Miller, D. H. (1959). Transmission of insolation through pine forest canopy, as it affects the melting of snow. In A. Kurth (Ed.), Mitteilungen / Schweizerische Anstalt für das Forstliche Versuchswesen: Vol. 35/1. Festschrift. Zum siebzigsten Geburtstag

Transmission of Insolation

through Pine Forest Canopy, as it Affects the Melting of Snow

David H. Miller

Department of Geography and Geology, University of Georgia, Athens

1. lntroduction

The long and thorough investigations of Dr. Burger into the influences of forest on hydrologic processes impress upon his readers the complexity of nature, and the necessity that we must first separate many intermingled phenomena if we are eventually to arrive at an understandig of any one. The effect of forests on snow, for example, is not a single problem but many. The forest acts on aerodynamic processes that govern the deposition of snow, and also intercepts a fraction. lt acts differently on transfer of heat that melts the snow; moreover, it acts differently on each avenue of heat .flow - short-wave radiation, long-wave radiation, convection, and condensation. Melt-water runoff from the wooded Sperbelgraben is 15-20 percent less than that from the mainly bare Rappengraben; this figure is the composite or summation of the ways in which forest affects the individual processes of heat flow, increasing some over their rate in the open, decreasing others.

One of the avenues by which energy reaches the snow in a forest stand is solar radia- tion transmitted through the canopy. In this paper I report briefly some studies of this process and some relations of transmission to physical dimensions of stands. I note some implications of transmission, and its complement, absorption of energy in the crowns, for the climatology and hydrology of snow-and-forest regions, and discuss problems of obser- vation.

The hydrologic processes of snow melting and evaporation are also thermal processes, and are not completely understood if considered only as functions of air temperature.

They require established amounts of heat, rather than a number of degrees of tempera- ture, fQr each centimeter of water melted or vaporized. The heat-balance method of estimating snow melting has made steady progress in the United States

^1,

as the older temperature method has proved inadequate. The older, or degree-day method is parti- cularly in error when a sudden change occurs in the radiation budget of a drainage basin,

1 lndebtedness to fundamental research in glaciology by such men as Sverdrup and Ahlmann is great.

«Mitteilungen der Schweizerischen Anstalt für das forstliche Versuchswesen, Bd. 35, Heft l»

as may happen when a spring snowstorm lays a highly reflective mantle of new snow over the old pack. The net radiation budget of the snow abruptly decreases. This decrease may not be indicated by any change in air temperature, but exerts a marked, immediate effect on stream flow.

In the more recent heat-balance method, the rate of each of the

incoming and outgoing flows of heat is measured or estimated, and a budget struck, which represents heat surplus available to the snow pack. This method requires know- ledge of short-wave radiation intensity, and of its depletion before it reaches the snow.

2. Transmission in Relation to Crown Closure

Many botanists and ecologists have been concerned with light at the forest floor, in research on growth of herbaceous plants or young trees. These men have usually looked to crown closure as the relevant dimension or parameter of the forest stand. So we first will consider some work in the western United States in terms of crown closure.

Radiation within forest stands was measured during several periods in an extensive observational program on snow accumulation and meltin

g, carried on from 194.S to 1950

under auspices of the Corps of Engineers and Weather Bureau

¹

of the Federal govern- ment, and from 1950 to 1956 by the Corps of Engineers alone. The instrument was the Eppley pyrheliometer, with a recording potentiometer sensitive to the whole solar spec- trum and recording all fluctuations during the day.

California

In fall 1951,

diffuse solar radiation was measured under lodgepole pine

(P. contorta

var. murray

ana) at the Central Sierra Snow Laboratory in the crest region of the Sierra

Nevada of California (latitude 39°20' N., elevation 6900 ft). The trees form an agglo- merated pattern with open spaces that are even more evident from the air than from the ground. Canopy cover, determined over circles of 25- and 50-ft radius on air photographs, averaged about 32 percent at eigths stations. On cloudy days, 8-10 calories/sq cm and hour was recorded, 30 pcrcent of the total insolation. Observations on clear days omitted sunflecks, but about half of the diffuse or sky radiation was transmitted

.

M.ontana, 1948

In fall 1948,

a series of day-long observations were made at Upper Columbia Snow Laboratory ( 48° 18' N. Iatitude, 4800 ft elevation), near Glacier Park, Montana. Eight

1 With cooperation from the Geological Survey and Bureau of Reclamation. Certain aspects are included in a new program of the Forest Service and State of California.

stations on a line reaching nearly through a stand of young lodgepole pine were occu- pied in daily rotation. Crown closure, measured for each station on photographs taken upward, averaged 64 percent at five stations in the interior of the stand; it averaged 52 percent at three stations closer to the edges. Daily totals of transmitted radiation ( and of insolation in the open) are published (U.S., Corps of Engineers, 1952)

1 •

Transmis- sion at the interior stations averaged 7 percent (see Table 1).

Montana, 1950-51

Transmission was measured during winter 1950- 51 at a single station in the Montana

stand of lodgepole, with closure 30 percent. Eliminating days when snow fell, or had fallen

on the day before (and might remain on tree branches), the 66 days remaining were grouped by cloudiness. On days that were clear or nearly clear, transmission of insolation averaged 13 percent; on days of moderate cloudiness, averaging

⁷

/ioths, transmission was 18 percent; on overcast days, it averaged 22 percent. Insolation from a plane, rather than a point source penetrates the canopy much more deeply. Insolation from all angles can find more points of entry into the stand than a single beam can, especially if the single beam comes in at a low angle. lt is likely that open spaces penetrated by the single beam from the low sun refract light at their edges, and that such refraction would total

.a

considerable sum if the spaces are numerous and small

^2.

On clear days, direct insolation in these sunflecks is the largest component of the total received at the forest floor. Evans (1956), in a study of light measurement problems in a tropical rainforest, finds that sunflecks make up about three-quarters of the total. Oving- ton and Madgwick (1955) show a decrease of transmission through canopy of P. nigra when intensity in the open increases, in the same month (April) ; tripling of intensity in the open, presumably caused by decrease in cloudiness, is associated with halving of percentage transmitted.

The Montana observations show no marked trend as insolation changes, separate from the effect of cloudiness change. The range of variation

in winter is probably too

small to produce a definite relationship.

An average value of transmission, omitting 20 days when daily insolation in the open was less than 100 calories/sq cm, is 17 percent. Standard deviation is 5 percent. Daily values range from less than 10 to more than 25 percent. The average of all days in May, last month of the series, was 21 percent, a high value that indicates cloudiness associated with late-spring maximum in precipitation and hence greater incidence of diffuse inso- lation, as well as the higher angle of the sun on clear days.

1 A base intensity of downward diffuse insolation of about 0.02 calorie/sq cm and minute was not registered, and is added to the published values for five hours each day. There are 23 days in the series.

2 Salisbury (1930) notes that sunflecks on the forest floor are lower in ,intensity than full sunlight;

this is presumably caused by refraction.

Montana, 1947

Brecheen ( 1951) presents daily totals of transmitted insolation in the same stand of lodgepole pine for summer and fall of 1947. Eight stations

¹

were occupied in daily rota- tion. Transmission at the five interior stations averaged 8 percent

^2,

at the edge stations 18 percent. Figures in parentheses in Table 1 were adjusted by me on the basis of a rela- tionship between transmission and distance from the edge, to reduce effect of side light.

Also in Table 1 are figures for overcast days.

Brecheen's curvilinear analysis of effects of cloudiness and insolation in the open shows that if insolation remains constant, transmission increases with cloudiness, as Gast (1930) and others note. Pairs of days from Brecheen's data illustrate this effect:

Staion A, 16 •10 closure Station F, 36 °/o Station H, 62 °10

Date: 6 Sept. 25 Oct. 26 Aug. 27 Sept. 12 Aug. 1 Nov.

Insolation, cal/sq cm 232 283 369 373 227 233

Cloudiness, tenths 10 0 10 2 8 6

Transmission, percent 34 30 14 10

11

4

In the period observed, insolation in the open was not closely

correlated with clou- diness, being more dependent on season, and was found to have an appreciable effect on transmission. For an increase in daily insolation of 100 calories/sq cm, transmission increases about 2 percent. This change is probably relatcd to darkening and growth of pine needles

³

and to change in angle of incidence of the direct ray of the sun

4 •

Transmission at Other Values of Closure

In order to fill out the relation between transmission and canopy closure, data were

obtained from investigations reported in the literature

5,

where closure was stated by the investigator or could be estimated by use of stand tables from other measurements. These data are listed in Table 1; comments on them follow.

Observations by Shirley (1945)

were made in jack pine stands that had been cut by

various amounts; I estimate that uncut stands of 60 years age have a closure of 40 per-

1 Closure of crowns directly above individual stations ranges from 16 to 79 percent. However, in- solation at any station is so affected by cover at the others that I have grouped the eight into interior and edge. These values of closure, sampled Irom ground photographs taken upward, differ from samples on aerial photographs, which, however, were smaller in scale and had less contrast between foLiage and background.

2 The last five days, when transmitted insolation was near zero, were omitted.

3 The effect of growth of needles has often been noted. For example, Ovington and Madgwick (1955) report a decrease in transmission from 9 percent in April to 4 percent in September and October.

4 Shading by a ridge at beginning and end of the day may have been a minor factor.

6 Geiger (1957) and Kittredge (1948) have br,ief summaries. More work has been clone with deci- duous stands than coniferous, and more with fir and spruce than with pine.

Transmission of Insolation in Pine Stands

Aikman, 1936

Brecheen, 1951 interior stations overcast only edge stations overcast only adjusted Bums, 1916

Clements, 1910

Gast, 1930 monthly values monthly values Oosting and Kramer, 1946 Sakharov, 1949

windy (15 mph) Scheer, 1953

Shirley, 1945 thinned stands

uncut stand U. S. Coop. Snow lnvest.

Montana, 1948 Montana,1950-51 Calif., 1951 Wellner, 1946

Wright, 1943

1 Days of little cloudiness 13 Days of moderate cloudiness 18

Overcast days 22

Transmission

of Insolation, Crown as percent of that Closure,

in the open percent (*=light)

5 82

7½ 64

8

18 52

(18) 14

6 68

8* 60

76, 65, 50, 45 40 34, 30, 28, 26 85

6* 80

6* 80

12*

27* 65

83 10

51 20

37 31

27 40

7 64

17¹

(std. dev. = 5) 30

30 32

94 -

73 -

70 -

61 -

53 -

48

-

45

-

37

-

27

-

17 -

46* 25

Table 1

Stern Density,

inches per acre

- 6200

-

- - 2200 3600

- -

- 700 1600 2400 2800

6200 M1

-

M2 3000 M3

600 800 900 1100, 1300 1400, 1700 1900 2400 2100 2600 2900

-

cent¹ and reduce this proportionately in the cut stands. Gast (1930) made a series of observations under a rather thin, high canopy of mature white pine. His figures for clo- sure are visual estimates and seem a little high 2 • Values for individual months from summer into fall are in Table 1. Burns (1916) reports both light and crown closure.

For Clements' (1910) measurements in young lodgepole pine, closure of 60 percent is assumed. For Aikman's (1936) measurements in white pine, closure of 80 percent is assumed. For Wright's ( 194,3) measurements in lodgepole pine, closure of 25 percent is assumed, since the stand was so open that he could make readings every twelve paces while cruising³• For observations of Oosting and Kramer (1946) under old shortleaf pine, closure of 80 percent is assumed ^{4 •}

Sakharov (1949) observed transmission of light in pine stands of 80 percent closure with special reference to wind, which he found not only increases the range of transmis- sion, but also increases the mean. Scheer (1953), in a stand of 65 percent closure, was studying thc effect of illumination on activity

oI

birds, so made observations at dawn, when the whole sky is the source. In his plot of brightness against fraction of sky covered, deciduous and coniierous stands lie along the same line. Here the concept of the crown as a thin plane without absorption in depth seems valid. Transmission is larger than in studies involving insolation Irom a point source predominantly.

Table Ja Transmission of Insolation in Fir and Spruce Stands

1

Transmission, 1

Crown Closure, perceat percent

Baumgartner, 1952 5 90

Berger, 1953 14 70

Knuchel, 1914 34* 25

15* 64

Nägeli, 194-0 spring 8* 60

fall 4*

Schimitschek, 1948 10-15* 60

5-10* 75

1 This was probably a stand of less than average density. Data in Brown and Petheram (1926) for basal area and number of trees per acre at various degrees of closure confirm the estimate of 40 percent.

The more dense Station of the two is shown by a map to be near openings, and considerable inso- lation might have come from the side, beneath the base of the canopy, 65 ft above the ground.

3 The stand was not so dense tliat light reflected from tree trunks was significant.

4 Correspondence of light-meter readin,gs with those of a spherical thermocouple suggests that light from the side was not important.

A few data for transmission under dense coniferous stands are included in Table 1 for comparison. Values of closure are assumed for the spruce stands studied by Knuchel (1914),Nägeli (1940),andSchimitschek (1948).Baumgartner's (1956_) workinspruce emphasizes net radiation, but from his data I compute that of the insolation about 5 per- cent reaches the forest floor; closure is 90 percent. Berger ( 1953) measured closure under mature fir as cover projected on a plate of unit area, or hemispherical cover;

averages are for five stations

1•

Discussion

Figure 1 displays the data on transmission of insolation through pine stands presen- ted in Table

1.

With considerable scatter, it shows a decrease of transmission as the crowns close. This decrease is most rapid in open forest. Concavity of the relation indi- cates an excess of interception of insolation in open forest, to the extent that a curve through most of the points would lie below the diagonal of the graph (lightly shown).

This excess interception is the result of repeated reflection of the beam of insolation by the foliage, absorption at each incidence depleting the beam by half or more

2 •

Some- times the beam is even reversed in direction. A much smaller part reaches the ground than would if the canopy were a thin plane with holes but without vertical dimension

3•

Only at high closures in Figure 1 is transmission greater than the diagonal. Here transmission represents stand light, with negligible contribution from the direct solar beam. This light has undergone at least one reflection, and has travelled a devious path through the porous canopy. In stands of moderate closure, stand light is significantly augmented by sky light, i. e., diffusely scattered solar radiation that comes from the sky as a plane source. In the mountains where the observations first presented were made, diffuse radiation is 10-20 percent of the total or «global« radiation on a clear day, and I have shown a dotted line in Figure 1 extending from 15 percent at left edge to suggest the contribution of sky light and stand light

4•

Radiation above this line is mainly direct insolation, i. e., sunflecks. The higher the sun the greater this contribution.

The effect of sun angle is particularly noted in the winter observations in Montana (M

2

in the figure), which were made when the sun was only 20 or 30 degrees above the horizon at midday. Gast's data (1930) show a decrease in transmission as the sun alti- tude declines from June to September, especially in the more open stand. This situation can be clarified by Krinov' s ( 1953) report that reflection of insolation from a stand of fir depends on angle; a ground observation horizontally against the side of the stand

1 Attempts to define closure as the fraction of the sun's path obscured by foliage (ecliptic cover) did not yield useful results.

2 The albedo of needles is only 0.12-0.15, so each reflection takes a large toll. As a result, albedo of the crown as a whole, with its many holes and shadows, is still smaller.

3 On the other hand, interception of rain or snow is relatively small. lt could be represented in Figure 1 by curves, convex upward, above the diagonal.

-4 At low elevations and in humid air masses this line would be higher.

0 100

\\

20

Figure 1 40

90

80

\~

1-

z

w

u

ll: w

Q.

.

z

0 1-<t ...J 0

Cl)

z

"-

0

70

60

50

40

Z 30

0

Cl) Cl)

:::E 20

Cl)

z

<t 0:

t- 10

\

---- ----

---

\ \

\ \

\

^•G

\

-~

\sh

\ •M3

\.sh

•M2

\ \

- - -

^t----_

_{- - ---}

20 40

60

\

80 100

TRANSMISSIO N RELATIVE TO CROWN CLOSUR E

s

IN PINE STAND

\

^•G

.s,1\

~ \

_ c.

•B

1\

-- -

^{- •':::--.} o •• s

Mr ^•

^Bu 1 ^{1 •A}

\

60 80 100

CROWN CLOSURE,PERCENT

A AIKMAN M3 CALIF. 1951 DATA

B BRECHEEN 0 00STING

Bu BURNS s SAKHAROV

C CLEMENTS Sch SCHEER

G GAST Sh SHIRLEY 1945

M1 MONTANA 1948 DATA

w

WRIGHT

M2 MONTANA 1950-51 DATA

gave an albedo of 0.08, while an aerial one looking down into the stand gave 0.02. The difference represents light that penetrates the canopy from above and is absorbed throughout its depth or at the ground. lt shows the importance of sun angle in stands where direct insolation makes the major contribution to the total reaching the forest floor.

Conversely, as the whole sky becomes the radiating source, the sun angle comes to have less meaning than the fact that more of the total insolation comes from overhead;

and so penetration of insolation into the forest increases

1 •

W e then have, in essence, two parallel planes opposite each other - sky and crowns. Transmission approximates the percentage of open area in the crown, and so transmission plus closure approaches 100 percent. In Scheer's study, 27 percent transmission and 65 percent closure add to a sum of 92 percent. The diagonal line in Figure 1 passes through points for which transmis•

sion and closure total 100 percent

2 •

3. Transmission in Terms of Other Parameters of a Forest Stand

CrownDepth

Scatter of the individual observations in Figure 1 is large. Clearly other dimensions or parameters than fraction of crown closure, as area projected on a horizontal surface, are relevant to transrnission of insolation. lt has been suggested that the difference bet•

ween a plane source and a point source of radiation is important, as well as the location of the source in terms of angular height above the stand. These meteorological factors draw attention to other parameters of the crown, most notably its depth.

Radiation is probably not absorbed in direct ratio to depth of crown, but follows some form of the Bouguer-Lambert law that would take account of the non-homogeneous nature of foliage. Only a few data are available to me on vertical attenuation of insolation, and from those of Schimitschek (1948) for visible light in spruce, I have computed extinction coefficient, y, in the law Iz = 1

0

e•rz, in which Iz is insolation at any depth z,

1 Dirmhirn (1953) gives a lower value of albedo for forests on a day when the sky is cloud- covered than on a clear day, when intensity of infra-red radiation äs higher. Infra-red is strongly

reflected by chlorophyll and penetrates more deeply into the stand as well as being reflected more strongly from the top of the crown; correspondingly, less is absorbed by the foliage.

2 lt may be noted in passing that some of the observations of transmission in the literature were made for the purpose of obtaining a value of closure, implicitly accepting this Statement, which, as we have seen, is not valid for deep crowns.

Figure 1. Transmission of solar radiation relative to closure of pine crowns. Transmission is ex- pressed as percentage of insolation in open site. Diagonal line indicates stands in which transmission and closure add to 100. Solid curved line is the approximate relation between the two variables;

distance below the diagonal represents absorption of insolation through depth of the crowns. Broken curved line indicates stand light and sky light (see text). Points Mi, M2, and M3 are from analyses in this paper; other points are from published studies in which crown closure is reported or can be estimated.

1

0

is insolation at the top of the canopy, and e is the base of natural logarithms. For com- parison, the extinction coefficient of dry snow (Mantis, 1951) ranges from 0.07 to 0.20 cm-

^1,

ten times the coeHicients shown above for spruce

^1.

These figures apply to the visible range; for the whole solar spectrum the coefficients would be smaller, because of the greater reflection and hence penetration of infra-red radiation. The extinction coeffi- cient in pine would also be smaller than in spruce, because of pine's vertical habit

2 •

Depth of crown is clearly important to transmission of insolation; it is likely that crown depth, crown length and closure all are important.

Average intensity Extinction Height, meters of light, percent coefficient, _cm-1

26 (top) 0.90

³

0.0052

23 0.19

0.0024

22 0.15

21 0.13 0.0011

19 0.11 0.0008

15 {lowest 0.07

⁴

0.0011 branches)

12 0.07

2 0.08

Stem Density

Unfortunately, crown depth is not commonly

recorded in published studies of insola- tion transmission. A partial solution is

offered by another index to the mass of tissue in the crown

-

the stem density. This index, which is the summation of diameters of all stems in an acre of stand, has been used successfully

by

Shirley (1945) and Wellner (194,6,

1948). Kittredge (1948, p.51), from

observations of

Burns

(1927),

develops a

relation of transmission to number of trees per acre in a planted stand. Since these trees probably are uniform in size, stem density is proportional to number.

Values of stem density are presented in Table 1 for those stands in which iL was rcpor- ted, or in which enough other information is given that

I

can compute it wilh some con-

1 Although the top of the canopy is the densest level, low branches also affcct transmission. Näge1i (1952) reports that light under spruce incrcused from 1.9 pcrccnt to 2.6 percent after dcad bran- ches were cut away, to 3.9 percent aftcr light cutting of the lowest living branches, and to 4.6 percent after heavy cutting of these brancl1cs.

2 Baumgartner (1955) compares light transmission in young spruce, having a rapid decrease at top of the crown, with transmission in grass, wh.ich, after a small decrease at the top is fairly uniform nearly to the ground. Transmission in pine may resemble that in grass, and display smaller values of the extinction coefficient than those computed above, especially in the top layers. Baumgartner also notes that infra-red radiation is not cut off so much in the upper layers as visible is.

3 Insolation reduced by 0.10 for reflection from top branches of crown.

4 Estimated same at base of canopy as at 12 meters. Columns 1 and 2 from Schimitschek (1948);

column 3 computed.

Figure 2

Transmission of solar radiation relative to sterri density of the pine stand. Transmission is expressed as percentage of insolation in open site. Points M1 and M3 are from analyses reported here; other points are derived from studies in which stem density is reported or can be estimated; see text.

10 0

90

80 1-z

11.1

~ 70 11.1 0..

z„

0 60 1-<X

_J

~ ⁵⁰ z

IL .O 40

z 0 u, u, 30 ::E u,

z

<X

~ 20

10

0 0

\ ·w

\sh

TRANSMISSION

RELATIVE TO

~

STEM DENSITY

IN PINE STANDS w

Y\W

_"

~ _:;h\W ^{·w .-}

·w

1\

y - ~

l u w - G

~~ ~

w.

~

~

1000 2000 3000 4000 5000

STEM DENSITY, INCHES PER ACRE

B BRECHEEN

M1 M0NTANA 1950-51 DATA M3 CALIF. 1951 DATA G GAST

Sh SHIRLEY W WELLNER

--- ^M1

⁸

6000 7000

fidence ^1• These data, plotted in Figure 2, show a better pattern than data on closure in Figure 1. Gast's observations again plot high, probably due to side light under the high

1 Presence of an understory often goes unrecorded in field work because of small size of the stems.

Y et a dense growth of small trees intercepts a great deal of insolation, and use of the stem den- sity index gives such an understory proper weight, frorn the heat standpoint.

canopy, mentioned earlier. Deviations may also be the result of inaccuracies in compu- ting stem density, and by the fact that this index is not a complete representation of the mass and distribution of plant tissue that intercepts radiation

1•

Some authors use basal area of a stand as a parameter related to transmission of inso- lation, but this gives little weight to small trees.

In fact, trees smaller than four inches

( or other definition of merchantable size) often are ignored in stand measurements, although in sum they form an absorptive part of the forest formation, as Kittredge notes

(1948, p.49).

Moreover, as trees age, basal area continues to increase. Conversely, stem density de- creases with age, as suppressed trees die, and this corresponds with a rise in transmission, as is shown by Mitscherlich (1940) and Shirley (1945), and discussed by Kittredge (1948)

2 •

Jackson and Harper (1955), on the other hand, consider basal area a satis- factory parameter of transmission. Final decision in this question is hampered by incom- plete reporting of understory and small trees; too few of the published studies of insola- tion at the forest floor contain adequate stand descriptions.

Stern density is superior, in any case, to crown closure as a measure of radiation trans- mission, the more so as depth of crown increases. The tendency to regard forest crowns as two-dimensional planes is an over-simplification of the complex network of branches and leaves; nature is not so simple.

4. Implications of Insolation Transmission for the Climatology and Hydrology of a Forested Region

Climate of the Region

We have seen that transmission of insolation through conifer crowns is less than clo- sure would suggest; absorption of energy is therefore very large. Only a small fraction of the insolation incident on a stand, even a sparse one,

escapes

again to outer space.

This very small

albedo has important consequences for the region where stands of coni-

fers occur.

In the crest region of the Sierra Nevada of California, open stands of lodgepole pine

occupy a third of the landscape, which is covercd by a cleep snow pack until Mayor June each year. This snow-ancl-forcst rcgi on has an albedo

in winter of about 0.60, taking

together the open snowfielcls ancl the snowy forests. Albedo of a snow-covered landscape without trees is about 0.80. A similar diffcrcncc exists in spring.

1 A difference is seen between stands that are naturally understocked, in which indtvidual crowns have expanded, and Stands that have been thinned, in which ]arge open spaces remain for a few years. Thinned stands of the same stem density as understocked stands transmit more insolation, until the crowns expand into the vacant spaces (Miller, 1955, p. 90).

2 Crown length and width are found by Arnold (194,9) to be related with annuaJ increment in basal area. lt is reasonable to th.ink that in the years when the tree is growing most rapidly it has the greatest amount of foliage intercepting and absorbing insolation to make this growth possible.

The additional energy thus made available to the region plays a part in the following series of phenomena. The canopy of the pines transmits about 40 percent of the insola- tion, reflects less than 10 percent, and absorbs about half. The absorbed energy produces marked heating of the needles above air temperature, and heat is given off from them by long-wave radiation to the sky and snow, by convection to the air, and by transpiration.

The large input of heat into the local air brings about high daytime temperatures, ano- malous in the presence of ckep snow and contrary to the accepted theory of influence of snow cover on climate. Exchange between local air and the free atmosphere usually is hampered by anticyclonic subsidence, so that the local air responds weil to the heat sup- plied by the crowns. Daily maximum temperature during periods between storms in January is 39° F, in April 54° F, far above the temperature of the snow surface

1 .

The pine stands are thus important in the climatology of the region (Miller, 1955, Ch. 3; also 1956). Transmission of more insolation through the crowns would mean more loss of heat, since most of the radiation reflected by the snow would escape back through the crowns to space. Transmission of less insolation means that energy is absorbed in the foliage and produces high air temperature over forested and unforested parts of the region alike.

Climate of the Stand

With regard to climate of the stand itself, transmission of insolation determines the level of maximum heating: at crown top, within the crown, or at the ground. Geiger ( 1957, p.188) graphically shows different levels of heating in low plant cover, and Baumgartner (1956) for young spruce. In the Sierra, absorption of insolation in pine stands produces a strong temperature inversion. Maximum temperature occurs above the 50-ft level at night; during the middle of the day, when the sun penetrates the stand most directly, the level of maximum temperature descends to a level below 35 ft, then rises again as night approaches (Miller, 1950 b).

Snow M elting in a Region

Hydrologie implications of transmission and absorption of solar radiation in forest crowns are shown by rapid melting of a regional snow pack, and less clearly by different melting rates in adjacent open and forested sites.

Rates of snow melting in the Sierra Nevada have been observed to exceed two inches per day. Over two weeks in spring, 1946, ablation averaged 1.4 inches per day. Stream flow, from snow melting alone over a four-square-mile basin, reached peaks of 50 cubic feet per second and square mile ( Miller, 1950 a) . In May 1950, runoff from this basin exceeded 23 inches

(U. S. Corps Engrs., 1956, Table 4-3), and the regime of melting

1 For comparison, daily maximum temperatures at Davos during periods between storms, adjusted for the difference in elevation, average 31

°

F in January and 48

°

F in April (Sw.itzerland, 1950).

rate (Ibid., Plate

4~7)

averages an inch of water equivalent per day in May, and 1.5 inches per day in June. These rates indicate a daily heat surplus at the snow surface averaging

200-300

calories/sq cm.

On

days of high melting late in spring, the heat sur- plus approaches or surpasses

400

calories

1,

a ma jor fraction of total daily insolation.

Surpluses of this size occur only because forests are present to convert much

oI

the solar radiation into sensible and latent heat, which moves from the dark stands to snow in both open and Iorest, and into long-wave radiation, which goes to snow in the forest. With about the same insolation, the heat surplus in summer in treeless Lapland averages

145

calories/sq cm (Wallen,

1949)

andin Svalbard

70

calories (Sverdrup,

1935).

In regions of denser forest, such as the Cascade Range in Oregon, transmission is smaller and absorption still greater than in the Sierra. Downward long-wave radiation and sensible and latent heat given off by the irradiated canopy supply most of the heat the snow receives; equal amounts of heat flow upward from the canopy as transpired vapor (U. S. Corps Engrs.,

1956,

p.

210).

By efficient utilization of solar energy, this dense forest produces heavy snow melting at the same time it is using large amounts of heat in transpiration.

M elting Rates in F orest and Open Sites

Transmission of solar radiation also plays a role on a smaller scale, in the difference between melting rates

oI

snow within stands and outside them, in the same region 2 • For example, Burger's investigations in the Emmental

(1943, 1954)

show differences of

20-30

percent.

Because shading is easy to see, it has sometimes becn credited with more influence on snow melting than it deserves. We do not sense the other modes of heat transfer, notably by long-wave radiation, and while we may feel high air temperatures we cannot easily perceive the sources and sinks of the heat being transported. Yet these media of heat transfer also affect melting rates.

In eight major melting periods during the years

1927

to

194, 2,

runoff from the com- pletely forested Sperbelgraben was

30.2

mm per period and that from the one-third forested Rappengraben

37.4

mm (Burger,

1943). In

terms of heat equivalent3, runoff

1 1n·periods of strong advection of heat, melting rates larger than these values conceivably could occur, though it is doubtful that they would be much !arger. The discussion here is of heat locally generated within the locai" region.

lt may be recalled tliat strict isolation of forest influences is difficult. As was found in studies

~f the influence of forcsts on precipitation, their effect often is felt over a whole region, inclu- ding open areas. Similarly, air warmed in forest stands drifts out over adjacent openings and supplies heat to the snow in them. As discussed earlier, forests raise thc heat budget of the entire region, andin so doing obscure local differences between stand and open area.

3 Runoff values probably underestimate the rates of melting at the snow surface. Meltwater may refreeze lower in the snow, or may infiltrate into the ground and add to soil moisture content or ground water, rather than to runoff. I calculated ablation rates from reported changes in depth of snow, assuming density 0.3 through the melting period, and obta.ined higher rates than those given above. However, becausc of thc possibility of compaction of the snow pack during the period, I use only the runoff values.

represents daily values of 48 calories/sq cm in fall, 45 calories in spring in the Sperhel- graben. The Rappengraben has higher values: 64 calories/sq cm in fall, 55 in spring.

Melting rates (i

.e., runoff) in the forested basin average about 46 calories/sq cm and

day. In the Rappengraben, melting rates of wooded and open areas are combined; if we assume that the melting rate of the Sperbelgraben applies also in the forested portion - 31 percent - of the Rappengraben, we compute melting rate in the open part as 68 calo- ries/sq cm in fall, 60 in spring; the average is 64. The melting rate in the forest in then

46fo4

ths of that in the open, or 72 percent.

Calculations based on data in a later report (Burger, 1954

,) yield daily melting rates

in the forest of 31 calories, in the open 40. The melting rate in the forest is 78 percent of that in the open.

In the Sierra Nevada, during periods of clear anticyclonic weather in spring, melting

rates in forest and open are shown by the following heat analysis (Miller, 1955, p. 165) :

Snow in Open

pine stands snowfields

Insolation absorbed by snow 160 350

Net loss of heat by long-wavc radiation

from snow to sky and foliage

-

40 -155

Convection of heat from air to snow 65 75

Heat loss by evaporation -20

-

50

Total heat surplus 165 220

( calories/sq cm and day)

Melting rate in the forest is 75 percent of that in the open; interception of solar energy by the pine stands is made up in part by long-wave radiation from them to the snow b.eneath, reducing net loss from the snow by this avenue of heat flow. Calculations (Mil- ler, 1955, p.117) of melting rate from published observations, mostly in the western United States, confirm this general ratio.

Anderson's (1956) equation relating spring ablation of the Sierra snow pack to shade by trees south of a sampling point and shielding by trees north of it, indicates that in open forest with 50 percent shade and some shielding, snow melts about 75 percent as fast as in an open area. Kittredge, in his study (1953) of snow in forests lower in the Sierra than those discussed earlier, says that the influence of forest cover in retarding snow melting is «quite small»

1 .

Forest crowns reduce heat transfer by short-wave radiation much more than they do the total heat transfer to the snow by all avenues.

1 He gives melting rates of more than 0,65 inch per day in open and cutover areas, and 0.46-0.65 in various types of forest, the lower values pertaining to fir. Rates about three-quarters of those in the open occur fo stands of 20-40 percent crown cover. Kittredge (lbid., p. 79) quotes the late E. A. Colman for a relation between daily decrease in snow depth and closure. This shows, if snow density is assumed 0.5, that melting is 1.5 inches per day in the open, and decreases by 0.008 inch for each percent increase in cover. Where cover is 40 percent, melting is 1.18 inches, or 79 percent of the rate in the open. Rosa's (1956) nomograph relating melt rate fa forest and open is in general agreement with the ratios given above. This paper gives no descriptions or data, but employs both closure and stand volume as parameters.

Evaporation and Transpiration

Evaporation is another hydrologic process in which insolation transmission through forest crowns is important. The canopy determines the ratio between evaporation from the forest floor and transpiration from the foliage.

If

a large part of the insolation reaches the soil, quick depletion of moisture in the top layer will result; with early decrease in evaporation, the total loss is relatively small. If, on the other hand, much of the insolation is intercepted by the canopy, energy is available to the trees, which can draw upon water at considerable depth in the ground; water loss continues longer and the total amount is large.

Burger's (1954) water-balance data show annual evapotranspiration of 861 mm from the Sperbelgraben over the period 1927/28-1951/52, and 696 mm from the Rappen- graben. Heat equivalents are 51,000 and 4,1,000 calories/sq cm, respectively ^{1 .} To some extent, the heat requirements of the forcsted Sperbelgraben may be supplied by advec- tion. Budyko's small-scale maps of insolation and net radiation (1958, figures 16 and 20) show that yearly insolation in this area is about 110,000 calories/sq cm, and net radia- tion (solar and long-wave comhincd, both upward and downward fluxes) about 40,000.

Little heat must go to warm the air, because evapotranspiraLion requires at least as much heat as net radiation supplies. Evcn in late summer Lhe soil rcmains wet and evapotrans- piration active, according to Burger ( 1945, p.171). Heat used in evapotranspiration during a late-summer monlh is approximately 5500 calories/sq cm, as much as in almost any other mid-latitude climate, and nearly as much as in tropical climates^{2 •}

Since the forest can draw on a !arge reservoir of soil moisture and continue to use water during periods without rain, a dense canopy produces heavy evapotranspiration because it absorbs more solar radiation. From Burger's figures for the Emmental basins, one can compute heat loss by evapotranspiration from open meadows and pastures as 36,000 calories/sq cm during the year, in contrast with 51,000 from the forest. The diffe- rence represents two factors: (a) the forest, drawing upon deep storage of moisture in the soil not available to grass, keeps evapotranspiration active more of the time than the grass does; (b) the forest has a lower albedo than grass, by perhaps 0.08, according to Dirmhirn (1953), and during the snow-free season may absorb 6000-7000 calories of heat more than the grass does. This second factor, low albedo, is a consequence of the depth to which solar radiaLion penclrales the vegetation Iormation and is subject to absorption on downward and upward palhs. Transmission

oI

insolalion is thus impor- tant to evapotranspiralion, as it is to snow melting.

1 Heat consumed in melting the maximum wintcr accumulation of snow in these basins does not exceed 1000 calories/sq cm. In 'the Mclera Valley, however, water balance data (Burger, 1945) indicate a heat requirement of 38 500 calories/sq cm for evapotranspiration and 2500 for snow melting.

2 Graphs of heat-balance regime (Budyko, )958) show that, for example, in Saigon, Viet Nam, heat consumed in evapotranspiration excreds 5500 calories/sq cm in only one month of the year.

5. Problems and Suggestions

A major problem in reaching definitive relations between transmission of solar radia- tion and any parameter of a forest stand, whether it be crown closure, stem density, or basal area, is the lack of information describing the stands in which light or insolation is observed. The feeling of some investigators is that radiation at the forest floor is a

«given», an element of the environment of seedlings or herbaceous flora. lt is not thought of as the result of a physical process of interception, reflection and transmission 1•

lt should be recognized, however, that no good way to describe the intricate tangle of limbs and foliage in the canopy is available to these investigators. Optical estimates are known tobe inaccurate. Instruments, other than those measuring closure2, are those that measure light - and this means that a stand is to be described in terms of the effect it has on light.

lt

is as if we described a stand only in terms of the energy it releases if it bums, instead of using basal area, volume or other dimensions.

We need means of characterizing forest canopy from aerial photographs, perhaps using alhedo and texture. Present methods of photograph analysis can probably be used to derive number and stem size, from which stem density can be computed, but a more fundamental approach is desirable in the long run. This lack of a rational means of des- cribing forest stands in their physical (rather than botanical or commercial) aspects may be regarded as part of a larger gap in scientific knowledge. This is the lack of a quanti- tative analysis of the landscape in general. In contrast, climate has long been the subject of numerical description, perhaps too much so. However, interest is increasing in lands- cape analyses, and measures of drainage texture, slope distributions and other dirnen- sions are being developed, for both explanatory and applied purposes, by a variety of hydrologists, geographers, and geologists. Some day forests may be subjected to the same scrutiny.

Other problems arise from the fact that standard instruments for measuring insola- tion are not common or inexpensive, if continuous recording is desired. Spot observa- tions do not integrate the complicated pattern of light and shade on the forest floor on clear days. This problem is easy to recognize, but the solution is not so easy. The attempt to avoid clear days and observe only when the sky is overcast introduces considerable bias.

This bias is acceptable only when the objective is to compare stands in relative terms;

but today we need absolute values of as many parameters and processes as we can get.

1 The same feeling may be seen with respect to air temperature. There are many measurements of air temperature in the environment of the trunk space of a forest, but few in which it is related to the phenomena that bring about a given level or regime of temperature. There are still fewer that treat such a relation quantitatively. As Lowry and Chilcote (1958) advocate, biologists might make profitable use of the energy budget concept, at least as a «reference system for the study and description of climatic environments ... ».

2 Instruments with mirrors on which sampling grids are inscribed, for example, the spherical den- sitometer of Lemmon (1956), are available, but give only closure information. lf measurements of horizontal visibility through the trunk space (as explored by Drummond and Lackey, 1956) are found useful in estimating stem density, thought might be given to adaptation of meteorologi- cal equipment for recording visibility.

Careful statistical sampling may obviate having to take records over the entire day, but it would be wise to test such a scheme against continuous records in order to assess its reliabili ty.

Light meters or photocells are more easily available than are radiation instruments that cover the entire solar spectrum, but they usually do not provide continuous records

1 •

Moreover, by not covering the whole spectrum, their readings tend to he low, because leaves reflect strongly in the infra-red wave lengths. More infra-red penetrales the stand than visible light, as a pair of photographs hy Anderson, Rice and West (1958) graphi- cally demonstrates. The visible range may suffice for some botanical studies, but we should also look on the forest as an energy converter that responds to the whole spectrum

2 •

Photocells have limited value in this work

^{3 •}

The prohlems discussed - those of ohserving dimensions of · a stand, of registering transmitted radiation in its fluctuations in space and time, and of covering the whole spectrum - lead one to venture certain suggestions. Some of these are radical, hut most require nothing more than auxiliary observations during a study to acquire additional data to round out our knowledge of the stand and its radiation relations.

(a) Observations should be made within uniform stands, and locations chosen by

slatistical design, as Wilm (1943) suggests for studies of rainfall in forest, or as Evans

(1956) used in thc rainforest. In stands having large amounts of edge, the individual trees become important, and their situations should be in mind when stations are set out

4 •

(b) A range of stands should be sampled, to represent different ages, densities of

stocking, thinning treatments, and species, as well as understories.

(c) The stands should be fully and quantitatively charactcrized by field measure- ments and analyses of ground and air photographs.

Such parameters as basal area,

crown lengths and depth, stem density, and perhaps some measure of foliage weight or area, should all be determined by size classes.

Small trees and brush should particularly

be included, since a later investigator cannot reproduce this information from stand tables. The general absence of knowledge of the physical dimensions of stands is, as Evans ( 1956) states, a handicap to laboratory simulation of ecological or botanical pro- cesses. lt is also a handicap to research on hydrologic and thermodynamic processes.

( d) Radiation over the whole spectrum should be measured. That in the visible range may be separately mcasurcd if desired, and long-wave radiation may also be included.

( e) Radiation

should be

measured during the entire day, and it must be measured when the sun shin

es dircctly on the instrument as well as when it does not. The discussion

1 Fairbairn (1954,) descrföes a barrier-layer cell that integrales over a day or more, without need of a recorder. However, it covers only the visible range.

Complete investigations into microclimate of forest also cover radiation in the longwave-lengths emitted by the leaves. For example, Baumgartner's work (1952, 1956) in young spruce empha- sizes net radiation.

3 One almost comes to believe that cheapness and availability of a particular meteorological fo.

strument become disadvantages, because they lead to over-use of the instrument and its readings in problems in which they are not relevant. Air temperature, easily measured, has in my opinion been injected into problems in which it can, at best, have no more than an index value.

See Anderson (1956), and Anderson, Rice and West (1958).

of stand light, sky light, and sunflecks shows ho,-v necessary it is to include all of these components. Occasional measurements of each component separately would be of value, as would measurement of diffuse and direct solar radiation 1 .

(f) All days in a fairly long period should be included in the observational program, or else a strictly random sampling of days should be followed, for the purpose of obtain- ing a valid climatic cross-section. The inffuence of such climatic factors as cloudiness and wind has been shown; restriction of observations to either clear or overcast days, or to calm days, lowers the value of the material for cümatologic or hydrologic research, and may even bring into question ecological conclusions drawn from biased samples.

(g) Climatic factors should be measured during the observations of transmission, not only to determine separate effects of cloudiness, cloud type, and wind, but also to isolate the effect of the crowns alone. Date or sun angle should also be recorded.

6. Conclusion

Some observations of insolation transmitted through pine crowns in mountains of the western United States have been analyzed with respect to crown closure, cloudiness and sun angle. The relation was extended over a wider range by use of published studies i'n which stand parameters could be interpreted in terms of crown· closure, and shows strong interception of radiation in even sparse stands, caused by absorption in depth. lncom- plete expression of crown depth by closure results in departures from the relation, and a better relation is found when stem density is employed.

Radiation transmission and absorption are important, on both a regional and a local scale, in climatological analyses of forest as a heat source in a snow-covered region, and in hydrologic analyses of forest effects on snow melting and evapotranspiration. Illustra- tions show how the presence of forest stands affects snow melting over an entire region, and how melting rates differ in forested and open sites. Finally, some problems aud sug- gestions for field work are offered, looking toward more complete reporting of physical dimensions of forest stands, and radiation observations that cover the solar spectrum as well as the great variations within a day and within a stand. Such procedures would make available more material fo:r long-range research, as well as for the immediate ques- tions of botany, ecology, and hydrology.

Acknowledgements: Observations of radiation in the snow-research program owe much to many people, of whom F. F. Snyder and

R. W.

Gerdel may be mentioned in parti- cular. My own work was further broadened through contact with Joseph Kittredge arid John Leighly of the University of California at Berkeley.

1 Possible difference in spectral composition of stand light, sky light, and the direct beam lends biological interest to such a resolution of the radiation at the forest floor.

Einfluß der Strahlungsdurchlässigkeit des Kronenraumes von Föhrenwald auf die Schneeschmelze

(Zusammenfassung)

Der Einfluß von Kronenschluß, Bewölkung und Sonnenstand auf die Strahlungs- durchlässigkeit von Föhrenkronen wird analysiert. Diese Untersuchungen ergeben, daß die Strahlung auch in lichten Beständen stark auf gefangen wird infolge der tiefen Staf- felung des Kronenraumes. Wird die Kronentiefe durch Angabe des Kronenschlusses nur unvollständig charakterisiert, so ergibt die Verwendung der «Stammdichte» eine bessere Beziehung zur Strahlungsdurchlässigkeit (Stammdichte ist definiert als die Summe der Stammdurchmesser pro acre).

Strahlungsdurchlässigkeit und -absorption sind wichtig für klimatologische Analysen (Wald wirkt in schneebedeckten Gebieten als Wärmequelle), sowie für die hydrologische Analysierung des Einflusses von Wald auf Schneeschmelze und Evapotranspiration. Bei- spiele illustrieren die starken Unterschiede der Schneeschmelze in Wald und Freiland, sowie die Wirkung des Waldes auf die Schneeschmelze ganzer Gebiete.

Schlußendlich werden Anregungen für weitere Untersuchungen gegeben, wobei eine eingehendere Erfassung der physikalischen Eigenschaften von Waldbeständen gewünscht wird. Ebenso sollten Strahlungsmessungen nicht nur das ganze Spektrum erfassen, son- dern auch die großen Schwankungen während des Tages und innerhalb des Bestandes.

De I'influence exercee par le couvert de forets de pin sur la fonte de la neige suivant sa permeabilite au rayonnement

(Resume)

L'auteur etudie l'influence du couvert, de la nebulosite et de la heuteur du soleil sur le rayonnement que laissent passer les cimes des pins. On peut deduire de ces recherches que les rayons du soleil sont aussi fortement absorbes dans des peuplements clairieres a

cause de l'echelonnement des couronnes dans le sens de la hauteur. Si on ade la peine a

caracteriser l' epaisseur des couronnes en indiquant seulement le degre de densite du cou- vert, on peut avoir recours au concept de la «densite des arbres» qui est mieux en rapport avec la permeabilite au rayonnement ( on cntend par «densite des arbres» la somme des diametres par rapport a l'unite de surface).

La permeabilite aux rayons du soleil et leur absorption par les cimes des arbres sont

des facteurs importants dans les analyses climatologiques comme aussi dans la determina-

tion de l'influence de la foret sur la fonte des neiges et «l' evapotranspiration». ( La foret

agit en effet comme une source de chaleur dans les regions recouvertes de neige.) Des

exemples illustrent la dif ference marquee entre la fonte de la neige en foret et en terrain

decouvert, comme aussi l'influence de la foret sur la fonte des neiges de regions entieres.

Enfin, l' auteur propose d' entreprendre de nouveaux travaux de reeherehes dans ce domaine en portant l' aeeent sur la neeessite d' etudier plus a fond les eonditions physiques des peuplements forestiers

.

Les mesures eoneernant le rayonnement doivent non seule- ment englober le speetre eomplet, mais eneore les grandes variations qui interviennent pendant la journee a l'interieur d'un peuplement.

Influsso della permeabilita alle irradiazioni, dello spazio occupato dalle corone di una pineta sullo scioglimento della neve

( Riassunto)

Aleune osservazioni sulla permeabilita alle irradiazioni delle eorone del pino vengono analizzate nei riguardi del eombaeiamento delle eorone, dei momenti di annuvolamento e di sole e poste su piu ampia base eon riferimenti ad altri lavori, sempre ehe gli stessi eonsentano di mettere in relazione talune proprieta del boseo eon il eombaeiamento delle eorone. Queste indagini dimostrano ehe le irradiazioni vengono fortemente assorbite anehe nei bosehi radi, a eazisa dello sviluppo in profondita delle eorone. Sela profondita delle eorone viene insuf fieientemente espressa dal eombaeiamento delle eorone, allora l'impiego del eoneetto di «jittezza dei tronehi» e piu pertinente per esprimere la per- meabilita alle irradiazioni ( «Fittezza dei tronehi» e definita eome la somma dei diametri dei tronehi per acro)

.

La permeabilita e l' assorbimento dei raggi sono importanti per le analisi climatolo- giehe (il boseo nelle regioni rieoperte di neve ha l'effetto di una sorgente ealoriea), non- ehe per l' analisi idrologiea dell'influsso del boseo sullo scioglimento della neve e sull' eva- potraspirazione. Gon diversi esempi si illustrano le forti dif f erenze in f atto di seiogli- mento della neve tra boseo e aperta eampagna, nonehe l'influenza del boseo sullo seiogli- mento della neve di intere regioni.

I nfine si da ineitamento per ulteriori indagini, sottolineando quanto sia desiderabile

eonoseere esaurientemente le proprietil fisiehe dei bosehi. Le misurazioni delle irradia-

zioni dovrebbero estendersi non solo all'intero spettro, ma anehe alle grandi variazioni

durante il giorno e nell'interno del boseo.

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