15

Agricultural and Forest Meteorology, 37 ( 1986) 15- 28 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

MOBILE SAMPLING OF SOLAR RADIATION UNDER CONIFERS

GYULA PECH Petawawa National Forestry Institute, Chalk River, Ontario, KOJ lJO (Canada) (Received September 23, 1985; revision accepted December 3, 1985)

ABSTRACT Pech, G., 1986. Mobile sampling of solar radiation under conifers. Agric. For. Meteorol., 37: 15-28.

Estimates of transmitted global radiation beneath a red pine canopy were made on

seven consecutive clear days in August and on one clear day in October, using three mobile and three stationary pyranometers above the forest floor and one that was placed above the canopy. The mobile sensors were moved back and forth continuously at a

speed of 4m min-1 on 20m long north -south oriented tracks, and the signals from the

seven sensors were integrated continuously and summed by independent integrators

each day from dawn to dusk. The results demonstrate the reproducibility of mobile

transmission records and indicate that mobile sampling of transmitted global radiation

is more sample-efficient, and gives a more reliable estimate of radiation within a forest,

than the use of stationary sensors.

INTRODUCTION

According

to

a

theory

of

characterizing

visible

radiation

in

plant

communities (Pech and King, 1967), solar radiation in forest stands can best be evaluated with a mobile sensor. A pyranometer is moved on a north­ south oriented track and the analog signals are integrated continuously from dawn to dusk. The theory takes into account the short- and long-term temporal variations of global radiation above the forest, and the spatial variations of transmitted radiation beneath the canopy owing both to the structural inhomogeneity of the stand and to the variable density of biomass that obstructs radiation. The method makes use of both the apparent movement of the sun in the sky, scanning the stand from dawn to dusk to account for different trans­ missions at various angles of incidence, and the movement of the sensor itself on a horizontal track, to sample for spatial variations of transmitted radiation arising from stand architecture. The analog signal is continuously integrated and summed for a period of a full day to provide a precise estimate of the global radiation available beneath the canopy. The theory is based on four premises the implications of which are important for measuring solar radiation in the forest. The most fundamental assumption is that, for a given level of accuracy, fewer sensors are needed *

1ly min-1

=

41.9kJ m-2 min-1

0168-1923 /86/$03. 50

© 1986 Elsevier Science Publishers B.V.

16

when the signals are integrated for a whole day than for shorter periods of measurements. Reifsnyder et al. (1971/1972) found that, with an allowable radiation error of 0.01 ly min - 1 , 174 pyranometers would be needed in a red pine stand when direct beam radiation was averaged for one hour, but only 10 pyranometers when signals were integrated for a day. Gay et al. (1971) concluded that when daily totals of below-canopy radiation were compared, no significant differences were found among measurements on four sample plots each containing five sample points. They found that daily totals beneath the canopy approached a normal distribution much more closely than did short-term measurements, and that the maximum reduction in deviations resulted from averaging radiation both in time and in space. Mukammal (1971) compared the hourly average output of a fixed sensor to the corresponding hourly average output of a moving sensor in a mixed stand of mature red and white pine and reported differences of 80% to 100% for two consecutive clear days in June. The daily outputs for these two days differed by 3% only. Differences in hourly outputs of fixed and moving sensors in September exceeded the June figures, varying between 60% and 260%, with daily output differences of 2% to 9% only. The theory provides for continuous integration of analog signals as opposed to digital sampling at chosen intervals. The reason for this is that, at any location below the canopy, global radiation is affected not only by the amount available above the canopy, the direction of the majority of radiation, and by the architecture of the canopy, but also by the higher frequency movements of leaves and branches under the influence of wind. Thus, in addition to the vertical and horizontal distributions of the solar radiation, the short- and long-term temporal fluctuations of the radiation flux density also influence the required frequency of sampling when the signal is not continuous. Furthermore, intermittent sampling is more sensitive to the time­ constant of the pyranometer and, also, to the position of the sensors within or below the canopy. Sinclair et al. (1974) demonstrated quantitatively that, close to the top of the canopy, deviations of radiation records from the mean were mostly positive. Less frequent sampling tended to over­ estimate the true mean by failing to record a sufficient number of the relatively few shaded events at that level. The opposite effect was observed near the bottom of the canopy as deviations were mostly negative. The less frequent rates of sampling there tended to underestimate the true mean, as they failed to include enough of the small number of exposures to direct beam radiation. Continuous integration of analog signals is free of these problems. Finally, the theory implies that one mobile sensor provides as precise an estimate of below-canopy global radiation as several stationary sensors at that level when averaged for a day. To the author's knowledge there have been only two studies reported in the literature on comparisons between

17

below-canopy solar radiation records obtained with a mobile sensor and those measured with one or more stationary sensors. Some of Mukammal's (1971) results have already been mentioned. He used one stationary pyranometer below the canopy to compare with a mobile one mounted on a 30-m long track. Because he treated the signals from both sensors identically, using mechanical integrators, and integrated incoming global radiation above the canopy as well, he could compare the mobile and stationary estimates of below-canopy radiation both hourly and daily, and make these comparisons valid after relocating the stationary sensor. He reported that moving the fixed sensor to another location in September altered the output relationships observed earlier between the moving and stationary sensors. The daily output differences increased from between 2% and 9% to as much as 11%. Mukammal concluded that mobile sampling was superior to stationary methods, and that stationary measurements were inadequate if hourly values of radiation were needed. The other paper (Brown, 1973) was entitled "Measuring transmitted global radiation with fixed and moving sensors", but the published results had little quantitative basis for comparing the two sampling schemes. Eight stationary pyranometers were placed below the canopy close to a mobile sensor for three or four hours on three days in a Douglas-fir stand and for seven hours on one day in a lodgepole pine forest. The results suffer on several counts, perhaps most from the lack of simultaneous above-canopy radiation records, the standard against which the two methods of measure­ ment could have been compared. Also, the mobile and the stationary pyranometer signals were sampled and recorded in a different manner, introducing a bias related to the effect the relative position of the sensors has on the required frequency of sampling (Sinclair et al., 1974). By confining the measurements to short periods of a few hours about solar noon, periods characterized by the "greatest differences between these methods" (Brown, 1973, p. 118), the estimates of transmitted radiation from the moving sensor differed markedly from those with the fixed sensors. Brown observed that the data were insufficient for any statistical analysis. He concluded from the qualitative observations that at all locations the hourly estimates were different, and that on one day, when the estimates were averaged over longer than six hours, the mobile and stationary systems were in close agreement. It appears then that while a number of recent solar radiation studies made use of the method of mobile sampling (Mukammal, 1971; Rodskjer and Komher, 1971; Sinclair and Knoerr, 1972), and some compared the radiation meausred with one or more stationary sensors to results obtained with a mobile one (Mukammal, 1971; Brown, 1973), none has attempted to establish experimentally whether the mobile records represented the true transmission at that level, nor to ascertain whether the results of the mobile records were reproducible at other locations in the stand. In the summer months of 1978 the author had an opportunity to compare

18

Fig. 1. Mobile sensors traverse back and forth on 20m long north -south oriented tracks

in a red pine plantation.

several clear days of stationary radiation records below and above a red pine (Pinus resinosa Ait.) forest with records from mobile sensors (Fig. 1). This paper describes the mobile integrating system used and the solar radiation measurements obtained with three mobile and four stationary pyranometers. MATERIALS AND METHODS

The site selected was a uniform 40-year-old red pine plantation in the Larose Forest about 50 km east of Ottawa at lat. 45°25'N, long. 75°30'W. The pertinent mensurational characteristics of the stand at the experimental site (Table I) reveal a young, thin-crowned monoculture, a fairly open stand with uniformly distributed trees spaced about 3 m apart. There was no understorey or minor vegetation beneath the trees at the site. Crown closure was estimated with a moosehorn (Robinson, 1947) to be 70% and uniform. Some 150 m distance into the stand a 20 m long track was constructed about 1.3 m above the forest floor. Angle iron was used for supports and, on top, two aluminum rails in 2 m sections were laid horizontally, parallel and 50 cm apart, in the north�outh direction. A trolley, carrying a large instrument platform, was pulled back and forth on the rails with a cable driven by a reversible motor. Microswitches at each end of the track controlled the direction of the travel automatically. The trolley was pulled at a steady speed of 4 m min-1 in both directions.

19

Three mobile sensors were lined up on the instrument platform along the east-west direction. They were separated by distances of 35 and 45 cm respectively from the one in the centre. Two stationary sensors were located some 20 m on either side, and one stationary sensor south, of the track. All three were at the same level (1.5 m) above the forest floor as the mobile sensors. About 10 m north of the north end of the track a scaffolding was used to raise a sensor above the tree tops to measure incoming global radiation. A small air-conditioned mobile laboratory at the base of the scaffolding housed the electronics. Gasoline-fired power generators provided alternating current to drive the reversible motor for the pulley. The signal integrating and recording devices were run on rechargable 12 volt DC batteries. Moll-Gorczynski type pyranometers (Kipp and Zonen Ltd.) were used for measuring solar radiation. Typical of these sensors is a 90% response in 2.8 s with a sensitivity of 8 mV/41.9 kJ m-2 min-1 (Monteith, 1972). The analog signals from seven pyranometers were independently summed by seven integrators of the Pike design (Pike, 1972). The printed circuits were manufactured for our purposes by Science Associates Inc. The heart of the integrating circuit is a Philbrick 1701 chopper-stabilized operational amplifier, a relatively inexpensive device that draws less than 3 rnA from the 12 volt DC supply. With such low drain a battery life of over two months was typical in trials prior to the field program. The output pulses from the seven integrators drove electromagnetically controlled event pens on an Esterline-Angus analog/event recorder (Model A609C). The chart drive of this recorder is spring-wound, the recorder has adjustable chart speeds, and two 6 volt DC lantern batteries operate the event pens. These features make the recorder very useful in field applications away from alternating current sources. As the output of the integrators were adjusted to 1 event/ 41. 9 kJ m-2 min 1 , a chart speed of 7.5 cm h-1 allowed easy resolution for even the highest rates of events marked on the chart. The field program ran intermittently between late July and early October in 1978, mostly on cloud-free days. Each day the site was readied half an hour before sunrise and closed down shortly after sunset, or when clouds rolled in. Each morning, at the startup, the six below-canopy pyranometers were rotated to eliminate sensor-specific systematic errors. The sensors were levelled and their glass domes were cleaned of dew or dust. The recorder was started up with the chart set to correct time, and the track and trolley system was inspected for trouble-free operation. From mid-September on, after one of the pyranometers became in­ operational, the instrument platform was rotated by 90° and two pyranometers were placed on it at the north and south ends of the platform to run in each other's path back and forth on a track shortened to 16 m. The objective of this exercise was to see how reproducible north­ south running mo bile records were. The separation distance between the two sensors was 1 m which meant that their paths coincided on 14 m out of the -

20 TABLE 1 Mensurational data for the red pine plantation at the experimental site Basal area

Number of stems

Average diameter at breast height Average tree height

2 1 3 3 m ha1

1,12 5ha20cm

15m

Average crown closure

70%

Age of trees

40y

Spacing between trees

3m

total 16 m they travelled in each direction. At the turn-around points at the south and north ends of the track the two mobile sensors acted as stationary ones at different locations while waiting a few seconds for the start of the return trip. RESULTS AND DISCUSSION

To demonstrate the significance of integrating below-canopy radiation for a whole day, the hourly records of mobile and stationary sensors were examined. The hourly records of one clear day in August are summarized in Table II. The most obvious feature is that hourly-integrated radiation is both smallest and most variable among sensors during the early morning and evening hours when most, if not all, of the solar radiation is intercepted by tree trunks and canopies. What global radiation there was below the canopy came as diffuse radiation. Sensor-to-sensor variation at low solar elevation is a function of canopy structure at individual sensor locations. The larger the canopy gap the more scattered the radiation was as received by the stationary sensors. Mobile sensors did not show this variation among the different tracks. The higher the sun rose above the horizon the less the variation from track to track. Once the above-canopy hourly global radiation surpassed 1,250 kJ m -2 the mobile sensors varied considerably more from hour to hour than amongst each other during any one hour. It appears that the distribution of global radiation, even under such uniform canopies, is a local phenomenon governed almost entirely by solar elevation and canopy structure. Note for example in Table II that while maximum incoming global radiation occurred around noon above the forest, on this day mobile sensors on different tracks all received their maxima identically during the same hour between 10 and 11 a.m. and displayed a secondary one-hour peak between 12 noon and 1 p.m. In contrast to this the stationary-sensor records were different at each location. At West-stationary there were three peaks for the hours ending at 10 a.m., 12 noon, and 2 p.m. At East-stationary the maximum peaked at 10 a.m. and was followed by two hours of almost equally high radiation periods.

TABLE II Global radiation (kJ m-2 ) in each hour ending at E.S.T.a shown , and for the whole day, on a clear day in August Daily

Time reference 0600

0700

0800

0900

1000

1 100

1200

1300

1400

1500

1600

1700

1800

1384

2223

2516

2894

3 103

3103

2894

2432

2055

1468

797

1900 total

Above the forest 84

797

252 26002

Mobile sensors below canopy Eastern Track:

Central

Track:

Western Track:

42

126

210

377

629

377

4 19

252

168

126

84

94

188

470

658

282

470

188

282

94

94

126

2 10

4 19

587

335

4 19

252

2 10

168

42

42

2810 2820 2810

Stationary sensors below canopy West: East:

South:

a At

42 108

42

167

501

167

626

250

501

209

125

42

42

2714

42

377

7 13

67 1

67 1

252

2 10

2 10

2 10

42

42

3440

433

541

433

54 1

433

108

2 16

2 16

108

3 137

this longitude Local Apparent Time is 2.5 min behind Eastern Standard Time (E.S.T.).

t>:> �

22

TABLE III Daily global radiation (kJ m -2) above (Open) and below the canopy at mobile and stationary locations Mobile sensors Date Aug.

Eastern track

5

3020

2915

2978

2684

2633

2600

10

2810

2820

2810

11

2810

2727

2726

12

2 139

1881

2097

13

2349

2 163

2307

18

2706

2474

2257

3

Stationary sensors Date Aug.

Oct.

Western track

7

Southend mobile

Northend mobile Oct.

Central track

10 1 1

1008

Open

West

East

South

5

25950

2253

4068

3031

7

2 1934

2295

3355

2706

10

26002

2714

3440

3137

11

2533 1

2838

3 145

3139

12

19627

1920

2307

2 165

13

19040

2253

2936

2381

18

24660

2402

3923

2432

3

15266

924

1251

798

Finally, at location South-stationary, hourly radiation had two identical maxima in the hours ending at 10 a.m. and at 12 noon that were considerably less than the daily maximum at any other stationary or mobile location below the canopy. While the spacing of the trees was uniform and the distribution of gaps in the canopy appeared even, the variability of hourly-integrated records gave rise to concern over the relatively small separation of distance between the mobile sensors. The question arose as to whether the mobile data constituted independent observations or whether the closely spaced mobile sensors viewed the same or similar transmission features of the canopy over the tracks. Owing to multiple reflections and scattering of solar radiation by the forest, during the middle part of the day the diffuse component of global radiation is largely uniform over the forest floor (Gay et al., 1971). Thus, the answer to whether mobile sensors provided independent observations depends on how independently these sensors measured the direct-beam component on their separate tracks.

23

Calculated speeds with which the shadows of the top of an average-size

tree and of its lowest living branch moved at the level of the sensors are

0.21 m min-1 and 0.12 m min- 1 , respectively, an order of magnitude slower

than the speed at which the mobile sensors moved at 4 m min- 1

•

Further­

more, if one assumes that sunflecks moved at speeds somewhere in between

the speeds of these shadows, the implication is that when one mobile sensor encountered a sunfleck while the others were in shade, something commonly

observed in this study, it would be unlikely that the same sunfleck could be encountered by the other sensors.

The physical reality, however, is that sunflecks do not move. They form

and form anew continuously, their size, shape, and spatial distribution

varying at any horizontal level owing to the movement of the radiation

source and to the three dimensional distribution of canopy gaps; different

size gaps line up at different times at different angles of incidence. Because

it is the direct-beam component of global radiation in the forest that varies

spatially on clear days, one must conclude that the three mobile sensors

provided independent samples of the direct-beam component of global

radiation.

The maximum hourly radiation integrated by the three mobile sensors

did not always occur simultaneously, or at the same time of the day. For example, on day 1 these maxima occurred during the hour ending at 1 p.m.

above the forest and at 11 a.m. at the mobile locations. On day 7 the

maximum hourly amount of radiation above the canopy occurred for two

consecutive hours ending at 12 noon and at 1 p.m. The East-mobile and

Central-mobile sensors had their maxima during the hour ending at 1 p.m.

while the West-mobile records showed it at 11 a.m. In contrast to the

relatively small spacing of the mobile sensors, the stationary ones were some

40 m distance apart. Still, on three out of seven days the maximum hourly

amounts of global radiation were recorded for the same hour at each

stationary location, and on the other four days at least two of the three stationary sensors registered maxima for the same hour of the day. It appears that hourly totals of global radiation below canopy were influenced primarily by the amount available above the forest. Canopy

features, under which the records were collected, played a secondary role.

Hence, whenever the hours of maxima coincided for several sensors on any

day, the amounts of radiation varied from sensor to sensor, and one could not conclude that these sensors had viewed identical transmission features of the canopy, only that they measured more global radiation during that hour than in other hours. The independence of the data from the various sensors was difficult to test because of the common underlying patterns of high and low radiation

days, and of high and low radiation periods within a day; high at midday, low at the start and end of a day. An approximate comparison between the

two categories of sampling was done by calculating a correlation coefficient for each pair of the six below-canopy sensors (Table IV), using both hourly and daily data (Table III).

24 TABLE IV Correlation coefficients (1') for each pair of the six below-canopy sensors using hourly and daily integrated global radiation

Mobile-mobile

Hourly radiation

Daily radiation

Eastern track and Central track

0.84

0.81

Central track and Western track

0.66

0.76

Eastern track and Western track

0.87

0.79

Stationary--stationary

Hourly radiation

Daily radiation

West and East

0.38

West and South

0.29

0.58

East and South

0.64

- 0 . 15

Mobile- stationary

Hourly radiation

Eastern track and South

0.41

0.53

Central track and South

0.35

0.73

- 0. 16

Daily radiation

Western track and South

0.65

0.85

Eastern track and East

0.58

0.38

Central track and East

0.61

0.5 1

Western track and East

0.63

0.12

Eastern track and West

0.16

0.34

Central track and West

0.16

0.23

Western track and West

0.17

0.33

It appears that the mobile-mobile correlations were higher than the stationary-stationary ones both for hourly and daily records. While the mobile-mobile correlation coefficients were about the same from hourly and daily records, the stationary-stationary ones were higher from hourly data than from daily radiation records. This may be an indication of the strong influence the above-canopy radiation exerts on the below-canopy radiation estimates. The higher coefficients among mobile sensors was not the result of the mobile sensors receiving radiation through identical canopy gaps more often than the stationary ones, but because below-canopy radiation fluctuated with above-canopy radiation and its mobile integration below the canopy was more sample-efficient than stationary integration. When signals were integrated over an entire day, the location-to-location variations were further reduced oy the apparent movement of the sun scanning the various canopy features from dawn to dusk. Seven clear or nearly clear days in early August provided the daily integrated records (Table III) for a statistical comparison of the mobile and stationary sampling methods. The technique used was the "Randomized Block" analysis that separated the variation from the overall mean of transmitted global radiation into three sources:

25

% radiation = overall mean

error In

+ sensor location effect + date effect + random

this model the interaction effects between location and date were

included in the random error. The analysis of variance is summarized in Table V. The basic questions to be answered by the analysis were as follows:

(1) Which of the two methods of sampling resulted in estimates of trans­

mitted global radiation least variable from location to location? The F-test

of the ratio of mean square differences gave: F =

MS (stationary location - error) MS (mobile location - error)

72.3[Fo.9S(2 .2 )

=

=

27.961 -1.644 0.612 -0.248

19.0]

This was significant at the upper 5% level, indicating that mobile sensors had significantly less variation from location to location than stationary

sensors. This result confirms known analyses of the response of moving

radiometers (Herrington et al., 1972) according to which the travel of a

sensor through high and low frequency signals reduces the peak amplitudes at higher frequencies without affecting mean values. Because the higher

frequency data are removed the variance and higher-order statistics are

reduced in magnitude. It is not possible in the current study to separate

the effects of the apparent movement of radiation source above the stand from the movement of the radiometers below the canopy.

(2) Were the three mobile locations significantly different among them­

selves? The F-test compared variations due to location of the mobile sensors

against variations due to random error

F

0.612

MS (mobile locations) =

MS (error)

=

0.248

=

2.47 [FO.9S(2 .12 ) = 3.89]

This was found not significant, indicating no variation among the mobile

locations other than that caused by the random error attached to each record.

(3) Were the three stationary locations significantly different among

themselves?

The

F-test

compared

the effects due to locations of the

stationary sensors to those of random error

F=

MS (stationary locations)

27.961 =

MS (error)

1.644

=

17.0 [FO•99(2 .12 ) = 6.93]

This was highly significant at the upper 1% level, indicating that location

affected measurements obtained '.'lith stationary sensors.

(4) Was the location to location variation of daily transmitted global

radiation a function of the total global radiation above the stand? To

examine this question the mean per cent radiation on each date for both

26

TABLE V The analysis of variance of transmitted global radiation on seven clear days in August

to compare mobile and stationary records

,

Mobile sensors Source

Location Date Error

adf

=

dfi

Sum of

squares (SS)

Stationary sensors Mean squares (MS)

Sum of

Mean

squares (SS)

squares (MS)

2

1.224

0.612

55.923

27.961

6

11.381

1.897

10.093

1.682

12

2.971

0.248

19.734

1.644

degrees of freedom.

mobile and stationary locations was plotted against the global radiation above the stand. There was no indication of any trend for either mobile

or stationary locations.

To test whether the random error present in the data was significantly

greater for the stationary than the mobile locations, the root-mean-square

average random error components were calculated as follows random componen�mobiles)

= MS (errorm ) 1/2

random component(stationary)

=

0.248112 = 0.498

= MS (errors) 1I2 = 1.644112 = 1.282

The F-test was set up as

F=

MS (errors) MS (errorm)

=

1.644 0.248

= 6.63 [F 0.99(12,12) = 4.16]

The random error component at all radiation levels was found to be significantly greater at the upper mobile locations.

1% level for the stationary than the

To illustrate the importance of the sun elevation in affecting the choice of the sampling method, the hourly records of one clear October day are shown in Table VI. The two mobile sensors ran on a single track on an identical path along 14 m of the 16 m total track length. With low sun angles,

considerably

less

radiation

penetrated

the

forest.

The

mobile

sensors gave an average transmission of 6.61%. There was less variation

among the stationary records this time compared to the seven days in August.

The

two

mobile

sensors gave identical results confirming the

conclusion based on the seven earlier clear days, namely, that the mobile

records are reproducible. CONCLUSIONS

While the analyses considered in this work are restricted to clear days at one time of year and uniform pine stands, they are conclusive on the reproducibility of mobile records, and indicate that the mobile method

'

TABLE VI Global radiation (kJ m -2) in each hour ending at E.S. T. a shown, and for the whole day, on a clear day in October Time reference 0700

0800

Daily

0900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1342

1845

2055

2391

2265

1971

1384

755

335

84

total

A bove the forest 42

797

15266

Mobile sensors below canopy on virtually identical paths Northend

Southend

Mobile:

Mobile:

126

126

210

168

168

84

84

42

42

126

211

169

169

126

84

42

42

1008 1011

Stationary sensors below canopy West: East:

South: a At

42

126

126

126

168

126

84

84

42

924

83

125

167

167

376

125

83

83

42

1251

42

84

126

168

84

126

84

42

42

798

this longitude Local Apparent Time is 2.5 min behind Eastern Standard Time �E.S.T.).

t>:> -J

28

of characterizing global radiation transmitted through a forest canopy is more sample-efficient than the use of stationary sensors. Hourly and daily integrated radiation records were analyzed to examine the assumptions basic to the theory of mobile sampling, and dawn to dusk integration of radiation was shown to be significant in overcoming spatial and temporal variations in global radiation in a relatively uniform stand. It was evident from the analysis that, for situations similar to those in the experiment, a single mobile sensor would give more accurate results than a single stationary sensor. Because of the efficiency of the mobile method, relative gain from additional mobile sensors would be less than for adding stationary sensors when mobile sampling could not be done. ACKNOWLEDGEMENTS

Mr P.J. Litwin constructed the mobile system and was responsible for the collection and evaluation of radiation records. The statistical comparison of the mobile and stationary sampling was done by Mr. D.A. MacLeod. REFERENCES Brown, G.W.,

1973. Measuring transmitted global radiation with fixed and moving

sensors. Agric. Meteorol., 1 1: 115-121.

Gay, L.W., Knoerr, K.R. and Braaten, M.O., 1971. Solar radiation variability on the floor of a pine plantation. Agric. Meteorol., 8: 39-50.

Herrington, L.P., Leonard, R.E., Hamilton, J.E. and Heisler, G.M., 1972. The response of moving radiometers. Boundary-Layer Meteorol., 2: 395-405.

Monteith, J.L., 1972. Survey of Instruments for Micrometeorology. I.B.P. Handbook No. 22, Internat. BioI. Program, London, 263 pp. Mukammal,

E.!.,

1971. Some aspects of radiant energy in a red pine forest. Arch.

MeteoroI., Geophys. BioklimatoI., Ser. B, 19: 29-52.

Pech,

Gy.

and

communities.

King, In:

K.M.,

Proc.

1967.

First

Characterization

Canadian

Conf.

on

of

visible

radiation

Micrometeorol. Part

Transport, Met. Branch, Toronto, Canada, 1965, pp. 5 1-81.

in

plant

I. Dept.

Pike, J.M., 1972. A stable integrator for millivolt signals. In: Facilities for Atmospheric Research, No. 21 Nat. Ctr. for Atmospheric Res., Boulder, CO, U.S.A., pp. 1 1-13.

Reifsynder, W.E., Furnival, G.M. and Horowitz, J.L., 1971/ 1972. Spatial and temporal distribution of solar radiation beneath forest canopies. Agric. Meteorol., 9: 21-37.

Robinson, M.W., 1947. An instrument to measure forest crown cover. For. Chron., 3: 222-225.

Rodskjer, N. and Kornher, A., 1971. Uber die Bestimmung der Strahlungsenergie im

Wellanliingenbereich von 0.3-D.7 f.1 in Pflanzenbestanden. Agric. Meteorol., 8: 139150.

Sinclair, T.R., Desjardins, R.L. and Lemon, E.R., 1974. Analysis of sampling errors with traversing radiation sensors in corn canopies. Agron. J., 66: 214-217.

Sinclair, T.R. and Knoerr, K.R., 1972. Measurement of radiative transfer processes in a loblolly pine forest. Triangle Res. Site, Eastern Deciduous Forest Biome, Durham,

U.S.A., Memo Rep. No. 72-75, 13 pp.