snow interception evaporation

8/2/2019 Snow Interception Evaporation.

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1Division of Water Resources Research, Lulea University of Technology, Sweden2Department of Earth Sciences/Hydrology, Uppsala University, Sweden

Snow interception evaporation. Review of measurementtechniques, processes, and models

A. Lundberg1 and S. Halldin2

With 6 Figures

Received June 28, 1999

Summary

A global warming, primarily affecting wintertime conditions

at high latitudes will inuence the functioning of the borealforest. The least known term of the winter water-balanceequation is evaporation of snow intercepted in forestcanopies. Several investigations stress the importance ofsnow-interception evaporation in coniferous forests andevaporation fractions of gross precipitation as large as 0.2

0.5 have been observed by investigators in Scotland, Canada,and Japan. Evaporation rates as high as 0.56mm h1 arereported. The largest differences between the rain and snowinterception evaporation processes are the differences instorage. Snow storage (both mass and duration) is often anorder of magnitude larger than that for rain. Snow inter-ception changes the canopy albedo although some studiesindicate the opposite. Process knowledge is limited becauseof measurement difculties but it is known that canopyclosure, aerodynamic resistance (ra), and vapour-pressure

decit are important factors. Existing formulations of ra asfunction of storage location and age cannot fully explainobserved differences in evaporation rates. Operational hydrol-

ogy and weather models, and GCMs describe snow inter-ception in a very simplied way and might benet fromincorporation of more realistic schemes.

1. Introduction

A global warming, primarily affecting winter-timeconditions at high latitudes will affect the func-tioning of the boreal forests. Large increases intemperature have been predicted as a response toincreased atmospheric CO2. Even if these predic-tions are still very uncertain, it is clear that if a

change takes place, forest cover will change as aresult. Future redistribution of boreal forests couldinitiate important climate feedback, which mayalso extend to lower latitudes (Bonan et al., 1992).The boreal forest landscape is a mosaic ofdifferent land types that interact in a complicatedway resulting in large variations in microclimate.This is particularly marked when the vegetationinteracts strongly with the snow (Harding andPomeroy, 1996). Studies of land-surface processesat local to regional scales for a mixed land coverdominated by boreal forests is thus important.Investigations of the energy, momentum, waterand CO2 exchange, and the associated dynamics,between the soil, the vegetation and the atmo-sphere are essential.

NOPEX (a NOrthern hemisphere climate Pro-cesses land-surface EXperiment (Halldin et al.,1998) aims at studying exchange processes duringthe whole annual cycle, including the winter. Theleast known term of the winter water-balance equa-tion is evaporation, especially from forests. Sev-eral studies during the last decade have stressedthe importance of snow-interception storage andevaporation (e.g., Calder, 1990; Johnson, 1990;Schmidt, 1991; Pomeroy and Schmidt, 1993;Lundberg and Halldin, 1994; Harding andPomeroy, 1996; Nakai, 1996; Lundberg et al.,1998; Nakai et al., 1998; Hedstrom and Pomeroy,1998). Snow-interception evaporation, thus, seems

Theor. Appl. Climatol. 70, 117133 (2001)


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to be an important process in the boreal winterlandscape. Techniques to measure and model theprocess would greatly assist efforts to predict theenvironmental changes associated with logging,reforestation, res, climate change and vegetationsuccession (Pomeroy and Schmidt, 1993). Thispaper reviews, as a preparatory study for a comingNOPEX winter-time experiment, the 1998 state-of-the-art in snow-interception knowledge. Thereview focuses on publications during the lastdecade.

Measurement techniques and data on canopysnow-storage capacity and duration, albedo, andevaporation rates are summarised. The processesrelating evaporation rates and canopy closure, andthe importance of aerodynamic resistance aresummarised. Process-based snow-interceptionmodels are described and sensitivity of model-parameter values to measurement errors arediscussed.

2. Measurement techniques

2.1 Establishing magnitudes

Most studies before 1985 as well as some newstudies are comparisons of snowpack accumulationin forests (cut/uncut, before/after thinning) andclearings/open elds (e.g., Gary, 1974; Goldingand Swanson, 1978; Johnson, 1990; Nakai, 1996).The interception-evaporation and the snow-redis-tribution processes are difcult to distinguish inthese studies, but the magnitude of the seasonalinterception evaporation can be found. Compar-ison studies involve several assumptions, e.g., thatstemow is negligible or measured, that differ-ences in melt, water-holding capacity, and evap-oration are negligible between snowpacks ineld and forest, and that differences in snowdeposition and relocation between forest and eldare negligible.

The high wintertime stemow rates reported byHerwitz and Delphis (1997) make the assump-tion of negligible stemow questionable butKominami (1998, personal communication) didnot observe any winter stemow. Differences insurface melt between forest and eld cannot beexcluded a priori. Most measurements reported(e.g., Nakai, 1996) were made in February orearly March to avoid inuences of surface snowmelt commonly occurring at the end of the winter

season. Surface melt can, however, occur duringearly winter and sometimes also during mid-winter. Nakai (personal communication, 1997)measured soil-heat snowmelt in forests and elds.Fluxes ranged within 0.21.0 mm d1 but eld/forest rates could not be separated. Mature snow-packs can hold up to %5% by volume (%17% byweight for a snow density of 300 kg m3) of liquidwater against gravity (Lundberg, 1997). Drainagefrom the snowpack requires its water contents toexceed the water-holding capacity. No study ofdifferences in water-holding capacity betweensnowpacks in forests and elds seems to bepublished. The snowpack density can generallybe expected to be larger in forests than on eldsbecause of compaction when melting snow lumpsslide down from the trees. In areas with a largeamount of snow, the larger snow mass on elds ascompared to forests may create snowpack com-paction and larger densities on elds caused by theweight of the snow (Nakai, personal communica-tion, 1997). Evaporation rates from snowpack arelow at open sites (0.10.3 mm day1 in mid-winter(Kojima et al., 1985), or 1020 mm per winter(Bengtsson, 1980). Doty and Johnston (1969)report average daytime rates of the same magni-tude below a conifer canopy (0.110.16 mm d1

excluding night-time condensation).It is difcult to separate the effects of deposi-

tion pattern, wind redistribution and evaporation.When wind is blowing across a clearing the cross-sectional area for the wind eld is rst expandedand then reduced. The wind speed will accord-ingly rst decrease and then increase. Decreasedspeed causes increased snow deposition and viceversa. Gary (1974) measured increased depositionat the windward side of a small clearing anddecreased deposition at the forest edge at theleeward side. Leaf (1975) observed plumes ofdrifting snow above forest canopies at high windspeeds but Nakai et al. (1994), who used bagswith a 150-mm-mesh net attached at differentheights in a tower, failed to catch any driftingsnow during 3 high-wind-speed days. An opticaldevice designed to calculate blowing snow ux(Brown and Pomeroy, 1989) might be used toestimate canopy snow redistribution.

Assumptions of negligible deposition differ-ences can be justied if sites are chosen with care.Differences in snowpack evaporation and ground-heat-induced melt rates between forests and elds

118 A. Lundberg and S. Halldin


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are a minor problem if snow accumulation islarge. Differences between forests and elds insurface snowmelt are difcult to handle. A pos-sibility to ascertain correct initial accumulationvalues might be to make snow surveys when theearly winter melt period has passed. Melt duringmid-winter can be calculated with an energy-balance method. Midwinters when melt exceedsthe snowpack water-holding capacity should beexcluded from comparative studies. Additionalstudies of the assumptions of negligible stemowand canopy snowdrift are desirable.

The interception-evaporation magnitude canalso be quantied from paired-catchment studies,where runoff changes are measured after partial orfull clear-cutting in one of two similar watersheds(Bosch and Hewlett, 1982; Stednick, 1996). Thesnow-interception evaporation cannot be distin-guished from other evaporation processes in suchinvestigations.

2.2 Process-related measurements

A summary of observed snow-interception pro-cesses is given by Brundl (1997a). Process studiesof interception evaporation have been hampered bymeasurement difculties. All methods used forprocess studies (Calder, 1990; Schmidt, 1991;Lundberg and Halldin, 1994; Nakai et al., 1994;Brundl and Schneebeli, 1995; Brundl et al.,1998a; Harding and Pomeroy, 1996; Grelle et al.,1999; Nakai, 1996; Nakai et al., 1998; Lundberget al., 1998) have individual drawbacks. Criteria toidentify an ideal method for process studies(Lundberg, 1993) include undisturbed meteorolog-ical conditions and continuous measurements ofintercepted mass with a high time resolution. Anideal method should work during periods of meltand sublimation, and above rough forest surfaces.The review by Lundberg (1993) of establishedmethods to measure evaporation and canopystorage, shows that no technique fulls all criteriafor process studies of intercepted-snow evaporation(Table 1). Among the methods designed todetermine canopy storage, only the weighing-cut-tree and the gamma-ray-attenuation techniquesgive continuous records of intercepted mass. Acombination of these methods with techniques forcontinuous measurement of evaporation, through-fall and drip might provide a fairly complete setof data for process studies. Throughfall can be

measured either with plastic-sheet throughfallgauges (Calder, 1990) or with weighing gauges(Lundberg, 1993). The technique with heatedplastic sheets to measure the throughfall appliedby Calder (1990) and Lundberg et al. (1998),might, if applied in a colder climate, exaggerateevaporation because of the heating of sheets. The-ray technique is expensive and time-consuming,and the handling of a radioactive source is adisadvantage.

Tree-weighing techniques have difculties withlight snow blowing off branches and the techniqueis difcult to apply in closed canopies. No canopy-storage measurements can presently be recom-mended for used during periods with snowfallbecause of the low accuracy of snowfall measure-ments. Traditional precipitation gauges under-catch snow because of the distortion of the windeld around the gauges. This is still a problem inspite of all shields constructed to minimise thiserror (Tabler et al., 1990). A new gauge based onaerodynamic principles, which minimise windlosses (Wiesinger et al., 1993), may enable in-clusion of snowfall periods into future processstudies. It is difcult to discriminate between solidand liquid precipitation when the air temperatureis close to zero if manual observations are notmade. Optical gauges are claimed to have acapacity to distinguish both precipitation type andintensity. Lundberg and Johansson (1994), whoevaluated an optical gauge, showed that it isdifcult to discriminate between rain and snowmeteors at high wind speeds.

Hancock and Crowther (1979) presented atechnique whereby the bending of individualbranches, measured with displacement transdu-cers, was used to estimate the mass of interceptedrain in a canopy. Canopy-snow-storage durationand mass have been estimated from digitisedvideo images of branch deection (Brundl andSchneebeli, 1995; Brundl et al., 1998b). Branchstiffness increases with decreasing temperature atsubfreezing temperatures (Schmidt and Pomeroy,1990; Brundl et al., 1998b). The distribution of thesnow load (close to or distant from the trunk) mustbe known and bridging of snow between branchesmust not occur if a unique relation betweenbranch deection and intercepted snow mass isto be found. These problems explain why thebranch-bending technique has not been used ex-tensively for snow-interception studies.

Snow interception evaporation review of measurement techniques, processes, and models 119


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Table1.Classicationofmethodstoestimateevaporationfrominterceptedsnow(slightlymodiedfromLundberg,1993)

Method

Criteria

Undisturbed

Works

with

Time

Space

Worksduring

Works

during

Measures

meteorological

rough

resolution

resolutio

n

meltoccasions

sublim

ation

intercepted

conditions

surface

s

occasions

mass

Catchmentstudies

Y

F

Mass-balancetechniques

Precipitation&throughfallmetho

ds

D

F

Weighing-cut-treetechniques

M-H

T

Weighing-leaforbranchmethods

M

L-B

Weighing-lysimeterstechniques

M-H

T-S

Non-weighinglysimeters&soil-

W

S

moisturemeasurements

Micrometeorologicalmethods

Bowen-ratiotechniques

H

F

Prolemethods

H

F

Eddy-correlationtechniques

H

F

Surface-temperaturetechniques

H

L-R

Miscellaneousmethods

Chambermethods

M

B-T

Gamma-raytechniques

H

S-F

M

Min;H

Hour;D

Day;W

Week;Y

Year;L

Leaf;B

Bran

ch;T

Tree;F

Forest;S

Stand;

R

Region.



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The intercepted snow mass have been estimatedwith help of fractal analysis of photographsshowing the area of snow intercepted on branches(Pomeroy and Schmidt, 1993).

The only direct method to measure the evapo-ration from intercepted snow is the eddy-correla-tion technique (Harding and Pomeroy, 1996;Grelle, 1997; Grelle et al., 1999; Nakai et al.,1999). This method gives the total evaporationfrom a forest and must be complemented withtechniques for separate measurements of tran-spiration and snowpack evaporation. Evaporationfrom the snowpack under a canopy (Doty andJohnson, 1969) and transpiration from groundvegetation and trees are small during winterconditions. For non-homogenous forest standsit is difcult to determine the ux-source area(Harding and Pomeroy, 1996; Grelle et al., 1997).

3. Processes

3.1 Canopy storage

The largest differences between snow and raininterception are the higher storage capacity(% one magnitude larger) and the longer duration(up to several weeks) of the snow storage. Snowinterception also inuences the canopy albedo.

A thorough review of studies dealing withcanopy snow accumulation and retention processes

was made by Hedstrom and Pomeroy (1998).Canopy snow accumulation studies have beencarried out for a variety of canopy surfaces, e.g.,freely suspended branches (Schmidt and Gluns,1991; Nakai, 1996) living branches (Brundl andSchneebeli, 1995; Brundl et al., 1998b), whole cuttrees (Nakai, 1996; Hedstrom and Pomeroy, 1998)and whole canopies (Calder, 1990; Hedstrom andPomeroy, 1998).

Branch bending under snow load, strength ofsnow structure, elastic rebounds of snow crystalsfalling on branch or on snow held on the branchare factors that inuence the collection efciencyof a branch (branch storage/total snowfall) accord-ing to Pomeroy and Gray (1995).

The denition of canopy storage C and storagecapacity (maximum possible storage) S is oftenimplicit and ambiguous since the values can begiven per unit branch area, per unit verticallyprojected crown/canopy area, or per unit groundarea. It is not always clear which denition isused. Subscripts B, C and G for the three types ofcanopy storage are used here.

Schmidt and Gluns (1991) and Nakai (1996)studied relationships between cumulative snowfalland SB for conifer branches. Both studies agreethat SB % 4 mm after % 8 mm of snowfall duringcold and calm conditions (Fig. 1). Schmidt andGluns (1991) also showed that the interception

Fig. 1. Snow interception storage on coniferous branches CB (per branch area) as function of cumulative snowfall PG. (Datafrom Schmidt and Gluns [1991] and Nakai [1996]). The lines are calculated using Equation (2) with SB (mm), P0 (mm) andk mm1 as 4.35 and 4.13; 3.71 and 2.58; 0.76 and 0.72 for Schmidt and Gluns (1991) and Nakai (1996) respectively. Thelines represent averages of 6 coniferous spieces for Nakai (1996) and 3 spieces for Schmidt and Gluns (1991). The symbolsshow calculated relationships for different speices. Measuremets performed in cold, calm conditions and with snow of lowspecic gravity



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catch was inversely proportional to the snowdensity in the specic gravity range 0.040.13.

Calder (1990) presented a relationship betweencumulative snowfall and CG for a closed conif-erous canopy in Scotland. The storage of inter-cepted snow per unit ground area CG continues upto SG 30mm (Fig. 2). SCb SB since snowbouncing from the top branches can be interceptedby branches underneath. Nakai (1996) observedSG 30 mm (coniferous forests) and Kominami(1998, personal communication) measured SC !50 mm, both studies were performed in Japan. Themaximum snow interception storage observed inCanada is much lower where Hedstrom andPomeroy (1998) estimated maximum measuredstorage to be SG % 3X5 and 7 mm (per groundarea) for a Jack Pine and a Black Spruce forestrespectively.

Lundberg and Halldin (1994), and Lundberget al. (1998) report CC ! 2mm (% rain canopy

storage capacity) during roughly one third of thewinter season in northern Sweden and Scotlandrespectively. Japanese observations in January andFebruary by Nakai (1996) and Kominami (1998,personal communication) show that CC exceeded2 mm during % 90% of the time. Brundl et al.(1997a) measured canopy-snow-storage durationat two locations in the Swiss Alps during twowinter seasons. There was snow on the canopyapproximately one third of the time at both loca-tions and the time fraction was highest in mid-winter. There were 1528 snow-interception event(from beginning of snowfall until trees were bareagain) per winter. The average duration of anevent was 34 days, but individual events couldlast 23 weeks (Brundl et al., 1997a) (Table 2;Fig. 3). Hedstrom and Pomeroy (1998) estimatedCG to be ! 2 mm during 25% and 50% of thetime for two different coniferous forests inCanada.

Fig. 2. Canopy snow storage CG as function ofcumulative snowfall PG for a mature SitkaSpruce forest in Scotland (Figure modied fromCalder, 1990). Line calculated using Eq. (3) andSG 30mm

Table 2. Average duration (L, in days) of snowfall events (from beginning of snowfall until the tree was bare again), number

(No) of snowfall events, and time fraction (Fr) with snowcovered canopy at two locations in the Swiss Alps during twowinter seasons. Data for the 3 two-month periods is extracted from diagrammes in Brundl et al. (1997a) whereas data for thewhole winter is supplied personally by Brundl (1997b)

Location Time period

Oct.Dec. Jan.Feb. MarchApril Winter

L No Fr L No Fr L No Fr L No Fr

Davos 93/94 3 9 0.38 5 7 0.71 1 10 0.25 3.5 26 0.44Alptal 93/94 7 4 0.26 3 7 0.48 3 4 0.26 4.5 15 0.32Davos 94/95 2 6 0.20 1 13 0.76 1.5 9 0.24 2.85 28 0.38Alptal 94/95 0.5 6 0.15 2 9 0.58 4 8 0.25 2.88 23 0.32Average 3 6 0.25 3 9 0.63 2.5 7.5 0.25 3.5 23 0.36



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3.2 Albedo

The albedo (short-wave reectivity) of a surfaceis essential for the energy balance. Typical albedovalues for snow on open elds are 0.60.9 for newand dry snow (Winther, 1993) and 0.4 for old

wet snow. Because of light extinction in forestcanopies, their albedo is normally much lower, butfew data on snow-covered-canopy seem to bepublished. Nakai (1996) measured above aTodo-r canopy and related it to CB. Nakai's datacan be interpreted as: 0X16 0X0056 CG toindicate 0X27 when CG 20 mm. Hardingand Pomeroy (1996) reported lower (0.120.14)above a snow-covered, slightly open jack pinecanopy. Pomeroy and Dion (1996) showed that is related to solar elevation. They report values

between 0.1 and 0.3 at different elevations but,surprisingly, nd a negligible inuence of inter-cepted snow. Their analysis was restricted to smallcanopy loads (`1X5 mm). These counter-intuitiveresults warrant further studies.

3.3 Evaporation rates

Recent studies show that evaporation rates fromsnow-covered canopies can reach 1.33.9 mmday1 (Table 3). Estimates of seasonal intercep-tion evaporation I from measurements in Europe,

North America, and Japan vary within a large range(Table 4) and the same holds for the interception-evaporation fraction IaPG of gross precipitationPG. The IaPG fraction was related to the sky-viewfraction SVF in Nakai's (1996) study. Kuzmin(1963) related net precipitation PN to grossprecipitation PG and forest-canopy-cover densityp (expressed as decimal fraction; p is the com-plement to SVF) as:

PN PG 1 0X37p 1

The observations of Nakai (1996) are in goodagreement with the ndings of Kuzmin (1963)(Fig. 4). Kominami (personal communication,1998) investigated the inuence of the location ofthe intercepted mass by measuring the evaporation

Fig. 3. Duration of snow canopy

storage events at two Swiss loca-tions. Basic data personal commu-nication Brundl (1997b)

Table 3. Maximum interception evaporation rates IMAX from coniferous forests measured with different techniques. Data arenot directly comparable since some refer to evaporation per unit vertically projected crown area while most of them are givenper unit ground area

Source Country IMAX Technique

(mmh1) (mm d1)

Calder (1990) Scotland 0.5 -rayplastic sheetweighing cut treeLundberg et al. (1998) Scotland 0.56 3.9 (mm/7 h) -rayplastic sheetweighing cut treeSchmidt (1991) USA 1.6 Weighing articial treeLundberg and Halldin (1994) Sweden 0.31 3.31 Weighing cut treeweighing throughfallNakai et al. (1994) Japan 2.32 Weighing cut treeweighing throughfallKominami (pers comm, 1998) Japan 0.70 2.33 Weighing cut treeweighing throughfallHarding and Pomeroy (1996) Canada 4.04 (mm/36h) Eddy correlationGrelle et al. (1998) Sweden 1.3 Eddy correlation

1Per vertically projected crown area, events with high wind speeds excluded.2Average during a two-week period.3Per tree area.4Calculated from reported energy uxes, short observation period.



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Table

4.Estimatesofseasonalsnow

interceptionevaporationI,evaporationfractionIaPG,skyviewfraction

SVFfordifferentspeciesandmeasurementmethods.Gross

precipitationPG

andnetprecipitationPN

aregivenasmmsnow-waterequivalent.LAI

leafareaIndex

Source

Country

I

IaP

G

SVForLAI

Species

Method

Johnson(1990)1

Scotland

105

0.3

7

Mostlyclosed

Sitkaspruce,50-yearold

PG

PN

PomeroyandSchmidt(1993)

Canada

0.3

3

Spruceandpine

PG

PN

ClaassenandDowney(1995)

US

%0

.5

PG

PN

Nakai(1996)2

Japan

%100

%0

.4

0.050.15

Conifers

PG

PN

Nakai(1996)2

Japan

%60

%0

.2

0.200.30

Dediciduousforest(Larix)

PG

PN

Nakai(1996)2

Japan

%15

%0

.1

%0.60

Dediciduous(Betula,

Alnus,

PG

PN

Quercus)

Kominami(perscomm,1998)

Japan

358

0.3

3

LAI

6.7

Cyprus

PG

PN


Japan

184

0.2

3

LAI

6.7

Cyprus

PG

PN


Japan

240

0.2

1

LAI

4.2

Cyprus

PG

PN


Japan

172

0.2

1

LAI

4.2

Cyprus

PG

PN

Lundbergetal.(1998)

Scotland

>200

0.3

0

Closed

Matureconiferous

Plasticsheet-ray

weighingcuttree4

Nakaietal.(1994)3

Japan

45

%0.1

Youngconiferous

Weighingcuttree

weighingthroughfall5

Grellepers.communication(1997)

Sweden

29

0.1

46

Closed

Matureconiferous

Eddycorrelation7

Grelleetal.(1998)

Grellepers.communication(1997)

Sweden

4

0.0

48

Closed

Matureconiferous

Eddycorrelation7

Grelleetal.(1998)

Nakaietal.(1998)9

Japan

%72

%0.1

Mixedspruce,22-yearold

Eddycorrelation

1Thevaluereferstoaone-monthperiod(13January10February,1984)

.AperiodwithI

07

wasrecordedinJanuary,1985.

2Three-yearaverageofmeasurementsatdifferentlocations.PG

wasinth

erangeof200800mm.

3Basedon73daysofmeasurements

4Measurementofcanopystorage(-ray),throughfall(plasticsheet)durin

glimitedperiods.Measurementofc

anopystorage(weighingcuttree)duringtwoentirewinters.

Seasonalestimatecalculatedbymul

tiplyingaveragemeasuredlimited-pe

riodinterceptionevaporationwithtimeforwhichcanopystorageexceed

ed2mm.

5Measurementsusedtodeterminera

.InterceptionevaporationIduringa

longerperiodwasdeterminedwith

Penman'sequation.Themeasurementtreewassmallerthan

surrondingtrees.

6Winterperiod

DecemberJanuary

7Measuredevaporation(Grelleperson

alcommunication,1997).PG

wasestimatedfromgaugeprecipitationinUppsala(at30kmdistance)(Bergstrom,personalcommunication,

1997)correctedforundercatchcausedbywindexposureofthegauge.C

orrectionfactor1.1forrainand1.5

forsnowwereused.

8NovemberMarch.

9Averagemeasuredmidwinterevapo

ration

0.6mmd1.Seasonalestimateiscalculatedas0.6120days(4

monthswithsnow)

72mm.



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from cubic ice-blocks mounted at differentheights in a mast located in a 15 m high conif-erous forest. The melt and evaporation rates weremeasured by weighing. The evaporation rate atthe lowest branches (located at 7 m height) wasapproximately 40% of the rate at the top of thecanopy (See Fig. 5).

4. Models

Different types of models have been developedto simulate snow interception storage (accumula-tion and duration), evaporation/sublimation andisotope enrichment in canopy snow during evap-oration. Except for such dedicated models, snow-interception processes are very crudely treated,

if at all, in operational hydrological models(Lindstrom et al., 1994) and atmospheric globalcirculation models (GCMs) (Harding andPomeroy, 1996).

4.1 Canopy storage models

Schmidt and Gluns (1991) and Nakai (1996)simulated the branch accumulation process forvarious coniferous branches using the equationrst proposed by Satterlund and Haupt (1967):

CB SB

1 ekPGP02

and tted the parameters SB (mm), P0 (mm) andk(mm1) for various species (See Fig. 1). Calder(1990) simulated the canopy storage CG accumu-lation shown in Fig. 2 with the relationship:

dCG

dPG 1

CG

SGX 3

Brundl et al. (1997a) propose a binary-regression-tree model to predict unloading and duration ofsnow interception events. The model is a based onfresh snow amounts, wind velocity, air tempera-ture and global radiation. The amount of freshsnow is the most dominant variable. The modelshows good agreement between simulated andobserved events with duration shorter than threedays, except for days with rainfall.

Hedstrom and Pomeroy (1998) suggested aphysically based accumulation and retention modelfor canopy snow storage. The model calculatesweekly interception storage and requires foreststand parameters, an unloading coefcient (func-tion of time) and measurement of initial canopystorage besides standard meteorological param-eters (wind, air temperature and precipitation).The model is very detailed and takes into account

Fig. 4. Snow interception evaporation fraction IaPG versussky view fraction SVF. Average values of year 9193, 95(11 values) and 9293, 95 (8 values) for ve differentlocations and 10 different species. The year 1994 excluded

due to large snow melt during mid-winter. Basic data fromNakai (1996). Hatched line IaPG 0X371 SVF (Equa-tion derived from Kuzmin [1963])

Fig. 5. Relative evaporation rate from ice cubesmounted at different heights in a 15 heighconiferous canopy as function of height. Twoexperiments and rate at 14 m taken as unity.(Data from Kominami (1998), personal commu-nication)



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e.g., variations in SG as function of snow density(snow density is calculated as function of airtemperature). The model also accounts for varia-tions in interception efciency as a function ofwind speed (snowakes affected by wind do notfall vertically and are more easily captured by thecanopy in a sparse forest). The required foreststand parameters are: Leaf area index, LAI, can-opy cover c, canopy height H and mean forestedfetch length J. Hedstrom and Pomeroy (1998)conclude that the initial validation of the modelwas promising but indicate a desire for furtherimprovement and verication in other environ-ments.

4.2 Evaporation/sublimation models

4.2.1 Combination-equation and bulk-transfermodels

Modelling of evaporation rates from interceptedsnow may be based on the combination of theenergy-balance and mass-transfer equations in theform pioneered by Penman (1948; 1953). Thistype of equation is often erroneously attributed toMonteith, (see Monteith, 1981). Calder (1990),who was one of the rsts to simulate the snow-interception-evaporation process, states that pro-cess-based modelling of snow accumulation anddepletion on a forest canopy is a formidable task.Calder (1990) presents a detailed model where thecombination equation for evaporation is modiedto account for the latent heat of melting. Canopystorage is divided into snow storage and liquidstorage (either held within the snow or as freewater drops). Sublimation or free-water evapora-tion combined with melting are assumed to prevaildepending on snow-surface temperature andcanopy-storage type (solid, liquid). Different aero-dynamic resistances are applied for the differenttypes of canopy storage. Calder (1990), who doesnot present any simulation results, states that themodel describe the general features of observa-tions surprisingly well for the majority of storms.Lundberg and Halldin (1994), Lundberg et al.(1998), and Nakai et al. (1994) also use com-bination equations. The model of Nakai et al.(1999), differs from Calder's (1990) by using abulk-transfer rather than a combination equationfor evaporation and different quotients of the bulk-transfer coefcients for sensible and latent heat

uxes was needed to simulate the evaporationfrom snow-covered and snow-free canopy.

4.2.2 Aerodynamic resistance

In the absence of stomatal control of evapora-tion, the aerodynamic resistance ra is one of thekey factors governing snow-interception evapora-tion. In the studies of Lundberg and Halldin(1994) and Lundberg et al. (1998) it is expressedas:

ra

ln2z d

zoM

!

2uz4

where z is height above ground (m), d displace-ment height (m), zoM roughness length (m) for

momentum, von Karman's constant, and uzwind speed (m s1) at height z. The roughnesslength for heat zoH (and vapour) is approximatedwith that for momentum zoM. Rutter et al. (1971/72) relate displacement height d and roughnesslength zo (for both heat and momentum) to standheight h by:

d 0X75 h and zo 0X1 hX 5

Lundberg and Halldin (1994) found fair agree-ment between measured and calculated evapora-

tion when Eqs. (4) and (5) were used to describera. They restrict their work to situations with wetor melting snow and low or moderate windspeeds. Lundberg et al. (1998) assumes that Eqs.(4) and (5) are valid for evaporation of interceptedrain (raL) whereas a special raS may be needed forsnow interception. On the basis of Calder's (1990)data they conclude that raL seems to produce fairresults for newly intercepted snow. Evaporationfrom older snow requires a special raS, an order ofmagnitude larger than raL. Nakai et al. (1994)

measured I and C and inverted the combinationequation to calculate ra for events with a largecanopy storage (CC % 4 mmYCB % 2 mm). Theypresented ra as a power function of uz:

ra 79X4 uz0X8X 6

Lundberg et al. (1998) illustrate that snow at topbranches disappear rst while snow at lowerbranches, less exposed to turbulence, remain for alonger time in the canopy. Observed differences inra may be caused by differences in location (top or



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lower branches) and by microscale differences inexposed surface (new or old snow) and Lundberget al. (1998) could not distinguish the two factors.The presence of liquid water on the canopypresents an additional complication discussed byLundberg et al. (1998). The exposed area for thesame intercepted mass is likely to be much largerif it is in the form of many small water drops thanas a few snow lumps. The macroscale surface areaof a snow-covered forest is also much smootherthan that for a rain-covered one.

4.2.3 Evaporation and interception storage

Evaporation can only prevail as long as there issnow left on the canopy. The reduction in evap-oration from its maximum value to the time when

the intercepted snow disappears has been model-led in the same way as for rain interception by,e.g., Lundberg and Halldin (1994), and Nakaiet al. (1994). According Rutter et al. (1971/72)this reduction for rain-fed interception evap-oration is linearly related to the quotient betweenthe intercepted mass and a threshold value T ( Sfor rain studies). Lundberg and Halldin (1994) usedTC 2 mm. They also tested other approaches tosimulate the reduction and found that the simu-lated evaporation is not very sensitive to model

selection. Nakai et al. (1994) found good agree-ment between measured and calculated evapora-tion using a threshold value of TB 2 mmTC % 4 mm.

4.2.4 Sphere-sublimation models

Schmidt (1991), and Pomeroy and Schmidt (1993)simulate snow-interception evaporation for sub-zero events. In those cases evaporation may alsobe called sublimation. The sublimation rate I(kgs1) is calculated as the product of an evap-oration-rate coefcient ISP, an exposure coefcientCe and the canopy storage mass M(kg) for asingle, articial, and freely standing tree:

I ISP Ce M 7

The evaporation-rate coefcient ISPs1 is the

change in mass per unit time divided by the mass(%0.5 mg) for a 1-mm ice sphere. The exposurecoefcient Ce is the surface-area-to-massquotient Q AaMm2kg1 for snow intercepted

by a tree divided by the same quotient for a singleice sphere QSP ASPaMSPm

2kg1:

Ce Q

QSPY 8

The exposure coefcient Ce is related to the inter-cepted mass M and snow age. This empiricalrelation was established from ISP, calculated fromthe energy balance (Schmidt, 1991) and from Mand I measured by weighing:

Ce k1MRELF 9

where k1 is a function of snow age (%0.00011 forfresh snow and %0.000055 for old snow) and F(%0.3 for a single tree) is a constant. MREL MaMMAX where MMAX is the maximum snowstorage. Fractal analysis of photographs of inter-cepted snow on branches taken in a canopy wasused to determine F for various part of a canopy(Pomeroy and Schmidt, 1993). F was found %0.3for the lower part and %0.4 for the upper part. Theobservations were more scattered in the upperthan in the lower part of the canopy. Ce is twiceas large for new snow as for old snow and theinuence of snow age seems much larger than theinuence of storage location except for situationswith very small intercepted mass (Fig. 6). Theinuence on Ce of location becomes larger thanthe inuence of snow age with an interceptedmass less than 3% of MMAX.

4.2.5 Isotope enrichment models

Claassen and Downey (1995) present a one-dimensional, physically-based, steady-state modelfor the enrichment of O18 and deuterium in inter-cepted snow that can be used to calculate snow-interception evaporation. The model describesviscous and diffusive uxes within the interceptedsnow, and between the snow and the surroundingatmosphere. Model simulations yield results simi-lar to observations and indicate that the evapora-tion process in the snow is dominated by diffusiveuxes in spite of the very high permeability offreshly fallen snow.

4.3 Snow interception in hydrological

and atmospheric models

Operational hydrological models often have avery simplied description of evaporation



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(Lindstrom et al., 1994). Lindstrom et al. (1994)present a test of an interception routine as part ofa possible modication of the evaporation modulein the HBV model (Bergstrom, 1992). The routinesimulates snow and rain interception in the samemanner. The storage capacity SG in the test wasset to 2 mm in forests and all evaporation from thestorage was assumed to be potential, dened bythe Penman equation. The tested interceptionmodel gave a poorer result than the originalmodel, but meant that more realistic snowfallcorrection factors could be used. Even if thesimulation results did not seem better (old errorsmay have compensated each other) Lindstromet al. (1994) conclude that some of the changesare realistic and should be kept. The interceptionroutine was introduced as an option in the newmodel version: HBV-96 (Lindstrom et al., 1997).According to Bringfelt (1998, personal commu-nication) a simple routine for snow evaporationhas been developed within a SMHI-project wherethe Penman-Monteith equation is used for calcu-lating evapotranspiration for the HBV model.Some preliminary tests have been made againstwinter evaporation data in Norunda (NOPEX area).Various aspects of snow and forest on climate asmodelled by GCM:s are treated by e.g., Thomasand Rowntree (1992), Bonan et al. (1992),Marshall et al. (1994), Beljaars and Viterbo(1994) and Gregory (1995) but atmosphericGCMs generally have a very simple representationof snow cover and an even simpler description ofthe interaction between snow and forest according

to Harding and Pomeroy (1996) and Nakai et al.(1999).

4.4 Sensitivity to measurement errors

Schmidt (1991), Lundberg and Halldin (1994),and Nakai (1996) have analysed their models withrespect to the sensitivity of calculated snow-inter-ception evaporation to errors in measured inputdata. Lundberg and Halldin (1994) reported theuncertainty in calculated evaporation estimatesfor 19 one-day events. Nakai (1996) calculatedthe sensitivity for annual evaporation estimates.Schmidt (1991) analysed the sensitivity for theevaporation of a 1 mm ice sphere with air tem-perature T 0 C, relative humidity RH 70%,wind velocity w 0.5 m/s and net radiation RN 100 Wm2. All three studies agree that evapora-tion sensitivity is low to uncertainties in measuredvalues of temperature and net radiation (Table 5).Sensitivity to errors in wind speed depend moreon the formulation of the aerodynamic resistancethan on wind-speed measurements. The sensitivityto errors in relative humidity is considerable; a 5%error gives an uncertainty between 16% and 30%in evaporation estimates. It is difcult to measurerelative humidity with this accuracy during coldand humid conditions according to Lundberg andHalldin (1994). The sensitivity to errors in canopystorage (when applicable) is variable. This vari-ability is caused by a threshold effect. Calculatedevaporation is independent of canopy storageabove a threshold value whereas relative errors

Fig. 6. Exposure coeffecient CeM calculated with Eq. (8) with F 0X3 (low branches), 0.4 (higher branches), k1 0X00011(fresh snow) and 0.000055 (old snow) as function of (a) MREL MaMMAX with M storage in the tree and MMAX maximumsnow storage in the tree (b) as function of tree snow storage M



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become large below the threshold (Lundberg andHalldin, 1994).

5. Discussion and conclusions

The most common technique to estimate seasonalsnow-interception evaporation is combined snow-course measurements in forests and elds. Thetechnique can be recommended in areas with largesnow accumulation provided that sites are selectedto avoid differences in deposition and that win-ters with substantial midwinter melt are omitted.Measurements are needed to assure that the as-sumption of negligible stemow and canopysnowdrift is justied.

Areally representative data on interception witha high time resolution is a prerequisite for theparameterisation of the interception process inhydrological and meteorological models. Inter-ception data of this kind should be available for abroad range of precipitation events and weatherconditions. Such data can only be guaranteed frommulti-annual, continuous time series because ofthe highly stochastic nature of precipitation. Pro-cess studies will primarily require measurement ofthe evaporation rate and the eddy-correlationtechnique seems to be the best suited method forthis purpose in spite of its difculties with source-area location. Development of eddy-correlationtechniques (Grelle and Lindroth, 1996) forunattended monitoring of eddy uxes has facili-tated multi-annual, continuous measurements.Accurate measurements, during different condi-tions, of the intercepted snow (mass, location[canopy top/canopy base], quality [wet/dry], age,exposed area) are needed to understand differ-ences between observed and theoretically deduced

values of ra and Ce. The intercepted mass can bemeasured with a -ray technique, a cut-tree tech-nique, or displacement transducers. The -ray anddisplacement-transducer techniques (the lattermodied to compensate for differences in dis-placement as function of canopy temperaturesbelow zero) may resolve the vertical distributionof canopy storage. A digital camera might provideinformation about the spatial distribution of inter-cepted mass and exposed area. Fractal analysis ofphotos of intercepted snow seems to be a feasibleway to gain information about the exposed area.Determination of intercepted snow quality (wet/dry) is a nonresolved issue. A digital cameramight perhaps be used. Another possibility mightbe to use the difference in dielectric constant be-tween water (KW % 80) and ice (KI % 3). Dielec-tric techniques are used in avalanche research(Denoth, 1994) and provide ground truth forremote sensing of snowpack wetness (Sihvola andTiuri, 1986). Problems with process studies beinginterrupted by periods of snowfall might bereduced if the new type of aerodynamically-designed precipitation gauge (Wiesinger, 1993)proves successful.

Maximum evaporation rates from interceptedsnow (Table 4) are much higher than correspond-ing open-eld snowpack values (around 0.06mm h1; Harding, 1986). Observed duration ofcanopy storage (Table 2) indicates that evapora-tion can prevail for long time periods and accu-mulate to signicant seasonal values. Such valuesare conrmed by estimates of 30% to 40% ofseasonal PG (Table 4) from net-precipitation andweighing methods. Investigations based on eddy-correlation techniques to continuously measureevaporation during an entire winter give a lower

Table 5. Sensitivity of calculated interception evaporation Ito observational errors in meteorological input data. The sensitivityvalues are expressed as percentages of the evaporation to achieve comparable values. Assumed error in temperature T 1 C,in relative humidity RH 57, in wind velocity u 0X3 m/s, in net radiation RN 1 0 W m

2 and in canopy storageC 307

Source Relative error in I(%)

T RH u RN C

Schmidt (1991) %6 %16 %20 %0.5 Lundberg & Halldin (1994)1 %5 %30 2 small 030Nakai (1996), Nakai et al. (1996) %4 %20 %14 %6 314

1Values were estimated from graphs.2Sensitivity to formulation of the aerodynamic resistance was larger than sensitivity to errors in measured u.



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seasonal fraction (Table 2). There is a need forintercomparison of methods as well as furthereddy-correlation studies covering entire winterseasons before one can know if such differencesare caused by methods or by characteristics of,and conditions during, the experiment.

Some authors prefer the term sublimation todescribe vaporisation of intercepted snow (dry ormelting). It is not always possible to know if thevaporisation goes from solid or liquid phase togaseous phase. It is preferable to use the termevaporation since this includes all phase transi-tions into the gaseous phase.

Schmidt (1991) considers evaporation of melt-ing intercepted snow to be of little importance fora site in continental North America. Lundberg andHalldin (1994) report high evaporation rates innorthern Sweden for melting snow. An argumentfor neglecting evaporation from melting snow isthat it easily unloads when melt temperatures areapproached. Three factors favour the unloading:the snow structure becomes weakened (Gublerand Rychetnik, 1991), branches becomes moreexible (Schmidt and Pomeroy, 1990), and windspeed often increases when air temperature ap-proaches zero (Calder, 1990) which increasesbranch movements. Other factors favour increasedevaporation: the exposed area increases (manysmall drops instead of a few large lumps) whenmelting gives rise to water drops. Increased windspeed will directly increase evaporation rates.

Harding and Pomeroy (1996) compared turbu-lent uxes from two sites one lake and one forest.The sites were studied during periods with snow-covered canopy and with dry canopy. Measuredlatent-heat uxes did not differ markedly betweenlake (7Wm2) and forest (18 Wm2) when thecanopy was dry. Forest evaporation (99 Wm2)exceeded lake evaporation (14 Wm2) with afactor 7 when there was snow on the canopy.Nakai et al. (1999) compare turbulent uxes fromdry and snow-covered canopies and report largedaytime latent heat uxes from snow-coveredcanopy (%80% of RN) and small for dry canopy(%10% ofRN). Sensible heat uxes were large forthe dry canopy and small for the snow-coveredcanopy.

A correct formulation of the aerodynamic resis-tance is a key issue for modelling of snow-inter-ception evaporation. The large reported variationsin r

ashould be related to intercepted snow quality

(wet/dry), storage location (top branches/lowbranches) and exposed area.

Observed evaporation rates from interceptedsnow (Lundberg and Halldin, 1994; Harding andPomeroy, 1996) are normally much larger than theavailable net radiation. Average net radiation was97Wm2 while latent heat ux was 132 Wm2

during events reported by Lundberg et al. (1998).Harding and Pomeroy (1996) state that the com-bined energy from net radiation and downwardsensible heat uxes could not provide sufcientenergy to supply the observed high evaporation.They discuss trunk heat storage and horizontaladvection as possible energy sources. The lackingclosure of the surface energy balance duringevents with rain interception has been discussedfor more than a decade and there is still nogenerally accepted explanation (Morton, 1984,1985; Calder 1985, 1986; Stewart, 1977; de Bruinand Jacobs, 1989). The observations of high snow-interception evaporation rates now give an addi-tional motivation to studies of the energy sourcesfor interception evaporation.

Since reported sensitivity analyses (Schmidt,1991; Lundberg and Halldin, 1994; Nakai, 1996)all show that models for snow-interception evap-oration are highly sensitive to errors in relative-humidity data, this is an incitement to improveand develop techniques for such measurements.

It is difcult to deduce generally applicableconclusions from existing studies of snow-inter-ception evaporation. The process is inuencedby precipitation patterns, by wind and humidityconditions, by forest type, by frequency of meltperiods, etc. Climatic conditions at reported studysites differ markedly. Pomeroy and Schmidt (1993)report air temperatures between 47 C and33 C at a Canadian site while air temperatureswere close to zero during the experiments ofBrundl et al. (1997a). It is important that resultsare interpreted in a similar context to the oneunder which the observations were made. If, e.g.,several studies show that snow-interception evap-oration is not signicantly dependent on availablenet radiation, one must carry in mind that notmany studies were carried out during spring whennet radiation can be large. Extrapolation of resultsfrom individual studies must be done with con-siderable care.

There are three types of model approaches tothe snow-interception evaporation. The combina-



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tion-equation approach (Calder, 1990; Lundbergand Halldin, 1994; Nakai et al., 1994; Lundberget al. 1998), the bulk-transfer-coefcient approach(Nakai, 1996), and the ice-sphere approach(Schmidt, 1991; Schmidt and Pomeroy, 1993). Itis easy to discern the effects of net radiation andventilation in the combination-equation approach(Lundberg and Halldin, 1994) and the widespreaduse of this approach in rain-interception studiessimplies possible generalisation of new ndings.Application of bulk-transfer coefcients methodsrequires better knowledge of the quotient of thebulk-transfer coefcients for sensible and latentheat uxes over forests (e.g., Hogstrom et al.,1989) and over melting snow (Male and Granger,1981). Since the ice-particle albedo (Schmidt,1991) is used when calculating ice-sphere evap-oration, effects of variations in canopy albedomust be included into the exposure coefcient.Ice-sphere models benet from the literature onblowing snow (Pomeroy, 1988, 1989).

Operational hydrology and weather modelsnormally treat rain and snow interception (andevaporation in general) in a very simplied way(Lindstrom et al., 1994). The same holds true formost atmospheric GCMs (Harding and Pomeroy,1996; Nakai et al., 1999). It is possible that in-clusion of this process in many hydrological andmeteorological models may lead to improvementssince several studies during the last decade agreeon the importance of intercepted-snow evaporation.

Acknowledgements

The work was carried out under contract ENV4-CT96-0324(WINTEX) with the Commission of the European Commu-nities. Dr Y. Nakai, Hokkaido Research Centre, Sapporo,Japan, has been of great help by allowing us to includeresults from his thesis. Dr. A. Grelle, Swedish University ofAgricultural Sciences, and Dr. H. Bergstrom, UppsalaUniversity, Sweden kindly provided evaporation and precip-

itation data for calculation of interception fractions.

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course measurements to approximate snow interceptionevaporation. Proceedings from XXI Nordic HydrologicConference, Uppsala, 2630 June, 2000. In: Nilsson T(ed) Nordic Hydrological Programme, NHP report 46:570577

Ohta T, Suzuki K, Kodama Y, Kubota J, Kominami Y, NakaiY (1999) Characteristics of the heat balance above thecanopies of evergreen and deciduous forests during thesnowy season. In: Hardy JP, Albert MR, Marsh P (eds)Hydrological Processes 13: 23832394

Pomeroy JW, Parviainen J, Hedstrom N, Gray DM (1998a)Coupled modelling of forest snow interception andsublimation. In: Taylor S, Hardy JP (eds) Hydrological

Processes 12: 23172337Pomeroy JW, Gray DM, Shook, KR, Toth B, Essery RLH,

Pietroniro A, Hedstrom N (1998b) An evaluation of snowaccumulation and ablation processes for land surfacemodelling. In: Taylor S, Hardy JP (eds). Selected papersfrom the 55th Eastern Snow Conference held in Jackson,New Hampshire, USA. Hydrological Processes 12: 2339

2367Pomeroy JW, Parviainen J, Hedstrom N, Gray DM (1998c)

Coupled modelling of forest snow interception and sub-limation. In: Taylor S, Hardy JP (eds) Selected papersfrom the 55th Eastern Snow Conference held in Jackson,New Hampshire, USA. Hydrological Processes 12: 2317

2337Storck P, Bowling L, Wetherbee P, Lettenmaier D (1998)

Application of a GIS-based distributed hydrology modelfor prediction of forest harvest effects on peak streamow in the Pacic Northwest. In: Taylor S, Hardy JP (eds)Hydrological processes 12: 889904

Authors' addresses: Angela Lundberg, Division of WaterResources Research, Lulea University of Technology, SE-971 87 Lulea, Sweden; Sven Halldin, Department of Earth

Sciences/Hydrology, Uppsala University, Norbyvagen 18B,SE-752 36 Uppsala, Sweden.


snow interception evaporation

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