Section 5.2 ESTIMATION OF DAILY SOLAR RADIATION OVER SOUTH AFRICA R.E. Schulze and R.D. Chapman

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1 Section 5.2 ESTIMATION OF DAILY SOLAR RADIATION OVER SOUTH AFRICA R.E. Schulze and R.D. Chapman Measurement and Estimation of Solar Radiation in South Africa: A Review up to the 1990s Systematic solar radiation measurements (commonly by a pyranometer or pyrheliometer) in South Africa commenced in the early 1950s and pioneering research on the spatial patterns of solar radiation, using very few data, was first published by Drummond and Vowinckel in Schulze and McGee (1978) updated summer and winter solar radiation patterns from subsequent radiation observations, while Reid (1981) used sunshine duration to derive solar radiation values over South Africa for each month of the year. Reid s distribution patterns, however, largely reflected the data from the network of sunshine recording stations he had at his disposal. Clemence (1992), realising that direct measurements of solar radiation (and even sunshine duration) were still relatively uncommon in South Africa, used over daily solar radiation observations from a wide geographic range of stations, and derived a single expression for South Africa to estimate solar radiation from extraterrestrial radiation (i.e. radiation at the top of the atmosphere, generated from first principles by standard equations), maximum daily air temperature (as a surrogate for solar radiation), and temperature range (as an index of humidity and cloudiness). Clemence s equation, explained in detail in the 1997 Atlas (Schulze, 1997) and mapped in that Atlas in conjunction with the 1 x 1 gridded temperature values, has been used as the most detailed study on the distribution of solar radiation in South Africa up to His equation is, however, a very general one, used to generate daily solar radiation across a region with widely divergent climatic conditions. A more region/season specific approach was therefore investigated by Chapman (2004) and subsequently by Schulze and Chapman, as reported in this section of the Atlas. The scientific background to the computations of solar radiation over South Africa is given in the shaded boxes. With the advent of automatic weather stations, most of which are operated by the SA Weather Service, the Agricultural Research Council, research organisations such as Universities and major agricultural sectors (e.g. the deciduous fruit and sugar industries), as well as with the potential to use satellite derived values of solar radiation, significant further improvements in the mapping of solar radiation patterns should be possible within the next decade. The Need for Accurate Daily Solar Radiation Estimates Since solar radiation (direct plus diffuse, R s ) provides the energy for photosynthesis, carbohydrate partitioning and biomass growth of individual plant components (Boote and Loomis, 1991) and, therefore, an entire crop or other vegetative cover in its various growth stages, it stands to reason that daily values of R s are required in estimations of crop yields and the effects of crop management practices (Mavromatis and Jagtap, 2005). Furthermore, solar radiation is the major driver and determinant of atmospheric water demand, i.e. potential evaporation (E p ) and daily estimates of R s are therefore required for detailed determinations of E p which, in turn, influence total evaporation (formerly termed actual evapotranspiration ) from a soil/vegetation surface, be it under irrigated or rainfed conditions. In the Penman-Monteith equation (Penman, 1948; Monteith, 1981), which has now become the internationally accepted reference for estimating E p, solar radiation is (under most conditions) the most sensitive input variable - further reason for daily estimates of R s, having to be made. However, the observation network of solar radiation stations in South Africa is relatively sparse, as well as not being representative of the physiography of the country and the records are frequently short, and often not of the desired quality either for direct use or for applications in model development as a result of instrument drift from calibrated values Section 5.2 Estimation of Daily Solar Radiation over South Africa 1

2 (Chapman, 2004). It has, therefore, become necessary to develop and verify techniques for estimating daily R s over South Africa using surrogate data. Approaches to Estimating Daily Solar Radiation A number of approaches have been developed to estimating daily R s at locations where it is not measured, the two main ones being stochastic weather generators, which are useful for risk analysis, but not for model verification or for the simulations of a specific historical period of time, as stochastic models do not generate values to match historical weather sequences (Liu and Scott, 2001); and empirically derived relationships, in which equations are developed relating R s to site specific surrogate variables which are readily obtainable or can be estimated for a given day and at a specific location with a high degree of confidence, and which have been found to be more accurate than weather generation. Many such empirically derived relationships have been presented and evaluated in the relatively recent literature, some notable and frequently used/cited ones being the R s equations by Bristow and Campbell (1984), Clemence (1992) for South Africa, Hunt et al. (1998), Liu and Scott (2001) or Donatelli et al. (2003) - all of which (plus others) have been reviewed and evaluated with South African data by Chapman (2004). Theoretical Basis for Deriving Empirical Equations for the Estimation of Daily Solar Radiation The estimation of daily R s is a complex one and the intensity of R s at any given location (including locations in hilly terrain) and time of year and day is influenced by five sets of factors (Robinson, 1966; Schulze, 1975), viz. astronomical, i.e. the solar constant, the radius vector (eccentricity of the earth s orbit) and solar declination (time of year), geographical, i.e. latitude and altitude (expressed through atmospheric pressure), physical, i.e. scattering by atmospheric aerosols (mainly dust) and the pure atmosphere (Rayleigh extinction) as well as absorption (mainly by water vapour), geometric, i.e. solar altitude and azimuth; slope steepness/gradient and hence topographic shading, and meteorological, i.e. cloudiness of the sky, as well as reflectivity from the earth s surface. From these five sets of factors, estimates of solar radiation on a horizontal surface at ground level may be partitioned into three components, viz. the determination of extraterrestrial radiation (astronomical and geographical factors), an estimation of the depletion of solar radiation under clear sky conditions, i.e. maximum transmissivity (geographical and physical factors), and the depletion due to cloud cover (meteorological factors). The practicalities of deriving empirical equations for estimation of daily R s revolve around the choice of commonly measured or easily determined surrogate climatic variables to account for variations in the depletion of solar radiation under clear sky conditions and the depletion due to cloud cover. The most commonly used variables are daily maximum and minimum temperatures, T mxd and T mnd, from which a daily temperature range, T ra, may be obtained. Justification of Use of Daily Maximum and Minimum Temperatures as Surrogate Variables to Estimate Solar Radiation The physical reasoning for choosing T mxd and T mnd is provided by Richardson and Reddy (2004): Clear skies result in high solar radiation loadings to reach the earth s surface, resulting in rapid warming of the surface/atmosphere (i.e. high T mxd ), but clear sky conditions will also allow terrestrial infrared (longwave) radiation to escape into space at night, allowing rapid cooling of the surface/atmosphere (i.e. low T mnd ), resulting in a large temperature range, T ra (i.e. T mxd - T mnd ). Conversely, cloudy conditions and rainfall reduce day time surface - incident solar radiation (because of a lower T mxd ), with the clouds also absorbing and re-radiation more terrestrial radiation at night, thereby restricting the cooling rate (ˆ higher T mnd ), resulting in a lower T ra Section 5.2 Estimation of Daily Solar Radiation over South Africa 2

3 (i.e. T mxd - T mnd ). Hence T mxd and T mnd, particularly when expressed through T ra, are highly suitable surrogate variables for use in estimating R s. The Bristow and Campbell Model for Estimation of Daily Solar Radiation The Bristow and Campbell (1984) model, which has been used in many studies and to which some important improvements have been suggested/developed over the past few years (e.g. Goodin et al., 1999; Liu and Scott, 2001), exploits (Mavromatis and Jagtap, 2005) the relationship between diurnal air temperature range and irradiance load to estimate the daily flux of incoming R s. This equation essentially describes solar radiation as an exponential asymptotic function of daily T ra as follows: where while R s = ar a [1 - exp (- bt ra c )] R a = extraterrestrial radiation = f (the solar constant, the earth s radius vector, latitude and solar declination, i.e. an expression of time of year) a = clear sky atmospheric transmissivity of R a = 0.75 in the Bristow and Campbell equation, and which represents the depletion of R a due to scattering by atmospheric aerosols (mainly dust) and the pure atmosphere (Rayleigh extinction), as well as absorption by water vapour b, c = empirical constants governing the depletion of the solar beam due to cloudiness and rainfall, and for which daily T ra is used as an estimator on the premise that cloudy/rainy conditions are associated with high atmospheric humidity and hence a low diurnal T ra while under clear skies high temperature ranges prevail. Modifications to the Bristow and Campbell Equation for Application over South Africa Since the Bristow and Campbell approach is fundamentally sound, it was used as the point of departure for determining daily R s at points where no direct observations of R s were made. A number of assumptions in the equation were revisited and modifications made for its application in South Africa. 1. Revisiting the Concept of a Clear Sky Transmission Constant Relatively little research attention has focussed on estimating variations, with location and season, in atmospheric transmissivity under clear sky conditions. On theoretical grounds Cngström (1929), in his turbidity formula on atmospheric transmissivity, separated water vapour absorption from dry, clear sky absorption and also from depletion due to scattering by dust particles. Brooks (1959), taking account of these three factors, presented an empirical formula which expresses transmissivity, a, of the direct beam of solar radiation. The formula, in the form rewritten by Gates (1962), gives a = exp[-0.089(pm a /1013) (wm a /20) (dm a ) 0.90 ] where and p = atmospheric pressure (mb), and a function of altitude w = total precipitable water vapour of the atmosphere in the zenithal direction (mm), and a function of dew point temperature, hence relative humidity d = concentration of haze and dust particles (particles/cm 3 ) m a = optical air mass, and a function of solar altitude, hence f (latitude, time of year and time of day) with the first term representing dry, clear sky absorption, the second water vapour absorption and the third term depletion due to dust scattering. Using this equation with a calibrated solarimeter at Pietermaritzburg, Schulze (1975) attained a value of r 2 = 99 and slope = 0.97 when estimating daily solar radiation loadings on cloudfree days throughout the year (r = 65). Despite the excellent performance of Brookes (1959) theoretically based formula for estimating clear sky transmissivity, perusal of some of the more Section 5.2 Estimation of Daily Solar Radiation over South Africa 3

4 recent literature on solar radiation estimation indicates that a variety of simple maximum transmissivity indices/values are used by researchers on solar radiation. Bristow and Campbell (1984) claim a transmissivity in excess of 60% under clear skies, but make no reference to the effects of changing seasons. Revfiem (1997) uses a maximum transmissivity of between 60% and 70%, again with no references to effects of changing seasons. Iziomon and Mayer (2002) focused on the effect that altitude plays on the transmissivity regime in mountainous regions of Germany, with clear sky transmissivity varying between 68% at lower altitudes and 77% at higher altitudes respectively. Thornton and Running (1998), working in the continental regions of the USA, employed clear sky transmissivities ranging between 70% and 77%. These values were found by them to be strongly correlated with altitude. Only Meek (1997) appears to have focused more specifically on the subject of clear sky transmissivity. Employing solar radiation data from just 5 climate stations located in the northern part of continental USA and Canada, he, like Brooks in 1959, claimed that the global solar radiation estimates were most sensitive to optical air mass and that the results were highly location specific. Chapman (2004), in an analysis of 10-day maximum transmissivities at 28 locations in South Africa with widely ranging climates, noted three broad trends, viz. rainy seasons, even on clear days, because of higher water vapour contents in the atmosphere. Based on the findings above it was therefore decided that, while retaining a transmissivity constant 0.75 as a point of departure, to modify it by an extinction function to account for atmospheric water vapour content. Transm issivi Transmissivit D e T u in Day of Year Joubertina Day of Year that the relationship between assumed clear sky a t and day of year was clearly hyperbolic at stations in the western half of the country which experiences a winter (i.e. April to September) rainfall, whilst this hyperbolic relationship tends to flatten out as one moves eastwards and northwards towards regions with a more even seasonal rainfall distribution, for the relationship to eventually become parabolic at the more humid eastern locations in the summer (October to March) rainfall regime (Figure 5.2.1). While Chapman (2004) notes some anomalies to these trends at certain stations, which would corroborate the findings of Meek (1997) that clear sky transmissivity curves can be highly location/site specific, the general conclusion is that atmospheric transmissivity is reduced in the respective Figure Transmissivit Funeray Day of Year Maximum 10 day atmospheric transmissivity curves against day of year (After Chapman, 2004) at De Tuin (winter, i.e. April to September, rainfall), Joubertina (all year rainfall) and Funeray (summer, i.e. October to March, rainfall) Section 5.2 Estimation of Daily Solar Radiation over South Africa 4

5 2. Modification of the Clear Sky Transmission Constant by a Water Vapour Related Extinction Function This modification took on the form of 1-1/T ra a on the premise that the higher the water vapour content (and by inference the lower the temperature range), the more the clear sky extinction would be. Clear sky solar radiation was thus expressed as R s = 0.75 R a [1-1/T ra a ] Using Liu and Scott s (2001) formulation of daily temperature range, viz. where T ra = T mxd - (T mnd + T mnd+1 ) / 2 T ra = diurnal temperature range ( C), T mxd = maximum temperature for the day, T mnd = minimum temperature for the day, and T mnd+1 = minimum temperature for the following morning the exponent a was optimised using clear sky solar radiation observations from stations which were grouped into four broad climatic regions in South Africa. Clear sky conditions were defined as days with no recorded rainfall on the day and a transmissivity These four regions (Figure 5.2.2) were defined as Eastern Seaboard, i.e. in more humid areas and with a distinct summer rainfall regime (8 stations; n = clear sky days); Northern Cape, i.e. semi-arid regions with low MAP ( mm) falling predominantly in summer (6 stations; n = clear sky days); Western Cape, i.e. humid and semi-arid regions with winter and allyear rainfall regimes (5 stations; n = 650 clear sky days); and Limpopo, in the more sub-tropical northern latitudes of South Africa, still with a summer rainfall, but more continental than the Eastern Seaboard (5 stations; n = 732 clear sky days). Figure Broad climatic regions used in modifications to the Bristow and Campbell equation for estimating daily solar radiation over South Africa The exponent a was optimised by iteratively changing its value in order to obtain a general best fit applicable in all four regions between R s and R a on clear sky days, not only with respect to r 2, but more specifically to attain a slope of the equation as close as possible to 1 and an intercept as close as possible to zero. Results of this optimisation are shown in Figure for the slope component of the R s /R a equation. The result was that clear sky solar radiation could be estimated with a high degree of confidence at individual verification stations (e.g. Funeray in Figure 5.2.4, left) as well as for groupings of stations within the broadly defined climatic regions in which individual station altitudes and MAPs could vary considerably (e.g. station altitudes range from 35 m to m in the Eastern Seaboard zone, and MAPs from 768 mm to mm; Figure 5.2.4, right). 3. Accounting for Regional and Intra-Annual Variations in South Africa in the Extinction Expression for Cloudy and Rainy Days If one considers the points beneath the clear sky R s / R a relationship in the hypothetical example of Figure 5.2.5, then those points represent solar Section 5.2 Estimation of Daily Solar Radiation over South Africa 5

6 Figure Slope Exponent 'a' Northern Cape Western Cape Limpopo Eastern Seaboard Example of the optimisation of the exponent a in the modification of the Bristow and Campbell equation for clear sky depletion of R s by atmospheric water vapour content radiation under cloudy and rainy conditions. The wide scatter of the points is the result of different cloud types, heights and thicknesses, ranging from relatively transparent high level cirrus to highly opaque cumulonimbus clouds, different fractions of cloudiness during the course of a day, and whether or not precipitation was occurring, and what the intensity and duration of the precipitation were. The above conditions vary by region, degree of aridity and season of dominant rainfall. It is for those reasons that in the Bristow and Campbell (1984) extinction function for actual meteorological conditions, which include cloudy and precipitation days, and which is expressed as [1 - exp (- bt ra c )] the constant b (already found in the literature to vary between and 0.019, e.g. Bristow and Campbell, 1984; Meza and Veres, 2000) and the exponent c were optimised for use in South Africa. This optimisation was R s R s Figure Individual Station, Eastern Seaboard: Funeray y = x r 2 = R a All Stations Combined, Eastern Seaboard y = x r 2 = R a Clear sky solar radiation estimates by the modified Bristow and Campbell (1984) equation for an individual station (Funeray) and a grouping of stations within a broad climatic zone (Eastern Seaboard) by broad climatic region (the four regions already mentioned above) and by month using, in total, over measured values of daily solar radiation from 24 stations considered to have high quality data (Chapman, 2004). Section 5.2 Estimation of Daily Solar Radiation over South Africa 6

7 Rs (MJ/m 2 /day) Figure Rs/Ra Relationships for Clear Sky and Cloudy/Rainy Conditions (Schematic) Ra (MJ/m 2 /day) Rs - Clear Sky Rs - Cloudy/Rain R s / R a relationships for clear sky and cloudy/rainy conditions (schematic) (2004) in South Africa found to improve estimates of daily R s. This function takes the form [1 - d P j-1 + ep j + fp j+1 + g] in which d to g = optimised regression coefficients, P j-1 = precipitation on the previous day, P j = precipitation of the day of estimation, and = precipitation on the following day. P j+1 In order to assess the degree to which this additional function would enhance results from the (by now modified) Bristow and Campbell equation, it was tested for spring, summer and autumn rainfall months on the dataset for the Eastern Seaboard of South Africa - a region characterised by relatively high rainfalls derived from a wide range of sources, from frontal to tropical to coastal to convective. Figure indicates the improvement in r 2 on a month-by-month basis when adding the explicit rainfall extinction function. The improvement is marked. From perusal of the scatter of points illustrated in the schematic illustrated in Figure 5.2.5, it stands to reason that the overall correlation of simulated vs observed R s will tend not to be particularly high. However, the above extinction equation also indicates that under clear sky conditions of high T ra and R s, when good estimates of R s are required, the extinction function will approximate 1 and under those conditions R s has been shown to be estimated accurately (Figure 5.2.4). On the other hand, under cloudy conditions when R s is low, the absolute error in its estimation is not so crucial. The optimised values of b and c by region in South Africa and month as well as the respective number of data points used, together with the r 2 between observed and estimated R s, is given in Table r Month 4. To Add or Not to Add a More Explicit Daily Rainfall Extinction Function to Improve Estimates of Daily Solar Radiation Liu and Scott (2001) added an explicit rainfall extinction function to the Bristow and Campbell equation which both they in Australia and Chapman Initial Value Improved Value Figure Improvements to r 2 in the Eastern Seaboard region of South Africa when adding an explicit rainfall extinction function to estimates of R s Section 5.2 Estimation of Daily Solar Radiation over South Africa 7

8 For purposes of mapping solar radiation over South Africa it was, however, decided not to pursue the option of adding the rainfall extinction function. The reason for that was that while temperature parameters, including the crucial T ra, can be estimated accurately in South Africa for long series of daily values on a fine raster (e.g. 1 x 1 latitude/longitude, i.e. ~ 1.7 x 1.7 km; as described by Schulze and Maharaj, 2004; and summarised in Section 2a), the same cannot yet be done with any accuracy at such a fine scale for a discrete event driven phenomenon such as daily rainfall (Lynch, 2004). General Conclusions on Improvements to Estimates of Daily Solar Radiation Over South Africa The development of an approach to estimating daily solar radiation loadings at unmeasured locations that is more rigorous and structured than that previously used for South Africa has been described. In modifying of the Bristow and Campbell (1984) equation, account is now taken of clear sky extinction of R s by water vapour by utilising temperature range as a surrogate for atmospheric water vapour content, while for cloudy/rainy days regression constants have been optimised by region and season to try and account for different meteorological conditions which can prevail. Indications are that an explicit rainfall function will improve daily estimates of R s even further. References (In the sequence in which they appear in this Section, with the full references given in Section 22) 1. Drummond, A.J. and Vowinckel, E. (1957) 2. Schulze, R.E. and McGee, O.S. (1978) 3. Reid, P.C.M. (1981) 4. Clemence, B.S.E. (1992) 5. Schulze, R.E. (1997) 6. Chapman, R.D. (2004) 7. Boote, K.J. and Loomis, R.S. (1991) 8. Mavromatis, T. and Jagtap, S.S. (2005) 9. Penman, H.L. (1948) 10. Monteith, J.H. (1981) 11. Liu, D.L. and Scott, B.J. (2001) 12. Bristow, K.L. and Campbell, G.S. (1984) 13. Hunt, L.A., Kuchar, L. and Swanton, C.J. (1998) 14. Donatelli, M., Bellocchi, G. and Fontana, F. (2003) Table Month Optimised values, by region in South Africa and by month, of b and c in the Bristow and Campbell extinction expression for cloudiness and rainfall Eastern Seaboard Limpopo b c n r 2 b c n r 2 January February March April May June July August September October November December Month Northern Cape Western Cape b c n r 2 b c n r 2 January February March April May June July August September October November December Robinson, N. (1966) 16. Schulze, R.E. (1975) 17. Richardson, A.G. and Reddy, K.R. (2004) 18. Goodin, D.G., Hutchinson, J.S., Vanderlip, R.L. and Knapp, M.C. (1999) 19. Angström, A. (1929) 20. Brooks, F.A. (1959) Section 5.2 Estimation of Daily Solar Radiation over South Africa 8

9 21. Gates, D.M. (1962) 22. Revfiem, K.J.A. (1997) 23. Iziomon, M.G. and Mayer, H. (2002) 24. Thornton, P.E. and Running, S.W. (1998) 25. Meek, D.W. (1997) 26. Meza, F. and Veres, E. (2000) 27. Schulze, R. E. and Maharaj, M. (2004) 28. Lynch, S.D. (2004) Citing from this Section of the Atlas When making reference to this Section of the Atlas, please cite as follows: Schulze, R.E. and Chapman, R.D Estimation of Daily Solar Radiation over South Africa. In: Schulze, R.E. (Ed) South African Atlas of Climatology and Agrohydrology. Water Research Commission, Pretoria, RSA, WRC Report 1489/1/06, Section 5.2. Section 5.2 Estimation of Daily Solar Radiation over South Africa 9