is combined with changed treatment of albedo (ALB1_NDG and ALB2_NDG; Fig. 7c and e), the earlier snow-off in southeastern Siberia and delayed snow-off in the Taymyr region become even more pronounced. In southeastern Siberia, the difference 5 to REF reaches locally −20 days. Figures 8 and 9 compare the snow-off dates in all ECHAM5 experiments with the snow-off dates derived from microwave satellite data and Russian snow course data, respectively. In spite of the inter-experiment differences noted above, all free-running (i.e., non-nudged) simulations show the same basic pattern of differences compared to 10 the satellite data ( Fig. 8): too early snow-off dates in the west, along with regions of delayed snow-off in eastern parts of northern Eurasia. The ALB1 and ALB2 experiments show some improvement in southeastern Siberia, where the positive bias in snow-off date is reduced but not eliminated. Furthermore, the negative bias in the Taymyr region is reduced in the ALB2 experiment with changed snow albedo parameterization, and 15 turned into a slight positive bias in ALB1, which uses observation-based CLARA-SAL albedo data.
Nudging eliminates entirely the positive bias in snow-off date in southeastern Siberia as compared with the satellite data. As a consequence, the REF_NDG experiment features an early bias throughout northern Eurasia (Fig. 8b), with largest biases in 20 the west. Likewise, for the nudged simulations with albedo changes (ALB1_NDG and ALB2_NDG), snow-off generally occurs earlier than in the satellite data, the most notable exception being that for ALB1_NDG, near-zero or even positive differences (i.e., delayed snow-off) appear in the Taymyr region.
It should be recalled that the early bias in snow-off dates compared with the satel- 25 lite data may be, in part, an artifact related to differences in the definition of snow-off time between the ECHAM5 simulations and the satellite data (Sect. 4). Indeed, when compared with the snow course data (Fig. 9), all free-running simulations feature delayed snow-off in eastern Siberia and in the Russian Far East. The differences between

REF, ALB1
and ALB2 are rather small in comparison with their biases with respect to the snow course data. Even for the nudged simulations (REF_NDG, ALB1_NDG, and ALB2_NDG), positive differences indicating delayed snow-off prevail for many measurement stations in Eastern Siberia and in the Russian Far East, although slightly negative differences occur for some stations. In the western parts of Northern Eurasia, 5 however, all simulations feature negative biases, snow-off occurring 10-20 days earlier than in the snow course data for many stations in western Russia. The negative biases are, in general, slightly larger for the nudged simulations, especially in the westernmost parts of Russia. Furthermore, as noted in Sect. 5.1 for the REF experiment, the negative biases are especially pronounced when compared with forest snow courses.

10
The changes in snow-off time are influenced by, and they feed back on, simulated 2 m air temperature (Fig. 10) and surface albedo (Fig. 11) in the sensitivity experiments. For brevity, only mean values over the months of April and May are shown. All experiments feature a cold bias in southeastern Siberia, which amounts down to −7 K in REF (Fig. 10a). Consistent with the earlier snow melt (Fig. 7), this bias is reduced in ALB1 15 (Fig. 10c) and ALB2 (Fig. 10e), and especially in the nudged experiments (Fig. 10b, d and f). A slight negative temperature bias (≈ −2 to −1 K) prevails in large parts of western and central Russia, and this feature varies only slightly between the experiments. Positive temperature biases are seen in all experiments in the Taymyr region and in parts of the Russian Far East. 20 Figure 11 displays surface albedo differences from the CLARA-SAL data for the REF, REF_NDG, ALB2 and ALB2_NDG experiments (for ALB1 and ALB1_NDG, the differences are zero by construction). It is seen that the high albedo bias in southeastern Siberia is reduced substantially in both REF_NDG and ALB2, and it is eliminated completely in ALB2_NDG. In the case of ALB2 and ALB2_NDG, the modified computation 25 of sky-view factor in the albedo parameterization for forested regions contributes to this. For REF_NDG, however, the change in surface albedo stems entirely from changes in meteorological conditions, the reduced negative temperature bias (Fig. 10b) leading to both lower snow albedo and reduced snow cover. However, all four experiments show 3689 some common biases, most distinctly an underestimation of albedo compared to the CLARA-SAL data in the northern parts of Northern Eurasia and in the Russian Far East. Interestingly, the use of a higher value for the albedo of "warm" snow (0.6 instead of 0.3 when T s ≥ 0 • C) in the ALB2 and ALB2_NDG experiments reduces somewhat the negative bias in the Taymyr region but does not eliminate it. Given that the Taymyr re-5 gion is almost completely snow-covered in May in the model simulations, this suggests that even the value of 0.6 is too low at least in this region.

Discussion
The analysis of the sensitivity experiments in Sect. 5.2 showed that nudging and changes in the treatment of surface albedo in the presence of snow alleviated some of 10 the model biases in snow-off dates, 2 m temperature and surface albedo. Nevertheless, many of the biases seen in Figs. 8-11 are quite similar for all experiments. Regarding the timing of springtime snow-off, the results are somewhat ambiguous for the eastern parts of Northern Eurasia, due to large differences between observational snow-off date estimates from satellite and snow course data, and hence in the resulting model 15 biases. For western Russia, however, comparisons with the satellite data and the snow course data indicate unanimously that snow-off occurs too early in ECHAM5 for all experiments, with only moderate variations due to nudging or changes in the treatment of surface albedo (Figs. 8 and 9). Moreover, surprisingly, the too early snow-off co-occurs with a slight negative temperature bias in the snow-melt season (Fig. 10). 20 To shed more light on the seemingly contradictory biases in temperature and snowoff dates, a detailed comparison of ECHAM5 results with observations at Sodankylä in Finnish Lapland is represented. The black line in Fig. 12a displays the mean seasonal cycle of snow depth measured at Sodankylä in 1979-2006, for days of year 1-165 (i.e., from 1 January until 14 June). The other curves show the corresponding seasonal cycle from the AVHRR-based CLARA-SAL dataset, the timing of snow melt coincides well with the observations. Figure 12b shows a comparison for the seasonal cycle of 2 m air temperature. From mid-March (day 75) onwards, all ECHAM5 simulations underestimate the average T 2 systematically. The average underestimate in the primary snow melt season (mid-April 10 to mid-May; days 105-135), is ≈ 1.8 K for REF, REF_NDG and ALB2, and ≈ 3.5 K for ALB1. Thus the Sodankylä site represents a case where snow melt (and snow-off) occurs earlier in ECHAM5 than in the observations, in spite of a negative temperature bias in the snow melt season.
The problems with representing correctly the relationship between snow melt timing 15 and temperature become even more obvious, when the temperature data are composited with respect to the snow-off date. Thus, for each year in 1979-2006, the snow-off date ("day 0") was defined as the first day after the winter's snow maximum completely without snow (in ECHAM5) or with snow depth equal to zero in the morning (in the observations), and the average T 2 was computed for each day in the range from 45 days 20 before snow-off to 15 days after snow-off (Fig. 12c). Note specifically that as "day 0" represents the first completely snow-free day, snow actually vanishes sometimes during "day − 1", and "day − 2" is (generally) the last day with snow persisting throughout the day. It is clear from Fig. 12c that ECHAM5 substantially underestimates T 2 in the snow 25 melt season. Strikingly, this depends quite little on the experimental details such as nudging or changed treatment of surface albedo. The negative bias in T 2 culminates just before snow-off, being ≈ −7 K on "day − 2". Furthermore, it is noted that in ECHAM5, the average T 2 reaches 0 • C as late as "day − 1", during which the snow vanishes in 3691 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the model. In the observations, the average T 2 reaches 0 • C already on "day − 20", and climbs to 7 • C by "day − 1". It is further seen that in ECHAM5, there is a substantial jump in temperature from "day − 2" (the last day with snow throughout the day) to "day 0" (the first completely snow-free day), 2.9-3.9 • C depending on the experiment, whereas the observed change is only 1.0 • C. A similar composite analysis of temperature with 5 respect to snow-off date was repeated for ECHAM5 for the entire northern Eurasia, and it confirmed that the behaviour seen in Fig. 12 is quite universal. In particular, throughout the region, the average T 2 stayed below 0 • C until and including "day − 2" (not shown). The likely main reason for the fact that T 2 simulated by ECHAM5 stays close to 10 0 • C in the snow melt season is that the surface energy budget (and hence surface temperature) is not computed separately for the snow-free and snow-covered parts of the grid cell. Rather, while snow cover fraction is taken into account in defining grid-mean properties like surface albedo and roughness length, a single snow-covered energy balance computation is performed (Eq. 1). 15 As explained in Sect. 2.1, the amount of snow melt is determined from the condition that, when the surface temperature T s would rise above 0 • C without considering snow melt, the heat consumed in melting snow restores T s to 0 • C (Eq. 2). Here, T s refers to the grid-mean surface temperature, not the temperature of melting snow. Therefore, as long as there is any snow left in the grid cell, T s is not allowed to rise above 0 • C, 20 irrespective of the snow cover fraction. Naturally, this acts to suppress the sensible heat flux (or even makes it negative), so 2 m air temperature cannot rise much above 0 • C either. In reality, in a region with partial (patchy) snow cover, surface temperature is kept to zero only in the patches of melting snow. In the snow-free patches, T s , and consequently, T 2 , can rise substantially above 0 • C. Furthermore, local temperature 25 advection from snow-free to snow-covered patches and subsidence associated with a "snow breeze" circulation can increase T 2 over the latter (e.g., Yamazaki, 1995;Liston, 1995).

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | In summary, the use of a single surface energy budget computation leads to a misrepresentation of grid-mean surface fluxes in the presence of fractional snow cover (Liston, 2004): too much energy is spent in melting snow, and too little in warming the air and the ground. Consequently, T 2 stays too low in the snow melt season (Fig. 12c). This likely explains why ECHAM5 features a persistent cold bias in springtime T 2 even 5 in regions where snow-off occurs earlier than observed (Figs. 8-10).
In addition, there is another factor related to the treatment of surface energy budget that may contribute to the too early snow-off: ECHAM5 does not include a canopy layer. In ECHAM5, forests influence the energy budget through changing the surface albedo and roughness length, but, for example, the shading of the surface by the canopy is 10 not considered. Since forests reduce the surface albedo in the presence of snow (or more precisely, the combined albedo of the surface and the canopy) in ECHAM5, this implies that the amount of solar radiation available for snow melt at ground is increased in forests. In reality, the opposite happens, which explains delayed springtime snowmelt in forests relative to non-forested areas (Strasser et al., 2011). This may explain why, in 15 comparison with the snow course data, ECHAM5's tendency toward too early snow-off is more pronounced for forest than field measurements (Fig. 3b-c).
Recently, Brutel-Vuilmet et al. (2013) found that, while there is still substantial intermodel dispersion among the CMIP5 models, on average the spring-time snow melt is slightly delayed in Northern Eurasia. Taken at face value, the default version of 20 ECHAM5 agrees with this result for the eastern parts of Northern Eurasia, while in the west, snow vanishes too early (Figs. 2 and 3). However, such regional features are not discussed in Brutel-Vuilmet et al. (2013), and moreover, a rigorous comparison with their results is difficult due to the different datasets and analysis methods used (e.g., Brutel-Vuilmet et al., 2013, used only monthly data). An interesting question for further 25 research is how well the CMIP5 models are able to represent the relationship between spring-time temperature and snow-off timing. In particular, is the problem of snow melt occurring at too cold grid-mean temperatures, as demonstrated in the current study, an exception or the rule for the CMIP5 models? 3693

Conclusions
In the present work, we have evaluated the timing of springtime snow-off in Northern Eurasia in the ECHAM5 (version 5.4) atmospheric GCM. Simulated snow-off dates were compared with a snow-off date dataset based on space-borne microwave radiometer measurements and with Russian snow course data. The primary conclusions 5 are as follows: -In general, the default version of ECHAM5 reproduces well the observed geographic pattern of snow-off dates, with earliest snow melt (snow disappearing in March) in the Baltic region, and latest snow melt (in June) in the Taymyr region and parts of the Russian Far East. However, compared to the satellite data, 10 snow-off occurs too early in the western parts of Northern Eurasia, and also in the northernmost regions like the Taymyr peninsula, with largest differences (locally over 20 days) in Northern Europe. On the contrary, in southeastern Siberia and in some far eastern parts of Russia, snow melts locally over 10 days later than in the satellite data. Comparison with the Russian snow course data confirms the 15 pattern of too early snow-off in the west and too late snow-off in the east, although the former is slightly less pronounced, and the latter more pronounced, than in the corresponding comparison with the satellite dataset.
-The later than observed snow-off in southeastern Siberia is associated both with overestimated snow accumulation during winter and a springtime cold bias, which 20 exceeds −6 K in April. The latter is, in part, related to an overestimation of surface albedo, which has been ascribed to insufficient shadowing of the snow surface by the canopy in ECHAM5 in the dormancy season of deciduous needleleaf trees. In contrast, surface albedo is underestimated in late spring especially in the Taymyr region, probably because an unrealistically low albedo (0.3) is assumed 25 for "warm" snow (T s ≥ 0 • C). This promotes too early snow-off in this region. -Several sensitivity experiments were conducted, where biases in simulated atmospheric circulation were corrected through nudging and/or the treatment of surface albedo was modified. Both nudging and surface albedo modifications alleviated some of the model biases in snow-off dates, 2 m temperature (T 2 ) and surface albedo. In particular, it proved possible to reduce substantially the biases 5 in snow-off date in southeastern Siberia and in the Taymyr region. In contrast, the early bias in snow-off in the western parts of northern Eurasia was not reduced appreciably in any of the experiments; rather it was slightly increased by nudging. Furthermore, surprisingly, this early bias in snow-off was accompanied by a slight negative bias (≈ −2 to −1 K) in springtime T 2 , both for the default version 10 of ECHAM5 and for the sensitivity experiments.
-The combination of a too early snow-off with a cold springtime temperature bias implies that temperature stays too low in the snow melt season. In fact, as long as there is any snow left on the ground, the daily-mean T 2 simulated by ECHAM5 rarely rises above 0 • C. In contrast, as demonstrated for the Sodankylä site in 15 Finnish Lapland, the observed daily-mean T 2 typically climbs several degrees above 0 • C before all snow has vanished.
-The likely main reason for the fact that T 2 in ECHAM5 stays close to 0 • C in the snow melt season is that the surface energy budget (and hence the surface temperature T s ) is not computed separately for the snow-free and snow-covered parts 20 of the grid cell. Thus, even if the diagnosed snow cover fraction is well below 1, the grid-mean T s is not allowed to rise above 0 • C. This acts to suppress the sensible heat flux (or even makes it negative), so T 2 cannot rise much above 0 • C either, and leaves too large a fraction of the grid-mean surface net radiation to be consumed in melting snow.

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-There is another factor related to the treatment of surface energy budget, which also likely contributes to the too early snow-off: ECHAM5 does not include a canopy layer. Thus, in particular, the shielding of snow on ground by the 3695 model may either improve or deteriorate the agreement with observations. An example of this is that for ECHAM5, the general tendency towards too early snow-off becomes clearer when biases in atmospheric circulation and temperature are corrected by nudging. This exposes more clearly the problems related to the treatment of surface energy budget, especially in the presence of partial snow cover and forests. Beyond that, an 15 obvious area for further development would be the snow scheme itself, which is rather simplistic in ECHAM5. Only the SWE and snow temperature are computed, with no consideration of snow density and snow grain size. Furthermore, the temperature dependent snow albedo scheme in ECHAM5 is very simple and, as demonstrated in this and previous work, to some extent unrealistic. 20 Finally, according to our preliminary tests, snow melt also occurs at too low (gridmean) temperatures in the Max Planck Institute's newest atmospheric GCM, ECHAM6 (Stevens et al., 2013). Like ECHAM5, ECHAM6 does not define separately the surface temperature for the snow-free and snow-covered parts of a grid cell. It is an intriguing question to which extent this issue pertains to other global and regional climate models.
In the Russian snow course data (Bulygina et al., 2011a), SWE measurements are typically provided at 10 day intervals in winter and 5 day intervals in spring (starting from March or April). A major issue in defining the snow-off date based on these data is, 5 however, that in the absence of snow, SWE measurements are generally not reported. Thus one cannot always be sure whether missing data indicates that there is no snow left to be measured, or that the measurement was not performed for some other reason. To define the snowmelt date, we adopted the following procedure.
1. The observation date with maximum SWE (d max ) for the winter was located. 10 2. The part of the SWE timeseries after d max was studied, and cases were sought in which a valid measurement of SWE was followed by missing data, with the corresponding dates denoted by d miss−1 and d miss .
3. In such cases, it was assessed whether the missing data could plausibly indicate the absence of snow. For this end, we evaluated the statistics of SWE changes 15 between two observation times (either 5 or 10 days apart from each other) within one month of the date in question, considering all years for which the station reported data. If the change in SWE from d miss−1 to d miss required for all snow to melt by the time d miss (i.e., ∆SWE_required = −SWE miss−1 ) was within two standard deviations (σ ∆SWE ) of the mean value (∆SWE) of SWE changes for the time 20 of the year, that is, it was assumed that the missing SWE value at day d miss indicates the absence of snow (SWE miss = 0). 4. If the missing value was deemed to be zero, all subsequent missing values were also interpreted as zero, until (possibly) a positive SWE value was found.
5. After the SWE time series was corrected as outlined above, the snow-off date was determined. Data for three observation days were used: the first observation day (d zero ) with corrected SWE = 0 after the winter's SWE maximum (d max ), and the 5 two observation days preceeding it with SWE > 0 (denoted as d m2 and d m1 , with SWEs of SWE m2 and SWE m1 , respectively). If linear extrapolation based on the values SWE m2 and SWE m1 suggested all snow to have melted before d zero , the snow-off date was computed as 10 otherwise, it was assumed that d snow-off = d zero .
6. Finally, if the SWE reached values higher than 20 kg m −2 after the determined snow-off date, the case was considered suspicious; thus this winter's data for this snow course were ignored in further analysis. Cases in which the above algorithm 15 failed to find a snow-off date were likewise ignored in the subsequent analysis.
Clearly, the above algorithm involves some arbitrary choices (especially the criterion of 2 standard deviations in Eq. (A1) and the limit of 20 kg m −2 in step (6) of the algorithm). However, a number of sensitivity tests were conducted regarding the choice of these parameters, and it was found that the statistics of model vs. observation differ-20 ences were largely insensitive to them. For example, changing the criterion of 2 standard deviations in Eq. (A1) to either 1 or 3 standard deviations changed the average model vs. observation difference in snow-off dates by less than 1 day. Lastly but importantly, to compare ECHAM5's snow-off dates with the snow course data as consistently as possible, the simulated SWE time series were first subsampled 25 according to the availability of the snow course data (i.e., including only the days with 3698 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |