Simulation of snow accumulation and melt in needleleaf forest environments

Drawing upon numerous field studies and modelling exercises of snow processes, the Cold Regions Hydrological Model (CRHM) was developed to simulate the four season hydrological cycle in cold regions. CRHM includes modules describing radiative, turbulent and conductive energy exchanges to snow in open and forest environments, as well as account for losses from canopy snow sublimation and rain evaporation. Due to the physical-basis and rigorous testing of each module, there is a minimal need for model calibration. To evaluate CRHM, simulations of snow accumulation and melt were compared to observations collected at paired forest and clearing sites of varying latitude, elevation, forest cover density, and climate. Overall, results show that CRHM is capable of characterising the variation in snow accumulation between forest and clearing sites, achieving a model efficiency of 0.51 for simulations at individual sites. Simulations of canopy sublimation losses slightly overestimated observed losses from a weighed cut tree, having a model efficiency of 0.41 for daily losses. Good model performance was demonstrated in simulating energy fluxes to snow at the clearings, but results were degraded from this under forest cover due to errors in simulating sub-canopy net longwave radiation. However, expressed as cumulative energy to snow over the winter, simulated values were 96% and 98% of that observed at the forest and clearing sites, respectively. Overall, the good representation of the substantial variations in mass and energy between forest and clearing sites suggests that CRHM may be useful as an analytical or predictive tool for snow processes in needleleaf forest environments. Correspondence to: C. R. Ellis (cre152@mail.usask.ca)


Introduction
Needleleaf forests dominate much of the mountain and boreal regions of the northern hemisphere where snowmelt is the most important hydrological event of the year (Gray and Male, 1981).The retention of foliage by evergreen needleleaf tree species during winter acts to decrease snow accumulation via canopy interception losses (Schmidt, 1991;Lundberg and Halldin, 1994;Pomeroy et al., 1998a) and greatly modify energy exchanges to snow (Link and Marks, 1999;Gryning and Batchvarova, 2001;Ellis et al., 2010).However, forest cover is often discontinuous, containing clearings of varying dimensions which may differ considerably in snow accumulation (McNay, 1988) and melt characteristics (Metcalfe and Buttle, 1995).As such, management of water derived from forest snowmelt is expected to benefit from the effective prediction of snow accumulation and melt in both forest and open environments.
Forest cover varies in its effects upon snow accumulation, with reductions of 30% to 50% of that in nearby clearings observed in cold Canadian and Russian mountain and boreal forests (Pomeroy and Gray, 1995;Pomeroy et al., 2002;Gelfan et al., 2004) to nearly even accumulations reported in temperate Finnish forests (Koivusalo and Kokkonen, 2002).Although numerous mechanisms have been proposed to explain decreased snow accumulations in forests, sublimation of canopy snow has been shown to be the primary factor controlling forest snow losses (Troendle and King, 1985;Schmidt et al., 1988;Pomeroy and Schmidt, 1993;Lundberg and Halldin, 1994;Parviainen and Pomeroy, 2000).Investigations by Pomeroy and Gray (1995) and Pomeroy et al. (1998a) found that 30 to 45% of annual snowfall in western Canada may be lost by canopy sublimation due to the increased exposure of intercepted snow to the above atmosphere.Thus, the estimation of canopy sublimation losses C. R. Ellis et al.: Simulation of forest snow accumulation and melt have often made appeal to physically-based "ice-sphere" models (e.g.Schmidt, 1991) which adjust sublimation losses from a single, small ice-sphere for the decreased exposure of canopy snow to the atmosphere.Such methods have been shown to well approximate canopy sublimation losses over multiple snowfall events through the coupling of the multiscale sublimation model to a needleleaf forest interception model (Pomeroy et al., 1998a).
Alongside interception effects, needleleaf forest cover also influences energy exchanges to snow.The forest layer acts to effectively decouple the above-canopy and sub-canopy atmospheres, resulting in a large suppression of turbulent energy fluxes (Harding and Pomeroy, 1996;Link and Marks, 1999).Consequently, energy to sub-canopy snow is dominated by radiation; itself modified by the canopy through the shading of shortwave irradiance while increasing longwave irradiance from canopy thermal emissions (Link et al., 2004;Sicart et al., 2004;Pomeroy et al., 2009).Forest cover may also affect sub-canopy shortwave radiation by altering snow surface albedo through deposition of forest litter on snow (Hardy et al., 2000;Melloh et al., 2002), or by influencing energy-controlled snow metamorphism rates (Ellis et al., 2010).As such, simulations of forest effects on energy to snow have largely focused on the adjustment of shortwave and longwave fluxes (Hardy et al., 2004;Essery et al., 2008;Pomeroy et al., 2009), although methods estimating turbulent energy transfer in forests have also been described (Hellström, 2000;Gelfan et al., 2004).
Since the first successful demonstration of snowmelt simulation using an energy-balance approach by Anderson (1976), numerous such snowmelt models have developed (e.g.EBSM, Gray and Landine, 1988;SNTHERM, Jordan, 1991;SHAW, Flerchinger and Saxton, 1989;Snobal, Marks et al., 1999).Due to the differing objective specific to each model, there is considerable variation in the detail to which snow energetics may be described, as well as forcing data and parameterization requirements.In general, more sophisticated snowmelt models possess information requirements that may prohibit their successful employment in more remote environments, where forcing data and parameter information is typically lacking or poorly approximated.Instead, more basic models that maintain a physically-based representation of forest snow processes in cold regions are expected to be better suited for such environments.
Although much focus has been placed on simulating forest snow accumulation and melt processes separately, fewer simulations over the entire snow accumulation and melt period have been demonstrated.To this end, this paper outlines and evaluates the simulation of snow accumulation and melt in paired forest and clearing sites of varying forest cover density and climate using the Cold Regions Hydrological Model (CRHM).CRHM is a deterministic model of the hydrological cycle containing process algorithms (modules) developed from field investigations in cold region environments, with modest data and parameter requirements.This paper exam-ines the potential for CRHM to be used to analyze and predict how changes in climate and forest-cover may affect snow processes in cold region forests.

Model description
Described in detail by Pomeroy et al. (2007), CRHM operates through interaction of its four main components: (1) observations, (2) parameters, (3) modules, and (4) variables and states.The description of each component below focuses on the requirements of CRHM for forest environments: 2. Parameters: provides a physical description of the site, including latitude, slope and aspect, forest cover density, height, species, and soil properties.In CRHM, forest cover need only be quantified by an effective leaf area index (LAI') and forest height (h); the forest sky view factor (v) may be specified explicitly or estimated from LAI'.The heights at which meteorological forcing data observations are collected are also specified here.
3. Modules: algorithms implementing the particular hydrological processes are selected here by the user.
4. Initial states and variables: specified within the appropriate module.

Modules
The following provides a general outline of the main modules and associated algorithms in CRHM.

Observation module
To allow for the distribution of meteorological observations away from the point of collection, appropriate corrections are applied to observations within the observation module.These include the correction of air temperature, humidity, Hydrol.Earth Syst.Sci., 14, 925-940, 2010 www.hydrol-earth-syst-sci.net/14/925/2010/ and the amount and phase of precipitation for elevation, as well as correction of shortwave and longwave irradiance for topography.

Snow mass-balance module
In CRHM, snow is conserved within a single defined spatial unit, with changes in mass occurring only through a divergence of incoming and outgoing fluxes.In clearing environments, snow water equivalent (SWE) [kg m −2 ] at the ground may be expressed by the following mass-balance of vertical and horizontal snow gains and losses where t is the time step in the model calculation, SWE o is the antecedent snow water equivalent [kg m −2 ], P s and P r are the respective snowfall and rainfall rates, H in is the incoming horizontal snow transport rate, H out is the outgoing horizontal snow transport rate, S is the sublimation loss rate, and M is the melt loss rate [all units kg m −2 t −1 ].In forest environments Eq. ( 1) is modified to in which I s is canopy snowfall interception rate, U l is the rate of canopy snow unloading, I r is the canopy rainfall interception rate, and R d is the rate of canopy rain drip [all units kg m −2 t −1 ].
The amount of snowfall intercepted by the canopy is dependent on various physical factors, including tree species, forest density, and the antecedent intercepted snowload (I s,o ) [kg m −2 ].In CRHM, a dynamic canopy snow-balance is calculated, in which the amount of snow interception (I s ) is determined by where C l is the "canopy-leaf contact area" per unit ground [], and I * s is the species-specific maximum intercepted snowload [kg m −2 ], which is determined as a function of the mean maximum snowload per unit area of branch, S [kg m −2 ], the density of falling snow, ρ s [kg m −3 ], and LAI by Sublimation of intercepted snow is estimated following the Pomeroy et al. (1998) multi-scale model, in which the sublimation rate coefficient for intercepted snow, V i [s −1 ], is multiplied by the intercepted snowload to give the canopy sublimation flux, q e [kg m −2 s −1 ], i.e.
q e = V i I s . (5) Here, V i is determined by adjusting the sublimation flux for a 500 µm radius ice-sphere, V s [s −1 ], by the intercepted snow exposure coefficient, C e [], i.e.
in which C e is defined by Pomeroy and Schmidt (1993) as where k is a dimensionless coefficient indexing the shape of intercepted snow (i.e.age and structure) and F is an exponent value of approximately 0.4.The ventilation wind speed of intercepted snow may be set as an observed within-canopy wind speed, or approximated from above-canopy wind speed by where u ξ [m s −1 ] is the estimated within-canopy wind speed at a fraction ξ of the entire forest depth [], u h is the wind speed at the canopy top [m s −1 ], and ψ is the canopy wind speed extinction coefficient [], which is determined as a linear function of LAI' for various needleleaf species (Eagleson, 2002).Unloading of intercepted snow to the sub-canopy snowpack is calculated as an exponential function of time following Hedstrom and Pomeroy (1998).Additional unloading resulting from melting intercepted snow is estimated by specifying a threshold ice-bulb temperature (T b ) in which all intercepted snow is unloaded when exceeded for three hours (Gelfan et al., 2004).

Rainfall interception and evaporation module
Although the overall focus of this manuscript is that of snowforest interactions, winter rainfall may represent substantial water and energy inputs to snow.(Rutter, 1971) in which a single storage is determined and scaled for sparse canopies by C c (e.g.Valente et al., 1997).Evaporation from a fully-wetted canopy (E p ) [kg m −2 t −1 ] is calculated using the Penman-Monteith combination equation (Monteith, 1965) for the case of no stomatal resistance, i.e.
For partially-wetted canopies E is reduced in proportion to the degree of canopy saturation, i.e.
where Q m is the energy for snowmelt, dU /dtis the change in internal (stored) energy of snow, K * and L * are net shortwave and longwave radiations, respectively, Q h and Q e are the net sensible and latent heat turbulent fluxes, respectively, Q g is the net ground heat flux, and Q p is the energy from rainfall advection [all units MJ m −2 t −1 ].In Eq. ( 11), positive magnitudes represent energy gains to snow and negative magnitudes are energy losses.The amount of melt (M) is calculated from where ρ w is the density of water [kg m −3 ], B is the fraction of ice in wet snow [∼0.95−0.97],and λ f is the latent heat of fusion for ice [MJ kg −1 ].

Adjustment of energy fluxes to snow for needleleaf forest cover
For the purpose of brevity, the following section outlines the algorithms in CRHM estimating energy fluxes in forest environments only.For an overview of energy flux estimations by CRHM in open environments, refer to Pomeroy et al. (2007).

Shortwave radiation to forest snow
In CRHM, net shortwave radiation to forest snow (K * f ) is equal to the above-canopy irradiance (K ↓) transmitted through the canopy less the amount reflected from snow, expressed here as in which α s is the snow surface albedo [], the decay of which is approximated as a function of time subsequent to a snowfall event, and τ is the forest shortwave transmittance [], which is estimated by the following variation of Pomeroy and Dion's (1996) formulation (Pomeroy et al., 2009) where θ is the solar angle above the horizon [radians].

Longwave radiation to forest snow
As stated previously, longwave irradiance to forest snow (L ↓ f ) may be enhanced relative to that in the open as the result of thermal emissions from the canopy.Simulation of L ↓ f is made as the sum of sky and forest longwave emissions weighted by the sky view factor (v), i.e.
Here, ε f is the forest thermal where ε s is the thermal emissivity of snow [], and T s is the snow surface temperature [K] which is resolved using the longwave psychrometric formulation by Pomeroy and Essery (2010): where w a and w s are the specific and saturation mixing ratios [], ρ a is the air density [kg m −3 ], c p is the specific heat capacity of air [J kg and is the slope of the saturation vapour pressure curve [kPa K Determination of Q h andQ e in open and forest sites are made using the following semi-empirical formulations developed by Gray and Landine (1988): Q e = 0.08(0.18+ 0.098u mean ) (6.11 − 10ea mean ) where u mean is the mean daily wind speed [m s −1 ], T max is the maximum daily air temperature [ • C], and ea mean is the mean daily vapour pressure [kPa].For the case of rainfall to melting snow (i.e.T s =0 • C), the energy delivered to the snowpack via rainfall advection (Q p ) is given by where T r is the rainfall temperature [ • C], which is approximated by T a .The primary mass and energy balance calculation routines for both forest and clearing environments within CRHM are summarized in Fig. 1.

Model application
Simulations of snow accumulation and melt using CRHM were performed at five paired forest and clearing sites of varying location, climate, forest species, and forest cover density (Table 1  snow model inter-comparison project (SnoMIP2) (Rutter et al., 2009;Essery et al., 2009).This initiative involved the off-line simulation of snow accumulation and melt in paired forest and nearby clearing sites located in Canada, Switzerland, Finland, Japan and the United States.Hourly standard meteorological forcing data, site descriptions, and initial states were provided to each participant by the SnoMIP2 facilitators.All simulations in SnowMIP2 were executed "blindly" with the exception of the Switzerland location for the 2002-2003 season where SWE field data were provided to allow for the option of model calibration.Location, topography and forest cover descriptions for all sites are given in Table 1, and site pictures in Fig. 2. Simulations of snow accumulation and melt were performed for both forest and adjacent forest clearing sites at each location for the period extending from 1 October to approximately 1 June.For each simulation timestep, appropriate energy, mass, and state variables were outputted by the model.

Evaluation of model performance
Simulations of snow accumulation and melt by CRHM were evaluated in terms of the ability of representing: 1. the variation in mean and maximum seasonal SWE observed between all sites; and 2. the timing and quantity of SWE accumulation and melt at individual sites.
For 1 and 2 above, model performance was assessed by the following three measures: the model bias index (MB), the model efficiency index (ME), and the root mean square error (RMSE).These indexes were used as they provide a rather complementary evaluation of model performance, with the MB comparing the total simulation output to the total of observations, the ME an indication of model performance compared to the mean of the observations, and the RMSE a where x avg is the mean value of n number of x obs values.In Eq. ( 22), model efficiency increases as the ME index approaches 1, which represents a perfect match between simulations and observations; 0 indicates an equal efficiency between simulations and the x avg , with increasingly negative values signifying a progressively superior estimation by the x avg .The root mean square error (RMSE) is determined by www.hydrol-earth-syst-sci.net/14/925/2010/ Hydrol.Earth Syst.Sci., 14, 925-940, 2010

Simulation of mean and maximum winter SWE at all sites
Among all sites, considerable variation in mean and maximum seasonal SWE was observed, with mean SWE ranging from 20 to 160 kg m −2 , and maximum SWE from 29 to  295 kg m −2 .Large variations in SWE were also observed between paired forest and clearings, with forest accumulations ranging from approximately 30% of the clearing accumulation at the Alptal location (2003)(2004) to near even accumulations at the BERMS location.Simulated and observed mean and maximum SWE at all sites are shown in Fig. 3 with model performance index values given in Table 2. Here, simulations exhibit a small systematic under-prediction of mean SWE for all sites (MB=0.97),with a slightly greater under-prediction for the

Simulation of winter SWE accumulation and melt at individual sites
Simulations of snow accumulation and melt at individual sites exhibited considerable variation in the accuracy of predicting the quantity and timing of SWE.However, as seen in Fig. 4, model simulations are able to capture the general differences in the timing of accumulation and melt between paired forest clearing sites.Model performance indexes for simulations at individual sites, as well as the mean index values for forest, clearing, and all sites are given in  2002-2003 and 2003-2004 winters, respectively.Overall, the mean RMSE for all sites was 26.5 kg m −2 , with higher absolute errors for simulations at the clearing sites.Due to the discontinuity of SWE observations over the winter at each site, exact determinations of the start, peak, and end of seasonal snow accumulation were not possible.Alternatively, an evaluation of the timing of snow accumulation was provided by the determination of the MB, ME, and RMSE of simulated SWE at the first, last and maximum SWE observation at each site (Table 4).Here, results show for the first observation, SWE is slightly over-predicted at the clearing sites (MB=1.07),with a large under-prediction of forest SWE (MB=0.6).At maximum SWE, little systematic simulation bias occurs for SWE simulations at all sites (MB=0.99)due to the offsetting of the slight over-prediction and under-prediction at the clearing and forest sites, respectively.However, for the last observed SWE, the high MB values indicate a large over-estimation of SWE at the end of melt, suggesting a substantial lag in simulated snow depletion.Poor simulation of late-season SWE is also reflected in the low ME and high RMSE as compared to results for the first and maximum SWE observations.

Simulation of canopy snow sublimation
The above results show CRHM is generally able to represent the observed differences in snow accumulation between paired forest and clearing sites.Considering that these differences are largely the result of canopy sublimation losses, model performance in estimating canopy sublimation   is further investigated here.Evaluation of canopy sublimation was performed using canopy snowload measurements from a spruce tree suspended from a load cell at the Marmot Creek spruce forest site (Fig. 2).Changing tree weight was correlated to the intercepted snowload by the measured difference in snow accumulations between the forest and an adjacent clearing site (e.g.Hedstrom and Pomeroy, 1998).
Decreases in tree tare from desiccation and needleleaf loss were accounted for, as was snow unloading from the canopy by measurements of snow collected in three lysimeters suspended under the canopy.Simulation of canopy sublimation was performed for the period of 14 January to 3 March using precipitation and incoming radiation data from the adjacent clearing with observations of within-canopy wind speed and humidity at the suspended tree.Over the period, approximately one-half of snowfall was lost by canopy sublimation, with respective mean daily observed and simulated losses of 0.52 kg m −2 and 0.55 kg m −2 , giving a MB of 1.06 and a ME of 0.41.The time-series of hourly canopy sublimation losses in Fig. 5 (top) shows a general agreement between observed and simulated values, with higher rates corresponding to periods of relatively high wind speeds and low relative humidity (Fig. 5, bottom).Overall, the cumulative amounts of observed and simulated sublimation were similar, equal to approximately 24 and 26 kg m −2 over the period, respectively.

Simulation of energy fluxes to snow
To investigate CRHM's handling of energy fluxes, simulations of energy fluxes to snow were compared to measurements made at the Marmot Creek paired pine forest and clearing sites.Measurements from these sites include incoming and outgoing shortwave and longwave radiation, as well as ground heat fluxes.However, as no direct measures of sensible and latent heat were made, evaluation of the simulation of these fluxes was not possible.
Time-series plots of observed and simulated energy terms during snowcover in Fig. 6 and model indices in Table 5 show a good agreement for all shortwave radiation terms at forest and clearing sites, and good prediction of net longwave radiation (L*) at the clearing site.However, even with the good prediction of the individual incoming and outgoing longwave fluxes (L ↓ and L ↑) at the forest, the prediction of forest L* was poor, which contributed to degrading estimates of total net radiation to forest snow (i.e.Q n = K*+L*).Despite the large errors in estimating the ground energy flux (Q g ) at the forest and clearing sites, little effect on overall model performance resulted due to the small contribution of Q g to total energy (note that no energy to snow from rainfall, Q p , was observed or simulated).In terms of systematic bias, the small negative and positive values of L*, Q n andQ g observed (and simulated) provided MB values that were often misleading and not instructive to model assessment.Alternatively, the systematic model bias of energy terms was evaluated simply as the difference between the mean of simulated and observed values.Here, the offsetting of small negative and positive biases of individual energy terms resulted in low bias errors of total energy to snow (Q*) at the forest and clearing sites of −0.59 and −0.37 W m −2 , respectively.Furthermore, the close comparison of total simulated and observed energy terms in Fig. 7  able to characterise the substantial difference between forest and clearing energy balances, and provide a good estimation of total energy to snow.Also shown in Fig. 7 are the simulated sensible and latent energy totals, which were greater in absolute magnitude at the clearing to that of the forest, but provided approximately equal contributions relative to Q* at both sites.

Discussion and conclusions
Overall, results show that CRHM is able to well represent the quantity and timing of snow accumulation and melt under needleleaf forest cover and in open forest clearings.Good results were obtained in terms of characterising the substantial differences in snow accumulation and melt observed in open and forest environments at locations of varying location and climate.The accurate representation of the major energy terms between the pine forest and clearing sites suggests that despite modest data requirements, the physical basis of the model is sufficient for representing forest-snow processes in environments of varying forest cover and meteorology.Simulations of mean and maximum seasonal SWE exhibited little systematic bias at forest sites, clearing sites, or all sites.This suggests that much of the errors incurred were random in nature, resulting either from errors in observations or model parameterisation.For simulations of SWE at indi-  vidual sites, errors also appear to be random rather than systematic, considering that the best and worst model efficiencies were obtained for the same site over consecutive winters (i.e.Alptal forest).In all, the poorest model efficiencies of SWE determinations were realised at the 2003-2004 Alptal forest and Marmot pine sites, which had substantially lower accumulations relative to most other sites.Such results may be expected as shallower snowpacks would be more sensitive to simulation errors of mass and energy, thus giving larger relative errors.Notwithstanding these limitations, encouraging simulation results were obtained, as exemplified in the good representation of the extreme differences in forest and clearing snow accumulations observed over the two winters at the Alptal location.Although good prediction of SWE was made for the start and peak of winter accumulations, poorer predictions were made at the end of accumulation, suggesting a lag in simulated melt rates.Particularly large lags in simulated snow depletion occured at the Alptal (2003Alptal ( -2004) ) clearing and Marmot spruce clearing sites, where the substantial late-season snowfall may have resulted in an overestimation of the additional energy deficit to the snowpack.As such, improvement in CRHM's representation of snowmelt timing and rate may require addressing the handling of internal snow energetics with large snowfalls.
Compared to observations of canopy snow load changes from a suspended tree, satisfactory model simulation of canopy sublimation was achieved both in terms of daily and cumulative losses.The correspondence of periods of high sublimation with relatively high wind speeds and low relative humidity demonstrate the physically-based manner in which canopy sublimation is accounted for by CRHM.Accordingly, such approaches are likely necessary to predict differences in snow accumulation between forest and clearings resulting from variations in forest cover density and climate.However, sensitivity analysis has shown sublimation estimates in CRHM to be very responsive to errors in the intercepted snowload, which may have been brought about by the rather simplistic approach in the handling of canopy snow unloading by CRHM.Consequently, increased confidence in the model's representation of canopy sublimation losses would likely by gained through a better understanding of the physical processes controlling canopy unloading of snow.), and the difference between mean simulated and observed values of: shortwave irradiance (K↓), reflected shortwave irradiance (K↑), net shortwave radiation (K * ), longwave irradiance (L↓), longwave exitance (L↑), net longwave radiation (L * ), total net radiation (Q n ), net ground heat flux (Q g ), and total energy to snow (Q * ) (i.e.Q* = Q m + dU/dt) for pine forest and clearing sites at Marmot Creek, Alberta, Canada.Although simulations of energy fluxes were evaluated against observations at only a single paired forest and clearing site, results show the model able to well represent both the total energy to snow and the relative contributions of individual energy terms.Furthermore, all errors in estimating shortwave and longwave radiation were small and below the measurement error of the radiometers used in their observation.However, the presence of forest cover is seen to dramatically decrease the model's predictive capability of net radiation and total energy to snow, as seen in the decreasing model efficiency with the increasing number of combined energy terms.Yet, cumulative errors in estimating total energy to snow were relatively modest, owing in part to the error cancellation of individual energy terms.Although no evaluation of sensible and latent energy terms was possible, simulated magnitudes were similar to those observed in cold-region needleleaf forest environments by Harding and Pomeroy (1996) and estimated by Pomeroy and Granger (1997).

Site
Despite some uncertainly in model performance, results show CRHM is able to provide good characterisation of critical forest-snow processes in environments of highly variable forest cover and climate, with only modest requirements for site information and meteorological forcing data.As simulations were performed without calibration to any objective function, there is increased confidence that CRHM is capable of representing the effects on snow accumulation and melt brought about by changes in forest cover or climate.Consequently, results from this model evaluation are encouraging for the use of CRHM as a diagnostic or predictive tool in investigating needleleaf forest cover effects on snow processes in cold regions.

Appendix
1. Observations: CRHM requires the following meteorological forcing data for each simulation timestep, t (units in [ ]): a air temperature , T a [ • C]; b humidity, either as vapour pressure, e a [kPa] or relative humidity, RH [%]; c precipitation, P [kg m −2 ]; d wind speed, observed either above, or within the canopy, u [m s −1 ]; e shortwave irradiance, K ↓ [W m −2 ] (in the absence of observations, K ↓ may be estimated from T a ); f longwave irradiance, L↓ [W m −2 ] (in the absence of observations, L ↓ may be estimated from T a and e a ).

Fig. 1 .
Fig. 1.Schematic outlining the major mass and energy calculations involved in the forest component of the Cold Regions Hydrological Model (CRHM).
C. R. Ellis et al.: Simulation of forest snow accumulation and melt Alptal, Switzerland forest (left) and clearing (right).BERMS, Saskatchewan, Canada forest (left) and clearing (right).Fraser, Colorado, USA forest (left) and clearing (right).Marmot Creek, Alberta, Canada pine forest (left) and clearing (right).Marmot Creek, Alberta, Canada spruce forest showing the suspended spruce tree (left), the spruce clearing (centre) and reference radiation tower at the spruce clearing (right).

Figure 2 .
Figure 2. Photographs of meteorological stations located at forest and clearing sites at Alptal, Switzerland; BERMS, Saskatchewan, Canada; Fraser, Colorado, USA; and pine and spruce sites at Marmot Creek, Alberta, Canada (with the exception of the Marmot Creek sites, site photographs were provided by the SnowMIP2 facilitators).

Fig. 2 .
Fig. 2. Photographs of meteorological stations located at forest and clearing sites at Alptal, Switzerland; BERMS, Saskatchewan, Canada; Fraser, Colorado, USA; and pine and spruce sites at Marmot Creek, Alberta, Canada (with the exception of the Marmot Creek sites, site photographs were provided by the SnowMIP2 facilitators).

Fig. 3 .
Fig. 3. Observed and simulated mean and maximum snow water equivalent (SWE) accumulations at forest and clearing sites.

Fig. 4 .
Fig. 4. Time series of observed and simulated SWE at paired forest and clearing sites.

Fig. 5 .
Fig. 5. Top: observed and simulated hourly (and cumulative) canopy snow sublimation; bottom: corresponding observations of forest wind speed and relative humidity.

KFig. 6 .
Fig.6.Time series plots of mean daily simulated and observed shortwave (K) and longwave (L) radiation fluxes, as well as total net radiation to snow (Q n ) at pine forest and clearing sites at Marmot Creek, Alberta, Canada.

Fig. 7 .
Fig. 7. Observed and simulated net energy terms and total energy to snow (Q* = dU /dt + Q m ) at pine forest and clearing sites (note that due to no observations of simulated sensible (Q h ) and latent (Q e ) heat fluxes, observations are assigned the same value as simulations).

.4 Snow energy-balance module Energy
to snow (Q*) is resolved in CRHM as the sum of radiative, turbulent, advective and conductive energy fluxes to snow, i.e.

Table 1 .
Location, topography, and forest cover descriptions of paired clearing and forest sites used in simulations of snow accumulation and melt.

Table 2 .
Model bias index (MB), model efficiency index (ME), and root mean square error (RMSE) of simulated mean and maximum snow water equivalent (SWE) at clearing sites, forest sites, and all sites.

Table 3 .
Determined model bias index (MB), model efficiency index (ME), and root mean square error (RMSE) for simulations of snow water equivalent (SWE) at individual sites.
forest sites.In comparison, a greater under-prediction of maximum SWE at all sites was realised (MB=0.94).Yet, the high ME value indicates CRHM well represented the variability in mean and maximum SWE accumulations between sites.Similar to MB results, the ME shows superior prediction of mean SWE to that of maximum SWE, as well as better prediction for clearing sites relative to forest sites.However, due to less snow at the forest sites, the lower MB and ME indexes at the forest sites translate into similar magnitudes of absolute error to that at the clearings (i.e.RMSE=∼16 kg m −2 ), and even lower absolute errors for the prediction of maximum SWE.

Table 3 .
Here, only small systematic underestimations of SWE are realised at both forest and clearing sites, having corresponding MB values of 0.94 and 0.99.In all, the mean ME for SWE simulations at individual sites was 0.51, with slightly lower efficiencies at the forest sites.Among simulations, the highest and lowest ME were both obtained at the Alptal forest site, with ME values of 0.93 and −0.03 for the

Table 4 .
Model bias index (MB), model efficiency index (ME) and root mean square error (RMSE) for simulations of SWE at the first SWE observation, maximum SWE observation, and last SWE observation at clearing sites, forest sites, and all sites.