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Solar radiation variability on the floor of a pine plantation
Agricultural Meteorology - Elsevier Publishing Company, Amsterdam- Printed in The Netherlands
SOLAR RADIATION
V A R I A B I L I T Y O N T H E F L O O R OF A P I N E
PLANTATION L. W. GAY, K. R. KNOERR AND M. O. BRAATEN School of Forestry, Oregon State University, Corvallis, Ore. (U.S.A.) School of Forestry, Duke University, Durham, N.C. (U,S.A.) Department of Industrial Engineering, University of Missouri, Columbia, Mo. (U.S.A.) (Received April 2, 1970)
ABSTRACT GAY, L. W., KNOERR,K. R. and BRAATEN,M. O., 1971. Solar radiation variability on the floor of a pine plantation. Agr. Meteorol., 8: 39-50. Measurements of global radiation were made above and below the canopy of a pine plantation during eight consecutive cloudless days. Several analyses were to be made of the variation in time and space in global radiation reaching the forest floor. One analysis represented the measurements as deviations from the mean global radiation at the floor. This approach revealed that periodic samples would be required from at least three pyranometers in this stand to satisfactorily estimate means over short periods of up to a few hours. A statistical analysis of daily radiation totals showed that significant differences were still present among individual sampling points. However, no significant differences were found among measurements of daily totals on four sample plots, each containing five sample points. The analyses suggest some guidelines for sampling global radiation beneath a forest canopy. The measurements also demonstrated the scattering effects of the canopy. The diffuse component increased from 15~ of the global radiation above the canopy to 469/ooof the portion transmitted to the floor. The mean transmission was 17~o during the 8-day experiment. INTRODUC~ON T h e forester's interest in the role o f solar r a d i a t i o n in the h e a t b a l a n c e o f the e a r t h a n d in the p h o t o s y n t h e t i c processes o f p l a n t s is well d o c u m e n t e d in recent reviews o f p l a n t c o m m u n i t y effects on r a d i a t i o n exchange (ANDERSON, 1964; MmLER, 1965; REIFSNYDER a n d LULL, 1965). M a n y studies cited in these reviews d e m o n s t r a t e a l a c k o f u n d e r s t a n d i n g o f the exchange processes involved. A c o m m o n p r o b l e m t h a t does n o t yet a p p e a r to be a d e q u a t e l y t r e a t e d is t h a t o f m e a s u r i n g solar r a d i a t i o n b e n e a t h a p l a n t canopy. Because o f the i m p o r t a n c e o f this p r o b l e m , the objective o f this study is to evaluate the effectiveness o f several time- and s p a c e - s a m p l i n g schemes in characterizing solar r a d i a t i o n t r a n s m i t t e d t h r o u g h the c a n o p y o f a pine p l a n t a t i o n . THE MEASUREMENT PROBLEM T h e q u a n t i t y o f solar r a d i a t i o n p e n e t r a t i n g t h r o u g h a p l a n t c a n o p y conAgr.~MeteoroL, 8~(1971) 39-50
40
L.W. GAY et al.
tinually changes with time. There are two interrelated factors involved in this timedependent variability. First, the transmitted radiation is affected by the systematic diurnal and seasonal changes in radiation reaching the canopy. These systematic changes are a consequence of the geometry of the solar system and the condition of the earth's atmosphere. Such diurnal and seasonal cycles need not be considered here because they are almost independent of the effects of the plant canopy. Secondly, the absorptive, transmissive, and scattering properties of the canopy create additional variability in the radiation field at the floor of the plant community. This is the aspect that has proven troublesome in the past. Let us consider the variability of this radiation field of shifting light and shadow with respect to radiation incident on the top of the canopy. A continuous measurement at one specific sampling point beneath the canopy will reveal a wide variation as the sun moves across the sky during its diurnal cycle. Additional variation would be observed if the sampling point could be moved across the floor of the community at one specific instant in time. There thus exist time- and space-dependent sources of variation in the radiation field beneath a canopy. Both are related to the structure and distribution of the elements that make up the canopy and to the quantity of radiation incident upon the top of the canopy. If a canopy were to consist entirely of uniformly dispersed elements of moderate density, then only uniformly diffused solar radiation would reach the floor. The radiation regime under such a canopy would be easy to evaluate. There would be slow changes with time throughout the day, but no differences would exist between sampling points on the floor. In other words, the time differences would be smoothed and the space differences would disappear. Such "ideal" canopies do not exist in terrestrial plant communities, however, and complex problems of sampling are present whenever canopy gaps allow direct-beam solar radiation to penetrate unattenuated to the community floor. Thus, whenever the sun is unobscured, the sampling technique on the floor of a plant community must characterize a radiation regime of two distinct components: one component consists of diffused solar radiation that is rather uniformly distributed over the floor by the scattering action of the canopy elements, the other consists of additional energy contributed by direct-beam sunflecks. The sampling problems created by the direct-beam sunflecks have been systematically avoided in the past. Too many studies have sampled only the diffuse component, either by restricting sampling to overcast sky conditions, or by shading the sample point. Measurement of only one component, however, cannot possibly characterize the complex solar radiation regime at the floor of plant communities. This study will consider both components, or "global" solar radiation. Global solar radiation (K~) is the sum of the direct and diffuse solar radiation received on a horizontal surface of unit area from a solid angle of 2zr (WORLDMETEOROLOGICAL ORGANIZATION, 1969). The flux-density units used here are calories per square centimeter per minute, or langleys per minute (ly/min). Agr. MeteoroL, 8 (1971) 39-50
SOLAR RADIATIONVARIABILITYON PINE PLANTATIONFLOOR
41
The question of how best to evaluate the two aspects of time-and-space variation in the global radiation field beneath a canopy has not yet been adequately treated. A solution of this problem appears essential for the design of sampling schemes suitable for characterizing the global radiation regime within plant communities. EXPERIMENTALPROCEDURE The problem was examined through periodic measurements of global radiation on the floor of a uniform stand. The site selected for measurements was a 32-year-old loblolly (Pinus taeda L.) pine plantation in the Duke Forest near Durham, North Carolina (36 ° N, 79 ° W). Values of three indexes frequently used to characterize stand development were as follows (1) basal area of 37.7 m2/ha (161 ft.2/acre); (2) mean diameter breast high of 25.8 cm (10.2 inches); and (3) stem density (sum of diameters) of 19,675 cm/ha (3,120 inches/acre). The 752 trees per hectare had an average height of 23.4 m. The stand was open and understory-free. Trunks in this well-stocked, although rather thin-crowned, stand were uniformly spaced about 3.7 m apart. A tower-mounted pyranometer ~ sensed global radiation incident upon the top of the canopy; five checkerboard pyranometers (GAY, 1966) at a height of 1.5 m sensed the global radiation transmitted through the canopy to the forest floor. Data were recorded at 5-min intervals with a digital data logger that sampled at a rate of about one data point per second. Thus the basic data are essentially instantaneous observations taken at 5-min intervals. The five pyranometers on the forest floor were spaced in a grid with about 8 m between sample points. The configuration of the grid was fixed by the signal cables; its dimensions are shown in Fig.1. This grid was randomly moved to establish a new plot every other day during the 8-day sampling period (October
"--Q RADIOMETERS
o, 0
I
0
I'
I
I0 DISTANCE
0
I
20
I
30
(m)
Fig.1. Dimensions of the sampling grid beneath the canopy.
1 Kipp en Zonen, Delft, The Netherlands.
Agr. Meteorol., 8 (1971) 39-50
42
L.W.
GAY et al.
26-November 3, 1965). The data from the forest floor can thus be grouped into periodic samples at five points over two consecutive days on each of four plots. Global radiation conditions prevailing during this period were nearly ideal; the skies were clear and daily totals incident upon the canopy varied approximately 5 o~, about the 8-day mean of 374 ly/day. RESULTS AND DISCUSSION
The number and frequency of samples, in combination with the clear weather, make two analyses possible. The first characterizes the short-term, timedependent variation present beneath the canopy, and the second evaluates daily variation between the four plots and among the sample points within each plot. Short-term variation
The variable nature of the global radiation observations on the forest floor is illustrated in Fig.2 by data from a single point sampled at 5-min intervals throughout the course of one clear day. The upper trace of dots, labeled K,~, is the observed global radiation incident on the canopy; the more scattered small circles are the transmitted global radiation measured at one sample point on the floor. The integrated totals for incident and transmitted K]. for the 8-hour period
' OCT
I 30,1965
' ...
'
I ..,-
........
...
I
I
"•..
,..
". K~ ~" 0 . 8
_J
0.6 I-Z a 0.4 x m It.
0.2
,
I0
1
~i i"
12 HOUR ( E,S,T, )
14
16
Fig.2. Global solar radiation (K + ) above a pine plantation c a n o p y a n d at one point o n the floor.
Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR
43
in Fig.1 are 385 and 68 ly, or about 18 ~ . The average transmission for the entire 8-day measurement period was 17 ~ . There is a uniform trend in the observations of the morning and afternoon hours beneath the canopy; this contrasts sharply with the variability present during the midday period. This midday variability results from direct-beam radiation penetrating to the floor. Since the minimum values of global radiation measured on the floor must represent diffuse radiation, the measurements can be separated into diffuse and direct-beam components by passing a smooth curve through the lower values of transmitted global radiation. Diffuse radiation beneath the canopy is estimated by this procedure to be 31 ly, or 46 ~o of the transmitted total. Our other measurements indicate that approximately 15 ~o of the global radiation above the canopy is diffuse under the cloudless conditions that prevailed on this day. The pine canopy thus transformed the ratio of diffuse to global radiation from 15 ~o to 46 ~ . This ratio is obviously related to the canopy structure. A wider study of this ratio may reveal that there is a characteristic "canopy scattering index" associated with different forest types. The amount of diffuse radiation beneath the canopy has received little attention elsewhere. BERGER(1953) estimated that one-third of the global radiation transmitted to the floor of a dense fir stand in Oregon was diffuse. AIZENSHTAT'S (1958) observations in Soviet Central Asia revealed that diffuse radiation under cloudless skies increased from 1 4 ~ in the open to 38~o beneath a dense saxaul (Haloxylon sp.) canopy. The midday variability evident in Fig.2 also demonstrates an apparent change in distribution and density of the canopy elements through the day. The dimension of crown depth plays a role that has often been overlooked. The thickness of the canopy in this stand was about 9 m. The effective size of canopy gaps will therefore vary as the distance of the sun from the zenith varies throughout the day. Several important points regarding the time-dependent nature of global radiation beneath the canopy can be deduced from examination of the measurements plotted in Fig.2. First, one notes the change in variation with time of day. This confirms that caution is required in analysis of observations collected at different hours, or, more generally, when the sun is at different zenith angles. Secondly, direct-beam radiation can create an obviously non-normal distribution of observations about a mean-intensity curve. This prevents the accuracy of the mean from being estimated with probabilities based upon an assumed normal distribution. A third point, not evident from Fig.2, concerns possible differences in the levels of incoming radiation on different sample days. This refers not only to differences in total amount of energy, but also to the relative proportions of direct-beam and diffuse radiation. These three points have not generally been considered in the past work, so the interpretation of many analyses is open to question. Because of these problems, our observations were visualized as deviations
Agr. Meteorol., 8 (1971) 39-50
44
L.W. GAY et al,
from the mean global radiation present beneath the canopy. This approach allows examination of the relative effectiveness of (a) averaging in time through a series of periodic samples at one point; (b) averaging in space among samples obtained at different points; (c) combining several intensities of both time and space sampling. Before beginning the analysis, it was necessary to correct for differences that existed between days. Therefore, the data were first adjusted for the small (less than 5~o) differences in daily global radiation. This was accomplished by multiplying each observation by a ratio of the 8-day mean to that day's total above the canopy. Then since the diurnal cycle of incoming global radiation was symmetrical about noon (solar noon equaled local noon), the number of samples was effectively doubled by "folding" or combining the afternoon observations into the morning period. The folding operation utilizes our knowledge that samples made in the afternoon are of different portions of the canopy than those in the morning. After the data were combined in this manner, the experiment was viewed as periodic samples at ten points between sunrise and solar noon, instead of samples at five points throughout the day. After the data were thus adjusted and combined into a half-day period, the mean global radiation at the forest floor was fitted to a logarithmic function of time between 07h00 and 12h00. The regression equation obtained for the morning period: loglo ( K $ ) =
- 1 0 . 3 2 6 2 - 1.64 ( h ) -
0.06991 (h z)
(1)
expressed the mean global radiation transmitted to the forest floor at any instant in time, when hours (h) were expressed in hundredths and all afternoon times were adjusted in their equivalent morning time, i.e., 10:45 a.m. = 10.75 h, and 3:30 p.m. = 08.50 h. This function was used in calculating the deviations at each sample time. The distribution of deviations about this function, as deduced earlier from Fig.2, was not symmetrical about the mean. Therefore, two groups of deviations, one positive and one negative, were formed for separate treatment. The relative effectiveness of the several sampling and averaging schemes may be examined in Fig.3. Because of the non-normal distribution of the deviations, the average of deviations about the mean line is used in Fig.3 to indicate the relative deviation size. The procedure for obtaining the deviations can best be explained by examination of the curves in Fig.3. The family of curves in Fig.3A were developed from the individual observations made with all five of the pyranometers on the forest floor. The outer envelope (solid lines) of this family shows the average deviations of the individual observations that were collected at 5-rain intervals throughout the 8-day sample period. The analysis may be more readily interpreted if we look closely at the development of this outer envelope. Consider a specific time, say 101100, and recall that 14h00 is the afternoon equivalent. There are Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATIONVARIABILITYON PINE PLANTATIONFLOOR
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/ 7
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i
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7
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I I0 ( P..,,.~.l
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Fig.3. Average deviations from the mean global radiation at the forest floor. Observations are grouped by corresponding morning and afternoon hours, i.e., 09h30 and 14h30 are considered equivalent points on the abscissa. A. Curves derived from measurements with five individual pyranometers. B. Curves derived from the mean of measurements made with three pyranometers. C. Curves derived from the mean of measurements made with five pyranometers. 5 x 16 = 80 samples of transmitted global radiation at this time (five pyranometers on each of 8 days at 10h00, and five pyranometers on each of 8 days at 14h00). The pooled, folded data thus contain 80 samples of transmitted global radiation at each 5-rain interval between 07h00 and 12h00, for a total of 4,800 samples. The deviations at 10h00 were obtained by subtracting the estimate of the mean as given by eq. 1 at that time from each of the 80 observations. This procedure was repeated at each 5-min interval between 07h00 and 12h00, to yield a total of 4,800 deviations about the mean line. Two additional regressions were then run: the first to express the positive and the second to express the negative deviations as functions of time. These regressions were used to draw the positive and negative envelope for the family of curves. The outer, solid lines thus represent an average of all deviations about the mean global radiation on the forest floor. The interior curves in Fig.3A (dashed and dotted lines) show effects of successively averaging the 5-rain series of observations over successively longer periods before computing the deviations from the mean curve as explained above. Averaging periods shown are for 15, 30, 60, and 120 min. Again, the positive and negative deviations for these time-averaged observations were expressed as functions of time. These functions were used to draw the interior curves. It is evident that a large reduction of mean deviations can be achieved by averaging observations over successively longer time periods. The two families of curves shown in Fig.3B, C illustrate additional effects
Agr. Meteorol., 8 (1971) 39-50
46
L.w. GAY et al.
of averaging among sample points in space. Fig.3B is based on observations from the three pyranometers most widely separated in the sampling grid. The observations from these three instruments at each sample time were averaged together before deviations from the mean curve were calculated. Thus these curves show the average deviations found after space averaging among three sample points; the outer envelope is based on the 5-rain time series of observations, and the interior curves again show improvement obtained by further averaging the 5-min time series over successively longer time periods. The curves in Fig.3C were developed by a similar procedure. The deviations in this family were obtained after first averaging among all five of the pyranometers at each sample time. Once again, the outer envelope shows the average deviations based on the 5-rain time series, but the interior curves show an improvement to be gained by successively averaging over a greater period of time. The graphs in Fig.3 for the first time allow comparisons to be made between effectiveness of averaging global radiation at the forest floor in space versus time. As an example, let us compare the curves in Fig.3A and 3C. The dotted line shows in each instance the average deviations found after averaging in time for one hour. Note that the magnitude of the dotted line in Fig.3A is about the same as that of the solid outer line in Fig.3B, regardless of time of day selected on the abscissa. This indicates that the grand mean appears to be equally well defined by either averaging a 5-rain time series observed by one pyranometer over one hour (twelve observations), or by averaging one set of observations collected simultaneously from five widely spaced pyranometers (five observations). A space average thus appears to be considerably more effective in reducing deviations about the mean curve than is the time average.
Long-term variation Analysis of Fig.3 shows that the average deviations approach the mean more closely as the period of integration is lengthened. Whenever global radiation is integrated over the entire day, the point-to-point variations may be averaged out by relative movement of the sun with respect to the forest canopy throughout the day. This is generally expected to be true if sampling is rather frequent and the canopy elements rather uniformly distributed. No statistical analysis of daily totals of transmitted global radiation beneath a uniform canopy under cloudless skies is known to us. The data collected in this study lend themselves to analysis of the point-to-point and plot-to-plot variation among daily totals. The following hypotheses will be tested in this analysis: (1) no significant differences exist between daily totals of global radiation received at individual sampling points within each plot on the floor of the pine plantation; (2) no significant differences exist between the mean daily totals of global radiation received in plots on the floor of the pine plantation. The data described in the analysis of short-term variation forms the basis Agr. Meteorol., 8 (1971) 39-50
47
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR TABLE I ADJUSTED GLOBAL RADIATION TOTALS (LY/DAY) AT b = 5 POINTS IN EACH OF a = 4 PLOTS,
n :
2 TOTALS PER POINT
Plot, i (i : 1...a)
Points, ij ~] = l...b)
Totals Xijk
Xo.
X~..
1
1 2 3 4 5
62 61 65 70 47
64 66 71 64 47
126 127 136 134 94
617
1 2 3 4 5
58 58 70 81 54
58 53 68 80 57
116 111 138 161 111
637
1 2 3 4 5
56 64 74 64 66
64 65 79 62 72
120 129 153 126 138
666
1 2 3 4 5
72 62 60 73 55
73 75 64 73 56
145 137 124 146 111
663
X...
2583
for testing these hypotheses. The experimental design has already been defined. It is only necessary to integrate the periodic observations at each sample point into daily totals. These integrated totals are tabulated in Table I. The daily totals beneath the canopy approach a normal distribution much more closely than do the previously described short-term measurements. The hypotheses were thus tested by analysis of variance after first adjusting the daily totals to account for the small changes (5 % or less) in incoming radiation on each day. The adjustment seeks to remove the effect of small differences attributed to shifts in the level of incoming global radiation on different sample days. Such an adjustment will permit the data to be analyzed as if all four sample plots had been measured simultaneously, rather than sequentially. The analysis of variance seeks to evaluate the variance component attributed to random measurement errors at a point, the variance between points established within any one plot, and the variance attributed to the different plots. The model used in the analysis is similar to that described by SNEDECOR (1956, p.265): Agr. Meteorol., 8 (1971) 39-50
48
L . W . GAY et al. Xij k
:
(2)
~l -~- Z i -{- B i j q- 8ij k
w h e r e i = 1 ... a , j = 1 ... b, k = 1 ... n, A i = N(0, aA), B i j = N(0, an), eiik = N(0, a); w h e r e X is the daily total, A refers to plots, a n d B refers to p o i n t s within a p a r t i c u l a r plot. W i t h the design used here, a = 4 plots, b = 5 p o i n t s within e a c h plot, a n d n = 2 r e p l i c a t i o n s at a point. T h e r a n d o m e l e m e n t s a s s o c i a t e d with plots, points, a n d totals are a s s u m e d to h a v e n o r m a l d i s t r i b u t i o n s ( N ) w i t h z e r o m e a n a n d respective s t a n d a r d d e v i a t i o n s o f a A, a 8, a n d a. T h e m o d e l specifies t h a t each daily total is m a d e u p o f a m e a n , plus a v a r i a n c e c o m p o n e n t f r o m the plots, plus a c o m p o n e n t f r o m p o i n t s within e a c h plot, plus an e r r o r c o m p o n e n t a s s o c i a t e d with e a c h daily total. T h e o b j e c t i v e o f the analysis is to p a r t i t i o n the s u m o f s q u a r e s into these three sources o f v a r i a t i o n . W e will then be a b l e to test for significant differences within a plot a n d a m o n g plots. T h e e r r o r c o m p o n e n t associated w i t h e a c h daily t o t a l is e s t i m a t e d f r o m r e p l i c a t i o n o f the m e a s u r e m e n t s at e a c h p o i n t for a s e c o n d day. T h i s c o m p o n e n t s h o u l d be small, as it involves p r i m a r i l y the r a n d o m m e a s u r e m e n t e r r o r s a s s o c i a t e d with the r e c o r d e r a n d sensors. I f the days are identical, t h e n m e a s u r e m e n t s at the s a m e p o i n t s h o u l d be the s a m e f r o m d a y - t o - d a y . In a d d i t i o n , it is n o t strictly p r o p e r to e s t i m a t e the v a r i a n c e a m o n g the p o i n t s w i t h i n plots, since the p o i n t s are fixed in a grid r a t h e r t h a n being r a n d o m l y l o c a t e d w i t h i n e a c h plot. T h e v a r i a n c e b e t w e e n p o i n t s w o u l d be m i n i m i z e d by r a n d o m l o c a t i o n o f the s a m p l i n g points. T h e analysis o f v a r i a n c e is s u m m a r i z e d in T a b l e I1. T h e null h y p o t h e s i s m a y be tested as:
TABLE I1 A N A L Y S I S O F V A R I A N C E OF T R A N S M I T T E D G L O B A L R A D I A T I O N
Source o f Variation
df
SS
MS
Parameters Estimated
Plots (A) Points within a plot (B) Total at a point (X)
3 16 20
161.075 2308.200 228.500
53.6916 144.2625 11.4250
a s -t nab s + bnaA 2 a '~ ÷ nab 2 a2
39 C ~ (X...)2/abn = 25832/40 = 166,797.225 Totals = X~jxz -- C = (622 + ... + 562) -- C = 2,697.775 Points = X~j.2/n -- C = (1262 + ... + lllZ)/2 -- C = 2,469.275 Plots = X~.)/bn -- C ~ (6178 + ... + 6638)/10 -- C = 161.075 Points within a plot = Points -- Plots = 2,308.200 Totals at a point = Totals -- Points = 228.500 Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR
(1) tr2s = 0;
MS points within a plot F = MS totals at a point -
(2) t r 2 = 0;
MS plots 53.6916 F = MS points within a plot - 144.2625 = < 1 , f - - 3, 16
49
144.2625 _ 12.6,f = 16, 20 11.4250
For the first test, F is beyond the 1% point, 3.05, indicating that daily global radiation totals in this stand do vary significantly from point to point within a given plot. For the second, F is less than 1, a situation that could not occur even if aA 2 = 0. Sampling variation has either decreased the real mean square for plots, or increased that for points within plots, or both. The apparent negative variance between plots may be the result of the grid increasing the observed variance between points. Obviously, there is no evidence to cause us to reject the hypothesis that trA2 = 0. Therefore, from the evidence available here, we cannot conclude that a difference exists among the plot estimates of transmitted global radiation. CONCLUSIONS
The analyses considered here are restricted to a favorable combination of weather conditions and stand uniformity. They may serve as guidelines in the complex problem of sampling global radiation beneath canopies. It is evident that a substantial reduction in deviations was achieved in this stand by averaging three pyranometers in space. The observations from a single pyranometer would certainly be inadequate to characterize the global radiation transmitted through this canopy. The maximum reduction in deviations resulted from averaging both in time and in space. Despite the usual limitations on instruments available, at least five pyranometers would be required here for a study seeking to define means of transmitted global radiation over periods of less than a day in length. Similarly, it appears necessary to space-average among several observation points to obtain a precise estimate of daily totals on the floor. In this relatively uniform plantation, one such space-averaged plot appeared sufficient. ACKNOWLEDGEMENTS This research was supported in part by Rockefeller Foundation Grant R F 61026 and in part through a fellowship to the senior author from the Public Health Service, Division of Air Pollution, 1F3AP24, 123-01. REFERENCES
AIZENSHTAT, B.
A., 1958. The Heat Balance and Microclimate o f Certain Landscapes in a Sandy Desert. (Transl. from Russian, 1960.) U.S. Weather Bureau, Washington, D.C., 90 pp.
ANDERSON,M. C., 1964. Light relations of terrestrial plant communities and their measurement. Biol. Rev. Cambridge Phil. Soc., 39: 425-486. Agr. MeteoroL, 8 (1971) 39-50
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BERGER, P., 1953. Radiation in forest at Willamette Basin Snow Laboratory. U.S. Corps Engrs., Snow Invest. Res. Note, 12, 17 pp. GAY, L. W., 1966. The Radiant Energy Balance of a Pine Plantation. Duke University School of Forestry, Durham, N.C., unpublished. MILLER, D. H., 1965. The heat and water budget of the earth's surface. Advan. Geophys., 11: 176-277. REIFSNYDER,W. E. and LULL, H. W., 1965. Radiant energy in relation to forests. U.S. Dept. Agr., Forest Serv. Tech. Bull., 1344:111 pp. SNEDECOrt, G. W., 1956. Statistical Methods. Iowa State Univ. Press., Ames, Iowa, 534 pp. WORLD METEOROLOGICALOROANIZATION,1969. Guide to Meteorological Instrument and Observing Practices. W.M.O. Geneva, No. 8.TP.3: IX--46.
Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATION
V A R I A B I L I T Y O N T H E F L O O R OF A P I N E
PLANTATION L. W. GAY, K. R. KNOERR AND M. O. BRAATEN School of Forestry, Oregon State University, Corvallis, Ore. (U.S.A.) School of Forestry, Duke University, Durham, N.C. (U,S.A.) Department of Industrial Engineering, University of Missouri, Columbia, Mo. (U.S.A.) (Received April 2, 1970)
ABSTRACT GAY, L. W., KNOERR,K. R. and BRAATEN,M. O., 1971. Solar radiation variability on the floor of a pine plantation. Agr. Meteorol., 8: 39-50. Measurements of global radiation were made above and below the canopy of a pine plantation during eight consecutive cloudless days. Several analyses were to be made of the variation in time and space in global radiation reaching the forest floor. One analysis represented the measurements as deviations from the mean global radiation at the floor. This approach revealed that periodic samples would be required from at least three pyranometers in this stand to satisfactorily estimate means over short periods of up to a few hours. A statistical analysis of daily radiation totals showed that significant differences were still present among individual sampling points. However, no significant differences were found among measurements of daily totals on four sample plots, each containing five sample points. The analyses suggest some guidelines for sampling global radiation beneath a forest canopy. The measurements also demonstrated the scattering effects of the canopy. The diffuse component increased from 15~ of the global radiation above the canopy to 469/ooof the portion transmitted to the floor. The mean transmission was 17~o during the 8-day experiment. INTRODUC~ON T h e forester's interest in the role o f solar r a d i a t i o n in the h e a t b a l a n c e o f the e a r t h a n d in the p h o t o s y n t h e t i c processes o f p l a n t s is well d o c u m e n t e d in recent reviews o f p l a n t c o m m u n i t y effects on r a d i a t i o n exchange (ANDERSON, 1964; MmLER, 1965; REIFSNYDER a n d LULL, 1965). M a n y studies cited in these reviews d e m o n s t r a t e a l a c k o f u n d e r s t a n d i n g o f the exchange processes involved. A c o m m o n p r o b l e m t h a t does n o t yet a p p e a r to be a d e q u a t e l y t r e a t e d is t h a t o f m e a s u r i n g solar r a d i a t i o n b e n e a t h a p l a n t canopy. Because o f the i m p o r t a n c e o f this p r o b l e m , the objective o f this study is to evaluate the effectiveness o f several time- and s p a c e - s a m p l i n g schemes in characterizing solar r a d i a t i o n t r a n s m i t t e d t h r o u g h the c a n o p y o f a pine p l a n t a t i o n . THE MEASUREMENT PROBLEM T h e q u a n t i t y o f solar r a d i a t i o n p e n e t r a t i n g t h r o u g h a p l a n t c a n o p y conAgr.~MeteoroL, 8~(1971) 39-50
40
L.W. GAY et al.
tinually changes with time. There are two interrelated factors involved in this timedependent variability. First, the transmitted radiation is affected by the systematic diurnal and seasonal changes in radiation reaching the canopy. These systematic changes are a consequence of the geometry of the solar system and the condition of the earth's atmosphere. Such diurnal and seasonal cycles need not be considered here because they are almost independent of the effects of the plant canopy. Secondly, the absorptive, transmissive, and scattering properties of the canopy create additional variability in the radiation field at the floor of the plant community. This is the aspect that has proven troublesome in the past. Let us consider the variability of this radiation field of shifting light and shadow with respect to radiation incident on the top of the canopy. A continuous measurement at one specific sampling point beneath the canopy will reveal a wide variation as the sun moves across the sky during its diurnal cycle. Additional variation would be observed if the sampling point could be moved across the floor of the community at one specific instant in time. There thus exist time- and space-dependent sources of variation in the radiation field beneath a canopy. Both are related to the structure and distribution of the elements that make up the canopy and to the quantity of radiation incident upon the top of the canopy. If a canopy were to consist entirely of uniformly dispersed elements of moderate density, then only uniformly diffused solar radiation would reach the floor. The radiation regime under such a canopy would be easy to evaluate. There would be slow changes with time throughout the day, but no differences would exist between sampling points on the floor. In other words, the time differences would be smoothed and the space differences would disappear. Such "ideal" canopies do not exist in terrestrial plant communities, however, and complex problems of sampling are present whenever canopy gaps allow direct-beam solar radiation to penetrate unattenuated to the community floor. Thus, whenever the sun is unobscured, the sampling technique on the floor of a plant community must characterize a radiation regime of two distinct components: one component consists of diffused solar radiation that is rather uniformly distributed over the floor by the scattering action of the canopy elements, the other consists of additional energy contributed by direct-beam sunflecks. The sampling problems created by the direct-beam sunflecks have been systematically avoided in the past. Too many studies have sampled only the diffuse component, either by restricting sampling to overcast sky conditions, or by shading the sample point. Measurement of only one component, however, cannot possibly characterize the complex solar radiation regime at the floor of plant communities. This study will consider both components, or "global" solar radiation. Global solar radiation (K~) is the sum of the direct and diffuse solar radiation received on a horizontal surface of unit area from a solid angle of 2zr (WORLDMETEOROLOGICAL ORGANIZATION, 1969). The flux-density units used here are calories per square centimeter per minute, or langleys per minute (ly/min). Agr. MeteoroL, 8 (1971) 39-50
SOLAR RADIATIONVARIABILITYON PINE PLANTATIONFLOOR
41
The question of how best to evaluate the two aspects of time-and-space variation in the global radiation field beneath a canopy has not yet been adequately treated. A solution of this problem appears essential for the design of sampling schemes suitable for characterizing the global radiation regime within plant communities. EXPERIMENTALPROCEDURE The problem was examined through periodic measurements of global radiation on the floor of a uniform stand. The site selected for measurements was a 32-year-old loblolly (Pinus taeda L.) pine plantation in the Duke Forest near Durham, North Carolina (36 ° N, 79 ° W). Values of three indexes frequently used to characterize stand development were as follows (1) basal area of 37.7 m2/ha (161 ft.2/acre); (2) mean diameter breast high of 25.8 cm (10.2 inches); and (3) stem density (sum of diameters) of 19,675 cm/ha (3,120 inches/acre). The 752 trees per hectare had an average height of 23.4 m. The stand was open and understory-free. Trunks in this well-stocked, although rather thin-crowned, stand were uniformly spaced about 3.7 m apart. A tower-mounted pyranometer ~ sensed global radiation incident upon the top of the canopy; five checkerboard pyranometers (GAY, 1966) at a height of 1.5 m sensed the global radiation transmitted through the canopy to the forest floor. Data were recorded at 5-min intervals with a digital data logger that sampled at a rate of about one data point per second. Thus the basic data are essentially instantaneous observations taken at 5-min intervals. The five pyranometers on the forest floor were spaced in a grid with about 8 m between sample points. The configuration of the grid was fixed by the signal cables; its dimensions are shown in Fig.1. This grid was randomly moved to establish a new plot every other day during the 8-day sampling period (October
"--Q RADIOMETERS
o, 0
I
0
I'
I
I0 DISTANCE
0
I
20
I
30
(m)
Fig.1. Dimensions of the sampling grid beneath the canopy.
1 Kipp en Zonen, Delft, The Netherlands.
Agr. Meteorol., 8 (1971) 39-50
42
L.W.
GAY et al.
26-November 3, 1965). The data from the forest floor can thus be grouped into periodic samples at five points over two consecutive days on each of four plots. Global radiation conditions prevailing during this period were nearly ideal; the skies were clear and daily totals incident upon the canopy varied approximately 5 o~, about the 8-day mean of 374 ly/day. RESULTS AND DISCUSSION
The number and frequency of samples, in combination with the clear weather, make two analyses possible. The first characterizes the short-term, timedependent variation present beneath the canopy, and the second evaluates daily variation between the four plots and among the sample points within each plot. Short-term variation
The variable nature of the global radiation observations on the forest floor is illustrated in Fig.2 by data from a single point sampled at 5-min intervals throughout the course of one clear day. The upper trace of dots, labeled K,~, is the observed global radiation incident on the canopy; the more scattered small circles are the transmitted global radiation measured at one sample point on the floor. The integrated totals for incident and transmitted K]. for the 8-hour period
' OCT
I 30,1965
' ...
'
I ..,-
........
...
I
I
"•..
,..
". K~ ~" 0 . 8
_J
0.6 I-Z a 0.4 x m It.
0.2
,
I0
1
~i i"
12 HOUR ( E,S,T, )
14
16
Fig.2. Global solar radiation (K + ) above a pine plantation c a n o p y a n d at one point o n the floor.
Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR
43
in Fig.1 are 385 and 68 ly, or about 18 ~ . The average transmission for the entire 8-day measurement period was 17 ~ . There is a uniform trend in the observations of the morning and afternoon hours beneath the canopy; this contrasts sharply with the variability present during the midday period. This midday variability results from direct-beam radiation penetrating to the floor. Since the minimum values of global radiation measured on the floor must represent diffuse radiation, the measurements can be separated into diffuse and direct-beam components by passing a smooth curve through the lower values of transmitted global radiation. Diffuse radiation beneath the canopy is estimated by this procedure to be 31 ly, or 46 ~o of the transmitted total. Our other measurements indicate that approximately 15 ~o of the global radiation above the canopy is diffuse under the cloudless conditions that prevailed on this day. The pine canopy thus transformed the ratio of diffuse to global radiation from 15 ~o to 46 ~ . This ratio is obviously related to the canopy structure. A wider study of this ratio may reveal that there is a characteristic "canopy scattering index" associated with different forest types. The amount of diffuse radiation beneath the canopy has received little attention elsewhere. BERGER(1953) estimated that one-third of the global radiation transmitted to the floor of a dense fir stand in Oregon was diffuse. AIZENSHTAT'S (1958) observations in Soviet Central Asia revealed that diffuse radiation under cloudless skies increased from 1 4 ~ in the open to 38~o beneath a dense saxaul (Haloxylon sp.) canopy. The midday variability evident in Fig.2 also demonstrates an apparent change in distribution and density of the canopy elements through the day. The dimension of crown depth plays a role that has often been overlooked. The thickness of the canopy in this stand was about 9 m. The effective size of canopy gaps will therefore vary as the distance of the sun from the zenith varies throughout the day. Several important points regarding the time-dependent nature of global radiation beneath the canopy can be deduced from examination of the measurements plotted in Fig.2. First, one notes the change in variation with time of day. This confirms that caution is required in analysis of observations collected at different hours, or, more generally, when the sun is at different zenith angles. Secondly, direct-beam radiation can create an obviously non-normal distribution of observations about a mean-intensity curve. This prevents the accuracy of the mean from being estimated with probabilities based upon an assumed normal distribution. A third point, not evident from Fig.2, concerns possible differences in the levels of incoming radiation on different sample days. This refers not only to differences in total amount of energy, but also to the relative proportions of direct-beam and diffuse radiation. These three points have not generally been considered in the past work, so the interpretation of many analyses is open to question. Because of these problems, our observations were visualized as deviations
Agr. Meteorol., 8 (1971) 39-50
44
L.W. GAY et al,
from the mean global radiation present beneath the canopy. This approach allows examination of the relative effectiveness of (a) averaging in time through a series of periodic samples at one point; (b) averaging in space among samples obtained at different points; (c) combining several intensities of both time and space sampling. Before beginning the analysis, it was necessary to correct for differences that existed between days. Therefore, the data were first adjusted for the small (less than 5~o) differences in daily global radiation. This was accomplished by multiplying each observation by a ratio of the 8-day mean to that day's total above the canopy. Then since the diurnal cycle of incoming global radiation was symmetrical about noon (solar noon equaled local noon), the number of samples was effectively doubled by "folding" or combining the afternoon observations into the morning period. The folding operation utilizes our knowledge that samples made in the afternoon are of different portions of the canopy than those in the morning. After the data were combined in this manner, the experiment was viewed as periodic samples at ten points between sunrise and solar noon, instead of samples at five points throughout the day. After the data were thus adjusted and combined into a half-day period, the mean global radiation at the forest floor was fitted to a logarithmic function of time between 07h00 and 12h00. The regression equation obtained for the morning period: loglo ( K $ ) =
- 1 0 . 3 2 6 2 - 1.64 ( h ) -
0.06991 (h z)
(1)
expressed the mean global radiation transmitted to the forest floor at any instant in time, when hours (h) were expressed in hundredths and all afternoon times were adjusted in their equivalent morning time, i.e., 10:45 a.m. = 10.75 h, and 3:30 p.m. = 08.50 h. This function was used in calculating the deviations at each sample time. The distribution of deviations about this function, as deduced earlier from Fig.2, was not symmetrical about the mean. Therefore, two groups of deviations, one positive and one negative, were formed for separate treatment. The relative effectiveness of the several sampling and averaging schemes may be examined in Fig.3. Because of the non-normal distribution of the deviations, the average of deviations about the mean line is used in Fig.3 to indicate the relative deviation size. The procedure for obtaining the deviations can best be explained by examination of the curves in Fig.3. The family of curves in Fig.3A were developed from the individual observations made with all five of the pyranometers on the forest floor. The outer envelope (solid lines) of this family shows the average deviations of the individual observations that were collected at 5-rain intervals throughout the 8-day sample period. The analysis may be more readily interpreted if we look closely at the development of this outer envelope. Consider a specific time, say 101100, and recall that 14h00 is the afternoon equivalent. There are Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATIONVARIABILITYON PINE PLANTATIONFLOOR
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:
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/ 7
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,
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.:.
I 12
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i
i
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i
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9
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i
,
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I II
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7
I 8
I 9 HOUR
,.o
I I0 ( P..,,.~.l
I II
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7
I0
Fig.3. Average deviations from the mean global radiation at the forest floor. Observations are grouped by corresponding morning and afternoon hours, i.e., 09h30 and 14h30 are considered equivalent points on the abscissa. A. Curves derived from measurements with five individual pyranometers. B. Curves derived from the mean of measurements made with three pyranometers. C. Curves derived from the mean of measurements made with five pyranometers. 5 x 16 = 80 samples of transmitted global radiation at this time (five pyranometers on each of 8 days at 10h00, and five pyranometers on each of 8 days at 14h00). The pooled, folded data thus contain 80 samples of transmitted global radiation at each 5-rain interval between 07h00 and 12h00, for a total of 4,800 samples. The deviations at 10h00 were obtained by subtracting the estimate of the mean as given by eq. 1 at that time from each of the 80 observations. This procedure was repeated at each 5-min interval between 07h00 and 12h00, to yield a total of 4,800 deviations about the mean line. Two additional regressions were then run: the first to express the positive and the second to express the negative deviations as functions of time. These regressions were used to draw the positive and negative envelope for the family of curves. The outer, solid lines thus represent an average of all deviations about the mean global radiation on the forest floor. The interior curves in Fig.3A (dashed and dotted lines) show effects of successively averaging the 5-rain series of observations over successively longer periods before computing the deviations from the mean curve as explained above. Averaging periods shown are for 15, 30, 60, and 120 min. Again, the positive and negative deviations for these time-averaged observations were expressed as functions of time. These functions were used to draw the interior curves. It is evident that a large reduction of mean deviations can be achieved by averaging observations over successively longer time periods. The two families of curves shown in Fig.3B, C illustrate additional effects
Agr. Meteorol., 8 (1971) 39-50
46
L.w. GAY et al.
of averaging among sample points in space. Fig.3B is based on observations from the three pyranometers most widely separated in the sampling grid. The observations from these three instruments at each sample time were averaged together before deviations from the mean curve were calculated. Thus these curves show the average deviations found after space averaging among three sample points; the outer envelope is based on the 5-rain time series of observations, and the interior curves again show improvement obtained by further averaging the 5-min time series over successively longer time periods. The curves in Fig.3C were developed by a similar procedure. The deviations in this family were obtained after first averaging among all five of the pyranometers at each sample time. Once again, the outer envelope shows the average deviations based on the 5-rain time series, but the interior curves show an improvement to be gained by successively averaging over a greater period of time. The graphs in Fig.3 for the first time allow comparisons to be made between effectiveness of averaging global radiation at the forest floor in space versus time. As an example, let us compare the curves in Fig.3A and 3C. The dotted line shows in each instance the average deviations found after averaging in time for one hour. Note that the magnitude of the dotted line in Fig.3A is about the same as that of the solid outer line in Fig.3B, regardless of time of day selected on the abscissa. This indicates that the grand mean appears to be equally well defined by either averaging a 5-rain time series observed by one pyranometer over one hour (twelve observations), or by averaging one set of observations collected simultaneously from five widely spaced pyranometers (five observations). A space average thus appears to be considerably more effective in reducing deviations about the mean curve than is the time average.
Long-term variation Analysis of Fig.3 shows that the average deviations approach the mean more closely as the period of integration is lengthened. Whenever global radiation is integrated over the entire day, the point-to-point variations may be averaged out by relative movement of the sun with respect to the forest canopy throughout the day. This is generally expected to be true if sampling is rather frequent and the canopy elements rather uniformly distributed. No statistical analysis of daily totals of transmitted global radiation beneath a uniform canopy under cloudless skies is known to us. The data collected in this study lend themselves to analysis of the point-to-point and plot-to-plot variation among daily totals. The following hypotheses will be tested in this analysis: (1) no significant differences exist between daily totals of global radiation received at individual sampling points within each plot on the floor of the pine plantation; (2) no significant differences exist between the mean daily totals of global radiation received in plots on the floor of the pine plantation. The data described in the analysis of short-term variation forms the basis Agr. Meteorol., 8 (1971) 39-50
47
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR TABLE I ADJUSTED GLOBAL RADIATION TOTALS (LY/DAY) AT b = 5 POINTS IN EACH OF a = 4 PLOTS,
n :
2 TOTALS PER POINT
Plot, i (i : 1...a)
Points, ij ~] = l...b)
Totals Xijk
Xo.
X~..
1
1 2 3 4 5
62 61 65 70 47
64 66 71 64 47
126 127 136 134 94
617
1 2 3 4 5
58 58 70 81 54
58 53 68 80 57
116 111 138 161 111
637
1 2 3 4 5
56 64 74 64 66
64 65 79 62 72
120 129 153 126 138
666
1 2 3 4 5
72 62 60 73 55
73 75 64 73 56
145 137 124 146 111
663
X...
2583
for testing these hypotheses. The experimental design has already been defined. It is only necessary to integrate the periodic observations at each sample point into daily totals. These integrated totals are tabulated in Table I. The daily totals beneath the canopy approach a normal distribution much more closely than do the previously described short-term measurements. The hypotheses were thus tested by analysis of variance after first adjusting the daily totals to account for the small changes (5 % or less) in incoming radiation on each day. The adjustment seeks to remove the effect of small differences attributed to shifts in the level of incoming global radiation on different sample days. Such an adjustment will permit the data to be analyzed as if all four sample plots had been measured simultaneously, rather than sequentially. The analysis of variance seeks to evaluate the variance component attributed to random measurement errors at a point, the variance between points established within any one plot, and the variance attributed to the different plots. The model used in the analysis is similar to that described by SNEDECOR (1956, p.265): Agr. Meteorol., 8 (1971) 39-50
48
L . W . GAY et al. Xij k
:
(2)
~l -~- Z i -{- B i j q- 8ij k
w h e r e i = 1 ... a , j = 1 ... b, k = 1 ... n, A i = N(0, aA), B i j = N(0, an), eiik = N(0, a); w h e r e X is the daily total, A refers to plots, a n d B refers to p o i n t s within a p a r t i c u l a r plot. W i t h the design used here, a = 4 plots, b = 5 p o i n t s within e a c h plot, a n d n = 2 r e p l i c a t i o n s at a point. T h e r a n d o m e l e m e n t s a s s o c i a t e d with plots, points, a n d totals are a s s u m e d to h a v e n o r m a l d i s t r i b u t i o n s ( N ) w i t h z e r o m e a n a n d respective s t a n d a r d d e v i a t i o n s o f a A, a 8, a n d a. T h e m o d e l specifies t h a t each daily total is m a d e u p o f a m e a n , plus a v a r i a n c e c o m p o n e n t f r o m the plots, plus a c o m p o n e n t f r o m p o i n t s within e a c h plot, plus an e r r o r c o m p o n e n t a s s o c i a t e d with e a c h daily total. T h e o b j e c t i v e o f the analysis is to p a r t i t i o n the s u m o f s q u a r e s into these three sources o f v a r i a t i o n . W e will then be a b l e to test for significant differences within a plot a n d a m o n g plots. T h e e r r o r c o m p o n e n t associated w i t h e a c h daily t o t a l is e s t i m a t e d f r o m r e p l i c a t i o n o f the m e a s u r e m e n t s at e a c h p o i n t for a s e c o n d day. T h i s c o m p o n e n t s h o u l d be small, as it involves p r i m a r i l y the r a n d o m m e a s u r e m e n t e r r o r s a s s o c i a t e d with the r e c o r d e r a n d sensors. I f the days are identical, t h e n m e a s u r e m e n t s at the s a m e p o i n t s h o u l d be the s a m e f r o m d a y - t o - d a y . In a d d i t i o n , it is n o t strictly p r o p e r to e s t i m a t e the v a r i a n c e a m o n g the p o i n t s w i t h i n plots, since the p o i n t s are fixed in a grid r a t h e r t h a n being r a n d o m l y l o c a t e d w i t h i n e a c h plot. T h e v a r i a n c e b e t w e e n p o i n t s w o u l d be m i n i m i z e d by r a n d o m l o c a t i o n o f the s a m p l i n g points. T h e analysis o f v a r i a n c e is s u m m a r i z e d in T a b l e I1. T h e null h y p o t h e s i s m a y be tested as:
TABLE I1 A N A L Y S I S O F V A R I A N C E OF T R A N S M I T T E D G L O B A L R A D I A T I O N
Source o f Variation
df
SS
MS
Parameters Estimated
Plots (A) Points within a plot (B) Total at a point (X)
3 16 20
161.075 2308.200 228.500
53.6916 144.2625 11.4250
a s -t nab s + bnaA 2 a '~ ÷ nab 2 a2
39 C ~ (X...)2/abn = 25832/40 = 166,797.225 Totals = X~jxz -- C = (622 + ... + 562) -- C = 2,697.775 Points = X~j.2/n -- C = (1262 + ... + lllZ)/2 -- C = 2,469.275 Plots = X~.)/bn -- C ~ (6178 + ... + 6638)/10 -- C = 161.075 Points within a plot = Points -- Plots = 2,308.200 Totals at a point = Totals -- Points = 228.500 Agr. Meteorol., 8 (1971) 39-50
SOLAR RADIATION VARIABILITY ON PINE PLANTATION FLOOR
(1) tr2s = 0;
MS points within a plot F = MS totals at a point -
(2) t r 2 = 0;
MS plots 53.6916 F = MS points within a plot - 144.2625 = < 1 , f - - 3, 16
49
144.2625 _ 12.6,f = 16, 20 11.4250
For the first test, F is beyond the 1% point, 3.05, indicating that daily global radiation totals in this stand do vary significantly from point to point within a given plot. For the second, F is less than 1, a situation that could not occur even if aA 2 = 0. Sampling variation has either decreased the real mean square for plots, or increased that for points within plots, or both. The apparent negative variance between plots may be the result of the grid increasing the observed variance between points. Obviously, there is no evidence to cause us to reject the hypothesis that trA2 = 0. Therefore, from the evidence available here, we cannot conclude that a difference exists among the plot estimates of transmitted global radiation. CONCLUSIONS
The analyses considered here are restricted to a favorable combination of weather conditions and stand uniformity. They may serve as guidelines in the complex problem of sampling global radiation beneath canopies. It is evident that a substantial reduction in deviations was achieved in this stand by averaging three pyranometers in space. The observations from a single pyranometer would certainly be inadequate to characterize the global radiation transmitted through this canopy. The maximum reduction in deviations resulted from averaging both in time and in space. Despite the usual limitations on instruments available, at least five pyranometers would be required here for a study seeking to define means of transmitted global radiation over periods of less than a day in length. Similarly, it appears necessary to space-average among several observation points to obtain a precise estimate of daily totals on the floor. In this relatively uniform plantation, one such space-averaged plot appeared sufficient. ACKNOWLEDGEMENTS This research was supported in part by Rockefeller Foundation Grant R F 61026 and in part through a fellowship to the senior author from the Public Health Service, Division of Air Pollution, 1F3AP24, 123-01. REFERENCES
AIZENSHTAT, B.
A., 1958. The Heat Balance and Microclimate o f Certain Landscapes in a Sandy Desert. (Transl. from Russian, 1960.) U.S. Weather Bureau, Washington, D.C., 90 pp.
ANDERSON,M. C., 1964. Light relations of terrestrial plant communities and their measurement. Biol. Rev. Cambridge Phil. Soc., 39: 425-486. Agr. MeteoroL, 8 (1971) 39-50
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BERGER, P., 1953. Radiation in forest at Willamette Basin Snow Laboratory. U.S. Corps Engrs., Snow Invest. Res. Note, 12, 17 pp. GAY, L. W., 1966. The Radiant Energy Balance of a Pine Plantation. Duke University School of Forestry, Durham, N.C., unpublished. MILLER, D. H., 1965. The heat and water budget of the earth's surface. Advan. Geophys., 11: 176-277. REIFSNYDER,W. E. and LULL, H. W., 1965. Radiant energy in relation to forests. U.S. Dept. Agr., Forest Serv. Tech. Bull., 1344:111 pp. SNEDECOrt, G. W., 1956. Statistical Methods. Iowa State Univ. Press., Ames, Iowa, 534 pp. WORLD METEOROLOGICALOROANIZATION,1969. Guide to Meteorological Instrument and Observing Practices. W.M.O. Geneva, No. 8.TP.3: IX--46.
Agr. Meteorol., 8 (1971) 39-50