1. Introduction
Land regions with transient snow cover are particularly sensitive to climate change due to the snow albedo feedback (SAF). The SAF enhances warming through two physical processes: 1) as snow melts, the darker land surface underneath becomes more exposed, reducing the surface albedo; and 2) prior to melting, as the snowpack warms, the albedo of the snow itself decreases because of snow crystal metamorphosis and the concentration of light absorbing impurities within the snowpack. In both cases, the albedo reduction increases the surface absorption of shortwave (SW) radiation, resulting in surface heating that is conveyed through the lower troposphere via turbulent fluxes (e.g., Randall et al. 1994). Generally, the SAF is dominated by changes in snow cover, rather than snow metamorphosis (e.g., Qu and Hall 2007; Fernandes et al. 2009), except perhaps in regions where the snow is affected by impurities, for instance, dust or black carbon (Fernandes et al. 2009).
Midlatitude mountain ranges are especially susceptible to the SAF, as these regions often accumulate large snowpacks that persist through the late spring and into the summer when solar insolation is at its highest. This study is focused on the mountainous region of Colorado. The focus on this region stems, in part, from its societal importance, as it serves as the headwaters for many major river systems in the western United States. Throughout the paper, this region will be referred to as the Headwaters region (outlined in Fig. 1). On average, 70% of the annual runoff within the Headwaters region comes from high-elevation winter snowpack, making the snowpack in this region critical to the water resources in the western United States (e.g., Christensen et al. 2004). The seasonal snowpack also serves as the basis for the robust skiing and tourism industry. In the coming century, the snowpack in the western United States is expected to decrease significantly as the climate warms (e.g., Christensen and Lettenmaier 2007; Gao et al. 2011; Klos et al. 2014). Many studies already show snowpack declines in the western United States due to warming (Mote et al. 2005; Kapnick and Hall 2012), that have been attributed in part to anthropogenic climate change (Pierce et al. 2008).
The SAF has been well studied in the global context, where typically it is considered as part of the total surface albedo feedback. Global estimates of the surface albedo feedback generally range between 0.2 and 0.8 W m−2 K−1 (e.g., Cess et al. 1991; Colman 2003; Soden et al. 2008; Qu and Hall 2014). This places the surface albedo feedback below the combined water vapor–lapse rate feedback in regards to global importance (e.g., Soden et al. 2008). Regionally, however, the surface albedo feedback can be dominant. For example, Qu and Hall (2014) and Taylor et al. (2007) show regional springtime maxima in SAF strength
However, estimates of the SAF by GCMs over mountain ranges should be met with skepticism as topography has profound effects on patterns of precipitation, temperature, and snow that cannot be captured by GCMs. In particular, coarse-resolution models have been shown to perform poorly with respect to temperature and precipitation over complex terrain (Mass et al. 2002; Leung and Qian 2003; Ikeda et al. 2010; Rasmussen et al. 2011). Furthermore, any mesoscale features of the SAF in these regions are not resolved at all by GCMs, so its regional climate effects are unclear.
Recently, regional climate downscaling experiments using regional climate models (RCMs) have been used to investigate climate change in mountain regions. Several of these point to the SAF as a significant mesoscale feature of mountain climate change, responsible for regional variability in climate change and elevation dependent warming (e.g., Giorgi et al. 1997; Fyfe and Flato 1999; Salathé et al. 2008; Kotlarski et al. 2012). For example, Salathé et al. (2008) investigated regional climate change over the mountains of the northwest United States. In comparing the warming between their RCM and its parent GCM, they found increased warming (locally greater than 1.5°C) in the RCM spatially correlated with snow loss. These results provide evidence that over complex terrain the SAF strongly modulates climate warming in ways that are poorly captured by GCM experiments.
Regional snow loss, exacerbated by the SAF may also be important to summertime temperature and precipitation, as the earlier spring runoff and additional warming caused by snow loss can lead to a local decrease in soil moisture that persists through the summer, thus increasing temperature and decreasing precipitation (e.g., Hall et al. 2008; Im et al. 2010). The SAF in the Headwaters region is further complicated by the effect of snow impurities, in particular dust, that locally can lower the snow albedo by as much as 15% and enhance snowmelt (Painter et al. 2007; Qian et al. 2011; Oaida et al. 2015).
Overall, previous research suggests that the SAF is important in amplifying climate change over midlatitude mountain regions, yet, a thorough quantitive analysis of the SAF over complex terrain has not been performed using RCM output.
In this study we use output from the Weather Research and Forecast (WRF) Model configured as a high-resolution RCM to investigate the SAF over the mountains of Colorado. Key questions we address in this study include the following: 1) How can the SAF be quantified using RCM output? 2) How does the SAF vary spatially, diurnally, and seasonally over complex terrain? 3) How does the RCM-simulated SAF depend on model resolution? 4) What are the nonlocal effects of the regional SAF associated with regional energy transport? To address these questions, the paper will be structured as follows. In section 2 we develop a framework to quantify the regional SAF over complex terrain based on linear feedback and energy budget analyses. In section 3 we use this framework to examine the seasonality of the SAF, its spatial structure, and its sensitivity to model resolution and region. This framework is also used to investigate nonlocal effects of the SAF. Sections 4 and 5 will discuss and summarize the results of this study.
2. Data and methods
a. WRF Model experiment
Here we use output from WRF RCM simulations described in Rasmussen et al. (2014) to examine the SAF. Figure 1 shows the full model domain centered over the Headwaters region, which is the focus of our analysis. These simulations were run at three different horizontal grid spacings:
Topography of the full WRF Model domain (
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
Topography of the Headwaters region for varying model resolution. (a) High-resolution topography (0.008°), (b) WRF
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
The control simulations were run from October 2000 through October 2008. The North American Regional Reanalysis (NARR) was used to force the lateral boundaries every 3 hours. No grid nudging was applied within the WRF domain. A more detailed description of model setup can be found in Rasmussen et al. (2014). The simulated total precipitation showed good agreement with the observations from the Snowpack Telemetry (SNOTEL) network within the Headwaters region of Colorado (Rasmussen et al. 2014).
The pseudo-global warming (PGW) experimental framework (e.g., Schär et al. 1996) was used to test the regional climate response to large-scale climate change. The PGW approach applies an idealized climate perturbation to the control boundary forcing, rather than forcing the RCM boundaries with transient GCM output. Essentially, the PGW experiment provides boundary forcing with the same synoptic conditions as in the control, only on a shifted base-state climate. The advantage of this approach is that it isolates the effects of large-scale warming and moistening from the effects of changes in midlatitude large-scale circulation and storm tracks. This allows us to examine how large-scale thermodynamic changes in climate interact with local mesoscale processes to shape regional climate. Because the natural variability of the large-scale flow is essentially identical between the control and PGW simulations, a regional analysis is possible over a shorter simulation period than is typically required for transient climate change experiments.
For the PGW experiment, GCM output from the CCSM3 model was used to perturb the boundary conditions (Rasmussen et al. 2014). The climate perturbation was taken to be the 10-yr monthly mean difference between 2045–55 and 1995–2005 from the CCSM3 ensemble mean using the Special Report on Emissions Scenarios (SRES) A2 emissions scenario (IPCC 2000). Perturbations were applied, at all vertical levels, to temperature, water vapor mixing ratio, geopotential height, and wind. The monthly mean perturbations were linearly interpolated in time and added to the NARR boundary conditions. In addition to the boundary forcing, a radiative perturbation consistent with an increase in CO2 to 533 ppm (2050 concentrations from the A2 scenario) was applied as well. We only analyze model output starting in October 2001 to allow a full year for the land surface model (LSM) to adjust to the perturbed climate.
The Noah LSM (Koren et al. 1999; Chen and Dudhia 2001; Ek et al. 2003) was used in these simulations. The snow model component of Noah is highly simplified compared to the snow models used in several other common LSMs (Chen et al. 2014a). However, the simulations analyzed here were run with a version of Noah that includes recent improvements (Barlage et al. 2010). While Noah has four soil levels, it treats snow using a single vegetation-blended layer. Noah includes a variable snow density, fractional snow cover, and time-varying surface albedo. There is no explicit treatment of canopy interception.





The empirically derived coefficients A and B are equal to 0.94 (0.82) and 0.58 (0.46), respectively, during the accumulation (ablation) season. The term
This version of Noah has shown good skill simulating SWE throughout the winter and early spring months in the Headwaters domain. The simulated SWE compares very well to SNOTEL observations during the early accumulation season, but is too low during the beginning of the snow ablation season (Barlage et al. 2010; Rasmussen et al. 2014). The timing of peak SWE in Noah agrees well with SNOTEL observations, however, the ablation season lasts too long, with simulated SWE persisting well past its observed disappearance (Chen et al. 2014b; Rasmussen et al. 2014). Recent work also indicates that Noah also tends to overestimate
b. Linear feedback analysis
The term on the left-hand side of Eq. (2) represents the change in net top of atmosphere (TOA) solar radiative flux density (Q) per change in surface (2 m air) temperature (
Equation (2) is used to quantify the SAF on monthly time scales, spatially averaged over the Headwaters domain. The second term is calculated by differencing the two climate states (PGW-control) then spatially averaging monthly mean values of
Change in
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
The third term cannot be calculated as a simple difference between climate states as it involves a partial derivative. There are a number of different methods used to calculate this term (e.g., Taylor et al. 2007; Qu and Hall 2007; Donohoe and Battisti 2011). We use the method described by Donohoe and Battisti (2011), which relies on a single-layer representation of the atmosphere. We chose this method as it is relatively simple to apply using standard WRF Model output, and because it has shown good agreement with more robust kernel methods (Qu and Hall 2014). To apply this method,
c. Energy budget formulation








Monthly mean values of WRF output were used to calculate the energy budget terms at TOA and the surface. The energy tendency term
3. Results
a. Qualitative characterization of the SAF
We first characterize the SAF by examining spatial patterns in the changes of
Average (2002–08) pattern of warming and snow loss. (top) Temperature change (PGW-control) and (bottom)
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
In general, regions of enhanced warming are broader than regions of snow loss, suggesting that the SAF is able increase the temperature in areas where albedo is not changing. To quantify this nonlocal impact of the SAF, the Headwaters-domain-average warming at snow-free grid cells was compared to the domain-average fractional snow loss (Fig. 5). Snow-free grid cells are defined as grid cells with
The term
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To better examine the effect of the SAF on the Headwaters region as a whole, we consider the seasonal cycle of domain-averaged
Headwaters-domain averages of (a)
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
One complicating factor in this analysis is that the PGW forcing is derived from GCM output. Thus, the boundary forcing potentially incorporates SAF-enhanced warming simulated by the parent GCM, making the WRF SAF an underestimate of the total SAF. The extent to which this affects our results is unclear; however, we only expect a substantial influence of the GCM SAF on the boundary forcing during early spring when snow cover and the SAF extend to low elevations.
The excess warming during June–August is not associated with the SAF, as
Figure 7 shows the detailed spatial structure of April mean snow cover and surface warming for two individual years, representing a warm/low-snowfall year (2007) and cold/high-snowfall year (2008). In April 2007, snow cover was limited to the highest terrain within the Headwaters domain. In contrast, the April 2008 snow cover was widespread over most of the northern Headwaters domain. The spatial patterns of warming for each year reflect the differences in snow cover. In April 2007, there is very little enhanced warming within the Headwaters domain, and the warming occurs at high elevations only, on the snow cover margins. More substantial warming occurs northwest of the Headwaters region, in southwest Wyoming where a large area of partial snow cover is present in the control simulation. In April 2008, there is much more warming within the Headwaters domain, consistent with the larger snow-covered area.
April monthly mean snow cover and temperature change (PGW-control). The term
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To characterize the vertical structure of SAF-enhanced warming, vertical cross sections of
April monthly mean cross sections along line (a)–(b) from Fig. 7. Vertical cross section of
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To investigate the diurnal variability of the SAF, spatial patterns of monthly mean warming during April 2008 at 0400 LST (1200 UTC) and 1600 LST (0000 UTC) were examined (Fig. 9). There is notable diurnal structure in the SAF. Not only is the SAF-enhanced warming substantially stronger at 1600 LST, the spatial pattern in the warming is also different. At 1600 LST, localized strong warming occurs mainly along the lower slopes of prominent mountains and in high-altitude basins where snow cover is changing. At 0400 LST, the strongest warming is located in the valleys and basins within the Headwaters domain and there is less enhanced warming along mountain slopes. In some areas, the warming at 0400 LST is greater than the warming at 1600 LST. This is most notable in the area northwest of the Headwaters region. The diurnally dependent warming patterns suggest that topographically driven flows and cold air pools influence regional patterns of SAF-enhanced warming.
Diurnal variation of April 2008 mean
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
b. Linear feedback analysis: Seasonal and regional variability of the SAF
To better quantify the SAF and its variability, linear feedback analysis was applied to the Headwaters domain. The values of each term in Eq. (2) are in green in Fig. 10. These values are spatially averaged over the Headwaters domain and temporally averaged over the full 7-yr period for each month. The whiskers represent interannual variability (10th–90th percentile). There are two peaks in
Terms of the snow albedo feedback in Eq. (1), for the
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
Figure 10d shows the magnitude of the SAF,
The interannual variability in the SAF is quite high, particularly in March. During the late spring and early summer, the variability in SAF strength collapses. The high variability of the SAF during the early spring can be explained by the variability in snow cover at low-elevation areas within the domain (e.g., Figs. 6 and 7). High-snowfall years generally have a stronger SAF than low-snowfall years: the February–June (FMAMJ) mean control snow fraction is well correlated with the FMAMJ mean
The SAF for two other mountain regions within the full model domain was calculated for comparison: the Wind River Mountains in west-central Wyoming and the Uinta Mountain Range in northern Utah (Fig. 1). The seasonal cycle of the SAF in each of these regions shows similarities to the Headwaters seasonal cycle (Fig. 10). Both regions show spring and fall peaks in the SAF, with a dominant spring peak in April. They have a stronger SAF during the spring and a weaker SAF during winter than the Headwaters region, likely because the Headwaters region includes more low-elevation grid cells that do not hold snow into the late spring and early summer.
Interestingly, while the mean SAF was slightly positive during the late winter, in some years this term was negative. The negative sign of the SAF is associated with a positive correlation between
c. Linear feedback analysis: Sensitivity to model resolution
To investigate the sensitivity of SAF strength to model resolution, linear feedback analysis was applied to simulations using the three grid spacings (
Terms of the snow albedo feedback, for the Headwaters region at
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To understand the causes of this resolution dependence, spatial patterns of warming and snow loss at
Comparison of warming and snow loss between the
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To further understand the mechanisms by which terrain resolution affects the strength and timing of the SAF, we examined the resolution differences (4 km − 36 km) for April and June values of variables relevant to the SAF: terrain height,
Difference between control simulation results at different model resolutions (4 km − 36 km). (top) April and (bottom) June. Differences are for terrain elevation,
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
As a result of these differences, during April, snow is more sensitive to warming at
Differences in the control climate and, hence, the SAF are much more modest between 4 km and 12 km, consistent with findings from previous studies examining resolution dependence of mesoscale model simulations over mountainous terrain (Mass et al. 2002; Ikeda et al. 2010). These results suggest that a 12-km horizontal resolution is sufficient to capture the regionally averaged SAF over the Headwaters domain; however, higher resolution is required to capture finer-scale structures and variability in SAF enhanced warming.
d. Estimating the SAF from the seasonal cycle of 
and Ts

Our methods should be broadly useful for diagnosing the SAF in other RCMs. However, most RCM experiments do not include PGW-type simulations. For experiments without PGW output, the linear feedback framework can be used to calculate
Comparison between
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
e. Regional energy budget analysis: Nonlocal effects of the SAF
Here the energy budget framework described in section 2c is used to explore how SAF-enhanced warming is redistributed by horizontal energy transport caused be atmospheric circulations. Such energy transport may reduce the localized climate impact of the SAF, and allow the SAF to remotely cause warming in locations where snow cover does not change. The role of horizontal transport as it relates to climate feedbacks has been previously studied using simplified global modeling experiments (e.g., Hall 2004; Feldl and Roe 2013b; Merlis 2014). On global scales, horizontal energy transport significantly dampens the local temperature response to feedbacks and enhances warming at locations remote from the feedback processes.
Monthly mean values of each of the terms of Eq. (8) were calculated and averaged over the 4-km Headwaters domain from January to June. Figure 15a shows the seasonality of the various terms. During the midwinter and early spring, energy is converged into the Headwaters region via transport, balancing the TOA radiative imbalance between the SW and longwave (LW) fluxes. As
Monthly mean terms of Eq. (8) averaged over the Headwaters region: (a) control, (b) (PGW-control), and (c) change in cloud radiative forcing (PGW-control). The solid red line in (b) represents the domain average
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
To better understand the effects the SAF has on the domain mean energy balance, these terms were differenced between the PGW and control simulations (Fig. 15b). The red line plotted in Fig. 15b is a measure of the radiative impact of the SAF attained by multiplying
In the Headwaters domain, in March–May
Energy transport scattered against
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
Changes in
Negative values of CRF imply a net cooling effect due to clouds, and positive values imply net warming. Figure 15c shows the change in CRF (PGW-control). From February to May,
To gain a better understanding of how changes in the energy budget terms relate to the regional terrain, spatial patterns of changes in the terms of Eq. (8) were investigated (Fig. 17) . For this analysis, we focused on the San Juan Mountains in southwest Colorado, and used 7-yr means for April. The hatching in Fig. 17 indicates regions experiencing snow loss:
Changes (PGW-control) in April energy flux terms from Eq. (8). Values are 7-yr averages (2002–08). (a)
Citation: Journal of Climate 28, 19; 10.1175/JCLI-D-15-0166.1
Interestingly, there is substantial horizontal energy convergence
4. Discussion
Figure 9 indicated substantial diurnal variability in the pattern of SAF-enhanced warming. This suggests that diurnally driven topographic flows redistribute SAF-enhanced warming throughout the region. For example, Bossert and Cotton (1994) show terrain-forced diurnal flow regimes over the Headwaters region that include regional-scale upslope and downslope flows that may help ultimately determine the regional patterns and effects of the SAF. Furthermore, these wind systems themselves may be modulated by snow loss and the SAF. In addition, amplified nighttime warming in valleys and basins may relate to changes in nocturnal cold pools caused by changes in snow cover. Because snow cover increases cold pool strength by enhancing surface LW cooling (e.g., Whiteman et al. 2001), we expect weaker surface LW cooling in basins with substantial snow loss. Accordingly, snow cover loss may weaken nocturnal cold pools and facilitate more rapid cold pool destruction by convection during the day.
Energy transport was found to damp warming where the SAF was active (Fig. 16), enhance warming over nearby snow-free regions (Fig. 5), and enhance snowmelt over completely snow-covered regions (Fig. 16). These result have implications for experiments that force LSMs with surface meteorological conditions representative of possible future climate and are run in “offline” mode (e.g., Elsner et al. 2010; Vano et al. 2012). In these experiments, the LSM-simulated surface conditions do not feedback into the forcing data. Thus, nonlocal effects of the SAF are not incorporated into the LSM forcing, since changes in surface albedo associated with snowmelt do not affect meteorological conditions elsewhere. Therefore, in regions where the SAF is relevant, these experiments may underestimate the rate of snowpack ablation, warming, and evapotranspiration.
There is a need for observational constraints on the SAF simulated by RCMs. The best way to observe regional snow cover at high spatial resolution is through use of remote sensing platforms. Recent work performed by Wrzesien et al. (2015) used fractional snow cover estimated from MODIS satellite data using the MODIS Snow Covered-Area and Grain size retrieval algorithm (MODSCAG; Painter et al. 2009) to evaluate RCM simulations over the Sierra Nevada Mountains. They considered simulations using both the Noah LSM and the more sophisticated Noah-MP. While they found significant improvement in snowpack simulation using Noah-MP, both LSM’s substantially overestimated
5. Summary and conclusions
The aim of this study was to provide a better understanding of the snow albedo feedback (SAF) in simulations of regional climate change over the complex terrain of the Colorado Headwaters region. The SAF is most active throughout the spring months during the snow ablation season, when snow cover is particularly sensitive to temperature and when solar radiation is high. During the spring, spatial structures in warming are strongly correlated with snow loss, indicating a significant contribution from the SAF. Averaged over the Headwaters region, the enhancement of warming by the SAF may be as much as 1.5°C, with localized warming greater than 5°C. SAF-enhanced warming is most active during the afternoon on the margins of the snowpack. Although this warming is generally reduced at night, it is pronounced overnight in valleys and basins. We speculate that this diurnal structure is due to regional-scale diurnal wind systems and changes in cold pool evolution. The SAF-enhanced warming is generally confined to the boundary layer but has increased vertical penetration along steep mountain slopes.
Linear feedback analysis was used to quantify the magnitude, seasonality, and the interannual variability of the SAF. The SAF is strongest during April with a mean of approximately 4 W m−2 K−1. There is high interannual variability in SAF strength within the Headwaters region, which is largely caused by interannual variability of regional snow cover. The SAF is strongest during high snowfall years because 1) more of the region is covered by snow, so the SAF is active over a larger area, and 2) snow cover persists later in the spring when incoming solar radiation is strong. The February–June average SAF strength is largely independent of variations in model grid spacing from
The nonlocal effects of the SAF were investigated by examining changes in the atmospheric energy budget. The direct effect of the SAF is an increase in net SW radiative flux at the TOA. Energy transport by atmospheric circulations is the primary process that balances these SW changes. This transport facilitates nonlocal effects wherein the SAF enhances warming and snowmelt in locations that do not experience a loss of snow cover.
The uniqueness and complexity of the regional terrain means that the specific results from this study cannot be directly applied to other mountain regions. Furthermore, the effects of snow impurities are not included in these simulations, and the SAF strength and timing may be substantially different in a model that includes these effects (e.g., Oaida et al. 2015). However, the methodological framework used here is generally applicable and can be used to diagnose the SAF in other RCM experiments and to help further the overall understanding of regional climate change in midlatitude mountain regions.
Acknowledgments
Support for this work was provided by the NSF Grant AGS-1349990. Initial work on this research was the result of a visit to NCAR by JRM funded by the NCAR Research Applications Lab visitors program. The NCAR Water System program funded by the NSF supported the generation of the RCM simulations analyzed here. We thank Kyoko Ikeda and Changhai Liu for providing assistance in accessing the RCM output and details of the model configuration. Roy Rasmussen provided helpful comments on an earlier version of the manuscript. High-performance computing support was provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the NSF. We are grateful to the anonymous reviewers for their insightful comments and suggestions, which helped improve the quality of this paper.
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In this analysis monthly mean values are centered at the beginning of each month, rather than in the middle, to make the seasonal