Physically Based Estimation of Seasonal Snow Accumulation in the Boreal Forest

Transcription

1 59th EASTERN SNOW CONFERENCE Stowe, Vermont USA 22 Physially Based Estimation of Seasonal Snow Aumulation in the Boreal Forest J.W. POMEROY 1, D.M. GRAY 2, N.R. HEDSTROM 3, J.R. JANOWICZ 4 ABSTRACT Aumulation of snow under forest anopies is known to deline with inreasing anopy density and leaf area beause of snow intereption and sublimation in the anopy. Seasonal snow aumulation measurements olleted over a deade from various forest stands in western Canada were used to test and develop methods to relate forest snow aumulation to stand properties and observations of either small learing seasonal snow aumulation or seasonal snowfall. At substand sales, the variability of seasonal snow aumulation was not well related to stand leaf area, seasonal intereption or small learing seasonal snow aumulation. At the stand-sale, physially-based snow intereption equations predited seasonal snow aumulation from the stand leaf area and the seasonal snow aumulation or snowfall in adjaent learings. A simple parametri form of these equations showed the sensitivity of seasonal snow aumulation to leaf area at the forest stand sale and suggested a relationship to extrapolate snow aumulation or snowfall measurements from learings to forests. These relationships, developed from Canadian boreal forest observations, are onsistent with Kuz min s (196) relationship between aumulation and anopy density derived from Russian observations, suggesting a good degree of transferability. Keywords: Snow aumulation; snow intereption; snowfall; Boreal forest; forest hydrology; water resoures predition INTRODUCTION Snow aumulation varies at marosales (1-1 km) due to variation in snowfall as influened by latitude, elevation, orography and water bodies; at mesosales (1 m 1 km) due to variation in terrain harateristis and vegetation over; and at mirosales (1-1 m) due to the influene of redistribution along airflow patterns and intereption (MKay and Gray, 1981). It is well aepted that at mesosales and mirosales, snow aumulation differs substantially between forested and open environments beause of proesses of intereption, sublimation and wind redistribution (e.g. Pomeroy and Gray, 1995). Intereption, sublimation and redistribution proesses operate at miro-sales or smaller (Pomeroy et al., 1998a) and yet result in harateristi 1 Centre for Glaiology, Institute of Geography and Earth Sienes, University of Wales, Aberystwyth, Wales, United Kingdom SY23 3DB john.pomeroy@aber.a.uk 2 Division of Hydrology, University of Saskathewan, Saskatoon, Saskathewan, Canada S7N W 3 National Water Researh Institute, Environment Canada, 11 Innovation Boulevard, Saskatoon, Saskathewan, Canada S7N 3H5 4 Water Resoures Division, Indian and Northern Affairs Canada, 3 Main Street, Whitehorse, Yukon Territory, Canada Y1A 2B5 93

2 snow aumulation patterns that are still evident at the stand sale (Pomeroy and Gray, 1995). In forested environments, the stand-sale orresponds to the extent of stands or learings of some harateristi speies mix, anopy density and leaf area harateristis and bridges the miro and meso sales noted by MKay and Gray. In natural forests, stand extent is often assoiated with aspet, moisture availability, soil type, hillslope loation, wind exposure, drainage and forest fire history. Forest learing and planting have imposed a manmade pattern on many forests, though there have been some reent attempts to mimi the spatial patterns of natural disturbane in forest harvesting operations in western Canada. Knowing the variation in seasonal (late winter maximum) snow aumulation amongst forest stand types and learings is essential to prediting athment-sale snow aumulation and melt, as most forested athments are overed by a mosai of learings and stands of varying density. Point or small area measurements and estimates annot be reliably extrapolated to areal estimates at the basin-sale without referene to the influene of the forest harateristis of the measurement site and of the larger basin on snow aumulation (Jeffrey, 1968). A primary problem for studies of snow aumulation in forested environments is: how do forest stand harateristis influene snow aumulation over a variety of sales? As more aurate and higher resolution maps of forest over type, density and leaf area have beome available, hydrologists with the answer to this question an take advantage of detailed basin landover information to develop detailed snowover information over spae. Two prominent pratial problems in hydrology may find solutions through a better understanding of the relationship between snow aumulation observed in a small learing and aumulation in adjaent forested environments. The first is that most meteorologial stations reording snow depth and snowfall in forested environments are loated in learings, rather than the forest, the seond is that snow remote sensing tehniques beome more unertain as forest density inreases and are most ertain for open sites. Trees, espeially evergreens, interept, emit, and satter visible, infrared, gamma and mirowave radiation in omplex manners. The result is that a dense oniferous stand an ompletely onfound attempts by remote measures, to detet the presene or water equivalent of snow underneath it. Tehniques that would relate snow aumulation in learings to that in the more heterogeneous and omplex forest landsape would help in extrapolating point observations and orreting remote sensing measurements to provide the areal representations of snow aumulation that are required by hydrologists. Comparison of measured snow aumulation between natural oniferous forests and learings demonstrates larger amounts of snow in learings (Golding and Swanson, 1978), though the degree of differene is often related to the size of the leared area. In southeastern British Columbia, Canada, Toews and Gluns (1986) report that snow aumulation in lear-uts ranged from 4 to 118% more than that in adjaent oniferous forests, with a mean differene of 37%. In the foothills of southern Alberta, Canada, Golding and Swanson (1986) report snow aumulation inreased from 2 to 45% from forest to learing. It is important to realise that in windy environments, learing size an have an important effet on snow aumulation. Very small learings are sheltered from snowfall by the nearby forest anopy, while larger learings an lose snow aumulation to wind transport via blowing snow erosion. Where mid-winter melts our, larger learings are more exposed to solar radiation and turbulent transfer, inreasing the melt rate (Pomeroy and Granger, 1997) Troendle and Leaf (198) demonstrated the effet of learing size on snow aumulation in wind-swept mountain forests in Colorado; the largest snow aumulation ourred in learings with dimensions five times the height of nearby trees. In the Alberta foothills, Swanson (1988) found the largest snow aumulation ourred in learings with dimensions two to three times the height of surrounding forest. In the boreal forest of entral Saskathewan, Pomeroy et al. (1997), however, found no differene between snow aumulation (away from the edges) of a large (km sale) and a small (1 m sale) learing. This was a relatively old and low winter wind speed environment ompared to the montane forests of Alberta and Colorado. The pratise in Canadian boreal forest harvesting is to leave trash from the treefelling and trimming operations on the lear-ut with the intention of retaining winter snowover to insulate soils. The roughness reated by this trash and the tall grasses and shrubs that quikly re-establish was suffiient to retain almost all of the seasonal snowfall as snow 94

3 aumulation in forest learings (Pomeroy et al., 1997). Melts in the learings were earlier than forest stands, but did not our until late Marh or April (Pomeroy and Granger, 1997). In suh regions, the ourrene of a suffiiently rough surfae to restrit blowing snow is more important than learing size in determining snow aumulation. Seasonal sublimation losses from interepted snow as a perentage of seasonal snowfall in a boreal forest varied from 13% in aspen/sprue mixed-wood, to 31% in mature pine to 4% in a dense sprue stand (Pomeroy et al., 1998a). These losses resulted in a fator of two differene in aumulation between adjaent dense and sparse forest stands, found within sales of hundreds of metres. Pomeroy and Gray (1995) suggested that stratifying aumulation into lasses by landsape type and then examining sub-landsape variability using statistial distributions ould reasonably aount for the hydrologially important variability in snow aumulation. Pomeroy et al. (1998b) and Faria et al. (2) provided evidene of the lognormal distribution of snow aumulation mass within forests stands and typial oeffiients of variation for various stand speies types. They noted that taller vegetation dampens the variability of aumulation assoiated with landform (wind redistribution), but that there was greater variability in small-sale aumulation in evergreen forests than deiduous forests due to mirosale effets of snow intereption and unloading. The purpose of this paper is to develop and evaluate simple tehniques to 1. desribe the between-stand variability of seasonal snow aumulation in forests, 2. desribe the within-stand variability of seasonal snow aumulation in forests, and 3. relate forest snow aumulation to that in adjaent small learings. Where possible the tehniques are based on popular physial measures of forest stands and retain a physial or theoretial basis. The study onentrates on old, boreal forests where snow aumulation proesses are not obsured by frequent or large mid-winter ablation events and defines seasonal snow aumulation as that aumulation at the time of maximum late-winter aumulation, just before ablation ommenes. THEORY Kuz min (196) suggested from extensive Russian measurements that the snow aumulation in a forest, S f, and in a learing, S, an be empirially related to forest winter anopy density, C (the ratio of anopy-overed area per unit area of ground), where, S = S 1.37C ) 1) f ( This expression has a useful simpliity, and while widely referred to, has not been extensively tested in North Ameria. The authors do not know the theoretial basis of Eq. 1. The following is an attempt to relate the possible theoretial basis of Eq. 1 with more reent forest snow intereption theories in order to develop pratial equations for prediting snow aumulation in forests from aumulation in learings. Presuming horizontal redistribution is negligible, over a snowfall event (period of snowfall), intereption, i, is defined as that snowfall whih does not reah the ground. If the snowfall, p, into a learing is the same as that to the top of a forest anopy, then p p i 2) f = where p f is the sub-anopy snowfall for some event. The intereption term defined in Eq. 2 was the subjet of theoretial and observational study by Hedstrom and Pomeroy (1998). They disussed results in terms of intereption effiieny, i/p = e i, whih was alulated from a physially based formulation. The snow intereption formulation of Hedstrom and Pomeroy (1998) relates intereption to leaf area index, tree speies, anopy density, air temperature, wind speed and snowfall. For a single snowfall event into a snow-free anopy, Hedstrom and Pomeroy s algorithm an be simplified to its primary fators, as C p 46 = = + I* i I * 1 e, where I* S p LAI '.27 3) ρ 95

4 and is an empirial unloading oeffiient found equal to.68, p is above-anopy snowfall during the intereption event, I* is intereption apaity, found as a funtion of the speies snow loading oeffiient, S p, effetive winter leaf area index, LAI (total horizontal area of stems, needles and leaves per unit area of ground) and density of fresh-fallen snow, ρ. Further generalising the omponents of Eq. 3 by assuming the density of fresh snow is 7 kg m -3, presuming that snowfall into a learing is equal to above-anopy snowfall and using an averaged speies snow loading oeffiient of 6.3 kg m -2 (range of measured values 5.9 to 6.6 kg m -2 ) provides, C p = 5.8LAI ' i 3.94 LAI' 1 e 4) where units are mm for the oeffiients 3.94 and 5.8, p and i; and LAI and C are dimensionless. Hedstrom and Pomeroy s intereption algorithm traked snow load in the anopy; the simplifiations shown as Eqs. 3 and 4 do not and hene are only valid for single snowfall events. Equations 3 and 4 lose their physial validity and auray when applied over longer periods of time with multiple snowfall events beause elapsed time inreases with preipitation. For every inrement of p, these equations assume that all interepted snow is retained as anopy snow load from the previous inrement. The assumption that snow load is preserved over the time between snowfall inrements is likely to be valid during individual snowfalls and for short periods after the snowfalls (up to one week in late winter, up to one month in mid-winter), but Pomeroy et al. (1998a) show that the anopy snow load for subsequent snowfall events is normally depleted by sublimation, melt or subsequent unloading between major snowfall events. In high sun periods of late spring this an take just a few hours. A onsideration of the full suite of interepted snow ablation proesses and the time-sales of their operation is neessary to employ Eq. 4 in a meaningful way. Interepted snow eventually sublimates, unloads or drips to the ground. Over a winter season it may be presumed that this has ourred. Seasonal sublimation E may then be found as P P U D E 5) f = where P denotes seasonal snowfall (subsripts and f refer as before to that to a learing and subanopy respetively), U, unloading and D, drip and the seasonal sum of intereption, i=e+u+d. Presuming that redistribution, surfae melt and surfae evaporation are negligible, the mass balane equations for the forest and learing redue to S = P and S f = P f - U - D, resulting in S = S E 6) f The sublimation term E was the subjet of investigation by Pomeroy et al. (1998a) and requires the solution of oupled mass and energy balane equations. A sublimation effiieny term, e s, may be defined as E/ i. This effiieny is expeted to be lower in humid temperate winter environments where in-anopy melt and unloading of wet snow from the anopy are large (e.g. Lundberg et al., 1998; Stork and Lettenmaier, 1999) and higher in old dry environments where sublimation proesses may proeed with relatively little hindrane (Pomeroy et al., 1998a; Parviainen and Pomeroy, 2). It is also expeted to vary with several other fators suh as snow age, amount of interepted snow, branh elastiity, wind and radiation penetration into the anopy, and anopy struture. Using the sublimation and intereption effiienies then Eq. 6 may be expressed as i S f = S Sesei = S (1 es ) 7) p where the effiienies e i = i / S or i = e i S and e s = E / i or E = e s i, must be evaluated from the same data set and for the same time interval. It is assumed that the seasonal effiienies an be approximated by the means of the ratios i / P (sine S P ) and E / i, for shorter time periods for whih Eq. 4 is valid: for example: 96

5 i P Seasonal i P i P et Monthly Weekly 8) By summing event-based intereption from intervals for whih it an be assumed that the anopy has beome initially snow-free, Eq. 4 an be employed. The intereption effiieny term may be summed to seasonal terms (the seasonal value being the summation of event intereption effiienies) as e i = i / S. With this presumption, Eq. 4 with its event-based (roughly weekly) time sale an be ombined with Eq. 7 to provide CPj 5.8LAI ' 3.94LAI ' 1 e S f = S 1 es 9) Pj where P j is the snowfall into a learing over snowfall event time interval j. Equation 9 provides a means of alulating seasonal snow aumulation in a forest, based on aumulation in a learing, the sublimation effiieny, the magnitude of individual snowfall events, anopy density and winter leaf area index. It is presumed that the anopy beomes snow-free over time interval j, therefore some estimate of snowfall amount over time interval j must be made. The expression uses two anopy parameters and an be further simplified by examining relationships between anopy density and leaf area index. For instane, Eq. 7 is similar in form to Kuz min s equation (Eq. 1) and omparison of the two equations suggests that his data give the produt e s e i equal to.37c. FIELD OBSERVATIONS Snow depth and density surveys were onduted during the snow season (usually Otober through April) in the Canadian boreal forest from 1993 through 22, on a weekly basis in the Prine Albert Model Forest, Saskathewan (PAMF) and a monthly basis at Wolf Creek Researh Basin, Yukon. Timing of surveys was sometimes varied slightly to apture a snowfall event or antiipate a melt period, but was onstrained by the operational requirements of the study programmes in the respetive areas. The loations provide a northern and southern example of the western Canadian boreal forest as shown in Fig. 1. Wolf Creek Researh Basin, Yukon Territory Prine Albert Model Forest, Saskathewan Western Canada Figure 1. Map of study sites in Saskathewan and Yukon, western Canada. 97

6 Stand harateristis are shown in Table 1. Leaf area index and anopy density were estimated in low-sun periods in wintertime using a LI-COR LAI-2 Plant Canopy Analyzer (Gower and Norman, 1991). The LAI-2 was programmed to alulate average anopy statistis from reords of 1 samples of irradiane through the anopy, referened to unobsured sky brightness. Samples were taken along snow survey transet lines. View angles were restrited to the 27 o of sky not inluding the operator or diretion of sun. In some ases multiple sample sets were used to determine mean anopy harateristis. Where forest regrowth was notied (young stands), stands were resampled to estimate anopy hange over the ourse of this study. Gower and Norman (1991) and Smith et al. (1993) noted that for needle-leaf anopies, the LAI- 2 measures the effetive LAI = LAI Ω, where Ω is the stand lumping index. Neglet of lumping an ause underestimation of LAI by 62%. Hedstrom and Pomeroy (1998) maintained that leaf area ontained in lumps is ineffetive in holding snow and therefore LAI, as measured by the LAI-2, is more relevant for snow intereption studies than the atual leaf area of the anopy. LAI and the fration of sky visible from under the anopy were estimated from radiation extintion by the anopy in various view paths as determined using LICOR algorithms (LICOR, 199) desribed by Gower and Norman (1991). Canopy density was alulated as the fration of sky not visible to the LAI-2 from under the anopy. Table 1. Seasonal (late winter maximum) snow aumulation (mm) derived from surveys of depth and density in the Prine Albert Model Forest (PAMF), near Waskesiu Lake, Saskathewan and the Wolf Creek Researh Basin, near Whitehorse, Yukon Territory Plantation Jak Pine Mature Jak Pine Mixed Aspen/ White Sprue Blak Sprue Burned Blak Sprue Clearing Loation PAMF PAMF PAMF PAMF PAMF PAMF Winter LAI Seasonal Snow Aumulation Clearing Wolf Creek White Sprue Wolf Creek C Wolf Creek Observations were made at Wolf Creek in the northern montane boreal forest of western Canada by Indian and Northern Affairs Canada as part of researh basin operations in support of the Arti Environmental Strategy and Makenzie GEWEX (Global Energy and Water Cyle Experiment) Study. Wolf Creek Researh Basin is loated 15 km south of Whitehorse, Yukon Territory. The athment oupies a 195-km² area in the headwater region of the Yukon River. The forested area represents about 43 km² of total basin area with an elevation of 75m at 6 36 N, W. Surveys foused on a white sprue (piea glaua) forest stand, whih was omposed of mature trees ranging from 12-18m in height. The snow ourse onsisted of 25-depth points spaed approximately 5 m apart with a snow density every 5th depth (25 m apart). The ourse diretion was random and did not deflet from dense brush. Snow density was measured with a metri Mount Rose or an ESC-3 ore sampler depending upon snow onditions (Pomeroy and Gray, 1995). Snowfall was reorded by a Nipher-shielded opper ylinder gauge in a nearby small (6 m wide) learing. Clearing snow aumulation was measured along a short five-point transet in 1-m 98

7 tall sparse brush near the snowfall gauge; the brush restrained wind transport. Unpublished surveys by Derek Faria (1999) and Susanne Hanson (21) suggest that fine sale (1-m inrement) measurements along this transet have the same statistial properties as the operational surveys. Prine Albert Model Forest Observations were made as part of Environment Canada s Prine Albert Model Forest study and the Makenzie GEWEX Study in a mid-ontinental southern boreal forest in western Canada. Three mature forest stands and a grassy small learing (55 m above sea level) near Waskesiu Lake, Saskathewan, Canada in the Beartrap Creek basin of Prine Albert National Park. The Park provided an undisturbed, natural environment. Two disturbed forests and a large learing were loated to the north and northwest of the Park in a ommerial forest zone managed by the provinial government. Snow surveys in forest stands and learings were taken along ten-point, randomly loated depth and density transets of approximately 1 m in length. Densities were measured at four of the depth loations using an ESC-3 ore sampler and weight sale (Pomeroy and Gray, 1995). The snow survey protool was tested by Faria (1999) who showed that sample lengths were suffiient to estimate mean areal SWE and that finer resolution (1-m inrement) samples had similar statistial properties to the operational surveys. Areas of dense brush were not avoided. Snowfall was olleted using a Nipher-shielded opper ylinder in the learings. Mature Jak Pine Site: this pine site is within the Beartrap Creek athment in Prine Albert National Park, at 53 o 52' N, 16 o 8' W. The jak pine (Pinus banksiana) stand has mature trees (5-7 years old) m tall, with a sparse understory of deiduous shrubs and mosses. Jak pine trees are sparsely branhed and variable in form. The needles of the jak pine are long (2-4 m) and grow in slightly twisted lusters. Due to the age of this stand, the trees are overed in lihens and mosses. The average distane between the jak pine trees measured on the ground is 2.4 m with an average tree diameter at breast height (DBH) of.174 m. Most of the anopy leaf area is onentrated in the top 5-7 m of anopy. Blak Sprue Site: this sprue site is within the Beartrap Creek athment in Prine Albert National Park at 53 53' N, 16 7' W. The blak sprue (Piea mariana) stand has densely spaed trees (5-9 years old) 1-14 m tall, with an understory of small bushes and mosses on a thik organi forest floor over. Blak sprue trees are slender and straight in form with sagging branhes. Needles are short, very sharp and four-sided. The average distane between the blak sprue trees measured on the ground is 1.1 m with an average DBH of.87 m. The blak sprue anopy leaf area is onentrated in the top 7-8 m of anopy. Mixed-wood (Aspen/White Sprue) Site: this mixed-wood site is within the Beartrap Creek athment in Prine Albert National Park, at 53 54' N, 16 7' W. Forest vegetation in this mature stand is a mixture of aspen (Populus tremuloides) and white sprue (Piea glaua) with an understory of grasses and kinnikinnik (bearberry). Approximately 75% of the trees are aspen m tall, the remainder being white sprue with heights up to 15 m. Burned Blak Sprue Site: this reent burn site is at 54 o 2' N 15 o 27' W in a utting exlusion zone managed by the provinial government. The site was previously overed with blak sprue up to 1-m tall, and burned ompletely in the "Monday Fire" of June, The fire left a anopy of standing harred trunks, with few branhes, no surviving vegetation and little organi soil. In the years after the fire, regrowth of a deiduous understory vegetation ourred, and standing trunks began to fall. Jak Pine Plantation Site: this regenerating lear-ut is in the Waskesiu River athment near Ehman Lake, at 54 2' N, 15 55' W. The site was logged, trenhed and replanted to jak pine (Pinus banksiana) in At the time of survey the vegetation was dominated by jak pine tree heights up to about 4 m but normally less than 3 m tall. Bittern Creek Clear-ut Site: this leared site is in the Bittern Creek athment on land managed by the provinial government and subjet to ommerial logging, and is loated at 53 59' N, 15 55' W. The initial forest of sprue with some aspen was logged after the summer of 199, trenhed and replanted to white sprue in During the surveys, grass bushes and small aspen trees dominated the vegetation with heights up to 1.5 m but typially less than 1 m tall. Muh of the soil surfae was exposed between very small sprue trees,.3-1. m tall, growing in sheltered 99

8 furrows. The aspen at this site were thinned as part of a stand management pratie in mid-june, RESULTS Statistial Properties of Snow and Canopy Over all stands, seasonal learing snow aumulation varied from 54 to 124 mm and stand-sale seasonal forest snow aumulation varied from 28 to 11 mm water equivalent with means of 86 and 59 mm for learing and forested landsapes respetively (Table 1). The ratio of forest to learing snow aumulation S f /S delined from values near 1. to near.5 as leaf area index, LAI and anopy density, C, rose from.2 to 4.1 and.95 respetively as shown in Fig. 2(a, b). The ratio S f /S was negatively orrelated to LAI and C with oeffiients of -.69 and -.72 respetively. 1.8 Sf/S LAI' a) Leaf area index (effetive winter) 1.8 Sf/S Canopy Density b) Canopy density (winter) Figure 2. Ratio of forest to learing snow aumulation as a funtion of stand harateristis. At the PAMF sites, the mean seasonal snowfall estimate of 78 mm was very similar to the mean aumulation in the learings, 85 mm, (differene 8.2%) suggesting that the assumption P S is aeptable for many purposes. The mesosale standard deviation and oeffiient of variation of the stand-sale means of SWE with respet to the PAMF mean for all PAMF sites were 16.4 mm and.28, averaged over five years of observation. At the miro sale, within-stand standard deviations ranged from 4.7 to 2. mm and oeffiients of variation from.5 to.37 respetively. As shown 1

9 in Fig. 3(a-d), neither within-stand sale statisti assoiated strongly with LAI, learing snow aumulation or seasonal snow intereption. The inrease of CV with forest stand density noted by Pomeroy et al. (1998b) is not learly evident in Fig. 3a. Any trend between CV for snow and leaf area would be due to the derease in the mean snow aumulation with inreasing leaf area as shown in Fig. 2a, as Fig. 3b shows that there is no assoiation between standard deviation of SWE and stand LAI. The similarity in relationships between leaf area and S f /S and anopy density and S f /S (Fig. 2 a, b) an be mainly explained by the strong assoiation between leaf area index and anopy density measurements shown in Fig. 4. A logarithmi form of a best-fit relationship between anopy density and LAI is: C =.29 ln( LAI ') ) for whih the R 2 is.97. Equation 1 suggests a possibly omparison between Kuz min s relationship and Eq. 9. It also permits a simplifiation of Eq. 9 to eliminate one of the anopy variables, whih will be explored later in the paper. CV of SWE LAI' a) Leaf area index (effetive winter) and the oeffiient of variation of seasonal snow aumulation 25 Standard Deviation of SWE LAI' b) Leaf area index (effetive winter) and standard deviation (mm) of seasonal snow aumulation. Figure 3 Influene of winter stand harateristis on within-stand variability of seasonal snow aumulation. 11

10 Standard Deviation of SWE in Forest Snow Aumulation in Clearing mm ) Clearing seasonal snow aumulation and standard deviation (mm) of seasonal snow aumulation in adjaent forest stands. 25 Standard Deviation of SWE in Forest Snow Intereption mm d) Seasonal snow intereption loss and standard deviation (mm) of snow aumulation in forest stands. Figure 3 Influene of winter stand harateristis on within-stand variability of seasonal snow aumulation (ontinued) Kuz min s Equation Kuz min s relationship between mean seasonal snow aumulation in forest stands and learing and anopy density was tested using the measurements and is shown in Fig. 5. Considering that the relationship was developed from measurements on another ontinent, the fit is quite good, with an R 2 of.77, mean differene (measured modelled) of 4.48 mm suggesting a systemati overestimate, and standard deviation of the differenes of 1.1 mm. Fitting the form of the relationship to the Canadian data gives: S = S 1.43C ) 11) f ( 12

11 with a R 2 of.79, mean differene (measured modelled) of.87 mm and a standard deviation of differenes of 9.5 mm. This fitting improves the overall overestimation, but provides a similar level of error in estimation. Canopy Density LAI' Figure 4. Canopy density and leaf area index (effetive winter) measurements for all stands, points are measurements and line is Eq Predited Forest Snow Aumulation Kuzmin Bf=.37 Kuzmin Bf = Measured Forest Aumulation Figure 5. Measured and modelled forest stand seasonal snow aumulation (mm) using Kuz min s (196) relationship, Eq. 1, and a modified form, Eq. 11, along with a 1:1 line for referene. Evaluation of Equation 9 To implement Eq. 9 the magnitude of p must be found and the behaviour of the sublimation effiieny, es, determined. It is proposed that for the boreal forest, the reommendation of Hedstrom (1998) is followed and that weekly snowfall be used to estimate p. Over three seasons (94-96) at PAMF for whih weekly data quality is highest, the mean weekly winter period snowfall into a learing was 5.1 mm. Mean monthly winter period snowfall at Whitehorse was 2.4 mm over four seasons (94-97) providing a weekly mean of 4.8 mm. A value for p of 5 mm was therefore adopted for subsequent analysis. An initial inspetion of the data (Fig. 6) shows that the ratio of sublimation to learing aumulation, E/S, is not well predited by the intereption effiieny, e i, where e i i = 12) p and j 13

12 C p j LAI ' = 5.8LAI ' e i e 13) p j and suggests that the sublimation effiieny, e s, is less than one. Solving for e s from Eq. 9 and measurements provides a mean e s of.72 with a standard deviation of.32. There were no trends of e s with leaf area index or learing snow aumulation. Sublimation/ Clearing Aumulation E/S LAI Figure 6. The measured ratio of seasonal interepted snow sublimation to learing seasonal aumulation, E/S, versus the effetive leaf area index shown as points, and modelled values of the intereption effiieny, e i, presuming snowfall event size, p, = 5 mm shown as line. It is evident that the intereption effiieny overestimates the ratio E/S suggesting that the sublimation effiieny must be less than 1.. A omparison of Eq. 9 using p = 5 and e s =.72 with measurements is given in Fig.7, with a R 2 of.8, mean differene (measured modelled) of.48 mm and a standard deviation of differenes of 9.4 mm. The omparison of Eq. 9 to measurements is similar to that of the alibrated Kuz min relationship (Eq. 11), the goodness of fit due to the use of a alibrated value for sublimation effiieny. DISCUSSION At the stand-sale, both Kuz min s relationship and Eq. 9 have a physial basis and make use of fitted oeffiients. Equation 9, though linked to intereption theory, is relatively omplex for predition and upsaling purposes. Its use of LAI is desirable however, as this parameter is diret linked to intereption effiieny and is beoming widely available for forests from remote sensing produts and allometri relationships. An examination of the sensitivity of intereption effiieny e i to LAI an provide a simpler form. Figure 8 shows the intereption effiieny alulated from Eqs. 4 and 1 as 1(.29 ln( LAI ') +.55) p j 3.94 = 5.8LAI ' e i LAI ' 1 e 14) p j and as the fitted logarithmi form e i =.1984 ln( LAI ') ) whih has a R 2 of.99 when ompared to Eq

13 Predited Forest Snow Aumulation Measured Forest Aumulation Figure 7. Points indiating measured seasonal forest snow aumulation (mm) and that predited using Eq. 9 using snowfall event size, p,,of 5 mm and sublimation effiieny, e s, of.72 and a 1:1 line for referene..8 Intereption Effiieny LAI' Figure 8. Modelled intereption effiieny from the physially based alulation (Eq. 14) solid line and the parametri alulation (Eq. 15) dashed line against leaf area index (winter effetive). From Eqs. 7 and 15 a parametri equation to predit snow aumulation in forests based on that in learings and leaf area index is: S f = S ( 1 es (.2 ln( LAI ') +.31)) 16) Equation 16 has a mean differene with measurements of 1.24 mm, standard deviation of differenes of 9.72 and a R 2 of.79 (Fig. 9). Interestingly, assuming the sublimation effiieny is.72, then this equation and the modified Kuz min equation (Eq. 11) are almost idential when Kuz min s equation is plaed in terms of LAI using the relationship between LAI and C (Eq. 1). The two forms (parametri, modified Kuz min) are then: S f = S [ 1 (.144 ln( LAI ') +.223) ] parametri Canada 17) and S f = S [ 1 (.125 ln( LAI ') +.237) ] modified Kuz min 18) Both forms provide a good fit to measurements and an be easily used to predit forest snow aumulation from LAI and learing snow aumulation. Using Eq. 1 they ould also be stated in terms of anopy density if that is the forest desriptor available for an appliation. The similarity of the modified Kuz min equation from his original equation derived from Russian data 15

14 suggests that these forms may be appliable to the old limate forests of both western Canada and Russia. The similarity of P and S values from the Prine Albert Model Forest, and Kuz min s (196) reommendation from Russian experiene, suggest that if aumulation data is unavailable, then umulative snowfall ould be substituted in the previous analysis. Predited Forest Snow Aumulation Measured Forest Aumulation Figure 9. Performane of the parametri forest snow aumulation equation (Eq. 16) presuming that sublimation effiieny is.72; measured and modeled aumulation (mm) as points with a 1:1 line for omparison. At the within-stand sale, the lak of assoiation between the standard deviation of SWE and the leaf area index (and by inferene anopy density, Eq.1), snow aumulation in learings (and by inferene seasonal snowfall) or snow intereption in anopy is instrutive. These parameters are fundamental to anopy intereption proesses and therefore snow aumulation under the anopy (Eqs. 7 and 9). Other fators that influene the nature of unloading of snow from the anopy, for instane snow wetness, branh temperature, and degree of wind redistribution vary from season to season and with geographial loation in the boreal forest and may play important roles in the ultimate distribution of snow under the anopy (Pomeroy and Gray, 1995). The within-stand spatial variability of LAI may also be an important fator; however the measurements needed to assess this variability were not olleted in this study Predited CV of SWE Measured Coeffiient of Variation of SWE Figure 1. Predited oeffiient of variation of forest snow aumulation (Eq. 19) and measured values shown as points; the 1:1 line is for referene. To see if the stand-sale mean SWE preditive relationship an help desribe within stand variability, the average of the individual standard deviation for all stands StDev (SWE) was taken 16

15 and found as 9.76 mm. The oeffiient of variation for an individual stand CV(SWE) was then estimated using Eq 17 as, StDev( SWE) CV ( SWE) = 19) S (1 (.144 ln( LAI ') +.223)) and is shown in Fig. 1. The mean differene between measured and modelled CV is.9 and the standard deviation of differene is.836, whilst the R 2 of modelled and measured values is.2 suggesting a poor preditive power. The low orrelation suggests that a bulk standard deviation from all stands and estimates of snowfall and anopy harateristis for a speifi stand annot be used to aurately predit the statistial harateristis of snow aumulation within a speifi stand. CONCLUSIONS The within-stand variation of snow aumulation in a forest as desribed by the standard deviation of snow water equivalent is not assoiated with seasonal maximum snow aumulation in small learings, seasonal snow intereption or leaf area index. The oeffiient of variation of snow aumulation is not well assoiated with mean stand leaf area index. Standard deviations have a large variation (4-21 mm) about their mean, suh that even if the mean snow aumulation an be estimated for a stand, the oeffiient of variation annot be reliably estimated from snowfall and stand harateristis. Seasonal snow aumulation in forests at the stand sale is shown to sale with leaf area index following the intereption theory of Hedstrom and Pomeroy (1998); the funtion is one of delining aumulation with inreasing leaf area. It is antiipated that the assumptions underlying this relationship are valid where mid-winter melts, wind redistribution and surfae evaporation are infrequent or small. The relationship between snow aumulation and leaf area is onsistent with Kuz min s (196) relationship between forest snow aumulation and anopy density, as leaf area and anopy density are strongly related in boreal forests. Knowledge of the distribution of leaf area index an therefore provide the distribution of snow aumulation at medium to large sales. Very similar relationships between forest stand parameters and forest snow aumulation our between western Canada and Russia, suggesting the transferability of the results between North Ameria, eastern Europe and Siberia. ACKNOWLEDGEMENTS The authors wish to note the high quality of snow surveys onduted by Dell Bayne, Glenn Ford, Kerry Paslawski, Glen Carpenter, Cuyler Onlin, Derek Faria, Brenda Toth, Jason Parviainen, Steve MCartney, John Bastien and others over a deade of study. Funding was provided by the Prine Albert Model Forest Assoiation, Arti Environmental Strategy, Makenzie GEWEX Study, National Siene and Engineering Researh Counil of Canada, Indian and Northern Affairs Canada, Environment Canada, Canadian Forestry Servie, Natural Environment Researh Counil (UK), British Counil (Canada) and the Sientifi Affairs Division of NATO. REFERENCES Faria, DA Distributed energetis of boreal forest snowmelt. Masters of Siene Thesis. Division of Hydrology, Department of Agriultural and Bioresoure Engineering, University of Saskathewan: Saskatoon, Canada; 14. Faria DA, Pomeroy JW, Essery RLH. 2. Effet of ovariane between ablation and snow water equivalent on depletion of snow-overed area in a forest. Hydrologial Proesses 14:

16 Golding DL, Swanson RH Snow aumulation and melt in small forest openings in Alberta. Canadian Journal of Forest Researh 8: Golding DL, Swanson RH Snow distribution patterns in learings and adjaent forest. Water Resoures Researh 22(13): Gower ST, Norman JM Rapid estimation of leaf area index in onifer and broad-leaf plantations. Eology 72(5): Hedstrom NR Development and Evaluation of a Cold Regions Snow Intereption Model. Masters of Siene Thesis. Department of Agriultural and Bioresoure Engineering, University of Saskathewan: Saskatoon, Canada; 79. Hedstrom NR, Pomeroy JW Measurements and modelling of snow intereption in the boreal forest. Hydrologial Proesses 12: Jeffrey WW Snow hydrology in the forest environment. In Snow Hydrology, Proeedings of a Workshop Seminar. Canadian National Committee for the International Hydrologial Deade. Queen s Printer: Ottawa, Kuz min PP Formirovanie Snezhnogo Pokrova i Metody Opredeleniya Snegozapasov. Gidrometeoizdat: Leningrad. Published 1963 as Snow Cover and Snow Reserves. [English Translation by Israel Program for Sientifi Translation, Jerusalem]. National Siene Foundation: Washington, DC LI-COR In., 199. LAI-2 plant anopy analyser, tehnial information. LI-COR In.: Linoln, NE. Lundberg A, Calder I, Harding R Evaporation of interepted snow: measurements and modelling. Journal of Hydrology 26: MKay GA, Gray DM The distribution of snowover. In, Handbook of Snow: Priniples, Proesses, Management and Use. Gray DM, Male DH (eds.) Pergamon Press: Toronto; Parviainen J, Pomeroy JW, 2. Multiple-sale modelling of forest snow sublimation: initial findings. Hydrologial Proesses 14: Pomeroy JW, Granger RJ Sustainability of the western Canadian boreal forest under hanging hydrologial onditions - I- snow aumulation and ablation. In, Sustainability of Water Resoures under Inreasing Unertainty, Rosjberg D, Boutayeb N, Gustard A, Kundzewiz Z, Rasmussen P (eds). IAHS Publ. No. 24. IAHS Press: Wallingford, UK; Pomeroy JW, Gray DM Snowover Aumulation, Reloation and Management, National Hydrology Researh Institute, Siene Report No.7, Saskatoon, Environment Canada, p Pomeroy JW, Granger RJ, Pietroniro A, Elliot J, Toth B, Hedstrom NR Hydrologial Pathways in the Prine Albert Model Forest, NHRI Contribution Series No. CS-974, National Hydrology Researh Institute, Environment Canada: Saskatoon; 154. Pomeroy JW, Parviainen J, Hedstrom NR, Gray DM. 1998a. Coupled modelling of forest snow intereption and sublimation. Hydrologial Proesses 12: Pomeroy JW, Gray DM, Shook KR, Toth B, Essery RLH, Pietroniro A, Hedstrom N. 1998b. An evaluation of snow aumulation and ablation proesses for land surfae modelling. Hydrologial Proesses 13: Smith NJ, Chen JM, Blak TA Effets of lumping on estimates of stand leaf area index using the LI-COR LAI-2. Can. J. For. Res. 23: Stork P, Lettenmaier DP Prediting the effet of forest anopy on ground snow pak aumulation and ablation in maritime limates. Proeedings of the Western Snow Conferene, 67; Swanson RH The effet of in situ evaporation on pereived snow distribution in partially lear-ut forests. Proeedings of the Western Snow Conferene; 56; Troendle CA, Leaf CF Hydrology. An Approah to Water Resoures Evaluation of Non- Point Silviulture Soures. U.S. Environmental Protetion Ageny; Athens, GA.; Toews DA, Gluns DR Snow aumulation and ablation on adjaent forested and learut sites in southeastern British Columbia. Proeedings of the Western Snow Conferene, 54;