Monthly average solar radiation in panama—Daily and hourly relations between direct and global insolation

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  • SolarEnerg3, Vol. 39, No. 5, pp. 445-4.53, 1987 00384)92X/87 $3.00 + .00 Printed in the U.S.A. Pergamon Journals Ltd.



    P. BECKER* Smithsonian Tropical Research Institute, P.O. Box 2072, Balboa, Rep. of Panama

    Abstract--Regressions are developed to estimate daily global and direct radiation and the hourly distribution of direct radiation for Barro Colorado Island, Panama from monthly mean values observed 35 km away at Chiva-Chiva. The ratio model of Liu and Jordan and the logarithmic model of Anderson for estimating direct from global radiation are compared. Both gave satisfactory results after accounting for "seasonal" variation, but the ratio model was preferred in this case for the smaller number of separate regressions required. The ratio model fitted for diffuse radiation at Chiva-Chiva agreed closely with regressions for stations at similar latitude. For a given value of the clearness index, the direct component of solar radiation was relatively (but not absolutely) reduced during the dry season com- pared with the wet season. A likely explanation for this unexpected result is increased marine and terrestrial aerosol during the dry season when offshore winds are stronger and burning of crop and wasteland occurs. The models of Whillier and of Gamier and Ohmura, which assume constant at- mospheric transmittance throughout the day, gave unsatisfactory fits to the hourly distribution of direct radiation. They were also unable to mimic an observed morning/afternoon asymmetry that was strongest in the wet season. Hourly direct radiation was accurately estimated from hourly global radiation by quadratic polynomials fitted separately to the morning and afternoon data. The resulting regressions will enable estimation of radiation in forest understory from measurements of insolation in the open by computerized image analysis of hemispherical canopy photos.


    Quantification of solar radiation in forest under- story has been a long-standing problem for ecologists and foresters due to extreme spatial and temporal variability, especially for the direct component seen as sunflecks. A promising approach is the analysis of hemispherical canopy photos to estimate radia- tion at forest sites from measurements of solar ra- diation in the open[l-2]. The necessary observa- tions are monthly means of daily direct and global insolation and the hourly distribution of direct ra- diation on a horizontal surface. SYLVA, a newly developed, computerized image processing system, greatly facilitates application of this technique. Ecologists at the Smithsonian Tropical Research Institute's field station on Barro Colorado Island, Panama, will apply it to correlate plant growth, sur- vival, and distribution with insolation.

    Several thousand canopy photos were taken dur- ing 1982-1985 on Barro Colorado, but measure- ments of direct radiation were unavailable for this period. Global radiation measurements were avail- able for only some of the time. It was necessary, therefore, to obtain empirical relations to estimate the necessary radiation components for Barro Col- orado from more extensive observations made by the U.S. Army Met Team at Chiva-Chiva Antenna Farm 35 km to the southeast. These data are of general interest and there has been no previous pub- lication of solar radiation patterns in Panama. This

    * Current address: % World Wildlife Fund, 1250 Twenty-fourth St., N.W., Washington, D.C. 20037, U.S.A.

    article thus has the twofold purpose of preparing the database for the canopy photo analyses on Barro Colorado and of illustrating the relations among solar radiation components in Panama.



    Global radiation was measured at Chiva-Chiva Antenna Farm (902'N, 7935'W, 16 m a.s.l, ele- vation) with a 15-junction Eppley pyranometer mounted horizontally at an open, sloping site cov- ered with grass. The sensor was calibrated yearly against one of the same type maintained for this purpose and traceable to an Eppley absolute cavity pyrheliometer. Monthly reports are filed at the Technical Information Center of the U.S. Army Tropic Test Center, Ft. Clayton, Panama. Figure 1 shows monthly and annual variation in mean daily global radiation at Chiva-Chiva during 1972-1985. The dry season typicaUy begins in December or January and ends in mid-April or early May. Global radiation is about 1.5 times greater during this pe- riod than in the cloudier months of the wet season.

    Global radiation was measured at Barro Colo- rado Island (99'N, 7951'W, 90 m a.s.1.) by the Smithsonian Institution's Environmental Sciences Program. Readings were made with a Li-Cor LI- 200S pyranometer mounted horizontally atop a tower about 8 m above the canopy of semiever- green, tropical moist forest. The tower is at the base of the Lutz catchment, 450 m from the shore of Lake Gatun. Data were available for March 1983 through May 1985, during which period several fac- tory-calibrated sensors were used without recall-


  • 446



    N d 15

    1o d F M A M d d A S 0 N O MONTH

    Fig. t. Tukey box plots of monthly mean daily global ra- diation at the Chiva-Chiva Antenna Farm, Panama, during 1972-1985. The median, interquartile range, and adjacent values are indicated by the central line, box, and whisker ends, respectively. More extreme points are plotted in- dividually. N = 13 for January (data unavailable for 1972);

    N = 14 for remaining months.

    bration. The LI-200S sensor is not spectrally ideal, but no correction was made as the error for daily totals is typically

  • Monthly average

    estimated and observed values in December prob- ably resulted from eight days of missing data for Chiva-Chiva at the beginning of the month. This led to an overestimate of the average daily radiation there in this transitional month between wet and dry seasons.



    Over periods of at least a day, diffuse radiation is quite regularly related to the effective transmit- tance coefficient of the atmosphere, as first noted by Liu and Jordan[8]. This relation has been veri- fied at a large number of temperate and tropical sites[3, 9-11]. Because the direct and diffuse com- ponents of global radiation are complementary, a similar, but inverse, relation exists for direct radia- tion~ A lesser known model by Anderson[12] pro- posed a logarithmic relation between hourly or daily totals of direct and global radiation. The article ver- ifying this relation was apparently not published by the Quarterly Journal of the Royal Meteorological Society as cited by Anderson[12]. I therefore com- pared the Liu and Jordan and the b~nderson models, hereafter called the ratio and log models, respec- tively. For uniformity, I have generally adhered to the mathematical nomenclature of ref. [3]. For the sake of the canopy photo analyses, however, ref- erence is primarily made to the direct component of solar radiation instead of the traditional emphasis on the diffuse component.

    Diffuse radiation was measured at Chiva-Chiva during February 1972 through November 1980 with a 15-junction Eppley pyranometer mounted hori- zontally under an Eppley shadow band. For this study, monthly mean daily direct radiation was cal- culated as the difference between monthly mean daily global and diffuse radiation. The latter was corrected for shadow band obstruction using the monthly coefficients for latitude 10N in Table 1 of ref. [13].

    According to the log model, mean daily direct radiation Ht, is related to mean daily global radia- tion Hh as

    log Hb = a + b log nh (1)

    where a and b are empirical coefficients[12]. In the ratio model, Hb/Hh is related to Hhlno, the ratio of terrestrial to extraterrestrial radiation, which is the monthly average clearness index Kh (sensu ref. [3]). Substituting the spectral coefficients for lati- tude 9N in Table 2 of ref. [14], Ho (in ly day -a) as a harmonic series on the nth day of the year is given by

    Ho = 847.6 - 58.5 cos(2rm/365)

    - 35.7 cos(47rn/365) + 14.2 sin(2~rn/365) (2)

    + 14.0 sin(4rm/365)

    solar radiation 447

    Monthly means of Ho from (2) evaluated for every day of the year differed < 1% from values calculated for the fifteenth day of the month (solar constant = 1360 W m -2) by equation (5) ofref. [8]. The latter was, therefore, used as an excellent approximation to Ho in calculating Kh.

    Seatterplots of monthly mean daily direct and global radiation appropriate for the log and ratio models are shown in Figs. 3 and 4, respectively. The relation is slightly curvilinear in the log plot and linear in the ratio plot. Linear, least squares regressions (not shown) fitted to the data overall are: log Hb = -- 1.98 + 2.33 log-Hh (r z = 0.90) and HJHh = -- 0.14 + 1.26Kh (r z = 0.90). In both plots there is a clear tendency for the values of certain months to occur above or below the overall regres- sion line. The coefficients a and b of (1) depend on the time of year and prevailing climate[12]. Sea- sonal variation in the ratio model has also been noted[3, 15].

    Two approaches have been taken to account for seasonal variation in the ratio model--grouping the data by sunset hour angle[3] and transforming the ratios to eliminate variation in multiple reflection of radiation between the earth's surface and at- mosphere[15]. At 9N latitude the annual range of the sunset hour angle (evaluated on the fifteenth day of the month) is only 1.50-1.64 rad, which cor- responds to just one of the three classes employed in ref. [3]. Moreover, the monthly patterns of the data in Figs. 3 and 4 are apparently unrelated to variation in sunset hour angle. The second method was not feasible in this study because it requires information on percentage cloud cover, which was unavailable. Least squares regressions were there- fore fitted to various combinations of months for the log and ratio models. My goal was to obtain the


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    n A I : , , , , I , , , , I , , , I I , , , ~'"i i.i i.E _t.3 1.4

    LOGIo GLOBAL MJ m -~

    Fig. 3. Relation between logarithms of monthly mean daily direct and global radiation at Chiva-Chiva during February 1972 through November 1980. Months are coded 1-9 for January-September, respectively; then O, N, D for Oc- tober-December, respectively Lines fitted by linear regression of Iogto-transformed variables with April 1976 excluded as an outlier: Y = -2.07 + 2.40X, r 2 = 0.95 (Feb., May, June, Sep., Oct.); Y = -2.06 + 2.36X, r z = 0.97 (Mar., Apr., July, Aug.); Y = -2.24 + 2.63X, r 2 = 0.98 (Nov., Dee.); Y = -1.39 + 1.93X, r 2 = 0.92


  • 448 P. BECKER

    O.B RATIOS OF MONTHLY .,,.i 0 7~ MEAN DAILY RADIATION _..,,22 .~,,,"-- t ~ RAY-JUN. AUG-DEC ~.,l;Yi/" :

    O.5F 5 070 _d-'3

    O ~ s ' - : s - "(7.3 0.4 0.5 0.6 0.7 GLOBAL/EXTRATEPRESTRIAL

    Fig. 4. Relation between ratios of direct/global and global/ extraterrestrial for monthly mean daily radiation at Chiva- Chiva during February 1972-November 1980. Months are coded as in Fig. 3. Lines fitted by linear, least squares regression with April 1976 excluded as an outlier: Y = - 0.224 + 1.39X, r 2 = 0.94 (Jan.-Apr., July); Y = - 0.218

    + 1.48X, r z = 0.86 (May-June, Aug.-Dee.).

    smallest number of groups consistent with a linear relation and minimal monthly pattern in the resid- uals. The group regressions finally selected are de- picted in Figs. 3 and 4.

    The present database was too small to allow des- ignation of independent subsets for development and validation of the empirical model. Instead, a limited but still useful evaluation was made by cal- culating the deviation between observed values and the corresponding regression estimates as

    % difference = 100 [ predicted Hb

    - observed Hb I/observed Hb

    The results summarized in Fig. 5 show improved fit of the group compared with the overall regressions,

    MONTHLY , , , . . . . . . . . ,

    I I I T I t I i I I I = 0 20 40 60 BO 100



    [] 0-5 [] 5-10 [] 10-35


    Fig. 5. Frequency distribution of the absolute percentage difference between predicted and observed monthly mean daily direct radiation at Chiva-Chiva during February 1972-November 1980. Predictions were made by linear regressions for the ratio and log models fitted separately for each month, to the groups in Figs. 3 and 4, and to all 106 observations. April 1976 and October 1980 were ex- cluded from the monthly regressions and April 1976 was

    excluded from the group regressions as outliers.

    especially for the log model. Additional improve- ments were obtained when regressions were fitted separately for each month (regression lines not shown or specified).

    Reduced sample size in the separate monthly regressions made detection of outliers more diffi- cult, and points with high leverage may have unduly influenced the regressions. Therefore, the group regressions were preferred for predicting direct from global radiation outside the observation pe- riod. Although some monthly pattern remained in the group regressions (values for October in Fig. 3 and for January and November in Fig. 4 tend to occur above their group lines), estimated values dif- fered by less than 10% from observed in more than 80% of the cases (Fig. 5). The group regressions of the ratio model were chosen over those of the log model to estimate direct radiation on Barro Colo- rado in 1982-1985 (Table A2 of the appendix). This was because their estimation accuracy was com- parable (Fig. 5) and the sample sizes for the ratio model were larger due to the smaller number of groups. Although the ratio model was linear in this study, the log model may prove to be a preferable alternative when this is not the case.

    The data in Fig. 4 show a strong tendency for the ratio of direct to global radiation HJHh to in- crease with increasing clearness Kk, as is typically observed[3, 8-11, 15]. The dry season (December or January to mid-April) tends to be clearer than the wet season. Surprisingly, however, the group regression for January-Apri l and July lies below that for the remaining months of the year. This rela- tively minor "seasonal" pattern runs counter to the expectation of reduced scattering and an increase in the direct component with decreasing cloudi- ness[15]. A possible explanation is that extensive burning of crop and wasteland during the dry sea- son in Panama increases atmospheric particulates. This then leads to increased scattering of solar ra- diation. On exceptionally clear days or days with high total radiation (Kh = 0.76) at Kew, England, depletion of direct radiation by suspended matter accounted for 21-46% of the total depletion[23] so this effect could be important. It would be consis- tent with December being distinct from the re-...


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