Land surface insulation response to snow depth variability

Transcription

1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jd012798, 2010 Land surface insulation response to snow depth variability Yan Ge 1 and Gavin Gong 1 Received 7 July 2009; revised 16 November 2009; accepted 7 December 2009; published 27 April [1] The existing literature on heat diffusion through a snow covered land surface deals primarily with snow cover presence or duration; however, the insulation property of a snowpack can vary substantially owing to the changes in snow thickness. Using SNTHERM, a one dimensional snowpack energy and mass balance model, we have isolated the heat diffusion response to varying initial snow depths, including snow free conditions, and assessed the magnitude of associated temperature and insulative energy flux anomalies within the entire snowpack soil column system. A clear and substantial land surface insulative response to snow depth is identified over hourly, intraseasonal, and interannual time scales. The overall snow soil system warms with increasing snow depth, but the surface snow layer cools slightly, generating decreased ground heat flux and increased sensible heat flux responses. This land surface thermal response is attributable to the increased insulative capacity of deeper snowpacks, which makes the underlying soil less responsive to solar radiation and air temperature fluctuations, and facilitates sustained warming by the bottom soil layer boundary. Furthermore, the overall effect of increasing snow depth due to insulation is comparable in magnitude to the effect of snow presence versus snow absence due to albedo. Citation: Ge, Y., and G. Gong (2010), Land surface insulation response to snow depth variability, J. Geophys. Res., 115,, doi: /2009jd Introduction 1.1. Background [2] A considerable body of research has explored the atmospheric consequences of anomalous land surface snow cover. For example, a near surface air temperature suppression associated with snow covered land has been well documented [e.g., Baker et al., 1992; Ellis and Leathers, 1999; Gong et al., 2004; Mote, 2008]. This local atmospheric response also propagates into overlying flow regimes and affects large scale circulation patterns, such as the Asian monsoon [Douville and Royer, 1996; Bamzai and Shukla, 1999] and the Arctic Oscillation [Cohen and Entekhabi, 2001; Gong et al., 2002], and even overall hemispheric climate [Barnettetal., 1989; Watanabe and Nitta, 1998]. [3] These local and remote climatic consequences are, of course, initiated by a more immediate snow forced change in the land surface energy balance, that is, energy fluxes acting on the surface, and temperatures within the snowpack and soil column. Thus, a detailed understanding of the thermodynamic impact of snow on the energy balance and thermal states within the land surface itself is of interest and serves as a foundation for characterizing, attributing, and quantifying the subsequent atmospheric and climatic 1 Department of Earth and Environmental Engineering, Columbia University, New York, New York, USA. Copyright 2010 by the American Geophysical Union /10/2009JD response. The goal of this study is therefore to provide a more detailed understanding of the land surface thermodynamic response to snow cover. [4] The shortwave radiation response to snow cover due to surface albedo changes is traditionally accepted as the dominant mechanism of snow forcing at the land surface [e.g., Cline, 1997; Marshall et al., 2003]. Other studies suggest that the insulating effects of snow cover on diffusive heat fluxes and the latent heat flux associated with snowmelt may also contribute to the overall surface energy balance response [Cohen, 1994]. The potential influence of multiple processes is more apparent when the depth of snow on the ground is considered as well as its presence or absence. The presence of a thin snow cover will dramatically influence the surface albedo but may not provide substantial insulation or snowmelt. Conversely, surface albedo increases asymptotically with a progressively thicker snow cover (owing primarily to increased fractional snow coverage on vegetated surfaces), whereas the insulation provided by thicker snow and the amount available for snowmelt can increase dramatically. [5] This study focuses on the insulative property of varying snow depth in an effort to establish this specific relationship as a substantial contributor to the overall land surface energy balance response to snow cover. The scientific literature on heat diffusion through a snow covered land surface deals primarily with snow cover presence or duration [Goodrich, 1982; Gosnold et al., 1997; Schmidt et al., 2001; Ling and Zhang, 2003], although some studies have recognized a measurable influence of snow thickness 1of11

2 snow depth increases; that is, the response is asymptotically nonlinear. [9] This conceptual model illustrates that the expected insulative response to increasing snow depth amounts to simple nonlinear warming, owing to diffusive heat flux acting over a greater distance subject to the same thermal boundary conditions. Three questions arise from this simple conceptualization: (1) Does the same behavior hold for more realistic situations? (2) Is the magnitude of the snowpack and soil column warming appreciable for a typical range of snow depth values? (3) How does the response to increasing snow depth compare against the response to the presence versus absence of a snowpack? A focused set of modeling experiments is presented here to address these questions. Figure 1. Conceptualized insulative response to varying snow depth. and its insulative capability [Smith and Riseborough, 1996; Gong et al., 2004; Grundstein et al., 2005]. A modeling approach is employed here to gain further insight by isolating the heat diffusion response to varying initial snow depths including snow free conditions and by assessing the magnitude of associated temperature and insulative energy flux anomalies within the entire snowpack soil column system Conceptualization [6] In order to help conceptualize the insulative effects of snow depth, an idealized multilayer snow soil system is depicted in Figure 1. For this hypothetical system, heat between individual layers is transferred solely by diffusion, and all snowpack and soil layers have the same thermal properties. The thickness of the snowpack varies, but the system is always constrained by the same fixed atmospheric and lower soil temperature boundary conditions. [7] Clearly, this idealization yields a simple linear temperature profile throughout the snow soil system. As illustrated in Figure 1, thicker snowpacks have higher snowpack and soil temperatures throughout the system, as a direct consequence of fixed upper and lower boundary conditions but with the upper boundary rising in elevation as snow depth increases. Thicker snow also has a smaller vertical temperature gradient throughout the snow soil column. At the snow soil interface, this results in a smaller rate of heat transfer from soil to snow, that is, a reduced ground heat flux term in the surface energy balance. [8] Note in Figure 1 that the average temperature of the uppermost layer of the snowpack cools slightly with greater snow depth as a result of the smaller temperature gradient, even though the snowpack as a whole warms. Sensible heat increases with snow depth as a result; that is, the upward sensible heat for this idealization decreases in magnitude. For all affected surface energy balance parameters, the magnitudes of the incremental responses diminish as the 2. Approach 2.1. SNTHERM Model [10] Modeling experiments are conducted using SNTHERM [Jordan, 1991], a one dimensional mass and energy balance snowpack model developed by the U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL). SNTHERM has been widely used in civil, military, and research programs for simulating the temporal evolution of snowpack properties and processes such as depth, accumulation, ablation, densification, and metamorphosis, in response to varying prescribed meteorological conditions. For example, the model is used by the National Weather Service s (NWS) National Operational Hydrologic Remote Sensing Center (NOHRSC) as part of its snow data assimilation system [Cline and Carroll, 1999]. In this study, a principal application will be to use SNTHERM in an inverse manner to evaluate the insulative response to different prescribed snow depth conditions. [11] In the SNTHERM model, snow and soil layers are divided into horizontally infinite control volumes with vertically homogeneous physical properties. Each layer is controlled by the governing equations for mass, momentum, and heat balance, subject to meteorological boundary conditions at the snow air interface (such as air temperature, wind speed, relative humidity, precipitation, and cloud cover) and a temperature boundary condition at the lowest soil layer. The model s initial conditions consist of temperature, density, grain size, and water content for various snow and soil layers. [12] The outputs of SNTHERM are thickness, temperature, phase, density, grain size, effective specific heat, and thermal conductivity for each model layer. The energy fluxes acting on the snowpack are S ¼ SW þ LW þ SH þ LH þ R þ GH; where S is the net energy flux (W m 2 ), SW is the net shortwave radiation, LW is the energy flux of longwave radiation, SH is the turbulent flux of sensible heat, LH is the turbulent flux of latent heat, R is the heat convected by rain or falling snow, and GH is the ground heat flux. GH is at the bottom of the snowpack, and all other energy terms are at the surface of the snowpack. The surface energy fluxes are defined as positive downward, and positive GH is from soil to snow (upward). Only SW can penetrate into the snowpack. Energy transfer between nodes in the interior of the ð1þ 2of11

3 Figure 2. Observed daily snow depth (SND) from the Global Historical Climatology Network (GHCN) and SNTHERMmodeled daily snow depth output at Minneapolis St. Paul International Airport for the snow season. snowpack is attributed to SW flux absorbed by snow, water, and vapor flux between layers and heat conduction due to temperature gradient of adjacent layers. [13] Previous studies have shown that SNTHERM does a good job of modeling snowpack conditions including both snow depth and snow density [e.g., Grundstein et al., 2005]. By comparing SNTHERM derived energy fluxes with measured data and aerodynamic profiles, previous research has indicated that SNTHERM provides accurate estimates of energy fluxes and appropriate representations of physical snowpack processes [e.g., Cline, 1997; Grundstein and Leathers, 1997; Ellis and Leathers, 1999]. SNTHERM applications have fully characterized these processes under varying conditions, including parameters for which observations were not readily available, such as thermal resistance [Grundstein and Leathers, 1999; Grundstein et al., 2005] Data [14] Minneapolis St. Paul International Airport, Minnesota (44.87 N, W), is used as the study site because of its historically reliable snow season duration and robust statistical relationships with local temperature [Cayan et al., 1996; Ge et al., 2009]. SNTHERM is run on the same hourly time step as the driving meteorological variables, which are obtained from the Unedited Local Climatological Data Hourly Observations Table provided by the National Climate Data Center (NCDC). An 11 year record is available for the study station, from hydrological year to Atmospheric boundary conditions, such as air temperature, relative humidity, and wind speed, are measured at 2 m above the ground. A soil temperature boundary condition of 277 K is applied at 4 m below the ground surface throughout all simulations. Daily precipitation and snow depth data, obtained from the Global Historical Climatology Network (GHCN Daily; oa/climate/ghcn daily/), are used to validate the SNTHERM outputs Validation of the SNTHERM Model [15] SNTHERM does a reasonably good job of modeling snowpack conditions at the study site. The correlation between the 11 year simulated daily snow depth (SND) and the observational SND from GHCN is strong and statistically significant (r = 0.89, p < 0.001). The time series of the observed and simulated SND are shown in Figure 2, using year as an example. SNTHERM by and large captures the general features of snow accumulation and ablation processes observed in the GHCN daily data. In general, SNTHERM replicates the major snow accumulation events during the snow season, and the overall snow ablation rates of the entire season from the observed data and the simulated results exhibit a good agreement. [16] A general underestimation of SND is observed, and such discrepancy exists throughout the 11 year simulation. The disagreement between observed and modeled SND is attributed, in part, to the fact that daily precipitation amounts reflected in the NCDC hourly input data are generally smaller than that for the GHCN validation data. Hourly trace values below detection limit in NCDC are treated as zero precipitation in the simulation but accumulate and contribute to the daily snow depths provided by GHCN. Another reason is the undercatch of snowfall by the NCDC input data, due to the effect of wind and wetting loss. Legates and DeLiberty [1993] estimated that for much of the United States, the resulting error in snowfall measurement often exceeds 25 percent. Bias adjustments have been developed and applied to SNTHERM [Mote et al., 2003]. However, such corrections are not utilized in this study, which focuses on the relative changes of temperature/energy fluxes as a function of snow depth, rather than their absolute values. [17] Another apparent discrepancy arises from the fact that the GHCN daily SND data used for model validation are provided in discrete intervals of m (1 inch). As a result, interstorm snowpack ablation appears as abrupt step changes for the GHCN data, in contrast to the more gradual daily ablation produced by SNTHERM. Taking this factor into consideration, SNTHERM appears to capture observed interstorm ablation rates and the overall seasonal ablation rate in Figure 2, which suggests that the model is effectively simulating snow density changes and metamorphosis at this site. Overall, the SNTHERM model validation is sufficient for conducting the SND perturbation experiments presented here Methodology [18] Three sets of experiments are conducted to evaluate the land surface insulative response to snow depth over diurnal, intraseasonal, and interannual time scales. Compared to the conceptualization presented in Figure 1, this set of simulations reflects increased complexity and realism, in that temporally varying atmospheric boundary conditions are applied, a full surface energy balance is computed including radiative terms, and heterogeneous snow and soil layer properties are applied. Furthermore, the specific atmospheric boundary condition applied in each of the experiment sets represents a different degree of atmospheric complexity. However, all experiments isolate the insulation response to snow depth from other processes. For example, SNTHERM does not account for spatial heterogeneity due to vegetation cover, so the surface albedo response to snow depth via fractional snow coverage is minimized. Also, all experiments focus on the winter season, where temperatures 3of11

4 Figure 3. The 10 day averages (days 41 50) of (a) temperatures within the snow soil system and (b) thermal resistance (TR), for Experiment 1. The x axis represents six different initial SND conditions (SND0 to SND0.5). are consistently below freezing, so the latent heat flux response to snow depth is minimized. [19] 1. In Experiment 1 a set of six simulations under idealized boundary conditions is performed to isolate the energy and temperature responses due to initial snow depth perturbations. The six initial snow depth conditions (0.0, 0.1, 0.5 m, hereinafter denoted as SND0, SND0.1, SND0.5) reflect a realistic range of snow depths at the study site. In these simulations the hourly meteorological conditions of 7 January 2008 are repeated for 50 days, representing a typical cold and dry winter day. The controlled and repeated atmospheric boundary conditions in Experiment 1 facilitate an analysis of the diurnal cycle response to snow depth. Precipitation is fixed at zero throughout the simulations, so that no more snow is added besides the prescribed initial snow depths. Hence the SND0 simulation remains snow free throughout, allowing for an explicit comparison of the effects of snow depth versus the presence of snow. The six simulations can be placed into three categories, with absent (SND0), thin (SND0.1), and thicker (SND0.2 SND0.5) snowpack. [20] 2. In Experiment 2 another set of simulations is conducted with different initial snow depths from 0.0 to 0.5 m. However, in this experiment each simulation is run from 1 December 2007 to 29 February The same 91 day observed meteorological time series (e.g., air temperature, humidity, wind conditions, and precipitation) are applied as boundary conditions for each of the six simulations. The inclusion of observed precipitation inputs throughout the simulations means that even the SND0 scenario will have a snowpack, since air temperatures are consistently below zero during this winter simulation so that precipitation falls as snow. The 91 day winter season duration of Experiment 2 captures the intraseasonal variability in atmospheric conditions, in addition to hourly variations. [21] 3. In Experiment 3 the SNTHERM model has been typically used to simulate the temporal evolution of a snowpack. A similar application is conducted in this experiment by applying historical snow and climate records as initial/ boundary conditions over an 11 year ( to ) period to look for interannual relationships between snow depth and the responses of temperature and associated energy fluxes. Thus Experiment 3 captures interannual variability in addition to intraseasonal and hourly variability. 3. Results 3.1. Experiment 1: Repeated Day Simulations With Different Initial SND [22] Snowpack temperature, surface snow temperature, soil column temperature, topmost soil temperature, and thermal resistance are averaged from days 41 to 50 and plotted with respect to the six different initial SND conditions (Figure 3). The results of the final 10 days of the simulation (days 41 50) are presented to allow the model to reach a pseudoequilibrium state for the simulated days. The snowpack (soil column) temperature is computed as the thickness weighted average of snow (soil) temperature at each layer. The topmost soil temperature is the temperature at the topmost soil layer, which extends to 3 mm below the land surface. [23] Thermal resistance (TR, Km 2 W 1 ) is a parameter used to describe the insulation capacity of a snowpack [Zhang et al., 1996]. TR i, the thermal resistance at each layer, is computed as TR i = H i /K i, where H i is the thickness of a snow layer (m) and K i is the thermal conductivity (W m 1 K 1 ). For a series system the total thermal resistance is TR = PN TR i, where N is the total number of layers. TR is i¼1 directly proportional to SND through H i but inversely proportional to SND through K i, which is related to snowpack density; thus, TR generally increases with SND. [24] Figure 3a shows that snow and soil temperatures warm nonlinearly with snow depth throughout the system 4of11

5 Figure 4. The 10 day averages (days 41 50) of (a) ground heat flux (GH), (b) sensible heat flux (SH), (c) shortwave radiation (SW), (d) longwave radiation (LW), and (e) latent heat flux (LH), for Experiment 1. The x axis represents six different initial SND conditions (SND0 to SND0.5). except for at the snow surface, where temperatures cool slightly. Figure 3b indicates that TR increases with SND, suggesting a minimal influence by density changes associated with thicker snowpacks. Thus increased SND translates into greater insulative capacity, allowing more of the upward heat conduction from the lower soil boundary to be retained in the snow soil system. This results in warming throughout the snowpack and soil column except at the snow surface, consistent with the premise drawn from the conceptual insulation model (Figure 1). [25] Note in Figure 3a that the topmost soil temperature difference varies substantially across the six simulations (T SND0.5 T SND0 = 5.7 K). Furthermore, the difference between thick and thin snow (T SND0.5 T SND0.1 = 2.5 K) is close to the difference between thin snow and bare ground (T SND0.1 T SND0 = 3.2 K). The soil temperature difference induced by snow depth changes is attributable primarily to added insulative capacity, whereas the temperature discrepancy caused by snow presence/absence is attributable primarily to the high albedo of snow covered ground. A similar observation holds for the soil column average temperature. Therefore, snow thickness exerts an insulative influence on soil temperature that is considerable and comparable in magnitude to the radiative influence of snow presence. [26] The 10 day averages of surface energy flux terms from days 41 to 50 are plotted with respect to different initial SND in Figure 4. Consistent with the Figure 1 conceptualization, a thicker snowpack nonlinearly reduces the rate of ground heat transfer from underlying soil (Figure 4a), owing to the warmer snow soil system (Figure 3a), and increases the rate of sensible heat transfer from the atmosphere (Figure 4b), owing to the cooler snow surface (Figure 3a). The change in ground heat flux induced by SND anomalies is substantial in magnitude; that is, GH SND0.1 GH SND0.5 = 6.6Wm 2, which represents a roughly 60% decrease from the GH SND0.1 value (10.6 W m 2 ). The change in sensible heat flux is more modest; that is, SH SND0.5 SH SND0.1 = 1.7 W m 2, which represents a roughly 5% increase from the SH SND0.1 value (35.9 W m 2 ). Shortwave radiation, longwave radiation, and latent heat changes with SND are negligible in comparison Figures 4c, 4d, and 4e indicating the predominant roles of ground heat and sensible heat in the SND driven land surface thermal response. Note that SND0 is not included in Figure 4 since the energy exchange for this simulation does not occur within the snowpack. [27] Hourly variations of topmost soil temperature, snowpack temperature, and ground heat flux are plotted in Figure 5. For each hour within a day, values are averaged over a 10 day period from days 41 to 50. Topmost soil temperature (Figure 5a) exhibits a clear diurnal cycle for bare ground, in response to the atmospheric boundary, that is, to air temperature and incoming solar radiation changes. The existence of a snowpack warms up the soil, dampens the amplitude of the soil temperature s diurnal oscillation, and delays the afternoon peak temperature. Thicker snowpacks further warm the soil and suppress and lag its diurnal temperature cycle. For SND0.5, the topmost soil layer exhibits only a slight diurnal cycle. Figure 5a also shows 5of11

6 Figure 5. Diurnal variation of (a) topmost soil temperature, (b) snowpack temperature, and (c) GH, for Experiment 1. For each hour, temperatures and GH are averaged from days 41 to 50. that the diurnal temperature response to a thicker snowpack (SND0.5 versus SND0.1) is comparable to the diurnal response to the presence of snow (SND0.1 versus SND0). [28] Figure 5b shows that the snowpack exhibits a diurnal temperature cycle for all snow depths. As for the soil, thicker snowpacks exhibit warmer temperatures and more suppressed and lagged diurnal cycles (Figure 5a). However, the sensitivity of snowpack s diurnal cycles to SND is far less than that for the soil, owing to the relatively large thermal conductivity of snow. Even for SND0.5, the snowpack still exhibits an appreciable diurnal cycle. Hence, the presence and thickness of snow progressively decouples the atmospheric boundary forcings from the underlying soil, so that the snowpack responds to the diurnal forcing more so than to the soil. [29] The direction and magnitude of ground heat flux are decided by the temperature gradient at the snow soil interface. At night when air temperature is low, the snowpack cools via upward sensible heat and longwave radiation flux, and this energy loss is compensated via diffusion from the underlying soil, so the direction of ground heat flux is from soil to snow (positive in Figure 5c). During the daytime, solar radiation and rising air temperature warm the snowpack, and the lower snow layers gradually start to release heat underground, as indicated by a negative ground heat flux in Figure 5c. In general, the GH diurnal cycle magnitude diminishes with SND, since it results from soil and snowpack temperatures whose diurnal cycles also decrease with SND. [30] Figure 5 suggests a second insulative function of a snowpack, namely, a mitigation of the thermal responsiveness of the soil to the atmospheric boundary conditions (e.g., the shortwave radiation and air temperature variability). This suppression of surface influence helps to facilitate the primary insulative function of the snowpack; that is, warming of the snow soil system occurs more consistently throughout the course of the day. Thicker snow contributes to both the overall warming and the diurnal suppression, to a degree comparable to the snowpack presence Experiment 2: Intraseasonal Simulations With Different Initial SND [31] An entire 91 day winter season is simulated in Experiment 2, rather than a single dry winter day repeated 50 times as in Experiment 1. This allows for an analysis of the intraseasonal variability of snow depth s influence on the insulation process, for example, the maximum extent of the surface temperature response that can be expected over the course of a season. The 10 day running means of snow depth, air and snowpack temperature, and topmost soil layer temperature are plotted in Figure 6. Thicker snowpacks yield higher temperatures in both the snow and soil, consistent with the conceptual model and Experiment 1. Snowpack temperature follows the same temporal pattern as air temperature variations (Figure 6b), but values are consistently higher than the overlying air temperature because of ground heat supply from the underlying soil. Meanwhile, the range of snowpack temperatures over the course of the season is less than that for air temperatures, and this range decreases with increasing snow depth owing to snowpack s insulative heat capacity. Similarly, thick snow has warmer and less variable soil temperature at the topmost soil layer (Figure 6c). 6of11

7 Figure 6. The 10 day running means of (a) snow depth, (b) air and snowpack temperature, and (c) topmost soil layer temperature at z = 3 mm, for Experiment 2 for six simulations with different initial snow depth conditions (SND0 to SND0.5). [32] The temperature changes across the six simulations vary considerably over the course of the season, reaching magnitudes of T SND0.5 T SND0 = 2.9 K for the snowpack temperature and T SND0.5 T SND0 = 4.8 K for the soil temperature. Note that these differences cannot be directly compared to those for Experiment 1, since the SND0 scenario is not snow free in Experiment 2. Likewise, the response to snow depth versus snow presence cannot be distinguished in Experiment 2. However, T SND0.5 T SND0 for Experiment 2 does portray the full range of the temperature response to insulation changes among the snow depths simulated here, which is upward of 5 K. As can be seen in Figure 6c, this response magnitude is approximately the same as the temporal range of soil temperature values that occur over the course of the snow season for the SND0 simulation (5.9 K). [33] Figure 7 shows the 10 day average temperature profile within the snow soil system computed from days 81 to 90. Note that the snow depths in Figure 7 vary from slightly above 0 m to 0.3 m, since precipitation and ablation during the snow season can lead to considerable deviations from the prescribed initial conditions (see also Figure 6a). Figure 7 demonstrates that the warming with increasing SND occurs consistently throughout the entire snow soil column. The only exception is the snow surface temperature, which decreases slightly with snow depth (T SND0.5 T SND0 = 0.17 K). The system temperature profile exemplified in Figure 7 has the same basic appearance as the conceptualized profile in Figure 1 and is consistent with the results from Experiment 1 shown in Figure 3a. [34] Figure 8 shows 10 day running means of ground heat and sensible heat fluxes, which decrease and increase, respectively, with initial snow depth, consistent with Figures 4a and 4b for Experiment 1. The 10 day running means of TR (not shown) indicate that thicker snow yields larger thermal resistance to heat, consistently throughout the simulated winter season. The 10 day running means of shortwave radiation, longwave radiation, and latent heat fluxes (not shown) do not show any appreciable difference between different initial snow depth conditions. These results are consistent with Experiment 1. However, note that in Figure 8 the ground and sensible heat flux change across the six simulations varies considerably over the course of the season, reaching magnitudes of GH SND0 GH SND0.5 = 15.7 W m 2 for ground heat and SH SND0.5 SH SND0 = 8.9Wm 2 for sensible heat. These changes due solely to snow depth insulation are appreciable, since the ground and sensible heat fluxes themselves are on the order of 10 W m 2 and vary by roughly W m 2 over the simulated season Experiment 3: Interannual Characteristics of Snow Depth Influence [35] Perturbation tests in Experiments 1 and 2 have demonstrated the influence of SND on land surface insulation for a single day and during a single winter season. The 7of11

8 Figure 7. The 10 day average temperature profile in the snow soil system computed from days 81 to 90 for Experiment 2. analysis is further extended to multiple winter seasons by conducting a single 11 year ( to ) historical simulation to look for interannual relationships between SND and the land surface energy balance that are consistent with the perturbation experiments. [36] For each year, winter SND, temperatures, and energy fluxes are computed as the average from December to February (DJF). Since this is a historical simulation, years with different SND will have different atmospheric boundary forcings, unlike the previous perturbation experiments, which prescribe different initial SND states for the same atmospheric forcing. Therefore, a direct comparison of SND versus temperature over multiple years is not informative. Temperature offset is used instead, defined as the difference between surface and air temperature for that year. Measuring the extent to which surface temperatures deviate from air temperature provides an alternative indication of the thermal response to SND. [37] Figures 9a and 9b present scatterplots of SND versus topsoil layer air temperature offset and surface snow layerair temperature offset. These parameters exhibit statistically significant linear relationships at the 95% significance level, and their linear regression lines and correlation coefficients are also shown. SND is positively (negatively) correlated with topsoil layer (surface snow layer) to air temperature offset, which indicates that thicker snow is associated with warmer soil (cooler surface snow) temperatures. Note that although significant linear relationships with SND are identified, close inspection of the scatterplots suggests that the relationships may, in fact, be nonlinear, with asymptotic changes as SND increases. Furthermore, the range of the temperature offset response to SND over 11 years is considerable. For example, the (topsoil layer air) temperature offset varies by 6.2 K. Finally, the negative relationship in Figure 9b indicates that the surface layer exposed to the atmosphere does not passively track air temperature variations when the land surface is covered by snow but rather is influenced by snow depth. These statistical relationships produced by a historical simulation are entirely consistent with the relationships produced by previous SND perturbation experiments, which suggests that SND influences land surface temperatures on interannual time scales as well. [38] Figures 9c and 9d present scatterplots of SND versus ground heat flux and sensible heat flux. These parameters also exhibit statistically significant linear relationships at the 95% significance level, so their linear regression lines and correlation coefficients are also shown. SND is negatively (positively) correlated with ground (sensible) heat flux, although again the relationships may, in fact, be nonlinear and asymptotic with increasing SND. The range of these diffusive heat flux values over 11 years is on the order of Figure 8. The 10 day running means of (a) GH and (b) SH, for Experiment 2 for six simulations with different initial snow depth conditions (SND0 to SND0.5). 8of11

9 Figure 9. Scatterplots for Experiment 3 of (a) soil air temperature offset versus SND, (b) surface air temperature offset versus SND, (c) GH versus SND, (d) SH versus SND, and (e) SW versus SND. 30 W m 2, notably larger than the response to SND in the perturbation experiments but likely reflecting atmospheric boundary variations in addition to SND variations. In contrast, latent heat and longwave radiation fluxes do not exhibit a significant relationship with SND (not shown). Once again, these results are consistent with Experiments 1 and 2, which suggests that the land surface insulation response to SND explicitly isolated and identified in perturbation Experiments 1 and 2 is also occurring in the historical simulation of Experiment 3. [39] Figure 9e presents a scatterplot of SND versus solar radiation flux and indicates a significant inverse linear relationship. However, for this energy flux term, a response to SND is not found for the perturbation experiments (Figure 4c), which indicates that insulative SND changes have no influence on solar radiation. Therefore, the empirical relationship shown in Figure 9e likely stems instead from solar radiation influencing snow depth; that is, years with greater solar radiation are subject to greater snowmelt and as a result have shallower snowpacks. [40] Note that the historical simulation experiment is not able to determine cause and effect between two significantly related parameters. In contrast, the perturbation experiments explicitly identify causal relationships whereby SND drives land surface energy balance conditions via the insulation process. Causal relationships for soil temperature, snowpack temperature, ground heat flux, and sensible heat flux have been so identified for Experiments 1 and 2. The fact that similar empirical relationships are found for Experiment 3 leads to the conclusion that SND also exerts an insulative influence on these land surface parameters at interannual time scales. This conclusion does not hold for solar radiation since the required consistency is lacking between the perturbation and historical simulation experiments. 4. Conclusions [41] In this study, the theoretical land surface insulative response to increasing snow depth, developed using an idealized multilayer snow soil system subject only to diffusive heat transfer and fixed boundary conditions, is confirmed and quantified via SNTHERM model simulations. Perturbation experiments with varying initial snow depths indicate that with increasing SND, the overall snow soil system warms but the surface snow layer cools slightly. The soil column also exhibits a suppressed diurnal cycle. The warmer land surface thermal state in turn generates decreased ground heat flux and increased sensible heat flux responses. The model simulations are designed so that this land surface thermal response is attributable to the increased insulative capacity of deeper snowpacks, which makes the underlying soil less responsive to solar radiation and air temperature fluctuations and facilitates sustained warming by the bottom soil layer boundary. This modeled response is entirely consistent with the idealized conceptualization. [42] The magnitude of the modeled land surface temperature response over a 0.5 m range of snow depths is generally on the order of 3 5 K. The corresponding ground and sensible heat flux responses are more variable, ranging from roughly 2 to 40 W m 2 depending on the specific energy term and experiment. Compared to the typical values that occur during repeated day simulations (Experiment 1) and the temporal ranges that occur during single season simulations (Experiment 2), the modeled response to snow depth 9of11

10 is quite substantial. Furthermore, although the thermodynamic response is asymptotically nonlinear with increasing snow depth, Experiment 1 showed that the overall effect of increasing depth due to insulation is comparable to the effect of snow presence versus snow absence due to albedo. Experiment 3 demonstrated that a land surface thermal offset consistently occurs in the presence of a snowpack, despite varying atmospheric conditions over multiple snow seasons, a finding that decouples both snowpack and soil temperatures from overlying air temperatures. Overall, a clear and substantial land surface insulative response to snow depth is identified over hourly, intraseasonal, and interannual time scales. Hence, snow depth variations are demonstrated to be an important contributor to the surface energy balance, via the insulative properties of the snowpack. [43] Results from Experiment 3 are generally consistent with previous studies in which winter snow explains a notable portion of air soil decoupling, owing to its thermal insulation of heat originating from the lower soil boundary. For example, Grundstein et al. [2005] performed a SNTHERM simulation very similar to Experiment 3 and revealed significant rank order correlations between the thermal offset of air and soil temperatures and various snow cover metrics such as thermal resistance (r = 0.81) or the annual number of snow covered days (r = 0.63). The perturbation simulations in Experiments 1 and 2 are helpful to isolate the specific insulative response to snow depth only and identify the causal factors for such linkages. [44] The warming of the snow soil system that occurs for deeper snowpacks can have a direct consequence on the overlying atmosphere. The additional heat retained within the snow soil system owing to a deeper snowpack represents energy that would otherwise be released to the atmosphere, so air temperature is likely to decrease as the snowpack gets thicker. This is consistent with the general understanding of surface air temperature response to snow cover reported in the literature [e.g., Baker et al., 1992; Ellis and Leathers, 1999; Gong et al., 2004], although the local air temperature suppression is usually attributed to albedo increases due to anomalous snow extent. The insulative property induced by thicker snowpack is also consistent with previous findings of the contributions of vegetation cover; that is, the air temperature depression was greater in areas with less vegetation [Mote, 2008]. Less vegetated land is covered with more snow than densely vegetated area with the same snow depth; thus more heat remains in the snow soil system instead of warming the overlying atmosphere. 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