VOL.
$, NO. 4
WATER
RESOURCES
RESEARCH
I•OURTH
QUARTER
1967
SnowCatchby ContierCrowns
DONALD
R.
SATTERLUND
WashingtonState University, Pullmar•
HAROLD
F.
HAUPT
Forestry SciencesLaboratory, Moscow,Idaho
Abstract. Study of interception storage of snow by two speciesof sapling conifers in
northern
Idaho
revealed
that
cumulative
snow catch follows
the classical law of autocata-
kinetic growth, or
'
I, = 8/[1 nt- e-•½•'-•'ø)
where I, is interceptionstorage,$ is the interceptionstoragecapacity of the tree, e is the
base of the natural logarithm, k is a constantexpressingthe rate of interceptionstorage,P is
accumulatedsnowfall,and Po is accumulatedsnowfallat the time of most rapid storage(i.e.,
the point of inflection of the sigmoid curve). Interception storage conformedto the law in five
storms in which snowfall began while the trees were bare, and in two storms in which snow
fell while snow from previousstormspersistedon the trees. Several small stormsyielded insufficient data to define the appropriate constants,but inspection indicated no serious deviation
from the generallaw. (Key words: Coniferoustrees; interception; snow; Idaho)
S is the interceptionstoragecapacityof the
INTRODUCTIO•I
vegetation;
Probablyno elementof the hydrologiccycle
has been as widely studiedas the interception
process,
wherebyprecipitationis caughtby veg-
e is the baseof the naturallogarithm;
P is stormprecipitationin inches;
R is the ratio of vegetationsurfacearea to
the projectedareaof the canopy;
E is the evaporationrate in inchesdepth per
hour duringthe storm; and
etation and redistributed to the atmosphere
and the ground.Interceptionloss,or the return
of precipitationto the atmosphere
by evaporation, wasobserved
by Horton [1919] to be the
sum of (a) the precipitation stored on plant
surfaces at the end of the storm (hereafter
termed interceptionstorage),and (b) evaporation from 'the precipitationheld by plant surfacesduringthe storm.
The interception loss equation. Merriam
[1960] developeda generalequationto describe
the interceptionloss processon the basis of
rain and snowfall data found in the literature
as follows:
L = $(1 -- e-r/s) nt- RET
(1)
where
L is interceptionlossin inchesdepth over the
projectedareaof the canopy;
T is the duration of the storm in hours.
The first term on the right-hand side of the
equation should be consideredinterception
storage,and the secondterm represents
evaporation during the storm.
During light or shortstorms,the interception
storageterm of the equationdominates,and the
evaporationduring the storm is minor to negligible. Similarly, very low evaporation rates
during long periods of precipitation have the
same tendency to cause the storage term to
dominate.Evaporation from interceptedprecipitation could be expectedto be high only
during short storms and to decreaseas the
storm continued,as demonstratedby Abraham
[1962] in his analysisof evaporationfrom fall-
1035
1036
SATTERLUI•D AND HAUPT
ing raindrops.Miller [1966], considering
the accumulatingrapidly and uniformly in a storm
low vaporpressure
of snowandthe lackof heat when the air temperature, initially slightly
energyavailable
duringthe coldand humid
above freezing, fell to near 30øF [Miller, 1964].
conditionsof snowfall,suggests
that evaporation The limited data suggestedthat interception
of interceptedsnowmust be very slightduring storage of snow may depart from the constorms. Therefore, snow interception losses vex upward form indicatedin equation 1.
Therefore, a study was set up to determine
mustprimarilybe limitedto losses
frominterthe factors influencingsnow catch by conifers.
ceptionstoragebetweenstorms.
Interceptionstorageo• snow. In moststudies This paper reports on the mechanismof interof snowfall interception, interception storage ceptionstorageduringsnowfall.
has been measuredindirectly as the difference
I•ETI-IOD
OF STUDY
between the amount of snowfall reaching the
Sapling Douglas-fir (Pseudotsugamenziesii
groundin the open and that reachingthe
vat.
glauca (Beissn.) Franco) and western
groundundera forestcanopy.As a result,many
of the data are of questionablevalue, because white pine (Pinus monticolaDougl.) trees were
all inaccuracies and errors of measurement are
suspendedin a very small openingin a sapling
includedin the residualterm, and becauseof lodgepolepine stand near the headquartersof
the questionable
assumption
that snowfallin a the Priest River Experimental Forest in northforestopeningis an accuratemeasureof snow- ern Idaho. The trees were suspendedby a light
cable that passedthrough an overhead pulley
fall above the forest canopy.
A few studies have been made by directly and was a•tached to a spring-tensionscale.
measuring
the amountof snowcaughtby con- Water level recorderswere modified to provide
iferoustrees.Goodell[1959] foundthat a small a continuousweight record of each suspended
Engelmannspruce(Piceaengelmannii
Parry) tree. A complete descriptionof the recording
held about 0.2 inch, water equivalent,after a apparatus and its constructionwill be reported
dry, cold snowfallof about 0.4 inch. Miller separately.
[1964]weighed
snowbeatenoff a younglodge- Each tree was suspendedfor a period of appolepine(PinuscontortaI)ougl.)asequivalent proximately one month, after which it was replacedby a freshlycut tree of the samespecies.
tomefta (Cryptomeria japonica?) tree was A quantitative descriptionof each tree is given
weighedcontinuouslythrough several snow- in Table 1.
to about 0.24 inch of water. In Japan, a cryp-
storms. The catch varied from storm to storm,
beingleastat low temperatures
near23øFbut
moderateto heavyat highertemperatures(32.34øF). The snowloadsaccumulated
in variable
fashion,closelyfollowingthe curveof accumulated stormprecipitationin a stormwhenair
temperatureremainedbetween25-27øF.,but
The hourly snow catch, in pounds,was converted to the depth in water equivalent over
the projected crown area of the tree to the
nearest 0.001 inch in each storm. Hourly precipitation recordswere obtainedfrom the headquartersweather station,about 100 yards away.
Also available
were continuous records of tem-
TABLE 1. Descriptionof Trees Used in Snow InterceptionStudy, 1967
Projected
Tree
Species
Douglas-fir
W. whitepine
No.
Dates
Suspended
Height
to Top Whorl,
Crown diam., Crown area,
ft
ft
Needled
SurfaceArea,*
sqft
sqft
I
1/10-2/2
13.7
10.68
89.58
514.61
2
2/2-3/8
12.8
7.90
49.02
119.39
I
2
1/10-2/2
2/2-3/8
12.0
12.2
10.00
8.12
78.54
51.78
95.31
97.07
* Needled surface area is the total surfacearea of needledbranchesmeasuredas needledbranch length
timesthe distancebetweenneedletips perpendicularto the branchaxis.
,Snow Catch
•
moist snowfallat higher temperaturesthan the
previoussnowfall.
Complete comparisonsof computedand ob-
z .075
DOUGLAS
1037
-FIR
o
served snow catch were made for all storms that
yielded sufficient data to define the curve. Ta-
,.. .d .050
bles2 and 3 presentthe data uponwhichfigures
i and 2 are based. Most
NHITE
o,.
PINE
.025
l-- Z
I
I
of the differences be-
tween computed and observedcatch were less
than 0.01 inch. The largest difference,0.036
inches,arosewhen snow slipping from a small,
I
overloaded branch fell and the force of its fall
dislodgedlarger massesof snow from lower
SNOWFALL,
INCHES,
branches.However, accumulationresumedand
WATER
EQUIVALENT
(P)
was approachingthe computed storage capacity when snowfallended.
Several small storms yielded insufficientsnow
(circles and crosses).
to definea relationshipbetweencatch and snowfall, but inspectionof the data gave no indication that the general form of the curve was
perature,relative humidity, and solarradiation. differentin smallthan in largerstorms.
z _
0
Accumulated
.10
wind
.20
movement
.30
.40
was measured
daily. Wind was not an important factor in this
study, as all snowfall occurred under calm or
nearly calm conditions.
RESULTS
DISCUSSIOlq'
Growth of any kind in which the substance
or structure itself acts as the base for the further accumulation of the same substance or
When accumulatedinterceptionstoragewas
plotted against accumulatedsnowfall for each
storm and tree, a surprisingsimilarity of form
appeared.Each plot, though differing in slope
.150
DOUGLAS-FIR
and varying in height, seemedto definethe
well known sigmoid growth function. Consequently, the formula for each curve was derived from the data accordingto methodsoutlined in Lotka [1956], and a computedcurve
wasfitted to the data. Figuresi and 2 illustrate
typical results.
The generalequationfor snowcatchis
I, = S/J1-[- e-•(P -- Po)]
.125
,,•
.•.
z
•,
--'
.1 O0
• "'
.075
WHITE
PINE
z •
(2)
where
S, e, and P are as previouslydefined;
I, is interceptionstorage;
k is the constant expressingrate of interceptionstorage;
'• •
050
I-. z
z
..
.025
Po is the amount of snowfall accumulated at
the time of most rapid storage (i.e., the
point of inflectionof the sigmoidcurve).
0
.10
WATER
Equation 2 held when the trees were bare of
snow at the start of the storm and when trees
loadedwith dry snowwere subjectedto a more
.20
SNOWFALL,
.30
.40
INCHES,
EQUIVALENT
(P)
Figure 2. Snow catch during storm of January
12, 1967. Computed curve fitted to field observations (circles and crosses).
1038
SATTERLUND
TABLE
2.
AND
HAUPT
Snow Catch by Douglas-firand WesternWhite Pine. TreesBare at Start of Storm. Priest
River Experimental Forest, Idaho. Storm of January 10, 1967
Interception Storage,Inches Water Equivalent
Cumulative
Hourly Snowfall,
inches,w.e.
Douglas-fir
Observed Computed* Difference
0.005
0.008
0.025
0.060
0.071
0.074
0.02
0.04
0.15
0.22
0.30
0.037
0.002
0.003
0.027
0.055
0.071
0.074
WesternWhite Pine
Observed Computed$ Difference
0.003
0.005
0.002
0.005
0
0
0.004
0.005
0.013
0.038
0.043
0.046
0.001
0.002
0.015
0.034
0.044
0.046
0.003
0.003
0.002
0.004
0.001
0
Temp.,
øF
32
32
32
32
32
33
* I, = 0.075/1 -+-½-2a.o7(P-o.175)
i I, = 0.047/1 + ½-2a.66(P-o.15o)
structure may be termed 'autocatakinetic'
growth [Lotka, 1956]. Accordingto this concept,
growth would continue. at an ever accelerating rate in the absenceof external constraints. In any complexsystem,however,constraints exist that limit growth at some point.
There are two points of equilibrium: a lower,
in which growth is absent for want of the
growth substance,and an upper, at which
growth is limited by the constraintsof the system. Starting at the point where the substance
is first present,growth beginsto accelerateand
continuesuntil the limits of the systemare approached,then deceleratesuntil a new equilibrium is establishedat the limits of the system.
For example, a bacteria population in a petri
dish containingagar definesthe locus of the
well knownequationof populationgrowth.
TABLE
3.
An analogoussituation existsin the development of interceptionstorageof snowby coniferous trees. The first snowflakesstriking the
canopy often bounce off the needlesand fall
through all but the smallest spacesbetween
them, bridging acrossthe smallest.With continued snowfall, more and more bridges are
formed acrosslarger and larger gaps,providing
a continuouslyincreasingplatform upon which
more
flakes can come to rest.
As the snow
builds up, however, most of the bridgeable
gaps are bridged, and the platform area increases at a slower rate. Heavier
snow loads on
flexible branchesbend them downward,and at
some point the tree can hold no more snow.
Thereafter, the excessslides or falls from the
canopy, as rapidly as it falls from the sky.
During calm periodsthe size, form, and wet-
Snow Catch by Douglas-fir and Western White Pine. Trees Bare at Start of Storm. Priest
River Experimental Forest, Idaho. Storm of January 12, 1967
,,
Interception Storage, Inches Water Equivalent
Cumulative
Hourly Snowfall,
inches, w.e.
0.02
0.05
0.13
0.17
0.23
0.27
0.29
0.37
Douglas-fir
Observed Computed* Difference
0
0.004
0.012
0.047
0.090
0.114
0.137
0.146
0.001
0.001
0.012
0.034
0.094
0.125
0.134
0.145
* I, : 0.146/1 -t- ,-29.75(r-0.210)
$ Io : 0.098/1 +
0.001
0.003
0
0.013
0.004
0.011
0.003
0.001
WesternWhite Pine
Observed Computedt Difference
0.001
0.012
0.023
0.053
0.075
0.097
0.097
0.094
0
0
0
0
0
0
0
OO2
005
026
049
080
091
093
0.097
0.001
Temp.,
øF
33
0.007
32
0.003
0.004
0.005
0.006
0.004
0.003
32
31
31
32
32
33
Snow Catch
ness of the snowflakes determine the rate and
degree of bridging during any given storm,
whereasthe form, surfacearea, and strengthof
the branches determine the ultimate snow load
that can be borne. There is an interaction be-
tween snow cohesionand branch strength, for
1039
Center, Pullman, project 1849. This investigation
was supported in part by Cooperative State Research
Service
Funds
from
the
McIntire-Sten-
nis forestry research program and was conducted
in cooperationwith the U.S. Forest Service, Intermountain Forest and Range Experiment Station, Moscow, Idaho.
snow bridges distribute the load so that
REFEREI•CES
branchesgive each other mutual support, inAbraham, F. F., Evaporation of raindrops,J. Geocreasingthe load capacity of the tree.
phys. Res., 67, 4673-4682,1962.
Interceptionstorageof snowthereforediffers Goodell,
B.C., Management of forest stands in
from interceptionstorageof rain. Liquid water
western United States to influence the flow of
forms a thin film surroundingthe existing surfacesof the tree, whereassnow bridgesacross
gapsand thereby createsits own surfaceupon
which further snowfall can be retained. In short,
there is no universal interception storage equa-
tion, and since interceptionstorageis the
snow-fed streams, Intern. Assoc. Sci. Hydrol.
Publ., 48, 49-58, 1959.
Horton, R. E., Rainfall interception, Monthly
Weather Rev., 47, 603-623, 1919.
Lotka, A. J., Elements of Mathematical Biology,
Dover Publications,Inc., New York, 465 pp.,
1956.
Merriam, R. A., A note on the interception loss
interceptionloss, there can be no universal equation, J. Geophys. Res., 65, 3850-3851, 1960.
Miller, D. I-I., Interception processesduring snowinterceptionloss equation.
storms, Pacific S.W. Forest and Range Expt.
Further consideration of the redistribution of
Sta. Res. Paper PSW-18, 24 pp., 1964.
interceptionstorageto the atmosphereand the Miller, D. I-I., Transport of interceptedsnowfrom
trees during snow storms, Pacific $.W. Forest
groundalsosuggests
differences
of greatmagniand Range Expt. $ta. Res. Paper PSW-33, 30
tude betweensnow and rain. But that is a sepdominant element in either snow or rainfall
arate questionand is alsounderinvestigation.
Acknowledgments.Scientific Paper No. 2977.
WashingtonState University AgricultureResearch
pp., 1966.
(Manuscript received June 1, 1967;
revised August 1, 1967.)