Influence of Photosynthetic Crown Structure on Potential Productivity of Vegetation, BasedPrimarily on Mathematical ModelsAuthor(s): Leland S. Jahnke and Donald B. LawrenceReviewed work(s):Source: Ecology, Vol. 46, No. 3 (May, 1965), pp. 319-326Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/1936335 .Accessed: 03/02/2012 09:29

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Spring 1965 PHOTOSYNTHETIC CROWN AND PRODUCTIVITY 319

mounds provide a drier habitat for goplhers in the spring. The sorting action of gophers in bringing fine and small gravels to the surface could explain the presence of mounds on Rocky Flats. The sorting, causing a decrease in bulk-density and consequent increase in volume, would explain the increase in relief of the mounds of 6 to 8 inches. Gopher activity can also accouint for the presence of pebbles in the surface of mounds and the lack of cobblestones and boulders in mloudlls.

LITERATURE CITED

Branson, F. A., R. F. Miller, and I. S. McQueen. 1962. Effects of contour furrowing, grazing intensities and soils on infiltration rates, soil moisture and vegeta- tion near Fort Peck, Mont. J. Range Manage. 15: 151-158.

Hack, John T. 1960. Interpretation of erosional topog- raphy in humid temperate regions. Amer. J. Sci. 258-A: 80-97.

Harrington, H. D. 1954. Maniual of the planits of Colorado. Denver Sage Books, Denver, Colo. 666 p.

Hillel, Daniel, and Naphtah Tadmor. 1962. Water regime anid vegetation in central Nagev Highlands of Israel. Ecology 43: 33-41.

Levy, E. B., and E. A. Madden. 1933. The poiint method of pasture analyses. New Zealand J. Agr. 46: 267-279.

Livingston, R. B. 1952. Relict true prairie commllunii- ties in cenitral Colorado. Ecology 33: 72-86.

McQueen, I. S. 1963. Development of a hand portable rainfall-simulator iiifiltrometer. U. S. Geol. Surv. Circ. 482. 16 p.

Malde, H. E. 1955. Surficial geology of the Louisville Quadrangle, Colo. U. S. Geol. Surv. Bull. 996-E, p. 217-257.

. 1964. Patterned ground in westerni Snake River Plain, Idaho, and its possible cold-climate origin. Geol. Soc. Amer. Bull. 75.

Scott, G. R. 1960. Subdivision of the Quaternary alluvium east of the Front Range near Denver, Colo. Geol. Soc. Amer. Bull. 71: 1541-1544.

. 1963. Quaterinary geology and geomorphic his- tory of the Kassler Quadranigle, Colo. U. S. Geol. Surv. Prof. Paper 421-A. 70 p.

Slatyer, R. 0. 1957. The influenice of progressive increases in total soil moisture stress on transpira- tion, growth, and internal water relationships of plaints. Aust. J. Biol. Sci. 10: 320-336.

U. S. Department of Agriculture. 1951. Soil survey mainual. U. S. Dept. Agr. Handbook 18. 503 p.

Van Horn, Richard. 1957. Bedrock geology of the Golden Quadrangle, Colo. U. S. Geol. Surv. Geol. Quad. Map CQ-103.

Ward, F. N., H. W. Lakin, F. C. Canney, and others. 1963. Anialytical methods used in geochemical ex- ploration by the U. S. Geological Survey. U. S. Geol. Surv. Bull. 1152, p. 89-92.

Washburn, A. L. 1956. Classificationi of patternied ground anid review of suggested originis. Bull. Geol. Soc. Amer. 67: 823-866.

Weaver, J. E., and F. E. Clements. 1938. Plant ecology. McGraw-Hill Book Co., Inc., New York. 601 p.

Weaver, J. E., and T. J. Fitzpatrick. 1934. The prairie. Ecol. Monogr. 4: 112-259.

Yarnell, D. L. 1935. Rainfall intensity-frequency data. U.S. Dept. Agr. Misc. Publ. 204. 68 p.

INFLUENCE OF PHOTOSYNTHETIC CROWN STRUCTURE ON POTENTIAI, PRODUCTIVITY OF VEGETATION, BASED PRIMARILY ON

MATHEMATICAL MODELS

LELAND S. JAHNKE AND DONALD B. LAWRENCE I)cpartmcot of Botany, University of Minnesota, Minneapolis, Mimiii.

Abstract. Productivity studies have shown that plants with marked vertical extension of photosynthetic crow n can be more productive per unit area of land or water occupied than plants whose photosynthetic surface is spread in a thin horizontal sheet on the earth's surface if environmental factors are not otherwise limiting. Geometric models including a flat disc and cones of several heights but constant base radius show that heightening cones intercept progressively more light. Amount of chlorophyll displayed per unit area of earth's surface can also increase greatly with vertical extension of aerial crown. These observations suggest that thickness, geometric configuration, and chlorophyll content of the photosynthetic portion of the vegetation per unit area of earth's surface, and light intensity incident on surfaces at right angles to suIn's rays should be measured and described as basic data in primary productivity studies.

I NTRODUCTION

The few reports we have founid that include data suitable for comlparisoin have showni that ver- tical extenision of photosynthetic crowns of plants brings al)out increased yield. For example, Ken- nard and Morris (1956), by careful studies with trol)ical yams (Dioscorca floribuinda) growni for

drugs in Puerto Rico, slhowed that tubers were much larger anid dry weight yield of tubers per unit land area was over three times as great if the plants were grown on vertical chicken-wire trel- lises 6 ft tall as if the vines were allowed to spread out horizontally in a single straight line along the row on the ground suirface. They did not coml-

320 LEI-AND S. JAHNKE AND DONALD B. LAWRENCE Ecology, Vol. 46, No. 3

pare amlounits of foliage, but a photograph showed nmuclh larger crowns onl the tall vines. Another study in Puerto Rico (Anonymous 1938: 51) slhowed yield by an edible variety of tropical yam of 12.5 g of tuber per gram of air-dry tops per hill, and a doubling of tuber weight with eaclh doubling of air-dry top weight up to the sixfold level.

Bray (1960) compared several kinds of native and miialnaged vegetation in central MIinnesota and found that with increasiing heiglht of the plants there was a generally increasing trend in chloro-

phyll contenit and in annultal accumulation of dry weight of tops.

Four main interrelations would seeml to govern the prodluctive potential of vegetation of level sur- faces wheni water, gas exclhanige, and nutrients are adequate, anid destructive agents are excluded. First is the ratio of the rate of photosynthesis to that of respiration for the whole plant body. Sec- onid is the amouint of chlorophyll exposed to in- cominiig ra(liationi, and the portion of the year (luring wlhiclh it is exposed. Third is the geo- mletric form of the crown, its reflectivity, and its traiusmlissivity, which are influenced by leaf shape, surface texture, orientationi, and thickness of the

plhotosynthetic part of the plant in relation to anigles of incidenit light. Fourth is the density of

spacing of the planits onl the portion of the earth's surface unider considerationi, which affects the ex-

pression of geomletric form and the amount of chlorophyll that can be displayed. In this paper we are mainly concernied with the second and third of these relationsliips, i.e. potential productivity as a funictioni of geonmetric form anid chloroplhyll exposure for the simple case of plants so widely space(l that the slhade they cast onl one another can he neglected.

( )f course in bothi natural anid artificial comimiilu- nities plants do slhade one another. In develop- ilng communluiiities, the taller they becomle, the more wi(lely spaced they must be to avoid such shading. Under naltutral condlitionis differential growth rates andl coml)etition bring about automatic thinninig. In agricultuiral crops and forest plantations favor- able sl)acing for later stages is attained artificially at planting tinme and through artificial thinniinig later onI. In nattural savanna situations widely spacedl tall plants cast their shadows either onl in- terveninig bare ground or on otlher kinds of plants of miuitch shorter stature whiclh, as we shall see, expose nmuch less chlorophyll per unit area of land and in less effective geonmetric fornms for light re- ception tlhan do plants witlh tall conical crowns. The present discussion purposely avoids considera- tionl of conmplexities that arise from close spacing and niuitutal shading.

The influenice of organizationi and movemenits of the plhotosynithetic parts of planit bodies onl po- tential productivity was considered long ago by Alnton Kerner (1894), and his ideas on the sub- ject are still of great interest. It is wortlhwlhile now to thinik those ideas througlh againi and to develop them further with the aid of models, and especially to extend our knowledge by nmaking measuremelnts with newly developed light meters and with infrared gas analysis apparatus for esti- mating rates of photosyntlhesis and respiration.

DEVELOPMENT OF A MATHEMATICAL MODEL FOR

ESTIMATING SOLAR ENERGY ABSORPTION

WVe are concerned first of all with developing a nmatlhematical model which will give predictions of eniergy absorption of certain shapes of planits as a funiction of time of year, time of day, anid heiglht of plant crown.

If all plant bodies were spread out flat oni a level surface as are the pads of pond and water lilies, and if the sun1 always shone down from directly above, the anmount of energy cominlg in would be very easily measured or calculated. But this situation holds true in nature onily instan- taneously even for a water lily growinig at the equator with its floating leaf blades exposed to equinioxial midday sun. The total energy absorbed could be predicted under such circulmistances by multiplying the true horizontal surface area by the light inteinsity falling on a unit area of upper sur- face per uniit time, by the duration of exposure, anid by one minus the proportion of energy reflected and transmitted. But the shapes of the photosyn- thetic surfaces of most vascular plants have an important tlhird dimension, being rouglhly spheres, cylinders, cones, or ellipsoids, or various truni- cated portions of these. Also, the angles at wlhiclh the sun1's rays fall upon a level surface differ with the latitude onl the eartlh's surface, time of year, and time of day (Fig. 1). It is readily uniderstood that the amount of direct sunlight falling upon a flat horizontal circle is nearly zero at sunrise and sunset and is maximum at midday. For an iso- lated tree with extended vertical axis the absorp- tive area for direct sunlight is maximum a little after sunlrise and before sunset, and minimumn at midday. The major objective of the present paper is to consider how the effective area exposed to direct illuminiationi for a simple three-dimenisional figure, a cone, changes as the height increases but the radius of the base remains the same, while the angle of incidenice of the radiation chaniges, and how these values differ from those for a simple circle of the same radius (Fig. 2). A symmlnetrical isolated Sierra redwood (Sequtojadendron gigan- teiimi (L.indl.) Buchholz) with its lowest branclies

Spring 1965 PIlOTOSY.NTHETlC CROWN AND PRODUCTIVITY 321

DIAGRAM OF SOLAR ALTITUDE AND AZIMUTH

FOR LAT. 45- N 35( NORTH o 3 0 20

33 I 0 30

320 n. 40

310 S4D 10

so~~~~~~1 - Jon 70

290 7

280 ?3z80

WEST o EAST

260 o0 ~ 00

240 120

220 2SE

Sun above 0 14'Applo. s. 190 SO2 I +23 27' Jur.* 2219 SO T 17

f201 t.y 21. J.1y024 015 7. 4Wy1 . 9,1 2 +*0 Ap, 16. A.9. 28

C 5 Ape of St 3 0 0 a 0 V., 21i Sp 2 3

Tm o o a c; 6 p.m 3 p.m.. List, Ro 9 a m -10_ Fb8 23 0c 20 So.l9.ho,,- AEf.-m.'ViCol T.blos, s .th *.18*d ed1tio".

F 1., (Upebr9. 3 Sof,. solaalitud Wohi,o, O.0C. -20 Ia..' 2lN-. 22 robl.. 869 8 170

-23'27 0.c 2.

Altitude of Sun above 0p 14 45o 65t 45s 14 0a

horizon

Cone of a lt itu de

8r

Cone of altitude

4r 4 4.07 4.03 3. 4.03 4.07 4

Cone of altitude 2 2.3 .7 2 2. .3

2 r

Circle 0.0 (j.1 .8 0.0

Time of day Sunset 6 p.m. 3 p.m. Noon 9 am. 6 am. Sunrise

FIG. 1. (Upper) Diagram of solar altitude and azimuth for latitude 450 N showing, from right to left, especially the path of the sun on May 21 and July 24 and its posi- tions at sunrise, 6 AM, 9 Am, noon, 3 Pm, 6 Pm, anid sunset.

FIG. 2. (Lower) Projected shapes, traced from actual cone shadows, and areas of exposure to direct sunlight for a horizontal circle and for erect cones of altitude 2r, 4r, and 8r at latitude 450 N on May 21 and July 24 for seveni times during the day. Projection ar-ea values inside figures are in square meters hasedi on r 1m using equation (2) except when altitude of sun is zero, in which case it is calculated by treating the cone as a triangle of height h and base 2r. The passage of time is presented from right to left in order- to facilitate rapid comiparisonis with Fig. 1 ahove.

lying oni the ground is a typical examiple of a tree withi coniical crown. One of our obj'ectives is to

l)resent the resuilts of a method (Fig. 3) for de- rivinig an equation for calcuilatinig amiouints of ra- diant energy absorbed by coniical-shiaped ob'jects.

Let uis n1ow look at the genieral assumilptionis mlade in the derivation.

Deri-vation This nmeth1od is illustrated in Fig. 3. The total

anmouint of radiant energy a p)lant receives can ibe treatedl in two (listinct plhases, the direct or solar radliationi, and the diffuise or sky radliationi. Elqua- tioIn (1) is the mlost general forml of thie radliant eniergy absorption e(quiation and(l show s hiow these two plhases of radianit energy are absorbed. The (lirect racliation is incidenit oIn oinly the effectiv,e suirface area A,0 whiclh is defined in e(qtiationI (2) for a cone. Factors wliclh are empirically (lerivedl are I, andl P.

The (liffuise ra(liatioin is inici(letit oni the entire

sturface area L wlhichl is the lateral surface area. ternmed the "cuirved suirface" in textbooks of solid geomletry. The eml)irical factor Ird rel)resents thie

(liffuse etnergy iincident per tunit area, per uinit timee. and R is the fraction of Ird absorbed.

Let uIs Inow retuirn to a (letailed analysis of A,, the effective suirface area. In (lealing with the amiiount of (lirect stuinliglht ahsorbed. it is uisefuil to realize that the slhadlow cast oIn level grotutn(d is merely a lhorizontal projection of the light-absorb- itig figture, i.e., the object itself. Tlhuis the area of the slhadlow is sotmie ftutnctiotn of the energy-ahsorb- inig area. It is niot a liniear funiction, since wlheni the stun is at the hlorizoni, the slhadlow cast is esseni- tially "infinitely" lonig, hut the object casting thie slhadow lhas a finiite area. Since the most coinveni- ienit miieasuiremenits of radiationi intenisity are mladle nornmal to the soturce of the radiationi, we will want the projected sturface area (A,) to be normlal to the stiu's rays. Simple trigoinometric considlera- tions show that the projected effective area (A,,) is a sin 61 ftunctioni of the horizointal area of the shadow. As showin in Fig. 3a, only three in(le-

leindent variables are involved: two geomletric variables, deternmining the size of the cone, altitudle h, and basal radlitus r, ', the angle of iniclinationi of the stun, is the other variable. As d(iagrammiiiied in Fig. 31), the area covered by the slhadow is calctulated in two components, one trianguilar, the other circular iminius a segmenit. The shadow area is the sLium of the two comlponents. Equation (2) slhows A, as a sin o ftunctioin of the area of the slhadow which is nmade uip of triangular area T

1 Where . is the angle of inclination of the sunI abov e

the horivon. Calculations in the past by physicists have considered the angle between the -enith and the sun's positioin as the "angle of incidence" of the son's rays. In the present study, the angle of the sun's rays above the horizon seems more appropriate.

322 LELAND S. JAHNKE AND DONALD B. LAWRENCE Ecology, Vol. 46, No. 3

:h Si~~~ = hadow a

r~~~~~~~~

3a 3 b~~~~~~~~

3b~~

'3'~~~~~~~~~~~1

3 c

GEOMETRY OF THE SHADOW FIG. 3. Derivation of equations for the direct and diffuse sunlight absorption of a cone. Equations and sym-

bols are on opposite page.

Spring 1965 PHOTOSYNTHETIC CROWN AND PRODUCTIVITY 323

plus the circular area -tr2 minus the segment S. In Fig. 3c, we see that the area of the shadow triangle T a1b. But since a1 -b tan y, and b = r sin , T r2 sin2 c tan c as indicated in

h r e(luation (3). Since a - S and cos y -' cos

- tan ~, hence g arc cos [htan as ah

shown in equation (4). The area of the segment S is calculated by the standard geometric formula:

wvr 2 2 r2 sin 2 y S- 3 60 2 shown in simplified form

as equation (5). L is simply the lateral area of the cone defined

by equation (6). L and A, substituted into equa- tion (1) yield equation (7) which is the specific equation for predicting energy absorption of a perfectly conical plant2 of basal radius r and height h with the sun at angle o above the horizon.

2 Transmission values of light through the side of coni- cal crowns to the interior are not considered here because much of that light should be absorbed by the inner foliage of the opposite side of the crown interior. The light transmitted completely through the crown is of course lost to the plant.

E = In PAO + I,d RL (I)

Aos (T + 1r2-S) sin e (2)

T . a, b

a,. b tan 0

b - r sin t

T b2 tan ' - r2 sin2 0 tan ? (3)

h tan E3

cos , r, r tan E3 a h

= arc cos hr tan e] (4)

S T1 r2 (p r2 sin 2 (5) 180 2

L = Trt (6)

-V'r~ + h2

E =In P (T +Tfr2 -S) sin e + I,d RT r (7)

KEY TO SYMBOLS: E = energy absorbed per unit time at solar altitude (E)

above the horizontal In - solar energy received per unit area at normal (901)

incidence to sun's rays per unit time P - fraction of direct sunlight absorbed Aos area exposed to direct sunlight projected normal to

sun's rays lxd diffuse (sky) energy received per unit area per unit time R = fraction of diffuse energy absorbed L = total lateral area of absorbing figure T = area of shadow triangle S = area of segment of circle e solor altitude above horizon (in degrees) h height of cone r= radius of base a = length of cone side (slant line)

9

,r Cones 8 Y h'8 r-l

1Vh 4 r.l

RIIh3 rh I

7 II h'2 r'l

I Circle, r I

6

;5 E

III

3

2 - -

I -, . . . :

0? 10? 20? 30? 40 50? 60? 70? 80- 90'

FIG. 4. Effective surface area, AO, in square meters, as a function of solar altitude -S, for cones of height 2, 3, 4, and 8 m, all with basal radius 1 m, and for a hori- zontal circle with radius of 1 m, calculated by equation (2).

Fig. 4 (curves II, III, IV, and V) is a graphical representation of only the effective surface area part of equation (7). Here we see A, in square meters as a function of .@, for four different cones with altitudes of 2, 3, 4, and 8 m shown by curves II to V, respectively, all with base radii of r 1 m. Curve I is the effective surface area (AO) of a horizontal circle of r - 1 m, as a function of -9. The vertical dotted line at 68' 2 is the maximum altitude the sun can rise in the sky at the latitude of Minneapolis (450) which occurs at noon at the summer solstice.

The equation for AO becomes inaccurate at values of 4 less than 0.5? if only four-place trigo- nometric tables are used. The equation cannot be meaningfully applied at = 0, since the area of the shadow approaches so and the sin of 9 be- comes zero.

Some of the interesting results of equation (2) are shown by comparing the solar altitudes at which the maximum effective areas are exposed to direct radiation. For a cone of h - 2, r - 1 this occurs at 45? N latitude at solar altitude 68' 20.

For h - 4, r = 1 it is at 240, and for h - 8, r - 1 the maximum occurs at 9 - 120. This means for conical plants with a height-to-base ratio of 8, much more direct radiation might be absorbed very early and late in the day, with relatively small amounts absorbed during the middle of the day, but with opposite results for very short conical or horizontal plant discs with the same radius. When the sun is close to the horizon the light scattering is increased so that the sky (diffuse) light inten-

324 LELAND S. JAHNKE AND DONALD B. LAWRENCE Ecology, Vol. 46, No. 3

sity would be proportionately increased and direc- tional differences would be greater.

At a height-to-basal-radius ratio of 3 (curve III), a cone has almost a constant area exposed at all times (Fig. 4). Thus there is similarity to a spherical plant which wouild always have coIn- stant area exposed to incidenit liglht of anly angle.

It slhould be kept in mind that the taller the plant becomes, and the more oblique the direct illumination from the sun, the longer is the shadow and the more area of lauid the shadow covers, so that the efficiency per unit area of land slhaded cannot l)e greatly increased. The greatest inicrease in efficiency of utilization of available light by tall trees should occuir wheni the sky is overcast so that the light source is spread over the wlhole dome of the sky. In this situationi which does occuir duirinig a large proportioin of the tillme in humiiid regionis such as the Pacific slopes of northwestern United States and Canadla, where trees are kinowni to grow very rapidly, only a sinigle much simpler equation would be needed since then it is only the diffuse energy (Ixd) and the fractioni (R) of that absorbed, and the total lateral area (L) of the absorbing figure which are involved.

An equation of the type that has been presented here may also be of use to ecologists concerned with problems of shadinig on level terraini, since the equation was derived in terms of the area of the shadow.

INFLUENCE OF CROWN STRUCTURE ON AMOUNT

OF CHLOROPHYLL THAT CAN BE DISPLAYED

In addition to geometric form of absorbing sur- face, reflectivity, transmissivity, and angle of inci- dent rays, we are concerned here with the range in mass of chloroplhyll that can be displayed over a unit area of land, or over, on, and under a unit area of water surface in relation to the geometric form of the plhotosynthetic apparatus. If all plant bodies were spread tlhin and flat on a level surface, the mass of green tissue that wotuld be exposed to light in shallow cylindrical shapes cotuld be ap- proximated by calctulating the volume of a cylin- der, xr2h, where h is the measured tlhickness of the chlorenchyma layer. If this thickniess, h, were .0001 m, the meastured thickiness of the palisade layer of a water lily (Nyinphaea) floatiing leaf blade, and the radius of the cyliider, r, were 1 m, then the volume of such a photosyntlhetic layer would be 3.14 X 10-4 1113, or 314.0 cc, and its mass 314 g3 (the specific gravity of the chloroplhyll tis-

'But the actual chlorophyll content per square meter of yellow pond lily floating leaf blade, shown in Table II, is only .44 g because according to data assembled by Rabinowitch (1945) the chlorophyll is contained solely within minute grana which occupy only about a sixth of the volume of the chloroplast (with chlorophyll conlsti-

sue being assumled for the sake of simplicity to be 1.0). When cone-slhaped figuires are considered, one way in which the minimumitn volume of tlhe chlorophyll apparatus miiiglht be estimated could he to consider it as a slheet of water lily leaf blade plastered over the whole curved suirface of a cone. This wotuld theni be tl-he volumle of a lhollow cone .0001 mI tlick.

But the plhotosyntlhetic apparatus of conie-slhaped evergreeni tree crowns is niot spread as a thliin layer over a smooth conical surface. Actuially it is dis- tributed tlhrouiglh mutclh greater depth, amouinting to an uiniknown fraction of the volumile of a solid cone. For preliminary considerations, in order to get somle understanding of param0ters withlini which muist lie the actual situationis of nature, raniginig froml horizontal water lily pad to conical tree crown, one might compare the relative volumnies of a cylinder of radius 1 m and .0001 nm higlh, a lhollow cone of the same wall thickness, and a solid cone, all of the same base radius (1 ni), the cones having an altitude of 2 r. The ratios would be rouglhly 1 to 2 to 6,700. These ratio values ap- proximately double with doubling of cone altituide wlhile radius of base is held constant.

The featuire to be especially observed is the much greater space theoretically available for con- taining chlorophyll as tlhe heiglht of the plant in- creases. Sonme actual weiglhts of clholorophyll -dis- played per square meter of earth's surface in nature are presented in Table I for comparison. There

TABLE I. Chlorophyll (a plus b) contenit of various p)ho- tosynthetic layers

Mean maximum thickness of Chlorophyll

Layer layer2 (m) (g/m2)

Nuphar variegatuml floating leaf blade ....... .0005 .44 Nymphaea odorata community1 .............. _ .35 Populus tremuloides individual layers3

Sun leaf May 31 ....................... .00018 .36 Aug. 3 ....................... .49

Shade leaf May 31 ..................... .00014 .26 Aug. 3 ...................... .38

Sun bark May 31 ..................... .00020 .50 Aug. 3 ...................... .31

Shade bark May 31 ............... .00033 .48 Aug. 3 .29

Soya max community4 ..................... .5 .91 Carex lasiocarpa community4 .............. . - 1.30 Zea mays community4 . . 1.9 2.66 Typha latifolia-angustifolia ..................

community4 ........................... 2.4 4.65 Populus tremuloides community4 ............ 18.1 5.95

1Data from Jon E. Sanger (personal communicatioii, Aug. 1963). 2For communities, this is the vertical distance from the highest photosyiitlietic

part to the ground. 3Data from Pearson and Lawrence (1958). 4Data from Bray (1960).

tuting only about 5% of the dry weight of the chloro- plast). The chloroplasts occupy only about half the volume of the chlorenchyma cell, and the cell walls also take up part of the space of the photosynthetic apparatus.

Spring 1965 PIIOTOSYNTHETIC CROWN AND PRODUCTIVITY 325

is 13.5 timiies more chlorophyll (lisplayed in the tall asI)en (Popululs) coimmunitiiity tlhani would be oIn the samiie area of water covered witlh a continutotus sheet of the floatiing leaf blade of yellow ponld lily (Nuiphar ) .

Thtus, the muclh greater chloroplhyll contenit of tail p)lants and comm iluIlities, wlhenl combined witlh the larger einergy absorptive capacity of p)lants witlh itncreasing lheight, as pointed otut earlier, slhotuld make p)ossible mutclh greater oplportunity to acctu- imutilate orgainic imiatter unider optimullll conditionis of water balance, gas exclhainge, ntutrienit stupply, anld toxic waste removal for tall greein plants thain

for those that are sl)read in a thlini filmll uipoIn the eartlh's surface. Possibly with furtlher sttudy we may discover imianiy times greater yield l)otenltial in tall trees than in flat plhotosynitlhetic sturfaces of the samiie projected lhorizonital area. These coIn- si(lerationis may well lhell) to explaini wlhy Ovingtoin and Heitkamp) (1960) fotunid as muctlh as 7%4 of the available radiatiotn received (on a flat horizonl- tal surface) stored in some evergreeni coniferotus tree planltationis in England, whiereas valuies of arounid 1% lhave been reported mtuclh more uisuially (\Vassiik 1959). The eniormous amotunits of chlorophyll that mutst be displayed in the tall coIni- cal crownis of ftully stocked stands of coast redlwood (Seqtuoia semlper-Zvircns (D. Don1) Endl.) in nlorthwesterni Californiia may well be accuimutlatinlg, anniiually, tuinexpectedly higlh percenitages of the available solar energy, especially since in that regiol p)ersistent fog anld overcast sky provide dif- ftuse light over the whole crown sturface anid the crowins do nlot cast deep shadows uipoIn oine ain- otlher.

Scieintists inlvolved in primary p)roduction sttudies miiay be initerested in testinig the e(quiatioins aind coIn-

cepts p)resented here by workinig out theoretical einergy absorptions and comparing tlhem with total ainnlual yields, and amotunts of chloroplhyll dis- played per unit area of level land, for example, of conifer stands of various ages anid heiglhts but all so fully stocked as to provide complete caniopy cover. This would tell tus whether we are getting a better tlheoretical understanding of the mechaniics of photosynithetic efficieincy of vegetatiotn.

Unfortuinately these studies are hanmpered by lack of adle(qtuate measuremenlts of direct sunliglht at normal (900) angle. Most of the meager avail- able data onI solar radiation are derived from Itpply pyrlheliometers exposed so as to receive radiant eniergy, both direct and diffuse, on a hori- zontal5 sturface. Sinice a telescope drive mecha-

4Estimated for ctirrcnit annual accumulation of energy in a 21-year-old plantation.

'Exposure in that positioin is reasonably satisfactory for measuring available light when it is all diffuse, as in humid regions of persistent fog and overcast.

nism for followinig the stuni is required for mleasur- ing normal incidenice light, biologists may perhaps be exctused for not havinig collected such data. But the recenit developmiient by Birkebak alnd Birkebak (1964) of an iniexpenisive solar radiationi integra- tor, as accurate as the standard Eppley but requir- inig lno external power, imiay soon be combined witlh a telescope drive to provide biologists at reasonable cost the equtipmiient that is really needed. Uintil stuclh devices become available and the nieeded data canl be accumutilated, there is muticlh to be done in finidinig out lhow the photosyntlhetic apparattus of various kinids of planits is distribtuted withlini the solid figures wlhiclh describe their crown formis. The nieedles are yotulngest at the cone surface and older inward in evergreeni coniferous tree crownis, anid their chloroplhyll conitenit decreases iinward witlh age; also they receive less intense light witlhin the crownis, so light intenisities miiust be mleasured witlhin as well as at the outer surfaces of the crowns. Areas of lumbering activity in a series of uniifornm-aged pure stands of evergreen conifers stuchl as coast redwood wotuld be ideal for acctumu- lating data oni dimiiensionis anid slhapes of crowns and amlotunts and distribution of needles of differ- eint ages anid clhlorophyll conitent within the crowns.

CONCLUSIONS

These observations suggest that thickniess and geometric conifigurationi of the photosynithetic por- tion of the vegetation, anid chloroplhyll content per tuniit area of eartlh's sturface shotuld be described, anid total liglht initenisity inicluding that incident on sturfaces at right anigles to the suin's rays should be mieasured at top anid bottom of the canopy and recorded as basic data in prinmary prodtuctivity sttudies.

ACKNOWLEDGMENTS

The writers express thanks for critical review of an earlier version to two anonymous reviewers, to T. Koz- lowsky, E. V. Bakuzis, A. Frenkel, J. R. Bray, E. Gor- ham, I. F. Hand, D. A. Fraser, J. Ian Richards, and Elizabeth G. Lawrence, but we accept full responsibility for any errors and misconceptions that may remain.

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