NEW EMPIRICAL RELATIONSHIPS FOR DETERMINING GLOBAL PAR FROM MEASUREMENTS OF GLOBAL SOLAR RADIATION, INFRARED RADIATION OR SUNSHINE DURATION

Transcription

1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 20: (2000) NEW EMPIRICAL RELATIONSHIPS FOR DETERMINING GLOBAL PAR FROM MEASUREMENTS OF GLOBAL SOLAR RADIATION, INFRARED RADIATION OR SUNSHINE DURATION S.O. UDO a, * and T.O. ARO b a Department of Physics, Uni ersity of Calabar, Calabar, Nigeria b Department of Physics, Uni ersity of Ilorin, Ilorin, Nigeria ABSTRACT Data on global solar radiation (H), global photosynthetically-active radiation (PAR), downward infrared sky radiation (IR) and sunshine duration (n) for a 2-year duration are analysed on monthly (monthly mean of daily values) basis at Ilorin (8 32 N, 4 34 E), Nigeria. The data were taken using a precision spectral pyranometer, quantum sensor, pyrgeometer and Campbell Stokes recorder, respectively. Two thermistor circuits were built into the pyrgeometer for monitoring the dome and body temperatures so as to take care of the dome heating effect. From monthly values of IR, PAR and H, a correlation model relating the three parameters was established and is of the form: IR= f p, where f p is the ratio of PAR to H. Further analysis showed that the use of maximum likelihood quadratic fit to relate the three parameters does not improve the coefficient of determination. Also from the monthly mean values of PAR and n, equations of the Angstrom Prescott one-parameter model of linear and quadratic forms are developed for the estimation of global PAR at this location and locations with similar climatic conditions. The advantage of these models over the traditional method of estimating PAR, by assuming it to be of constant ratio to insolation, is that PAR can be estimated even at locations where insolation values are not available since they make use of only solar-related astronomical parameters (extraterrestrial radiation and maximum sunshine duration) and duration of sunshine. The results show that in practice, the simple linear regression model is sufficient and hence the use of a quadratic model is only slightly justifiable. On developing the models based on the two seasons (rainy and dry) encountered here, the rainy season model showed a high correlation coefficient, R, of against the poor R of for the dry season. The poor correlation during the dry season period is probably due to large differences in the characteristics of the sky during this period. Copyright 2000 Royal Meteorological Society. KEY WORDS: global solar radiation; global photosynthetically-active radiation; downward infrared sky radiation; sunshine duration; empirical relationships; Nigeria 1. INTRODUCTION Radiation components used for this study are global solar radiation (H), global photosynthetically-active radiation (PAR) and downward infrared radiation (IR). Their importance and hence reasons for wanting to estimate them are highlighted below. Solar electromagnetic radiation is recognized as the primary and almost the sole source of energy for myriads of physical and biological processes on planet Earth. It is the most fundamental renewable energy source in nature. Detailed and reliable information on the spatial and temporal variability is needed to provide input in modelling solar energy devices and a good database is required in the work of energy planners and engineers. Apart from the broad-band information being important, information on the spectral distribution (e.g. PAR nm bandwidth) could also be useful for the estimation of the amounts of radiation which * Correspondence to: Department of Physics, University of Calabar, Calabar, Nigeria; soudo@unical.anpa.net.ng Copyright 2000 Royal Meteorological Society

2 1266 S.O. UDO AND T.O. ARO are available for photosynthesis processes of all biotic systems (Raschke et al., 1991). PAR is also one of the important components of microclimate critical for forest regeneration (Chen et al., 1993). Surface net energy is an important variable in the surface energy budget. It represents the energy flux available for the transport of the sensible and latent heat to the atmosphere above and the soil below (Duchon and Wilk, 1994). One important component of the surface net energy radiation is the downward infrared sky radiation. This longwave emission from the atmosphere is a very important energy flux, since in its absence, the global average temperature would be at C cooler than it actually is (Sellers, 1965). The knowledge of this component of the Earth s surface energy budget is necessary for many meteorological studies, e.g. forecasting of diurnal temperature variations, nocturnal frosts and fogs. Interest has also grown in the use of radiative cooling of buildings at night (Catalanotti et al., 1975). Infrared radiation is also an important element of the energy balance of buildings, greenhouses, solar collectors and vegetation leaves. Its quantification is necessary to estimate correctly the radiative heat loses of these systems (Aubinet, 1994). From available literature, relationships have been found to exist between global solar radiation and photosynthetically active radiation, downward infrared sky radiation and objective ground measured meteorological variables like air temperature, water vapour pressure and clearness index. However, no relationship has been reported relating global solar radiation, global PAR and downward infrared sky radiation together. Since a worldwide routine network for the measurements of PAR is not yet established (Gueymard, 1989a,b; Papaioannou et al., 1993; Udo and Aro, 1999b), the practice has been to calculate PAR as a constant ratio of the broadband solar radiation. Hence, many reports are available in the literature to estimate PAR from the more routinely measured parameter of solar radiation (McCree, 1966; Szeicz, 1974; Britton and Dodd, 1976; Stanhill and Fuchs, 1977; Stigter and Musabilha, 1982; Blackburn and Proctor, 1983; Howell et al., 1983; Rao, 1984; Weiss and Norman, 1985; Gueymard, 1989a,b; Karalis, 1989; Slomka, 1989; Papaioannou et al., 1993), light intensity (Nathan, 1984) and cloud amount (Nathan, 1986). Apart from fundamental models (e.g. Berdahl and Fromberg, 1982; Morcrette and Fouquart, 1985; Morcrette et al., 1986) which have little use for practical application, simpler models exist which relate infrared sky radiation and meteorological parameters measured at ground level for clear skies (e.g. Brunt, 1932; Swinbank, 1963; Idso and Jackson, 1969; Brutsaert, 1975; Satterlund, 1979; Idso, 1981) and cloudy skies (Berdahl and Fromberg, 1982; Centeno, 1982; Kimball et al., 1982); Ineichen et al. (1984), Aubinet (1994) and Udo (1999a) presented correlations between infrared sky radiation and objective ground measured meteorological variables. No relationship seems to exist relating the three radiation components in the literature. This is due to limitation of the data set in terms of duration or the fact that these three radiations are hardly measured simultaneously at a particular location. For example, hardly a whole year of data is reported for PAR. In this article, a relationship relating these three radiation components is presented. This relationship, it is hoped, will help in estimating any of these components provided any two of them is measured or estimated and will also open a new direction to researchers in the field. Several investigators have also demonstrated the predictive ability of the Angstrom-Prescott oneparameter equation correlating global solar radiation to relative sunshine in a simple linear form (for example, Angstrom, 1924; Black et al., 1954; Glover and McCulloch, 1958; Massaquoi, 1958; Swartman and Ogunlade, 1967; Rietveld, 1978; Ogelman et al., 1984; Turton, 1987; Veeran and Kumar, 1993; Bashahu and Nkundabakura, 1994) and maximum-likelihood quadratic form (Ogelman et al., 1984; Akinoglu and Ecevit, 1993; Fagbenle, 1993). However, no such relationship is reported correlating PAR to relative sunshine. As stated earlier, PAR has always been calculated as a constant ratio of global solar radiation. This therefore presumes that insolation values are available. In this work, a relationship is developed (similar to the Angstrom Prescott one-parameter model) between PAR and relative sunshine. This equation is important because it enables us to estimate PAR even if the insolation values are not known.

3 PAR, SOLAR AND INFRARED RADIATION RELATIONSHIPS 1267 Ilorin, the town in which the study site is located, is about the mid-point of Nigeria with coordinates: 8 32 N; 4 34 E; altitude 375 m. The prevailing winds in Ilorin, as in the whole West African sub-region, are the south-westerly (SW) and the north-easterly (NE) trade winds. The SW wind blows from the Atlantic Ocean and brings rain to the West African Coast from about April to October (this is the rainy season). The NE wind, a very dry wind, blows across the country between November and March bringing the Harmattan dust with it (this is the dry season). More information on the geography of Ilorin are reported in Udo and Aro (1999b). 2. DATABASE AND METHOD OF ANALYSIS The analysis is based on data collected at Ilorin for a 2-year period (September 1992 August 1994). The data were collected using the following radiometers: Precision Spectral Pyranometer (Eppley-PSP), quantum sensor (LI-Cor) and pyrgeometer (Eppley-PIR) for global solar radiation, photosynthetically active radiation and downward infrared sky radiation, respectively. The associated recording instrument was a Campbell-CR10 data logger and its peripheral, a storage module. The datalogger was programmed to 2-s sampling rate and 3-min integration time. The radiometers were calibrated at the beginning and end of the data collection. Data reduction in terms of downward infrared sky radiation was based on the Albrecht et al. (1974) equation which takes care of the dome heating effect. Quantification of the dome heating effect for this location is reported in Udo (1999b). Data analysis was on an hourly basis. Other details concerning the radiometers are described elsewhere (Udo, 1997; Udo and Aro, 1999a). The daily sunshine duration, n, was obtained from the Nigerian Meteorological Services, Oshodi, Lagos and was measured at Ilorin Airport (a distance of about 12 km from the project site). This is within the permitted range in which radiation-sunshine data can be reliably extrapolated (WMO, 1981; Baker and Skaggs, 1984). Daily sunshine duration were measured using a Campbell Stokes recorder with heat sensitive paper. The units (daily) of measurement of H and IR were MJ/m 2 while that of PAR was E/m 2. In this analysis, a relationship is sought between IR and f p (=PAR/H), which in effect gives the relationship relating IR, PAR and H. The values used in the analysis are monthly means of daily values. On the relationship between PAR and number of sunshine hours, the equations are of the form: K TP =a+bs, for the linear form, and, K TP =a+bs +CS 2, for the quadratic form. Here K TP (=PAR/H 0 ) is the PAR clearness index and S (=n/n 0 ) is the relative sunshine. All values are the monthly averages of the daily values. H 0 is daily extraterrestrial radiation and is determined as presented in Appendix A; n is the daily sunshine duration and N 0 is the maximum sunshine or daylength. N 0 is calculated as presented in Appendix A. The predictive efficiencies of the correlation models will be tested (dependent test) using the following parameters: mean bias error (MBE), mean absolute bias error (MABE) and root mean square error (RMSE). These terms are defined by the following equations: MBE= N 1 MABE= (y i x i ) N, (1) N 1 ( y i x i ) N, (2)

4 1268 S.O. UDO AND T.O. ARO Figure 1. Daily variation of the ratio of PAR to H, f p (E/MJ), and infrared radiation, IR (MJ/m 2 ) N (y i x i ) 2 1 RMSE=, (3) N where y i is the ith predicted value, x i is the ith measured value and N is the number of observations. Although MBE is not a good measure of fit because large positive deviations can be balanced by large negative to yield a small sum even when the fit is poor, this sum is informative about the long-term predictive values of the estimation (Akinoglu and Ecevit, 1993). For MABE, they observed that although it does not yield information on whether the correlation is overestimating or underestimating, it gives information about the performance of the correlation. They further asserted that a small number of large deviations of the calculated values from the measured values can substantially increase RMSE; however, it gives information on short term predictive quality of a correlation. 3. RESULTS AND DISCUSSION 3.1. Empirical relationship relating PAR, IR and H The daily values of f p and IR are presented in Figure 1, while their respective monthly values are presented in Table I. A look at Figure 1 and Table I shows that there is a strong relationship between these two parameters. Consequently, a regression equation was established relating these two parameters. The model was of the form: Table I. Comparison of measured and predicted (based on Equation (4)) infrared sky radiation Month f p IR (measured, P m ) (E/MJ) (MJ/m 2 ) IR (predicted, P p ) Absolute percentage difference (MJ/m 2 ) ( P p P m /P m ) 100% January February March April May June July August September October November December

5 PAR, SOLAR AND INFRARED RADIATION RELATIONSHIPS 1269 Figure 2. Daily variation of global solar radiation, H (MJ/m 2 ) and global photosynthetically-active radiation, PAR (E/m 2 ) IR= f p, (4) with a coefficient of determination, R 2, of (correlation coefficient, R=0.9347). The regression equation was significant at the 95% confidence level. The dependent test carried out shows that agreement with measured values was better than 4% (see Table I). This shows that the regression model is reliable, not minding the obvious limitation imposed by a dependent test. The MBE, MABE and RMSE values were , and MJ/m 2, respectively. From these values, the performance of this model is quite satisfactory. Following the methods of Ogelman et al. (1984) and Akinoglu and Ecevit (1993) for the relationship between global solar radiation and sunshine duration, a maximum-likelihood quadratic fit resulted in: IR= f p,+1.01f p2, (5) with R=0.9347, the same as the linear type of equation (Equation (4)). Hence, it can be seen that the use of the quadratic model is not justified. The existence of a strong relationship between f p and IR is expected. f p has been found to depend on the moisture content of the atmosphere (Udo and Aro, 1999b) besides other factors like cloudiness (McCree, 1966; Stigter and Musabilha, 1982; Howell et al., 1983; Rao, 1984; Papaioannou et al., 1993; Udo and Aro, 1999b), daylength (Szeicz, 1974; Britton and Dodd, 1976) and insolation (Britton and Dodd, 1976; Udo and Aro, 1999b); infrared sky radiation is also found to depend on moisture content (Aubinet, 1994; Udo, 1997) Empirical relationship between PAR and sunshine duration Since PAR is a component of and its pattern of variation is the same as that of global solar radiation, H (see Figure 2; Howell et al., 1983 for daily variations), and since there exists a relationship between clearness index K T (=H/H 0 ) and relative sunshine S, it was reasonable to suspect that there should also exist a relationship between what is referred to here as the PAR clearness index and S. The regression models obtained in terms of linear models were: and K TP = S, R=0.8715, (6) K TP = S, R=0.9001, (7) for 1993 and 1994 data sets, respectively. Using Equation (7) to predict 1993 data and Equation (6) to predict 1994 data (double cross-validation method) showed that the agreement with measured values is better than 10%. Hence, the method of data splitting and its accompanying double cross-validation technique introduced no difficulties, since the estimation data set and the prediction data set did not differ much in coefficient of estimates.

6 1270 S.O. UDO AND T.O. ARO Since the models developed from the estimation data sets were satisfactory predictors, one way to improve the precision of estimation was to re-estimate the coefficients using the entire data; in this case, the 2-year monthly averages. The regression model with its correlation coefficient was: K TP = S, R= (8) The value of a=0.47 is a measure of PAR received at the ground through an overcast sky as a fraction of the extraterrestrial radiation (i.e. PAR transmissivity of an overcast atmosphere). The coefficient b, which has a value of 0.99, expresses the rate of increase of K TP with increase of S. For a clear sky, S becomes unity and the parameter (a+b) which in this case is 1.46 is a fraction of extraterrestrial radiation that reaches the Earth surface; that is, the transmissivity of PAR under perfectly clear sky conditions. In using the above equation, one has to be aware of the different units used; PAR is in E/m 2 while H 0 is in MJ/m 2, hence the unit K TP and a are in E/MJ. The difference in units and problems associated with it have been discussed elsewhere (Howell et al., 1983; Udo and Aro, 1999b). Using the ratio of photon flux to PAR energy flux of 4.57 E/MJ proposed by McCree (1972), Equation (8) becomes: K TP = S. (9) To test further the predictive ability of Equation (8), the percentage difference (dependent test) between the measured and predicted values of PAR were determined (see Table II). The analysis shows that apart from the 11% difference obtained for the month of December, all other differences were much lower than 10%. This again shows that the regression model is reliable. The MBE, MABE and RMSE were , and E/m 2, respectively. The corresponding quadratic-fit model for the average of the two years (i.e. the equivalent of Equation (8)) was: K TP = S 1.85S 2, R=0.9324, (10) when a logarithmic fit was applied the model was: K TP = ln S, R= (11) From the values of R, it can be seen that the use of a quadratic or logarithmic model only slightly improves the relationship between PAR and S. Carrying out the analysis on a seasonal basis, dry and rainy, leads to a rather poor correlation coefficient for the dry season period (November April) probably due to the large differences in the characteristics of the sky during this period. The respective equations and correlation coefficients were: Table II. Comparison of measured and predicted PAR (from Equation (8)) Month H o (MJ/m 2 ) S Measured PAR, P m Predicted PAR, P p Absolute percentage difference (E/m 2 ) (E/m 2 ) ( P p P m /P m ) 100% January February March April May June July August September October November December

7 PAR, SOLAR AND INFRARED RADIATION RELATIONSHIPS 1271 K TP = S, R=0.5075, (12) and K TP = S, R=0.9793, (13) for dry and rainy season periods. A dry season at Ilorin consists of mainly two distinct periods: (i) the Harmattan period (mainly December and January) when cold and dust laden NE trade winds from the Sahara desert keep the atmosphere over Ilorin and its environs heavily overcast with dust for many days, with characteristic hazy and cloud-free weather conditions. Additionally, the site is surrounded by a large area of agricultural land and is subjected to a high dry season haze resulting from bush burning which is prevalent during this period; (ii) the cloud and dust-free period (November, February April) of mainly high irradiation and clear weather conditions. The rainy season (May October) model was quite satisfactory. The two equations are highly informative: as expected the coefficient, a, for the dry season is higher than that of the rainy season. However for estimation purposes generally, Equations (8) and (10) are preferred. It is suggested that more years of data are needed to validate satisfactorily the above models. Moreover, while it is appreciated that a number of meteorological and geographical parameters (e.g. sunshine hours, air temperature, relative humidity, cloud cover, latitude and altitude, precipitation) taken separately or jointly, may affect the magnitude of global PAR, the value of the correlation coefficient obtained in this study seems to point to the fact that the greatest influence is exerted by sunshine hours, as is the case for global solar radiation. No similar work is known to the authors in the literature for the comparison of these models. The lack of published work of this nature is probably due to the small data sets normally used hardly a full year of data are collected. The other reason could be that researchers are mostly used to the estimation of PAR as a constant ratio of global solar radiation. However, like the other Angstrom models, these models may be locality dependent, and as such may be applicable to localities with similar climatic conditions as Ilorin mainly. Therefore, data in terms of spread and duration are needed to test the universal applicability of this model. Again, though the equations may have limited applications, they do, however, open a new direction to researchers in the field. 4. SUMMARY AND CONCLUSIONS Analysis of the monthly mean values of daily global solar radiation, photosynthetically-active radiation and downward infrared sky radiation shows that these three parameters are highly related: hence Equation (4) could be used in estimating any of them if any two of these parameters are measured or estimated at this location and locations with similar climatic conditions, if not globally. The use of a higher power polynomial in establishing this relationship is found to be unjustified, as such models do not improve the coefficient of determination. With the corresponding monthly mean of daily values of sunshine duration, n, equations of the Angstrom Prescott one-parameter model of linear (Equation (8)) and quadratic (Equation (10)) forms are developed for the estimation of monthly mean daily PAR. This very important radiation component had always been calculated as a constant ratio of insolation. This presumes that insolation values are available. The advantage of Equations (8) or (10) is that PAR can be estimated purely by making use of the necessary solar-related astronomical parameters, extraterrestrial radiation and maximum sunshine hours, provided sunshine duration data are available. From the results it can be seen that in practice the simple linear regression model is sufficient and the use of the quadratic model or the logarithmic model is only slightly justifiable. The development of the models based on season is not justified even though a higher correlation coefficient (R=0.9793) is obtained for the rainy season period since the corresponding dry season model is rather poor (R= ), for the linear model.

8 1272 S.O. UDO AND T.O. ARO It is realized that more data are needed in terms of spread and duration to confirm these equations. They are mainly applicable in terms of seasonal (monthly or longer-term mean basis) estimations. For example, they may be very applicable for crop production estimations on a time scale of a growing season although it is insufficient for improving parameterizations of the dependence of stomatal conductance on absorbed PAR. However, it is hoped that these results will open a new chapter to researchers in this area. ACKNOWLEDGEMENTS The authors are grateful to the Department of Physics, University of Ilorin, Nigeria for providing the facilities used in this study. The expansion of the radiation centre to include a pyrgeometer, quantum sensor and data-logger was made possible by a grant from the USA Nigeria Cooperative Research Scheme, with Professor R.T. Pinker of the Department of Meteorology, University of Maryland, College Park, USA as the principal investigator and Professor T.O. Aro (co-author) as the other investigator. The guidance and contributions in terms of facilitating the measurements by Professor R.T. Pinker, Dr F. Miskolczi and Mr M. Iziomon are greatly appreciated. APPENDIX A. DETERMINATION OF H 0 AND N 0 H 0 (the daily extraterrestrial radiation) is evaluated from the equation (Iqbal, 1983): H 0 =(24/ )I sc E 0 {( /180) s (sin sin )+(cos cos sin s )}, where I sc =solar constant in energy unit=4921 kj/m 2 /h=1367 W/m 2 ; E 0 is the eccentricity correction factor of the Earth s orbit; is the solar declination; s is the sunrise hour angle; and is the geographical latitude. According to Spencer (1971): E 0 = cos sin cos sin 2, where, in radian, is the day angle and is defined by: =2 (d n 1)/365, where d n is the day number of the year. Solar declination is evaluated according to Spencer (1971) by: = cos sin cos sin cos sin 3 )(180/ ). (A4) The sunrise hour angle, s, is evaluated using: s =cos 1 ( tan tan ). The daylength, N 0 (=2 s ) when expressed in hours is as follows: N 0 =2/15 cos 1 ( tan tan ). (A1) (A2) (A3) (A5) (A6) REFERENCES Albrecht B, Poellot M, Cox SK Pyrgeometer measurement from aircraft. Re iew of Scientific Instruments 45: Angstrom A Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society 50: Aubinet M Longwave sky radiation parameterization. Solar Energy 53: Akinoglu BG, Ecevit A Comparison and discussion of eight sunshine-based correlations of global radiation. Turkish Journal of Physics 17:

9 PAR, SOLAR AND INFRARED RADIATION RELATIONSHIPS 1273 Baker DG, Skaggs RH The distance factor in the relationship between solar radiation and sunshine. Journal of Climatology 4: Bashahu M, Nkundabakura P Analysis of daily global radiation data for five sites in Rwanda and one in Senegal. Renewable Energy 4: Berdahl P, Fromberg R The thermal radiation of clear skies. Solar Energy 29: Black JN, Bonython G, Prescott JA Solar radiation and duration of sunshine. Quarterly Journal of the Royal Meteorological Society 80: Blackburn WJ, Proctor JTA Estimating photosynthetically active radiation from measured solar irradiance. Solar Energy 31: Britton CM, Dodd JD Relationships of photosynthetically-active radiation and shortwave irradiance. Agricultural Meteorology 17: 1 7. Brunt D Notes on radiation in the atmosphere. Quarterly Journal of the Royal Meteorological Society 58: Brutsaert W On a derivable formula for longwave radiation from clear skies. Water Resource Research 11: Catalanotti S, Cuomo V, Piro G, Ruggi D, Silverstrini V, Troise G Radiative cooling of selective surfaces. Solar Energy 17: Centeno VM New formula for the equivalent night sky emittance. Solar Energy 28: Chen JM, Black TA, Price DT, Carter RE Model for calculating photosynthetic photon flux densities in forest openings on slopes. Journal of Applied Meteorology 28: Duchon CE, Wilk GE Field comparisons of direct and component measurements of net radiation under clear skies. Journal of Applied Meteorology 33: Fagbenle RL Total solar radiation estimates in Nigeria using a maximum-likelihood quadratic fit. Renewable Energy 3: Glover J, McCulloch JSG The empirical relation between solar radiation and hours of sunshine. Quarterly Journal of the Royal Meteorological Society 84: Gueymard C. 1989a. An atmospheric transmittance model for the calculation of the clear sky beam, diffuse and global photosynthetically active radiation. Agricultural and Forest Meteorology 45: Gueymard C. 1989b. A two-band model for the calculation of illuminance and photosynthetically active radiation at the Earth s surface. Solar Energy 43: Howell TA, Meek DW, Hatfield JL Relationship of photosynthetically active radiation to shortwave radiation in the San Joaquin Valley. Agricultural Meteorology 28: Idso SB A set of equations for full spectrum and 8 to 14 m and 10.5 to 12.5 m thermal radiation from cloudless skies. Water Resource Research 17: Idso SB, Jackson RD Thermal radiation from the atmosphere. Journal of Geophysical Research 74: Iqbal M An Introduction to Solar Radiation. Academic Press: New York. Ineichen P, Gremaud JM, Guisan O, Mermoud A Infrared sky radiation in Geneva. Solar Energy 32: Karalis JD Characteristics of direct photosynthetically active radiation. Agricultural and Forest Meteorology 48: Kimball BA, Idso SB, Aase JK A model of thermal radiation from partly cloudy and overcast skies. Water Resource Research 18: Massaquoi JGM Global solar radiation in Sierra-Leone (West Africa). Solar Wind Technology 5: McCree KJ A solarimeter for measuring photosynthetically active radiation. Agricultural Meteorology 3: McCree J Test of current definitives of photosynthetically active radiation against heat photosynthetic data. Agricultural Meteorology 10: Morcrette JJ, Fouquart Y On systematic errors in paramerterized calculations of longwave radiation transfer. Quarterly Journal of the Royal Meteorological Society 111: Morcrette JJ, Smith L, Fouquart Y Pressure and temperature dependence of the absorption in longwave radiation parameterizations. Beiträge zur Physik der Atmosphäre 59: Nathan KK A note on the relationship between photosynthetically active radiation and light intensity. Arch Meteorol Geoph Bioclim Ser B 35: Nathan KK A note on relationship between photosynthetically active radiation and cloud amount. Idojaras 90: Ogelman H, Ecevit A, Tasdemiroglo E A new method for estimating solar radiation from bright sunshine data. Solar Energy 33: Papaioannou G, Papanikolaou N, Retalis D Relationships of photosynthetically active radiation and shortwave irradiance. Theoretical and Applied Climatology 48: Rao CRN Photosynthetically active components of global solar radiation: Measurements and model computations. Arch Meteorol Geoph Bioclim Ser B 34: Raschke E, Stuhlman R, Palz W, Steemers TC Solar Radiation Atlas of Africa. A.A. Balkema: Rotterdam. Rietveld MR A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine. Agricultural Meteorology 19: Satterlund DR An improved equation for estimating longwave radiation from the atmosphere. Water Resource Research 15: Sellers WD Physical Climatology. University of Chicago Press: Chicago. Slomka J Photosynthetic photon inflow, in relation to sunshine duration at Belsk. Publications of the Institute of Geophysics, Polish Academy of Sciences D32: Spencer JW Fourier series representation of the position of the sun. Search 2: Stanhill G, Fuchs M The relative flux density of photosynthetically active radiation. Journal of Applied Ecology 4: Stigter CJ, Musabilha VMM The conservative ratio of photosynthetically active radiation to total radiation in the tropics. Journal of Applied Ecology 19: Swartman RK, Ogunlade O Solar radiation from common parameters. Solar Energy 11:

10 1274 S.O. UDO AND T.O. ARO Swinbank WC Longwave radiation from clear skies. Quarterly Journal of the Royal Meteorological Society 89: Szeicz G Solar radiation for plant growth. Journal of Applied Ecology 11: Turton SM The relationship between total irradiation and sunshine duration in the humid tropics. Solar Energy 38: Udo SO Measurement and analysis of global solar and atmospheric radiations at Ilorin, Nigeria, PhD Thesis. Department of Physics, University of Ilorin, Nigeria. Udo SO. 1999a. On the relationship between downward infrared sky radiation and clearness index. Global Journal of Pure and Applied Science 5: Udo SO. 1999b. Quantification of solar heating of the dome of pyrgeometer for a tropical location: Ilorin, Nigeria. Journal of Atmospheric and Oceanic Technology (in press). Udo SO, Aro TO. 1999a. Measurement of global solar, global photosynthetically active and downward infrared radiations at Ilorin, Nigeria. Renewable Energy 17: Udo SO, Aro TO. 1999b. Global PAR related to global solar radiation for central Nigeria. Agricultural and Forest Meteorology 97: Veeran PK, Kumar S Analysis of monthly average daily global radiation and monthly average sunshine duration at two tropical locations. Renewable Energy 3: Weiss A, Norman JM Partitioning solar radiation into direct and diffuse, visible and near infrared components. Agricultural and Forest Meteorology 34: WMO Meteorological aspects of utilization of solar radiation as an energy source. Technical Note No. 172, WMO No. 557.