2.1 Sub-canopy longwave radiation in CLM4.5

Vegetation in CLM4.5 is parameterized as a single layer using a “big-leaf” approach (Oleson et al., 2013). Sub-canopy longwave radiation is calculated as the sum of atmospheric longwave radiation LW_atm and longwave radiation emitted by vegetation LW_veg, weighted by vegetation emissivity ε_v:

using the Stefan–Boltzmann law with the Stefan–Boltzmann constant $\mathit{\sigma }=\mathrm{5.67}\times {\mathrm{10}}^{-\mathrm{8}}$ W m⁻² K⁻⁴ and vegetation temperature T_v. Vegetation temperature is calculated based on an energy balance, net radiation minus turbulent heat fluxes. Radiative transfer of direct and diffuse shortwave radiation is calculated via a two-stream approximation (Sellers, 1985) considering one reflection from ground to canopy. Net longwave radiation is calculated from atmospheric longwave radiation, vegetation temperature, and (ground) surface temperature and determined by vegetation emissivity and emissivity of the ground. Calculation of turbulent heat fluxes in CLM4.5 is based on Monin–Obukhov similarity theory and described by Oleson et al. (2013). Vegetation emissivity depends on the leaf area index (LAI) and stem area index (SAI) and is calculated as

This parameter is a combination of emissivity in the physical sense and a weighing parameter based on vegetation density; however, we will stick to this denomination here for consistency with the nomenclature of the technical description of CLM4.5 (Oleson et al., 2013).

CLM4.5 subdivides grid cells based on land units, e.g. vegetated, glacier, or urban, and vegetated land units based on plant functional types (PFTs), with up to 16 possible PFTs as well as bare soil. Sub-canopy longwave radiation is calculated for each PFT present in a grid cell, with separate values of LAI, SAI, and vegetation temperature for each PFT. All PFTs within one vegetated land unit share a single column of snow and soil so that fluxes from vegetation to the ground are weighted averages over all PFTs. Consequently, changes in fluxes from an individual PFT affect snow cover beneath every PFT in a particular vegetated land unit.

2.2 Correction of sub-canopy longwave radiation in CLM4.5

For this study, a correction factor f_corr was implemented in CLM4.5 to reduce unphysical diurnal variations in sub-canopy longwave radiation. As atmospheric longwave radiation is an input variable to CLM4.5, from either forcing datasets or the atmospheric component of CESM (Community Atmosphere Model – CAM), correction factors were used to scale longwave radiation emitted from vegetation:

Conceptually, correction factors represent a vegetation structure consisting of multiple individual layers so that longwave radiation fluxes emitted upward and downward from the vegetation are no longer equal by design. In a multilayer canopy configuration, the uppermost layer contributes most to longwave radiation emitted upward to the atmosphere and directly absorbs incoming longwave and shortwave radiation fluxes. Conversely, the lowest layer contributes most to longwave radiation emitted downward to the surface but is insulated from atmospheric fluxes by the canopy layers above.

Using this multilayer canopy configuration as a guideline, longwave radiation emitted by the canopy was partitioned asymmetrically upward and downward in CLM4.5. The resulting above-canopy longwave radiation flux to the atmosphere was calculated as

with emissivity of the ground ε_g and temperature of the ground T_g. Ground emissivity in CLM4.5 is calculated as a weighted sum of emissivities of snow (0.97) and soil (0.96), weighted by the fraction of snow covering a grid cell. In Eq. (4), the first term represents atmospheric longwave radiation transmitted through the vegetation, reflected by the ground, and transmitted through the vegetation to the atmosphere; the second term represents longwave radiation emitted from the vegetation reaching the atmosphere; and the third term represents longwave radiation emitted by the ground and transmitted through the vegetation to the atmosphere. The second term combines longwave radiation emitted by the vegetation directly to the atmosphere (first term in brackets) and longwave radiation emitted downward from the vegetation, reflected by the ground, and transmitted through the vegetation to the atmosphere (second term in brackets). For f_corr>1, LW_above decreases as a reduction in the first term in brackets (2−f_corr) outweighs the increase in the second term in brackets $(\mathrm{1}-{\mathit{\epsilon }}_{\text{v}})(\mathrm{1}-{\mathit{\epsilon }}_{\text{g}})f_{\text{corr}}$, while LW_sub in Eq. (3) increases. For f_corr<1, LW_sub decreases and LW_above increases. Note that the sum of LW_sub and LW_above was not changed by the introduction of f_corr, which guaranteed conservation of energy. The calculation of vegetation temperature in CLM4.5 was not altered by this approach so that the temperature of the single vegetation layer represented an average of multiple (theoretical) layers suggested by asymmetrical upward and downward longwave radiation fluxes.

2.3 Global offline simulations with CLM4.5

Offline simulations of CLM4.5 were forced by prescribed atmospheric data, using the CRUNCEP Version 7 dataset, covering 1981 to 2016 and thus snow seasons 1981–1982 to 2015–2016 (Viovy, 2018). The impact of correction factors on longwave enhancement, snow cover, and snowmelt was assessed by comparing two simulations, a control run (henceforth CTRL) and a run in which correction factors were implemented (henceforth CORR). Correction factors were applied to evergreen needleleaf trees in CLM4.5, as given in Eqs. (3) and (4). Two PFTs, needleleaf evergreen boreal trees (NEBTs) and needleleaf evergreen temperate trees (NETTs), represent evergreen forests across snow-covered areas in CLM4.5, and grid-cell coverage by these two PFTs is shown in Fig. 1a. Plant area index (PAI), the sum of LAI and SAI, is shown in Fig. 1b as a weighted average of NEBTs and NETTs.

Figure 1Coverage of vegetated land unit within grid cell by combination of needleleaf evergreen boreal trees (NEBTs) and needleleaf evergreen temperate trees (NETTs) (a), plant area index (PAI) for combination of NEBTs and NETTs weighted by PFT fractions (b), and grid-cell average elevation (c) based on CLM4.5's ${\mathrm{0.9}}^{\circ }\times {\mathrm{1.25}}^{\circ }$ surface dataset.

2.4 Global observations of snow-off date

A blended dataset of five global observation-based SWE products (henceforth Blended-5) covering the period 1981 to 2010 (Mudryk et al., 2015) was used to estimate snow-off dates across the Northern Hemisphere and evaluate simulation of snowmelt in CTRL and CORR. In contrast to simulations, observations display snow persisting for physically unrealistical durations, which necessitates a SWE threshold to estimate snow-off dates (Krinner et al., 2018). While Mudryk et al. (2017) and Krinner et al. (2018) used thresholds of 4 and 5 mm, respectively, for estimates of the spatial snow cover extent, a smaller SWE value was necessary to represent the precise timing of melt-out within individual grid cells. A threshold of 1 mm was used in this study to define melt-out for the Blended-5 mean, and the snow-off date was defined as the first day of a year for which the SWE did not exceed this threshold. Sensitivity of snow-off dates to threshold values was tested for the range 0.5 to 4 mm; however, the overall conclusions of this study are unchanged for different thresholds.

4.1 Sub-canopy longwave radiation – case study Alptal, Switzerland

For the location of Alptal, in contrast to other forest stands used in this study, the forest stand and the CLM4.5 grid cell feature similarly high vegetation densities (PAIs of 4.1 and 3.7 m² m⁻², respectively) and thus similar vegetation emissivities ε_v (0.983 and 0.975, respectively). This allows for a comparison of diurnal cycles of sub-canopy longwave radiation as well as longwave enhancement between stand-scale measurements and offline simulations. Implementation of correction factors in CLM4.5 results in decreased sub-canopy longwave radiation during the daytime and increased sub-canopy longwave radiation during nighttime, thereby reducing diurnal cycles. For the grid cell representing Alptal, diurnal ranges decrease from about 70 to about 30 W m⁻² during the snowmelt season (Fig. 4a and b). Observations at the forest stand show an average diurnal range of about 15 W m⁻² during the snowmelt season. Simulations and observations display a similar range of intraseasonal variability but do not agree in evolution and daily average of sub-canopy longwave radiation. Implementation of correction factors increases average sub-canopy longwave radiation, as seen in Fig. 4b, for two reasons. Firstly, daytime correction depends on insolation, which changes throughout the snow cover season so that daytime correction varies to a higher degree than nighttime correction. Secondly, nights are longer than days prior to the boreal spring equinox, which leads to nighttime increases outweighing daytime decreases. Consequently, correction results in increased average sub-canopy longwave radiation even for equal magnitudes of daytime overestimation and nighttime underestimation.

Figure 4Hourly time series (a, c), diurnal cycles (solid in b and d), and JFM averages (dotted in b and d) of sub-canopy longwave radiation (a, b) and longwave enhancement (c, d) for the snowmelt season in 2006 at Alptal, Switzerland. Measurements at the forest stand (OBS; green) are shown for comparison with offline simulations CTRL (black) and CORR (red) for boreal evergreen needleleaf trees in the corresponding grid cell of Alptal, Switzerland. Gaps in measurements are due to quality checks and excluded from calculation of diurnal cycle and JFM average.

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Comparison of simulated and measured longwave enhancement is shown in Fig. 4c and d for Alptal. As for sub-canopy longwave radiation, the diurnal cycle of simulated longwave enhancement is reduced by implementation of correction factors with increased enhancement at night and decreased enhancement at daytime. Reduction of daytime longwave enhancement increases throughout the snowmelt season, which is due to increasing insolation and thus increasing reduction of sub-canopy longwave radiation during daytime. Longwave enhancement values vary between 1.1 and 1.4 in CTRL, which is predominately driven by diurnal cycles. The diurnal cycle of longwave enhancement is reduced by more than 50 % in CORR, resulting in a diurnal range similar to observations and increased daily average longwave enhancement. Simulated longwave enhancement displays little intraseasonal variability, with variations mostly due to the overestimated diurnal cycle. This indicates that intraseasonal variability in sub-canopy longwave radiation is largely due to variations in atmospheric longwave radiation. In contrast, measured longwave enhancement values range from less than 1 to more than 1.6 and display little diurnal variability but high variability on synoptic timescales, which results in a different daily average of longwave enhancement compared to simulations. Moreover, lower average longwave enhancement for observations indicates more overcast conditions, which lead to smaller diurnal cycles in sub-canopy longwave radiation compared to simulations. Therefore, correction factors improve the realism of diurnal cycles of sub-canopy longwave radiation and longwave enhancement, encouraging usage for evaluation of the impact on snow cover.

The contrast in variability between simulated and observed longwave enhancement can be seen in Fig. 5. Observations show a large range of longwave enhancement values that are closely tied to effective emissivity of the sky, which represents clear-sky (low ε_sky) and overcast (high ε_sky) conditions. Observed longwave enhancement increases for decreasing ε_sky as the contrast between vegetation temperatures (increasing due to higher insolation) and the effective temperature of the sky increase. Spread in observed longwave enhancement is small throughout the range of ε_sky, indicating little diurnal variability and the process of longwave enhancement depending on meteorological conditions. Simulations display a narrow range of ε_sky, which causes the lack of intraseasonal variability seen in Fig. 4c. The spread in simulated longwave enhancement values is substantially larger compared to observations for the respective range in ε_sky, representing overestimated diurnal cycles. Implementation of correction factors reduces the spread in longwave enhancement values and increases average longwave enhancement (see Fig. 4d); however, spread in longwave enhancement is still overestimated and average longwave enhancement is underestimated in CORR compared to observations for the respective range in ε_sky.

Figure 5Longwave enhancement measured (OBS; green) at the forest stand of Alptal, Switzerland, and simulated in CTRL (black) and CORR (red) for boreal evergreen needleleaf trees in the corresponding grid cell of Alptal, Switzerland, as a function of effective emissivity of the sky. Each data point represents an hourly average seen in Fig. 4c.

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Figure 6Frequency of days for 2004–2007 during which implementation of correction factors results in higher nighttime than daytime sub-canopy longwave radiation despite higher daytime than nighttime atmospheric longwave radiation.

4.2 Longwave enhancement and limited spatial variability in ε_sky

Lack of variability in simulated ε_sky, as seen for the grid cell of Alptal, across the Northern Hemisphere results in spatially similar correction factors that are largely dependent on insolation. However, variability in both insolation and diurnal ranges of atmospheric longwave radiation indicates small variations in meteorological forcing that are not represented by ε_sky. Therefore, ε_sky in simulations may indicate clear-sky conditions even when insolation and atmospheric longwave radiation suggest more overcast conditions, resulting in overestimated correction factors and overcorrection of sub-canopy longwave radiation. This overcorrection results in larger nighttime than daytime values of sub-canopy longwave radiation in contrast to atmospheric longwave radiation and occurs mostly along continental coasts (Fig. 6). Consequently, a contour line is used in the following to denote an overcorrection for 10 % of days.

Figure 7Averages in CTRL (a, c, e, g) and differences between CORR and CTRL (b, d, f, h) for longwave enhancement beneath evergreen needleleaf trees (a, b), snow surface temperature (c, d), cold content (e, f), and snow-off date (g, h). Longwave enhancement is averaged over December to May, while snow surface temperature and cold content are averaged over entire snow cover seasons. Differences between CORR and CTRL are calculated as averages of differences between each individual snow cover season. For panels (c–h), a mask is applied to filter out grid cells that are not perennially covered in snow. Black lines demarcate continental areas with less than 10 % of overcorrected days. Green lines demarcate areas with coverage by evergreen needleleaf trees of at least 50 %.

Figure 8Longwave enhancement beneath evergreen needleleaf trees as average over December to May in CTRL (a; as in Fig. 7) and as difference between CORR and CTRL over February and March (b) and over April and May (c). Differences between CORR and CTRL are calculated as averages of differences between each individual year. Black lines demarcate continental areas with less than 10 % of overcorrected days. Green lines demarcate areas with coverage by evergreen needleleaf trees of at least 50 %.

To demonstrate the impact of correction factors spatially, maps of longwave enhancement beneath evergreen needleleaf forests in CLM4.5 are shown in Fig. 7a and b. Averages over boreal winter and spring show an enhancement of longwave radiation beneath canopies by about 20 % to 30 % and display little differences across boreal forests, which is due to small spatial variability in both ε_sky and vegetation density (Fig. 1). CORR displays increased average longwave enhancement north of 40^∘ N, with an additional enhancement of longwave radiation of up to 5 % beneath dense boreal forests. Changes in longwave enhancement generally increase with latitude, as daytime correction factors vary with insolation while nighttime correction factors are independent of latitude. A higher increase in longwave enhancement can be seen for higher vegetation density within regions covered by boreal forests (Fig. 1b) due to weighting of contributions to sub-canopy longwave radiation (Eq. 3).

4.3 Snow cover and snowmelt

Changes in sub-canopy longwave radiation induced by the correction increase the net energy flux to the surface, which can be seen for grid-cell-averaged snow surface temperature (Fig. 7c and d). Simulated average snow surface temperatures are determined by latitude, topography, and continent, reaching values of less than −40 ^∘C in the mountainous regions of northeastern Siberia (Fig. 1c), and range between −20 and −15 ^∘C for boreal forests, the outlines of which can be seen in central Siberia and central North America. The impact of correction factors is limited to grid cells for which vegetation is dominated by evergreen needleleaf trees and implementation results in an increase in average snow surface temperature of up to 2 ^∘C. The lack of spatial variability is caused by little spatial variability in meteorological conditions, high vegetation density, and similarly high PFT coverage across boreal forests (Fig. 1a and b).

Cold content, the energy required to raise snow temperatures to 0 ^∘C, is used to quantify the impact of correction factors on the entire snow column. Average cold content simulated by CLM4.5 mostly reaches values of up to 4 MJ m⁻² and exceeds 5 MJ m⁻² only in glaciated grid cells (Fig. 7e). In CTRL, simulated average cold content ranges between 1.5 and 3 MJ m⁻² across boreal forests, with the lowest values in northeastern Europe and highest values in eastern Siberia, western Canada, and Quebec. Relative changes in cold content from CTRL to CORR display spatial differences, with cold content generally decreasing across boreal forests (Fig. 7f). Reductions in average cold content reach up to 30 % in northeastern Europe and western North America and up to 20 % in central North America. Across Siberian boreal forests, relative reductions decrease from west to east from more than 20 % to about 10 %. Spatial differences in relative reductions correspond to spatial differences in average cold content, with higher relative reductions for smaller averages, representing a more even spatial pattern of absolute reductions in cold content as indicated by changes in snow surface temperature (Fig. 7d).

Spatial patterns in the snow-off date are similar to those in cold content, with higher cold content corresponding to later melt-out (Fig. 7g and h). Changes in the snow-off date from CTRL to CORR display stark spatial contrasts, with melt-out happening up to 10 d earlier in central Europe and on the western coast of North America. Melt-out is advanced by about 5 d for boreal forests in northeastern Europe and western Siberia and slightly less for boreal forests in central North America. In contrast, melt-out is delayed in the mountains of southeastern Siberia (Fig. 1c), where melt-out occurs late among boreal forests.

As offline simulations lack spatial variability in ε_sky, latitude (through insolation) and duration of snow on the ground (through day length) control spatial differences in the impact of correction of sub-canopy longwave radiation on the snow-off date. Changes in longwave enhancement due to correction of sub-canopy longwave radiation before and after the boreal spring equinox, approximated by averages over February–March and April–May, display opposite signs across the Northern Hemisphere (Fig. 8), with shorter (longer) days than nights before (after) the equinox resulting in an increase (decrease) in daily average longwave enhancement. Generally, lower insolation at higher latitudes leads to a more positive impact of correction on daily average longwave enhancement, increasing (decreasing) positive (negative) changes in longwave enhancement with increasing latitude before (after) the boreal spring equinox. Across mid-latitudes, the increase in daily average longwave enhancement over February and March is roughly similar to the decrease in daily average longwave enhancement over April and May, while the increase over February and March outweighs the decrease over April and May across high latitudes, including most of the regions covered by boreal forests.

Reasons for spatial differences in changes of the snow-off date across Siberian boreal forests are explored in Fig. 9. Snow-off dates are similar spatially in CTRL, likely caused by higher elevations in southeastern Siberia compensating for less cold content, and melt-out generally occurs past the boreal spring equinox in northwestern and southeastern Siberia. However, higher insolation for southeastern Siberia results in higher reductions of daytime sub-canopy longwave radiation by correction factors and consequently smaller increases in daily average sub-canopy longwave radiation prior to the boreal spring equinox compared to northwestern Siberia. Although changes in sub-canopy longwave radiation are still positive in southeastern Siberia, when accumulated over the snow season, causing a decrease in cold content, reduction in daily average sub-canopy longwave radiation by correction factors past the boreal spring equinox cancels out the previous increase, and consequently, snowmelt is slightly delayed. In contrast to southeastern Siberia, melt-out is slightly accelerated in central North America, although both latitude and the melt-out date are similar, as relative reductions in cold content are generally higher. However, differences in changes in the melt-out date between central North America and southeastern Siberia are minor.

Figure 9Change in cold content and snow-off date from CTRL to CORR as a function of (a) snow-off date and (b) cold content in CTRL as well as elevation (c) for grid cells within the area 42 to 70^∘ N and 40 to 140^∘ E.

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4.4 Snow-off date in comparison to observations

Simulated and observed snow-off dates are compared in Fig. 10 for grid cells with consistent snow cover throughout the preceding December and coverage by evergreen needleleaf trees of at least 50 %. The simulations CTRL and CORR generally feature a narrower probability density function (PDF) of snow-off dates, indicating a shorter snowmelt season, and later melt-out compared to observations across the entire Northern Hemisphere (Fig. 10a). While shapes of observed PDFs are well represented by simulations over Eurasia (Fig. 10b and d), observations show a clearer, shorter peak of melt-out compared to simulations over mountainous western North America (Fig. 10c). Correction of sub-canopy longwave radiation displays little impact when accumulated over the entire Northern Hemisphere; however, it systematically reduces the delay of simulated snow-off dates throughout the snowmelt season. PDFs of snow-off dates for regional subsets reflect spatial patterns seen in Fig. 7h, with minor differences between CTRL and CORR over most of western North America (Fig. 10c) and eastern Siberia (Fig. 10d) but substantial acceleration of snow-off dates over western Siberia and eastern Europe (Fig. 10b) due to correction of sub-canopy longwave radiation.

Figure 10PDFs of snow-off dates and sample sizes n for CTRL (black), CORR (red), and observations (blue) over 1982–2010 across grid cells with coverage by evergreen needleleaf trees of at least 50 % and snow cover persisting through December. Observational estimates are shown for SWE thresholds of 1 mm (bold line) and 0.5 to 4 mm (shaded area). Panels show entire Northern Hemisphere (a), eastern Europe and western Siberia (b; 49 to 66^∘ N and 29.5 to 90.5^∘ E), western North America (c; 39.5 to 66^∘ N and 104.5 to 125.5^∘ W), and eastern Siberia (d, 44 to 66^∘ N and 90.5 to 135.5^∘ E). Panels (e) and (f) are as panels (a) and (b), respectively, but only for grid cells with average changes in snow-off dates of at least 3 d (as seen in Fig. 7h).

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The regionally limited impact of corrected sub-canopy longwave radiation is highlighted by filtering PDFs of the snow-off date for grid cells with average differences in the snow-off date between CORR and CTRL of at least 3 d (Fig. 10e and f). Correction of sub-canopy longwave radiation improves timing of melt-out in filtered grid cells especially over western Siberia and eastern Europe, where the filtered PDF for CORR, in contrast to CTRL, closely resembles observations. PDFs of snow-off dates derived from the Blended-5 SWE display sensitivity to threshold choices; however, this uncertainty is generally smaller than differences between simulations and observations.