It is established that the density of a larch forest strongly influences the snowmelt energy under its canopy. In the spring thaw of 1994, 1995, and 1996, the surface snowmelt at three different sites located at the southern foot of Mt. Iwate, Japan, was measured. These sites were surrounded by the same tree species with similar tree height, but with different forest densities [open (OP) site; sparse larch forest (SLF): 411 larch trees per hectare; dense larch forest (DLF): 1433 larch trees per hectare]. It was observed that at most periods under analysis, the snow surface albedo under the canopy decreased as the forest density increased. With this in mind, a simple empirical model for the balance of snow surface energy at a forested site shows that variations in below-canopy snow albedo, due to forest density, are important for estimating the snowmelt energy, especially at high forest densities. The importance of such variations lies in the fact that their inclusion is necessary to estimate accurately the net all-wave radiation in DLF—net all-wave radiation being the most important energy component that affects snowmelt. Taking into account variations in the weather conditions, net all-wave radiation does not usually decrease as forest density increases, because when forest density increases, there is an associated increase in longwave radiation that is counterbalanced by a decrease in below-canopy snow albedo. By contrast, net all-wave radiation does increase slightly when forest density increases. Variation in net all-wave radiation under the larch forest canopy depends upon the variation in below-canopy incident short-wave radiation and below-canopy snow albedo. Variations in below-canopy snow albedo, which are due to variations in forest density, affect the snowmelt energy as follows: (i) when the initial below-canopy snow albedo is low, the snowmelt energy decreases significantly as forest density increases, because the decrease in below-canopy incident shortwave radiation is more than the decrease of below-canopy snow albedo, both of which are due to increases in forest density. By contrast, (ii) when the initial below-canopy snow albedo is high, the snowmelt energy changes only slightly as forest density increases, because the slight increase in net all-wave radiation that occurs when forest density increases is caused by the fact that the decrease in below-canopy incident shortwave radiation due to increases in forest density is cancelled out by the decrease in below-canopy snow albedo that occurs in response to increases in forest density.
At middle and high latitudes in winters in the Northern Hemisphere, snow covers most high mountainous regions and land surfaces. This affects the above-canopy albedo. The above-canopy albedo of snow cover, in turn, strongly influences the present climate system (Bonan et al. 1992). Harding and Pomeroy (1996) showed that, compared to a lake site, a forested site with canopy snow has a lower albedo and a higher sensible heat flux.
In order to make use of meltwater, it is important to predict the rate at which snow disappears as it melts. Most snowy regions are at least partly forested, and many studies have examined the effect of forest cover on snowmelt (Price and Dunne 1976; Price 1988; FitzGibbon and Dunne 1983; Ohta et al. 1993; Hashimoto et al. 1994; Hardy et al. 1997; Yamazaki and Kondo 1992; Koike et al. 1995; Marks et al. 1998; Suzuki et al. 1999; Woo and Giesbrecht 2001). These studies found that the net all-wave radiation is the dominant energy component causing snowmelt, and that forest cover has a significant effect on below-canopy snowmelt.
Price (1988) and Ohta et al. (1993) suggested that the net all-wave radiation is the major heat flux component of snowmelt. This quantity decreases under a forest canopy because of the reduced solar radiation. Petzold (1981) and Nakabayashi et al. (1999) modeled solar radiation in order to estimate the below-canopy net all-wave radiation, and their studies confirmed that the net all-wave radiation decreases as density in a larch forest increases. Ni et al. (1997) used a model to evaluate incident shortwave radiation under a forest canopy based on stand-scale information, and their model can predict the probable transmission of shortwave radiation.
Simple models that have been developed for longwave radiation under forest canopies (Male and Granger 1981; Hashimoto et al. 1994) show that longwave radiation is important for below-canopy snowmelt. These models show that the downward longwave radiation actually increases with forest density. FitzGibbon and Dunne (1983) examined the relation between forest cover, the net all-wave radiation, and snowmelt, and found that the net all-wave radiation increases as the transmission of solar radiation through the canopy decreases. Suzuki et al. (1999) found that the net all-wave radiation does not vary with forest density during the snowmelt season, because of the effects of below-canopy snow albedo and downward longwave radiation.
By using the forest stand-scale model of Hardy et al. (1997) and Davis et al. (1997) showed that snow ablation depends on tree height and tree species, using forest parameters: horizontal crown radius, vertical crown radius, foliage area, volume density, stem density, and crown depth. Woo and Giesbrecht (2001) developed a trunk-scale model to evaluate the spatial distribution of snow cover, but this requires detailed forest stand information—canopy radius and canopy height for each tree, and location of each tree—when applied to large-scale basin snowmelt, as does the forest stand model. These models could describe the detail of snowmelt, but it is difficult to get the detail of such forest descriptions over the basin scales.
To obtain forest stand information on basin scales, satellite data are often necessary. Nemani et al. (1993) used remote sensing to estimate the leaf area index (LAI) by the Normalized Difference Vegetation Index (NDVI), and found that it strongly affected fluxes in a forested basin. Metcalfe and Buttle (1998) developed a model that uses forest canopy gap fractions derived from optical satellite data to estimate the LAI. It is important to understand the effect of gap fractions on both the LAI and, subsequently, on snowmelt.
The below-canopy snow albedo in winter has also been studied (Pomeroy and Dion 1996) and the effects of litter on snow cover have recently been investigated (Hardy et al. 1998, 2000). Hardy et al. (2000) noted that litter caused a greater reduction in below-canopy snow albedo in a forest site than in an open site, and concluded that the effect of litter cover on the snow surface did not depend on wind speed during the short melting season. Robinson et al. (2001) showed that wind speed determines the rate of litter fall on below-canopy snow cover by studying the same site as Hardy et al., but over a longer period. We believe that the effect of litter fall on the below-canopy snow surface depends on the tree species, wind speed, and forest density, and that further study is required to understand these effects.
In a previous study (Suzuki et al. 1999), we showed, using heat balance analyses, that differences in larch forest density cause variations in snowmelt and in other meteorological variables; below-canopy snow albedo and snowmelt under a forest canopy both decrease as the larch forest density increases. Based on these observations, we have developed empirical formulas for the relations between forest stand descriptors (plant area index, PAI) and meteorological variables. Our equations can be used to predict downward radiation, wind speed, and below-canopy snow albedo under larch forests of different densities.
Warren (1982) noted that the albedo at an open site depends on the snow grain size, contamination by soot, and solar zenith angle. Accordingly, the albedo at high latitudes can exceed that at low or middle latitudes during snow cover and thaw periods, because the solar zenith angle is large and the concentration of industrial soot is low at high latitudes, for example, in eastern Siberia.
However, empirical and theoretical studies of the way in which snowmelt energy varies with forest density are limited, and snowmelt studies that compare sites at different latitudes and altitude are scarce. The purpose of this study is to demonstrate the effects of varying larch forest density on below-canopy snow albedo, and, consequently, on net all-wave radiation and snowmelt energy. We discuss how larch forest density affects snowmelt and changes in snow ablation processes, based on a simple snow surface energy balance model of forested sites.
Table 1 gives a description of the observation site, including forest type and forest density. Figure 1 shows photographs of the three different forest-cover conditions on the southern slope of Mt. Iwate in northern Japan (39°48′N, 140°58′E). The observational site consisted of the southern slope which was about 10-km long and the mean slope angle was about 6°. Thus, we assumed that the observational site had moderate terrain and that the effect of slope was not significant to the meteorological valuables. One site was open (OP), the second was a sparse larch forest [(SLF); plant area index (PAI) = 0.48], and the third was a dense larch forest [(DLF); PAI = 1.05]. The PAI was measured by a plant canopy analyzer (LI-COR LAI-2000), and is defined as the summation of the area of one side of a tree per unit horizontal area. Details of the study sites have been given elsewhere (Suzuki et al. 1999). Figure 2 shows the variation in snow depth under the different larch forests during the periods analyzed. The snow depth increased as the larch forest density increased because wind drifted snow from sparser forest areas and the snow cover period increased as the larch forest density increased, over all sites. During this period, the snow surface density ranged between 370 and 400 kg m−3. Using snow data for Japan (Maeno and Fukuda 1986), the snow grain size was derived from the snow density, with the estimated mean snow grain size being about 1 mm at all three sites.
We also observed the spatial distribution of below-canopy incident shortwave radiation under the forest canopy at the two forest sites, by using 17 pyranometers (Hamamatsu G1118 silicone photo diode) at each forested site. The pyranometers were installed at the center of a main grid (30 m × 30 m) and at the apexes of nine subgrids (10 m × 10 m) at each forested site. Comparing the incident below-canopy shortwave radiation in the center of a main grid to the other below-canopy incident shortwave radiation in apexes of nine subgrids at each forested site, we found that the coefficient of variation in total daily below-canopy incident shortwave radiation to the center of a main grid in each forested site was less than 0.15 among the 17 pyranometers located at each forested site. Details of the observations and results have been given elsewhere (Hashimoto et al. 1997). We assumed that the spatial variations in below-canopy incident shortwave radiation were not significant, because the coefficient of variation in below-canopy incident shortwave radiation was less than 0.15.
In our previous study (Suzuki et al. 1999), we found that global solar radiation, wind speed, and below-canopy snow albedo were the meteorological factors most affected by larch forest density, and that air temperature and relative humidity changed only slightly. Figure 3 shows variations in the daily below-canopy snow albedo under the larch forest canopy. We calculated the daily below-canopy snow albedo as follows. The incident shortwave radiation and upward shortwave radiation were integrated on a daily basis. Then, to estimate the daily below-canopy snow albedo, the daily upward shortwave radiation was divided by the daily incident shortwave radiation. The pattern of variation in the below-canopy snow albedo differed from year to year, and the variation was smaller at each site when fresh snowfall occurred, but, generally, the below-canopy snow albedo decreased as the larch forest density increased. Snow albedo in 1994 at the OP site was larger than in 1995 and 1996. In 1994, the snow cover period began in the middle of December and ended on 8 April 1994. By contrast, in 1995 and 1996, snow cover at the OP site began in early December and ended on 10 April 1995 and on 15 April 1996, respectively. In 1996, the snow cover period was the longest and the snowmelt season was the latest. O'Neil and Gray (1973) demonstrated that the older age of snow surface at the mountain snowpack during the melting season caused the decrease of the snow albedo in 1995 and 1996. We assumed that the decrease of snow albedo at the OP site occurred in 1995 and 1996 because older snow covered the ground, especially in 1996. The below-canopy snow albedo of the SLF site was greater than that of the OP when the snow depth at the OP site was less than 10 cm. We believe that the albedo of the soil below the snow influences the below-canopy snow albedo at snow depths less than 10 cm. The reduction in below-canopy snow albedo due to the density of the larch forest will be explained in the discussion below.
The relations between the daily mean meteorological conditions at the open site and conditions below the forest canopy are modeled by a linear function: MF = a · MO + b, where MO is a meteorological variable at the open site, MF is the same variable at a forested site, and “a” and “b” are coefficients estimated by the least squares regression (see appendix for complete list of terms). Table 2 shows the estimates for a and b, and the determination coefficient R2 for each relation, from about 68 datasets of Suzuki et al. (1999). All R2 values exceed 0.85, and the linear relations suffice to evaluate the effects of forest density on daily meteorological variable values. The relations between a or b and PAI were also used. Table 3 shows mean meteorological data over the period of observation at the OP. Figures 4a and 4b shows the comparisons between the below-canopy solar radiation at the SLF and DLF sites, and solar radiation at the OP site due to the change of weather conditions. When the ratio of actual-to-possible sunshine duration was less than 0.5, below-canopy penetrations of solar radiation at the SLF and DLF sites were about 4% smaller than the value in Table 2. By contrast, when the ratio of actual-to-possible sunshine duration was greater than or equal to 0.5, below-canopy penetration of solar radiation was about 4% greater than the value in Table 2. Here, we believe that these variations in below-canopy incident shortwave radiation did not strongly depend on the weather conditions, because the penetration of below-canopy incident shortwave radiation did not strongly depend on the weather conditions (see Fig. 4). Thus, in the analysis below, we used constant below-canopy penetrations of incident shortwave radiation in Table 2.
b. Model description
Our model for snowmelt below a forest canopy now follows:
1) Energy balance for snow cover
The heat balance equation for the snow is written as
where QM is the energy for the snowmelt (W m−2), RN is the net all-wave radiation (W m−2), H is the sensible heat flux (W m−2), LE is the latent heat flux (W m−2), and QG is the heat storage in the snow cover.
The sensible and latent heat fluxes are estimated from bulk formulas as
where ρ is the air density (kg m−3); CP is the specific heat of air (J K−1 kg−1); L is the latent heat of evaporation (J kg−1); T, U, and q are the air temperature (°C), wind speed (m s−1), and specific humidity, respectively; RH is the relative humidity; and CH, CE are the bulk transfer coefficients for sensible and latent heat fluxes. A subscript “Z” denotes the reference height above the snow cover (approximately 1.3 m above S), and “S” denotes the height of the snow surface (m).
We include the snowmelt model of Kondo and Yamazaki (1990) in the following form:
where T0 = 0 (°C), CS is the heat capacity of snow (2.17 × 103 J m−3 K−1), ρS is the snow density (taken as mean value 3.9 × 102 kg m−3 at the open site), ZF is the freezing depth (m), lf is the heat of fusion for ice (lf is 0.333 × 106 J kg−1), W0 is the maximum water content of the snow cover, λS is the thermal conductivity of the snow cover (W m−1 K−1), ɛ is the snow emissivity (ɛ = 1.0), TS is the snow surface temperature (°C), and a subscript “n” denotes the nth discrete time interval. Kondo (1988) wrote λS as
where ρI is the ice density (ρI is 9.17 × 102 kg m−3).
By using Eqs. (1)–(6), this model can predict QM, TS, and ZF, from the meteorological valuables at reference height.
2) Forest density effects
where IF↓ and LF↓ are the global solar radiation and the downward longwave radiation at a forested site (W m−2), IS↓ and ID↓ are the diffusive and direct solar radiation above the forest canopy (W m−2), VH is the hemispherical view factor, VS is the view factor for a solar path that is not obstructed by canopy, LO↓ is the downward longwave radiation at the open site (W m−2), σ is the Stefan–Boltzmann constant (5.67 × 10−8 W m−2 K−4), and Ta is the air temperature at the reference height on the forested site (°C). When using Eq. (8), the diffusive and direct solar radiation must be estimated; so, to simplify Eq. (8), we do not separate IS↓ and ID↓, because there was insignificant difference in the daily transmission of incident shortwave radiation between cloudly and sunny days in shown Fig. 4. According to our observation (Hashimoto et al. 1997), we believe that spatial differences in the daily incident shortwave radiation at the forested sites are small and that VS ≅ VH if both direct and diffuse solar radiations are accumulated over a whole day. On the basis that the transmission of daily global solar radiation is the same as the hemispherical view factor, Eq. (7) can be approximated as
where IO↓ is the global solar radiation at the open site (W m−2).
To discuss the relations between heat balance characteristics and larch forest density, equations for estimating the effect of the PAI on meteorological conditions must be found. A function describing the relation between a and the PAI was obtained by the least squares method, with allowance for error. We found that, by and large, for the snow albedo a does not change as larch forest density increases, but that b decreases as the larch forest density increases. The snow albedo was, therefore, obtained by the least squares method using b. These functions are shown in Fig. 5. The empirical relations between PAI and the below-canopy meteorological variables are
where I↓ is the incident shortwave radiation, U is the wind speed, α is the below-canopy snow albedo, and subscripts “O” and “F” indicate open and forested sites, respectively. Thus, VH = e0.75PAI.
According to Suzuki et al. (1999), changes in air temperature and specific humidity with larch forest density are small. We, therefore, assumed that the air temperature and the relative humidity above the snow cover at the open site were the same as at the forested sites.
In summary, the meteorological data required as input to our model are the following: air temperature, relative humidity, wind speed, solar radiation, downward longwave radiation, the below-canopy snow albedo of the snow surface at the open site, and the PAI.
3. Simulation of energy exchange at the snow surface
a. Forcing meteorological data
To drive the simple model presented above, the relevant data were input on an hourly basis. First, to discuss the effect of weather on snowmelt during thawing, the incident shortwave radiation was evaluated from the formula (Kondo and Xu 1997)
where IO↓ is the incident shortwave radiation at an open site (W m−2), RS is the ratio of actual daily duration of sunshine to the maximum possible daily duration of sunshine over a full day, given the time of year, IEXT↓ is the extraterrestrial solar radiation (W m−2), and a and b are constants related to the Jordan sunshine recorder by Kondo (1988). Here we set a and b as 0.179 and 0.550, respectively.
At the open site, the downward longwave radiation was also determined using the ratio of actual-to-possible sunshine duration RS:
where IFIN↓, LO↓ are the atmospheric downward longwave radiation at the open site when the weather is, respectively, fine and cloudy (W m−2), and w*TOP is the total amount of effective water vapor (m). The incident shortwave radiation and the downward longwave radiation at the open site were evaluated hourly. Here, it is assumed that the ratio of actual-to-possible sunshine duration RS was constant throughout the day. Thus, the hourly ratio was derived from the daily mean value.
Other meteorological factors, such as air temperature, relative humidity, and wind speed were specified as their daily mean values. Figures 6a, 6b, and 6c show the diurnal variation in air temperature, relative humidity, and wind speed at the OP site normalized by the mean value over the observation period. Below, we discuss the daily value that comprises the mean of the hourly values for that day.
To evaluate the accuracy of this model we used two indexes of accuracy: the absolute error index (AEI) and the relative error index (REI), defined as
where QMe and QMo are the estimated and the observed snowmelt energy, n is the total number of days of observation of snowmelt, and QMo is the mean observed snowmelt energy for n days. Here, we transferred the observed snowmelt rate (mm day−1) by the snow-wire method to the observed daily snowmelt energy, using the energy for fusion of ice. For details of the observations, see Suzuki et al. (1999).
To verify the input data at the open site, Fig. 7 compares the estimated daily mean snowmelt [arrived at by using the observed daily mean meteorological values, the normalized diurnal variation shown in Fig. 6, and Eqs. (13)–(17)] and the observed daily mean forcing meteorological data at OP during the periods analyzed by Suzuki et al. (1999) (shown in Table 4). The data exclude the effect of unreliable observed snowmelt and snow depths less than 10 cm, because using the snow-wire method, we were unable to discriminate between metamorphism and snowmelt just after snowfall. The slope of the regression equation between estimated and observed snowmelt energy was 1.06 with R2 = 0.84, with 90% confidence interval from 1.00 to 1.20. The estimated maximum snowmelt energy to observed maximum snowmelt energy was overestimated by 7 MJ day−1 on 24 April 1996, because we assumed that the ratio of actual-to-possible sunshine duration was constant over the course of a day, thus, stipulating that the incident shortwave radiation would be unaffected by diurnal variations in cloud cover. However, downward longwave radiation was not affected by the hourly change of cloud conditions during a day. Table 5 shows the AEI and REI at the OP site. The AEI was 5.1 mm day−1 and REI was 0.21. The simulation reported below, on the effect of larch forest density effect, contains these errors because of the estimation of downward radiation at the OP site.
By using functions of the PAI, the meteorological variables, and Eqs. (10), (11), and (12), we estimated the energy balance at the forested site. The meteorological input variables were air temperature, relative humidity, global solar radiation, downward longwave radiation, albedo, and wind speed at the OP site (shown in Table 3). The air temperature and relative humidity at the OP site were equivalent to those at the forested sites. The heat balance model of Kondo and Yamazaki (1990) was used.
Figures 8a and 8b compare the observed and estimated snowmelt energy in the SLF and DLF, and Table 5 shows the accuracy of estimates for the snowmelt energy in the simulation. To estimate values excluding the effect of below-canopy snow albedo due to larch forest density, the albedo in the forested site was assumed to equal that at the OP site. The regression coefficients in SLF were 0.94 with 90% confidence interval from 0.94 to 1.19, when including the effect of below-canopy snow albedo due to the larch forest density, and 1.06 with 90% confidence interval from 0.94 to 1.19, when excluding the effect of below-canopy snow albedo due to the larch forest density. In SLF, the estimated values, including and excluding the effect of below-canopy snow albedo with larch forest density, were mostly similar with respect to accuracy.
However, the estimates that included the effect of albedo with larch forest density were better than those that excluded it, and were mostly in agreement with the observed values in DLF. When the effect of below-canopy snow albedo due to dense larch forest density was ignored, the snowmelt estimate was less accurate and was underestimated in the DLF, whereas including the effect of larch forest density on below-canopy snow albedo resulted in an AEI and REI that were less than 4.4 mm day−1 and 0.25, respectively. Furthermore, the regression coefficients in DLF were 0.99 with a 90% confidence interval from 0.86 to 1.13, when the effect of albedo due to the larch forest density was included, and 0.74 with a 90% confidence interval from 0.65 to 0.84, when the effect was excluded, respectively. Thus, the DLF density effect on below-canopy snow albedo is important.
The following discussion focuses on the effects of variation in the albedo on the snow surface energy balance, for differing larch forest density. From our snow surface energy balance model, we can test how variation in snow albedo affect the snowmelt energy and energy components at differing larch forest densities. The simulations below calculate hourly values using our simple model with a PAI from 0 to 3, and we discuss the variation in the accumulated snowmelt energy and energy components of the snowmelt energy for an entire day. To estimate the incident shortwave radiation, we used the data for 1 April and 40°N.
c. Variation in albedo of snow surface
The net all-wave radiation is strongly influenced by the ratio of actual-to-possible sunshine duration and the albedo of the snow surface. Most previous studies (e.g., Ohta et al. 1993; Hashimoto et al. 1994) examined the dependence of the net all-wave radiation on weather conditions only, and studies of the effects of albedo are rare. The snow albedo depends, in turn, on the grain size of the snow cover, solar zenith angle, and the amount of soot in the atmosphere. During the spring thaw, for example, the snow albedo is quite high at high latitudes, where there is little industry to discharge soot and the solar zenith angle is high (e.g., Siberia). According to Sokolov and Vuglinsky (1997), the monthly mean albedo at an open site in the Siberian taiga (55.2°N, 124.2°E) was 0.72 during the spring thaw in April 1980. By comparison, Suzuki et al. (1999) found that the daily mean albedo at an open site was 0.57 from the middle of March until the end of April in 1994, 1995, and 1996. We shall discuss how the albedo and ratio of sunshine duration RS affect snowmelt and the net all-wave radiation. Figures 9a–e show the relations between the net all-wave radiation estimated using the meteorological conditions from Table 3 and the PAI, based on variations in snow albedo and the ratio of actual-to-possible sunshine duration. Here, the PAI changed continuously in value from 0 to 3. Under clear-sky conditions, the net all-wave radiation decreased as the PAI increased, because the net shortwave radiation decreases as the PAI increases. In particular, for a low albedo with a high ratio of actual-to-possible sunshine duration, the net all-wave radiation decreased greatly as the PAI increased. However, under cloudy conditions, the net all-wave radiation changed only slightly as the PAI increased, and in the case of a low ratio of actual-to-possible sunshine duration, the net all-wave radiation increased slightly. The results are similar to previous simulation studies (Nakabayashi et al. 1999), in which net all-wave radiation showed marked changes if the albedo was more than 0.8.
According to our simulation, the net all-wave radiation has the following properties: 1) if the weather is cloudy it will increase slightly as PAI increases, even with a low albedo, and 2) when the albedo exceeds 0.6 there will be no variation in the net all-wave radiation with larch forest density, even on sunny days. Our observations (Suzuki et al. 1999) and those of FitzGibbon and Dunne (1983) support these simulation results.
We discussed above how albedo affects the way in which the net all-wave radiation varies with larch forest density. We next use the simulation to show how the net all-wave radiation influences the way in which snowmelt energy varies with larch forest density. Figures 10a and 10b show the relationships between snowmelt energy, net all-wave radiation, and the PAI, with various snow surface albedo values. The daily meteorological values in Table 3 were used, except that the albedo PAI changed continuously between 0 and 3. The net all-wave radiation is one of the most important energy inputs determining snowmelt. Changes in the net all-wave radiation depend strongly on the snow albedo. At high albedo, net all-wave radiation increases with larch forest density, whereas at low albedo the net all-wave radiation decreases strongly with larch forest density. However, a large change in the net all-wave radiation does not diminish the decrease in snowmelt energy, because the trend manifested by the results is a consequence of the decrease in sensible heat flux with increasing larch forest density. The present simulation reproduces the results of our previous study (Suzuki et al. 1999) in which we concluded that snowmelt differences at different forest densities are caused mainly by variation in the sensible heat flux.
This section discusses the reasons for the way in which below-canopy snow albedo varies according to larch forest density and a possible problem in applying the present model to other sites.
Recently, T. Watanabe (2002, personal communication) showed that the capacities for transmission of diffuse and direct photosynthetically active radiation (PAR), in the wavelength of range from 400 to 700 nm [mostly visible (VIS) range], and incident shortwave radiation under a deciduous forest canopy are largely the same during the winter season, when there are no leaves. Consequently, we assumed that the capacities for transmission of VIS and near-infrared (NIR) radiation under the larch forest canopy were the same, because larch branches and tree bark will have the same absorptive and reflective capacities as VIS and NIR lights. We, therefore, believe that the differences in snow albedo due to larch forest densities are caused by the size of the snow grains and debris on the snow surface.
We first discuss the effect of debris on the below-canopy snow surface. It has previously been shown that the albedo beneath a forest canopy is affected by litter (Hardy et al. 1998, 2000; Melloh et al. 2001). In our study, we ignored the effect of snow age because the beginning of the snow cover period was the same, and we compared the same date at the OP, SLE, and DLF sites. Thus, if the snow depth and grain size are similar for open and forested sites, it is debris from the canopy that causes differences in the below-canopy snow albedo. Here, larch trees are leafless during the period of snow accumulation. The debris should, therefore, be small branches or bark from the larch trees. We have just stated that the capacities for transmission of VIS and NIR are similar. Correspondingly, we assume that the spectrum albedo on VIS and NIR for such debris are the same (we do not have actual data on the spectrum albedo for larch branches or bark).
If we suppose that the snow grain size is the same at all sites, it is possible to model the effect of debris on the snow surface as follows:
where CL is the debris coverage ratio on snow surface (m2 m−2); CS is the pure snow surface coverage ratio (m2 m−2); and αO, αF, αS, and αL are, respectively, the albedos for open and forested sites, the pure snow surface, and debris. From these relations, we estimate the effect of debris in the SLF and DLF for the thaw period, except for snow coverage of less than 10 cm. Jones (1992) showed that the aL of conifer leaves is 0.12, and we suppose that the albedo of larch branches or bark is similar, and set aL to 0.12. We assume that the spectrum albedo of αL and αS is uniform. Table 6 shows below-canopy snow albedo values for the thaw period, which runs from the middle of March to the middle of April. Using Eq. (20) we obtained values for CL and CS. In the SLF, CL was 0.098, and in the DLF, it was 0.164. The amount of debris on the snow increases as the larch forest density increases. This trend is in accord with the results of Melloh et al. (2001).
Furthermore, Nakamura et al. (2001) showed that the size of the snow grains in the upper 3 cm of the snow cover strongly determined the spectrum albedo at the snow surface. In particular, the snow albedo in NIR decreased with increasing snow grain size. It was found that if snow grain size increased from 0.047 to 1.5 mm, the snow albedo of VIS would change from 0.84 to 0.79, and the snow albedo of NIR would change from 0.31 to 0.18. Even if the litter coverage on snow surface is the same, the size of the snow grains results in changes in the snow albedo. The spectrum components of snow albedo are, therefore, significant.
In summary, there are two reasons for the way in which the snow albedo varies with changes in larch forest density: 1) the increase in debris and 2) increase in snow grain size with forest density. Debris on snow not only affects snow albedo but also has different thermal properties, because the temperature of the snow never rises above 0°C, whereas that of the debris can exceed 0°C. Furthermore, the higher temperature of the litter might also affect the surrounding snow. Thus, debris might induce changes in the energy balance on the snow surface.
Further study is required to understand the effects of litter coverage and snow grain size on the energy balance of snow surfaces at varying forest densities.
b. Possible problems with the present model
This paper has presented a simple snowmelt model for estimating the surface energy balance under a larch forest canopy. The model was based on the relations between meteorological factors in open and larch forest sites on a moderate southern slope in the temperate climate of Japan. It is important to consider whether our findings may be extended to the sites of other tree species, and, in particular, to check the accuracy of the relations for the snow albedo and penetration of incident shortwave radiation under the canopy. If it were possible to obtain data on hourly downward radiation above a canopy, or on hourly cloud conditions, it would be better to use those data to estimate the below-canopy downward radiation.
Another limitation involves the snow grain size. By using the below-canopy snow albedo during the thaw period, we estimated the effect of larch forest density on the energy balance at the snow surface. The snow grain size was about 1 mm, the same as for granular snow. The snow grain size affects the spectrum of snow albedo; especially the NIR range of snow albedo decrease as noted by Nakamura et al. (2001). Thus, the albedo will vary with the snow grain size.
Our present model should be useful for quantifying the effect of larch forest density during the thaw season, but it is necessary to calibrate the relation between albedo and larch forest density in the period when snow accumulates.
We developed a simple empirical model for snowmelt under a forest canopy. Estimates for meteorological variables, especially for below-canopy snow albedo, as well as estimates for the PAI, were obtained from observations by Suzuki et al. (1999). Using our model and a snowmelt model (Kondo and Yamazaki 1990), we carried out various simulations for the snowmelt energy and heat balance components. The way in which below-canopy snow albedo varies with larch forest density, and our simulations of the resulting variation in snow albedo, are summarized in the following set of conclusions.
Our simple model described the observed surface energy flux under forest canopy. The results show that the PAI strongly influenced the surface energy balance under the larch forest canopy.
Net all-wave radiation is one of the most important energy sources for snowmelt. We found that the change of net all-wave radiation strongly depends on the ratio of actual-to-possible sunshine duration and snow surface albedo. Our simple model included the effect of below-canopy snow albedo, and it shows the importance of accounting for the effect of larch forest density on below-canopy snow albedo, because otherwise, net shortwave radiation in the dense larch forest will be underestimated. If the effect of below-canopy snow albedo due to the larch forest density were excluded, snowmelt in the dense larch forest would be underestimated.
Under cloudy conditions, the net all-wave radiation remains constant or, in the case of a low ratio of actual-to-possible sunshine duration, increases slightly as the PAI increases, even when the albedo is low. However, if the snow albedo is low and the ratio of actual-to-possible sunshine duration is high, the net all-wave radiation decreases greatly with increasing PAI. Taking into account variations in the weather conditions, the net all-wave radiation does not, as a general rule, decrease as the PAI increases, because of the associated increase in downward longwave radiation and the counterbalancing decrease in below-canopy snow albedo.
Variations in below-canopy snow albedo, which are due to variations in larch forest density, affect the snowmelt energy as follows: (i) when the initial below-canopy snow albedo is low, the snowmelt energy decreases significantly as larch forest density increases, because the decrease in below-canopy incident shortwave radiation affects the net shortwave radiation more than does the decrease of below-canopy snow albedo, both of which are due to increases in larch forest density. By contrast, (ii) when the initial below-canopy snow albedo is high, the snowmelt energy changes only slightly as larch forest density increases, because the slight increase in net all-wave radiation that occurs when larch forest density increases is caused by the fact that the decrease in below-canopy incident shortwave radiation due to increases in larch forest density is cancelled out by the decrease in below-canopy snow albedo that occurs in response to increases in larch forest density.
Observarions at the Mt. Iwate sites were made possible by Koiwai Noboku, Ltd., and Nishiyama Bokuya Kumiai. We thank Dr. Tsutomu Watanabe of FFPRI and Dr. Tsutomu Nakamura of Iwate University and Dr. Osamu Abe of NIED for their radiation data, and three anonymous reviewers who helped us to improve our manuscript. Part of this study was financially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture of Japan.
List of Terms
QM Snowmelt energy (W m−2)
RN Net radiation (W m−2)
H Sensible heat flux (W m−2)
LE Latent heat flux (W m−2)
L↓ Downward longwave radiation (W m−2)
L↑ Upward longwave radiation (W m−2)
QG Heat storage in the snow cover (W m−2)
PAI Plant area index (m2 m−2)
AEI Absolute error index
REI Relative error index
CP Specific humidity of air (W m−2 K−1)
ρ Density of air (kg m−3)
TZ Air temperature at the reference height (°C)
UZ Wind speed at the reference height (m s−1)
qZ Specific humidity at the reference height (kg m−3)
qS Specific humidity at the snow surface (kg m−3)
L Latent heat flux (W m−2 kg−1)
CS Heat capacity of snow (2.17 × 103 J m−3 K−1)
RH Relative humidity at the reference height (%)
qSAT(TZ) Saturated specific humidity of TZ (kg m−3)
ρS Snow surface density (kg m−3)
ZF Freezing depth within snow cover (m)
Δt Discrete time step (s)
T0 Melting snow temperature (=0°C)
lf Heat of fusion for ice (=0.333 × 106 J kg−1)
λS Thermal conductivity (W m−1)
ρI Density of ice (=9.17 × 102 kg m−3)
IF↓ Incident shortwave radiation under forest canopy (W m−2)
IS↓ Scattered shortwave radiation above canopy (W m−2)
ID↓ Direct shortwave radiation above canopy (W m−2)
VH Hemispherical view factor
VS Solar path view factor
LF↓ Downward longwave radiation under forest canopy (W m−2)
LO↓ Downward longwave radiation at open site (W m−2)
IO↓ Incident Shortwave radiation at open site (W m−2)
UF Wind speed under forest canopy (m s−1)
UO Wind speed at open site (m s−1)
αF Snow albedo under larch forest canopy
αO Snow albedo at open site
RS Ratio of actual-to-possible sunshine duration
IEXT↓ Extraterrestrial solar radiation (W m−2)
LFIN↓ Downward atmospheric radiation during fine weather (W m−2)
w*TOP Total amount of effective water vapor (m)
αS Pure snow albedo
CL Debris coverage ratio on snow surface (m2 m−2)
CS Pure snow coverage ratio on snow surface (m2 m−2)
Corresponding author address: Kazuyoshi Suzuki, Frontier Observational Research System for Global Change, JAMSTEC Yokohama Institute of Earth Science, 3173-25 Showa-machi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan. Email: firstname.lastname@example.org