Characteristics and simulation of snow interception by the canopy of primary spruce‐fir Korean pine forests in the Xiaoxing'an Mountains of China

Abstract Snow interception by the forest canopy is an important control on the forest hydrological cycle in the Xiaoxing'an Mountains within the northern temperate region of China. In this study, the effects of snowfall characteristics and stand structures on the snowfall redistribution of the canopies within primary spruce‐fir Korean pine forests are analyzed at the forest stand scale. Characteristics of snowfall, through‐canopy snowfall, and stand structure are continuously measured using positioning observations. A semiempirical theoretical model is used to conduct snow interception simulations in the Xiaoxing'an Mountain region. The results indicate that the snowfall, canopy density, slope gradient, and tree height have a significant effect on the through‐canopy snowfall. The interception efficiency gradually decreases with an increase in the amount of snowfall and is particularly sensitive to the snowfall and canopy density, although it shows no significant correlation with average diameter at breast height, tree height, basal area, canopy height, canopy width, leaf area, or slope gradient. Very similar results have been observed in Canada and Switzerland, suggesting the transferability of the results between North America, Western Europe, and China. However, although model results provide a satisfactory simulation of snow interception, further studies are required to optimize the model in this region.

conducted extensive studies on this process. In this respect , Miller hypothesized (1964) that snow interception is subject to the morphology characteristic of canopy, air temperature, and wind speed. Tennyson, Ffolliott, and Thorud (1974) used time-lapse photography to assess potential interception and found that the rate of snowfall interception storage on the uneven-aged stand of ponderosa pine increases in a nonlinear manner, with initial deposition being rapid, then slowing with time. Fitzharris (1975) suggested that snow interception by forest stands could be described using a linear equation of snowfall, and Strobel (1978) showed that under different stand densities, snow interception efficiency decreases with increasing snowfall. Harestad and Bunnell (1981) observed that canopy density and snowfall have significant effects on the efficiency of snow interception in coastal forests, and although McNay, Petersen, and Nyberg (1988) and Pomeroy and Gray (1995) found no significant differences in interception efficiency under different snowfall conditions, it was notably influenced only by the canopy density.
Furthermore, Calder (1990) studied the gamma ray attenuation of fir forests and found that snow interception efficiency is related to the speed and duration of snowfall and that snow interception can be described using a linear equation of snowfall depth. Pfister and Schneebeli (1999) found that air temperature has a significant influence on snow interception efficiency. Marsh (1999) and Garvelmann, Pohl, and Weiler (2013) also suggested that interception efficiency increases with increasing temperature and decreasing wind speed. Storck and Lettenmaier (2002) reported small differences in the maximum capacity of snow interception for different conifer species. Lundberg and Koivusalo (2003) showed that interception loss from gross precipitation increases with increasing forest density and approaches 30% for forests of the highest density class, and the results of Liu et al. (2010), Liu et al. (2012) showed significant differences with respect to snow interception from different types of forests, different snowfall intensities, and snowfall classes. It has also been determined that variations in the characteristics of forests and climate cause greater variations in the snow interception efficiency. Examples of this include the canopies of coniferous forests, which can store 60% of the snowfall in the cold temperate continental climate of North America (Strasser, Warscher, & Liston, 2011), and intercept 32%-35% of the snowfall in the temperate maritime climate of Scotland (Lundberg, Calder, & Harding, 1998), and intercept 12%-40% of the snowfall in the Xiaoxing'an Mountains within the northern temperate continental climate zone of China and in the Daxing'an Mountains (which are within the cold temperate continental climate zone) (Li, Cai, Sheng, & Yu, 2014;Zhang et al., 2015).
The process of snow interception by the forest canopy is relatively complex, but many researchers have established, tested, and optimized canopy interception models. For temperate climate conditions, Satterlund and Haupt (1967) felled and weighed young Douglas firs and white pine trees to observe the process of snow interception and develop an empirical statistical model on a single tree scale. It has been determined that interception efficiency is relatively low for branches of young trees under mild and high snow loads but is higher under moderate snow loads. It is also evident that snow interception is closely related to snowfall and the maximum intercepted snow load by the forest canopy, and in this respect, Schmidt and Glunns (1991) used a method involving cutting of spruce, fir, and black pine branches to weigh and observe the processes of snow interception. They also verified and revised the model of Satterlund and Haupt (1967), and establishing an empirical statistical model for a single branch scale.
The abovementioned models were developed for a single tree and single branch scale, respectively, and were established under temperate maritime climate conditions, where the snow interception preload for individual snowfall events was fixed to 0. However, the process is different under cold temperate continental climate conditions, and snow intercepted by the canopy can remain for days (Pomeroy & Schmidt, 1993); therefore, the snow interception preload is not 0. Hedstrom and Pomeroy (1998) and Pomeroy, Gray, Hedstrom, and Janowicz (2002) felled and weighed trees to develop a semiempirical theoretical model of snow interception at a stand scale based on the physical mechanisms in a cold temperate continental climate. Their model considers the effects on snow interception with respect to the snow stored on the canopy, canopy structure, and snowfall, which have clear physical significances. Andreadis, Storck, and Lettenmaier (2009) established a theoretical model of snow interception based on coupled energy and water balance at a stand scale, which divided the snow intercepted by the canopy into solid states and liquid states. However, to operate this model, multiple meteorological parameters are required for the canopy layer, and the calculations involved are relatively complex.
In summary, three types of models currently exist for canopy interception: (a) empirical models at single branch and single tree scales; (b) semiempirical theoretical models at a stand scale; and (c) theoretical models based on the energy and water balance mechanisms at a stand scale (Xiao, Zhang, & Song, 2017), and all have certain advantages and limitations. In this respect, empirical statistical models are easy to use but contain fewer ecological parameters, which mean that the effects of certain forest canopy characteristics and other factors are ignored with respect to the interception process. Theoretical models require a large number of meteorological parameters, which limits their usage in regions that lack meteorological data; they also involve complex calculations. In contrast, semiempirical theoretical models have a simple structure, require fewer parameters, and can better reveal the mechanisms of canopy interception process; however, although these models can be operated using canopy structure and snowfall parameters, further research is required on the applicability of these models in different climatic zones and types of forests.
The differences between snowfall and rainfall interception mechanisms are relatively large. For example, snow can remain on the canopy for a longer period of time than rain, which is only retained for a short period of time. In China, many researchers have studied the effects on rain interception within classical climate forests relating to nearly every forest types (Chen, Zhang, Yu, Shi, & Huang, 2013;Chen et al., 2015;Li et al., 2013aLi et al., ,2013bLiu, Sun, & Wen, 2003;Lu et al., 2015;Sun, Wang, Li, Liu, & Lin, 2011)

| Experimental design
Experiments were conducted under natural snowfall conditions from November 2013 to April 2015. At the research station, two 1-hm 2 plots (with a distance between them of 500 m) were designated for the long-term and fixed-point monitoring of snowfall, in The monitoring and examination methods employed in this study are described as follows:

Measuring amount of snowfall
Four snow troughs were at random installed in the opening sites at 20-m intervals to measure the amount of snowfall. The distance between the opening site and the borders of each plot was 200 m. The area at the bottom of the wooden snow trough is 1 m 2 with a 20-cm height at the edges in order to prevent wind from blowing snow off the snow trough. The edges of the snow trough were angled at 45°, so that the snowflakes falling on the edges can slide into the snow trough ( Figure 1). The snow troughs were placed on wooden frames at a height of 50 cm above the ground. To decrease the error caused by snow sublimation/ evaporation and windblown snow during the measurement process, measurements of snowfall were conducted immediately after each snowfall event. Using a steel ruler, the snow depth was measured at four points at 0.2-m intervals along the diagonal of the snow trough bottom. Three snow cores were randomly extracted by vertically inserting a 4.6-cm diameter polyethylene tube (of a known mass) into the snowpack within the snow trough, and snow density was estimated by weighing a known volume of the sampled snow cores. The mean snow water equivalent (SWE) was determined by: where, D is the mean snow depth, s is the mean density of freshfallen snow in the snow trough (g/cm 3 ), and w is the density of water (g/cm 3 ).

Measuring amount of through-canopy snowfall
Twenty-eight snow troughs were set up at 10-m intervals along the diagonals of the plots ( Figure 2). As in the previous case, a steel ruler was used to measure the snow depth and a polyethylene tube was used to collect snow samples to enable calculation of the amount of through-canopy snowfall in the snow troughs after each snowfall events.

Determining amount of the snow intercepted by the canopy
According to the principle of water balance, the amount of the snow intercepted by the canopy (mm), i, can be expressed as: where, P c is the secondary snowfall amount (mm), and T is the amount of through-canopy snowfall (mm). This equation ignores the amount of evaporation/sublimation of the snow intercepted by the canopy.

4.
Obtaining forest metrics, canopy density, and effective LAI Average tree DBH, basal area, and canopy width were investigated by conducting individual tree measurements conducted in the field during early October 2013. Tree height and canopy height were measured using an ultrasonic wave height indicator (Vertex IV 60), and a leveling instrument was used to measure the slope gradient and slope aspect of plots. The height from the top to the base of the tree and canopy was used as the measurement of tree height and canopy height, respectively. The geometric mean of the minimum and maximum crown diameter was used as the measurement of crown width.
On cloudy days or after sunset, a Nikon Coolpix 995 (f = 7-32 mm) camera, with a Nikon FC-E8 (f = 8-24 m) fish-eye lens was used to photograph the top of each snow trough within sampling plots ( Figure 3). The camera was kept level, and photographs were taken vertically skywards. A minimum focal length was used to capture the maximum photography area through the fish-eye lens. All-sky photographs of the stand were taken of a view that excluded those areas outside the sampling plot (Yao et al., 2015), and three hemispherical photographs were taken in each snow trough sampling point. Canopy density and effective LAI was averaged over the three photographs to obtain one value per snow trough sampling point. Fish-eye images were analyzed by the analysis system of the HemiView canopy to obtain canopy density and effective LAI at the top of each snow trough sampling point.

| Interception models
This study used a snow interception model, based on the physical mechanisms applicable to a stand scale, which was established by Hedstrom and Pomeroy (1998) and Pomeroy et al. (2002). This model assumes that the effective LAI, canopy density, and coniferous species can be used to determine the snow interception ability of the canopy. For individual snow interception events, the model takes the following form.
where, i is the amount of the snow intercepted by the canopy (mm), c is the empirical unloading coefficient of the snow intercepted by the canopy, p c is the snowfall amount (mm), C c is canopy density, I* is the maximum amount of the snow intercepted by the canopy, S p is snow load coefficient, LAI is the effective LAI in winter (total horizontal area of stems, needles, and leaves per unit area of ground), and s is the density of fresh-fallen snow (g/cm 3 ).

| Data processing
Statistical analyses were conducted out using SPSS. Simple regressions were used to evaluate trends in through-canopy snowfall and snow intercepted by the canopy with respect to 17 snowfall events. At each snow trough sampling point, correlation analysis and multiple regressions were computed for the dependence of through-canopy snowfall and snow intercepted by the canopy on the means of stand variables and terrain factors, which were obtained within a 5-m radius of the snow trough center (average DBH, average tree height, average basal area, average canopy height, average canopy width, canopy density, effective LAI, and slope gradient were used as independent variables in the analyses).

| Snowfall characteristics during observation period
The daily temperature during the storm period ranged from −0.

| Characteristics of snow interception in spruce-fir Korean pine forests
The average amount of snow intercepted by the canopy was calcu-

| Correlation analysis between through-canopy snowfall and snow intercepted by the canopy and stand structure characteristics and terrain factors at 56 snow trough sampling points in spruce-fir Korean pine forests
After each snowfall event, the amount of through-canopy snowfall in each snow trough was investigated and calculated. Stand variables and terrain factors were investigated precisely within a 5-m radius of each snow trough center in early October 2013 (Table 2)  The correlation analysis showed a positive correlation between through-canopy snowfall and DBH, canopy density, H, and slope gradient, but a negative correlation with BA, average canopy height, average canopy width, and LAI (Table 3)

| Regression analysis of through-canopy snowfall and snow intercepted by canopy, and stand structure characteristics and terrain factors at 56 snow trough sampling points in spruce-fir Korean pine forests
Through-canopy snowfall is influenced by snowfall and is closely associated with stand characteristics. Multiple regression analysis showed that through-canopy snowfall was positively correlated with canopy density, H, and slope gradient ( Table 4). The amount of through-canopy snowfall increased with a decrease in canopy density and an increase in the H and slope gradient.
The multiple regression equation for interception is represented by and stepwise multiple regression analysis indicates that snow interception and canopy density also have a significant positive correlation. Furthermore, canopy density is found to be the single most significant forest variable explaining snow interception by forest canopy.

| Model parameters
Snow interception of the stand as a whole was used to construct a model of snow interception during 17 snowfall events from 2013 to 2015. In the model, the original value set by Pomeroy and Hedstrom (c = 0.68) was used as the empirical unloading coefficient of snow interception. Schmidt and Gluns found that the snow load coefficient, S p , of pines and spruces to be 6.6 and 5.9 kg/m 2 , respectively, and Pomeroy and Hedstrom used an average value of the snow load coefficient for pines and spruces when constructing their model (S p = 6.3 kg/m 2 ). Korean pines were the dominant tree species in the sample plots in this study and represented the highest canopy level, while spruces and firs were auxiliary species representing the lower canopy level. Therefore, the snow load coefficient, S p , was also set at 6.3 kg/m 2 . For snowfall density,  Note. The symbol of ** denotes a significance level of 1%; the symbol of * denotes a significance level of 5%, and "n.s." implies "no significant correlation." was changed to i = 3.59LAI 1 − e −C c p c ∕5.28LAI' and used in simulations (see Table 5).
According to simulation results using the Pomeroy and Hedstrom model, snow interception from 17 snowfall events was 44.3 mm and the actual amount of snow interception was 48.1 mm. Therefore, the simulated value was lower than the actual value by 3.8 mm.
However, the amount of snow interception in the revised model was 43.4 mm, which is 4.7 mm lower than the actual value. The determination coefficient of the regression, R 2 , in the model by Pomeroy and Hedstrom and the revised model were 0.796 and 0.803, respectively; these results are consistent and relatively accurate (Table 5 and Figure 7). From the original model and the revised model, when the amount of snow interception was lower than 2 mm, the simulated and observed values showed good correspondence; however, when the amount of snow interception exceeded 2 mm, the differences between the values were larger.

| Relationship between through-canopy snowfall and snowfall and forest metrics in spruce-fir Korean pine forests
The amount of through-canopy snowfall increased with an increase in the snowfall grade, and through-canopy snowfall and snowfall Results of correlation analysis and stepwise multiple regression in this study show that through-canopy snowfall is adequately related to the canopy density, tree height, and slope gradient (Tables   4 and 5). However, the relatively high standard error of stepwise multiple regressions (

| Relationship between the interception and the snowfall and forest metrics in spruce-fir Korean pine forests
Interception capacity of forest canopy changed based on snowfall classes, and interception was also strongly associated with snowfall. When the observed snowfall class was lower than 20 mm, the amount of snow interception gradually increased with an increase in snowfall, but when the observed snowfall class was greater than 20 mm, the amount of the intercepted snow by the canopy decreased with an increase in snowfall amount (Figure 6a).When snowfall reached to 18.9 mm on 24 February 2015, the maximum amount of snow interception in 17 snowfall events was 6.6 mm with both these snowfall events, although the amount of snow interception was very different (6.6 and 3.3 mm, respectively). Therefore, the maximum amount of snow was not intercepted when snowfall was more than 18.9 mm.
Under similar stand structure condition, the interception efficiency is largely controlled by wind speed, snowfall density, and temperature (Schmidt & Gluns, 1991). It is evident that the interception process was synthetically influenced by the forest stand characteristics and local climate. Under different temporal and spatial conditions, there was a larger range in the interception efficiency variation between the various snowfall events, and the interception process thus changed dynamically. In this study, a larger difference in the interception efficiency was observed under different snowfall grades. For snowfall grades lower than 10 mm, the average interception efficiency was 35.1%; when the snowfall grade ranged between 10-20 mm, the average interception efficiency slowly decreased to 28.4%; and for snowfall grade larger than 20 mm, the average interception efficiency rapidly decreased to 18.1%. The interception efficiency significantly decreased with an increase in the snowfall class until it finally trended to a stable value (Figure 6b). This demonstrates the limitations of the forest canopy in its capacity to intercept snow.
Snowfall intensity changes constantly during the process of snowfall, and the interception capacity of forest canopy also alters correspondingly. In this study, the observed interception increased with an increase in the snowfall intensity during individual snowfall events (Figure 8a). Regression analysis indicates a significantly positive power correlation between snowfall intensity and interception (R 2 = 0.6898, p < 0.05), but not with interception efficiency (Figure 8b).
This study of snow interception in the spruce-fir Korean pine forests shows that canopy density has a significant effect on interception efficiency, and this result is consistent with those of Strobel (1978) and Harestad and Bunnell (1981). In this study, the average canopy density of spruce-fir Korean pine forests was 55% and the average interception efficiency was 31%. However, in a related study by Liu et al. (2012), the average canopy density of spruce-fir Korean pine forests was 87% and the average snow interception efficiency increased to 39.7%. This study showed a decreasing trend for interception efficiency with an increase in the snowfall amount, where the amount of snow interception was significantly influenced by canopy density. However, the current study results also indicate that the process of snow interception of spruce-fir Korean pine forests is mainly influenced by the amount of snowfall and canopy density in the Xiaoxing'an Mountains.

| Interception model
The snow interception model of forest canopy has an important role in understanding of the hydrological process involved in snow interception and redistribution. The characteristics of snow interception by the vegetation canopy are influenced by the amount of snowfall, air temperature, wind speed, humidity, air pressure, and the vegetation characteristics during the snowfall period. However, these parameters also limit the applicability of the canopy interception model to a great extent. In this study, the results of the correlation analysis and stepwise multiple regression showed that canopy density is the single most significant forest canopy variable in the prediction of snow interception. However, the relatively high standard error of stepwise multiple regressions (Equation (5) accurate. The simulated snow interception results for individual events showed that the data are better represented when the amount of snowfall is relatively small, thereby resulting in higher model precision (Figure 7). Therefore, model parameters, such as the snowfall amount and canopy structure, better explain most of the snow interception information, but the remaining information is explained by air temperature, wind speed, humidity, and air pressure.
Although the model disregards the sublimation/evaporation effects on the intercepted snow by the canopy during the observation period, the parameters included, such as air temperature, wind speed, humidity, and air pressure, and other microclimatic factors have a significant effect on the sublimation/evaporation process (Knowles, Blanken, Williams, & Chowanski, 2012;Li et al., 2013aLi et al., ,2013bLundberg et al., 1998). This may be attributed to the measured interception values of some snowfall events being larger than their simulated values. In addition, the empirical unloading coefficient and the snow load coefficient in the model were obtained from the observations of interception processes in the coniferous forests of North America. Therefore, long-term monitoring and studies of the coniferous ecosystem in the current region are required to improve the aforementioned coefficient and to optimize the model so that it is region-specific. This will provide a foundation for the analysis of the dynamic rules of snow interception and related causative mechanisms.

ACK N OWLED G M ENTS
The authors would like to thank Chunyan Song and Quanbo Wang for their assistance in conducting field measurement. We would like to thank the Fenglin State Natural Reserve Department of the

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interest.