Values Of Global Radiation Research Articles

UV and global solar radiation in Łódź, Central Poland

AbstractWith the overall aim of quantifying urban atmospheric effects on different parts of the solar spectrum, a multi year analysis of data collected at Łódź was undertaken. UV (290–400 nm) and global solar radiation measured by means of a Kipp and Zonen CUV3 radiometer and a Kipp and Zonen CM11 pyranometer in the center of Łódź between 1997 and 2001 are analysed. The mean annual sum of global and UV solar radiation equaled 3710.8 MJ m−2 and 154.1 MJ m−2, respectively. The minimum monthly total of solar energy occurred in December (48.7 M Jm−2—global; 2.1 MJ m−2—UV); however, the maximum monthly total occurred atypically in May (620.9 MJ m−2—global; 25.3 MJ m−2—UV). UV clearness index (Kuv) is approximately half of the clearness index of the global solar radiation, indicating greater attenuation of that part of the spectrum (Kuv 0.14 in December to 0.26 in May). A linear regression model was fitted to the daily values of UV and global (g) solar irradiation (Duv = a + Dgb). The slope coefficient b and the coefficient of determination equal 0.039 and 0.98, respectively. Cloudiness exerts an important control on the solar radiation flux at the ground level and for the relation between UV and global solar radiation. The convective clouds caused an increase of global and UV solar irradiance by about 10–20% compared to clear days, the enhancement resulting from reflections. On clear days, UV comprises 3.3–4% of global solar irradiance (10‐min values) on average, while during cloudy weather it increases to 8%. The results presented have implications for understanding the radiative transfer of UV and global solar radiation in the atmosphere over an urban area and the influence of clouds on transmission of solar radiation flux. Copyright © 2009 Royal Meteorological Society

Comparison of mass balances for Vernagtferner, Oetzal Alps, as obtained from direct measurements and distributed modeling

AbstractThe direct comparison of modeled glacier mass-balance distribution with field measurements could be problematic, as the methodology of determination and the processes considered at the point or catchment scale could differ strongly. Moreover, direct measurements cover only small parts of a glacier, and model performance is thus difficult to assess outside these regions. Remaining opportunities for model validation include comparison of snowlines, as derived from remote-sensing data, and maps of the mass-balance distribution, as interpreted by observers with local knowledge. This study compares such hand-drawn maps of the Vernagtferner (Oetzal Alps) mass balance with the modeled pattern as obtained from a distributed energy-/mass-balance model of intermediate complexity. The model is driven by measured daily values of temperature, global radiation and precipitation from a nearby climate station and grids of mean daily potential global radiation and climatologic annual precipitation sums. Compared with the direct measurements, the calculated mean mass balance and equilibrium-line altitude agreed very well in both balance years, although the spatial pattern of the mass-balance distribution displayed larger deviations in regions influenced by snowdrift or local topographic undulations. However, compared with the remaining snow as visible on a satellite image from 1999, the modeled snowline pattern for a larger sample of glaciers is in very good agreement.

A Method For Estimating Solar Radiation From Air Temperature Data In Samaru, Northern Guinea Savanna Of Nigeria

A major limitation to the application of weather data in engineering designs and agricultural engineering is the lack of solar radiation data, while temperature and rainfall data are relatively available. Four empirical model methods (Bristow-Campbell (BC model), Campbell- Donatelli (CD model), Donatelli- Bellocchi (DB model) and Donatelli-Campbell-Bristow-Bellocchi (Modular DCBB)) were tested by comparing their estimated global radiation values with measured solar radiation data obtained for several years from the meteorological station at Samaru, northern Nigeria with the aim of determining which model estimate correlates more with measured values. The CD model had the best slope of the regression estimated vs measured of 0.87 with the DB and BC models having a slope of 0.65. The CD model also had the lowest RMSE of 2.7 while the DB model had the highest value of 4.5. From the coefficient of residual mass (CRM), BC, CD, and DB models overestimates the global solar radiation while the DCBB model gave underestimated values. The CD model which accounts for situations in which the night air temperature cooling is less than the corresponding clear day and also accounts for the date by using the average air temperature proved to be a reasonably accurate method for estimating global solar radiation for Samaru. Keywords: Solar radiation, air temperature, model, northern NigeriaGlobal Journal of Engineering Research Vol. 7 (1) 2008: pp. 21-28

An Upper Threshold of Enhanced Global Shortwave Irradiance in the Troposphere Derived from Field Measurements in Tropical Mountains

Abstract Extraordinarily high values of global irradiance (up to 1832 W m−2) incident upon a horizontal surface were observed during a 4-yr meteorological field campaign in the southern Ecuadorian Andes Mountains (4°S). The unexpected magnitude gave rise to a thorough revision of the instrumentation and an assessment of the radiation database. Infrastructure at the sites and software were critically examined, and the sensor and datalogger manufacturers were contacted. The observed enhanced irradiance was quantified with a simple clear-sky model for global radiation. The efforts showed that atmospheric conditions and not artifacts had produced the high values. Cloud radiative effects could be singled out as the exclusive source of the “superirradiance.” Mean (bihourly) maximum enhancement was 119.6% of the potential (clear sky) irradiance; absolute maximum enhancement occasionally reached to over 170%. Thereby, under ideal conditions, the upper threshold of global irradiance is apparently ∼200% of the potential (clear sky) direct radiation [i.e., at the point of observation, downwelling diffuse cloud radiation can (almost) equal the magnitude of its apparent “source”]. The observations were made between altitudes of 1500 and 3400 m MSL in different climates ranging from perhumid to semiarid (i.e., in very cloudy climates and in less cloudy climates). The conditions that were found to explain the magnitude of the extremely enhanced irradiance are not confined to tropical or mountainous environments only, but rather they can occur at any spot in the troposphere where clouds exist. Therefore, the findings appear to be of general validity.

Characterization of new particle formation events at a background site in Southern Sweden: relation to air mass history

Particle formation events were analysed from aerosol number size distribution data collected at a background station in southern Sweden between February 2001 and May 2004. Events occurred on about 36% of all days and were favoured by high global radiation values. The clearest events (class I, 20% of all days) were observed when the formation rate of activated hypothetical clusters around 1 nm diameter, J1 was higher than 10(180*CondS-0.60), where CondS is the condensation sink (in s-1). The median condensable vapour concentration, observed formation rate at 3 nm, and growth rate during class I events were 3.0 × 107 cm-3, 1.1 cm-3 s-1 and 2.1 nm h-1, respectively. On 7% of all days, it was possible to observe growth of the newly formed particles exceeding 30 nm geometric mean diameter during event days in the evening, which is important for the regional particle population, and thereby the climate. A trajectory analysis revealed that cleaner air masses were relatively more important for the contribution of Aitken mode particles than polluted ones. Class I events were registered on 36% of all days when trajectories had passed over the open sea, indicating that ship traffic can contribute to particle formation and growth.

Estimation of monthly average daily global solar irradiation using artificial neural networks

This study explores the possibility of developing a prediction model using artificial neural networks (ANN), which could be used to estimate monthly average daily global solar irradiation on a horizontal surface for locations in Uganda based on weather station data: sunshine duration, maximum temperature, cloud cover and location parameters: latitude, longitude, altitude. Results have shown good agreement between the estimated and measured values of global solar irradiation. A correlation coefficient of 0.974 was obtained with mean bias error of 0.059 MJ/m 2 and root mean square error of 0.385 MJ/m 2. The comparison between the ANN and empirical method emphasized the superiority of the proposed ANN prediction model.

A new algorithm to estimate sky condition based on 5 minutes-averaged values of clearness index and relative optical air mass

This work describes a new algorithm to characterize sky condition in intervals of 5 min using four categories of sun exposition: apparent sun with cloud reflection effects; apparent sun without cloud effects; sun partially concealed by clouds; and sun totally concealed by clouds. The algorithm can also be applied to estimate hourly and daily sky condition in terms of the traditional three categories: clear, partially cloudy and cloudy day. It identifies sky conditions within a confidence interval of 95% by minimizing local climate and measurement effects. This is accomplished by using a logistic cumulative probability function to characterize clear sky and Weibull cumulative probability function to represent cloudy sky. Both probability functions are derived from frequency distributions of clearness index, based on 5 minutes-averaged values of global solar irradiance observed at the surface during a period of 6 years in Botucatu, Southeastern of Brazil. The relative sunshine estimated from the new algorithm is statistically comparable to the one derived from Campbell-Stocks sunshine recorder for both daily and monthly values. The new method indicates that the highest frequency of clear sky days occurs in Botucatu during winter (66%) and the lowest during the summer (38%). Partially cloudy condition is the dominant feature during all months of the year.

A case study to prepare for the utilization of aerosol forecasts in solar energy industries

Precise aerosol information is indispensable in providing accurate clear sky irradiance forecasts, which is a very important aspect in solar facility management as well as in solar and conventional power load prediction. In order to demonstrate the need of detailed aerosol information, direct irradiance derived from Aerosol Robotic Network (AERONET) ground based measurements of aerosol optical depth (AOD) was compared in a case study over Europe to irradiance calculated using a standard aerosol scenario. The analysis shows an underestimation of measurement-derived direct irradiance by the scenario-derived direct irradiance for locations in Northern Europe and an overestimation for the Mediterranean region. Forecasted AOD of the European Dispersion and Deposition Model (EURAD) system was validated against ground based AERONET clear sky AOD measurements for the same test period of February 15th to 22nd, 2004. For the time period analyzed, the modelled AOD forecasts of the EURAD system slightly underestimate ground based AERONET measurements. To quantify the effects of varying AOD forecast quality in their impact on the application in solar energy industry, measured and forecasted AOD were used to calculate and compare direct, diffuse, and global irradiance. All other influencing variables (mainly clouds and water vapour) are assumed to be modelled and measured correctly for this analysis which is dedicated to the specific error introduced by aerosol forecasting. The underestimated AOD results in a mean overestimation of direct irradiance of +28 W/m 2 (+12%), whereas diffuse irradiance is generally underestimated (−19 W/m 2 or −14%). Mean global irradiance values where direct and diffuse irradiance errors compensate each other are very well represented (on average +9 W/m 2 or +2%).

Analysis of satellite derived beam and global solar radiation data

Images from the GOES 8 satellite were used along with auxiliary information such as snow cover to produce an hourly solar radiation database on a 0.1° grid for the Pacific Northwest from 1998 through 2002 [Perez, R., Ineichen, P., Moore, K., Kmiecik, M., Chain, C., George, R., Vignola, F. 2002. A new operational satellite-to-irradiance model. Solar Energy 73(5), 307–317]. Both global and beam irradiance values were derived from the satellite images and diffuse values were calculated from the beam and global values. Data from the University of Oregon Solar Radiation Monitoring Network were used to help refine and validate the model used to produce the database from the satellite images. This article presents new and independent tests of this satellite database from one year with high quality data from Kimberly, Idaho that was not used in the original development and testing of the satellite model. The mean bias error of the satellite-derived global and beam irradiance values were 5% and 2% respectively. The standard deviation ranged from 22% for global values to 41% for beam values. The largest discrepancies occur on clear winter days when it is difficult to distinguish between frost or snow on the ground and low lying fog or clouds. It is suggested that ground-based solar or visibility measurements or auxiliary satellite data are needed to augment the satellite cloud cover and snow cover data to reduce errors that can occur during cold winter days.

On the use of the digital elevation model to estimate the solar radiation in areas of complex topography

AbstractThe development of solar energy as a power source in the next few years requires reliable estimation of available solar energy resources. At local scales, topography is the most important factor in determining the distribution of solar radiation at the surface. Interpolation techniques are usually employed to estimate solar radiation where stations are not available, but their usefulness is limited where topography is an important source of variability. The use of satellite data and more recently of models based on techniques GIS, have contributed to solve this difficulty. In this work the usefulness of a digital elevation model (DEM) in providing topographic information for the estimation of solar radiation in areas of complex topography is analysed. Daily global radiation values were generated using the Solar Analyst software, which uses topographic information to generate radiation data. The generated data were compared with the experimental data obtained from 14 radiometric stations located within the Sierra Nevada Natural Park (southern Spain), an area of complex topography. Results show the usefulness of the topographic information derived from a DEM to estimate the solar radiation in areas of complex topography. Nevertheless, results depend on the DEM resolution and it is important that other factors, such as the albedo, should also be taken into account to obtain better estimates. Copyright © 2006 John Wiley & Sons, Ltd.

A new simple parameterization of daily clear-sky global solar radiation including horizon effects

Estimation of clear-sky global solar radiation is usually an important previous stage for calculating global solar radiation under all sky conditions. This is, for instance, a common procedure to derive incoming solar radiation from remote sensing or by using digital elevation models. In this work, we present a new model to calculate daily values of clear-sky global solar irradiation. The main goal is the simple parameterization in terms of atmospheric temperature and relative humidity, Angstrom's turbidity coefficient, ground albedo and site elevation, including a factor to take into account horizon obstructions. This allows us to obtain estimates even though a free horizon is not present as is the case of mountainous locations. Comparisons of calculated daily values with measured data show that this model is able to provide a good level of accurate estimates using either daily or mean monthly values of the input parameters. This new model has also been shown to improve daily estimates against those obtained using the clear-sky model from the European Solar Radiation Atlas and other accurate parameterized daily irradiation models. The introduction of Angstrom's turbidity coefficient and ground albedo should allow us to use the increasing worldwide aerosol information available and to consider those sites affected by snow covers in an easy and fast way. In addition, the proposed model is intended to be a useful tool to select clear-sky conditions.

Simulação estocástica de atributos do clima e da produtividade potencial de milho utilizando-se distribuição triangular

O objetivo deste trabalho foi simular a produtividade potencial da cultura de milho, pelo método de Monte Carlo, utilizando um modelo agrometeorológico estocástico. O experimento foi conduzido em Piracicaba, SP, a 22º42'30''S, 47º38'30''W, e altitude de 546 m, o clima da região é do tipo Cwa (tropical úmido). Foram utilizados os valores médios diários de temperatura (de 1917 a 2002) e radiação solar global (de 1978 a 2002). Para comparar os dados reais com os simulados, foram utilizados índices de desempenho estatístico. Observou-se que os modelos probabilísticos, desenvolvidos para a simulação de dados médios diários de temperatura e de radiação solar global, geraram valores semelhantes aos observados por meio da distribuição triangular, a qual pode ser utilizada em modelo estocástico, para previsão da produtividade potencial de milho, nas diferentes épocas de semeadura.

A study of solar radiation climate at Cairo urban area, Egypt and its environs

The measured values of the hourly global solar radiation, G, and its diffuse component, D, on a horizontal surface for a 12-year period (1992–2003) have been collected and used to examine the solar radiation characteristics in the urban area of Cairo, Egypt. The corresponding values of the diffuse fraction of global radiation, K, have been calculated. Diurnal variations of the results have been investigated. Also, the daily total values and their monthly and seasonal means, as well as their frequency distributions, have been calculated and investigated. The results reveal that Cairo has annual mean values of G, D, and K equal to 18.57, 6.10 MJ m−2 and 0.35, respectively. The seasonal and climatic effects on the fluctuation of the results are discussed. These effects were particularly large during the winter and spring months owing to the high fluctuation of the atmospheric conditions with respect to the amount of water content, clouds, and concentration of aerosol and dust particles. It was found that the reduction of G due to the effect of clouds is small (2.8%), which in turn reflects the low degree of cloudiness over Cairo due to the impacts of urbanization. A comparative study has also been done to investigate the effect of urbanization processes on the global radiation values received at urban Cairo. It was found that G values received during the non-urbanized period (1969–1973) highly exceeded the radiation values received during the recent urbanized period (1999–2003) for all months of the year, and the annual mean of the relative reduction was found to be 17.63%. Copyright © 2006 Royal Meteorological Society

Cloud and radiance measurements with the VIS/NIR Daylight Whole Sky Imager at Lindenberg (Germany)

Ground-based cloud data acquired with the whole sky imager (WSI) are analyzed in relation to measurements of solar radiation performed at the Lindenberg Meteorological Observatory. Cloud fractions derived by the cloud detection algorithm from WSI images acquired during daylight hours between 2002 and 2004 are compared with conventional cloud observations for the two sites Potsdam and Lindenberg, and also with ceilometer data of cloud-base heights at Lindenberg. The comparison statistics are discussed in the context of different principles of measurement. A few case studies illustrate the strong scattering effect of clouds on solar radiance and irradiance measured at the ground in different spectral regions. Particularly clouds close to the apparent position of the sun lead to strong enhancements of solar diffuse irradiance incident on horizontal planes and hemispheres that substantially exceed corresponding clear-sky values. Irradiances derived from WSI sky radiance fields are shown in comparison to pyranometer data of diffuse irradiance and radiative transfer model calculations performed for clear sky conditions. Examples of spectral sky radiances with moving contrails illustrate the significant enhancement the contrails have compared to clear sky, even though they may have a relatively small direct effect on global irradiance values. As contrails are observed at Lindenberg for about 18 to 19% of daylight hours, and part of them become clouds, the indirect impact of these changes on solar irradiance received at the ground may not be negligible. (orig.)

Prediction of direct and global solar irradiance using broadband models: Validation of REST model

In the present paper, three parametric models Yang, CPCR2 and REST (without considering transmittance due to nitrogen dioxide) have been analyzed for four Indian stations, namely New Delhi, Mumbai, Pune and Jaipur over the period of 1995–2002, under cloudless conditions. These stations have different climatic conditions. The beam radiation at normal incidence as well as global solar radiation at horizontal surface was computed for these locations during all seasons except monsoon (June to September). The computed values of beam and global irradiance was compared with reference values in case of beam and measured values in case of global solar radiation on the basis of percentage root mean square error (RMSE) and mean bias error (MBE). The maximum RMSE is 6.5% in REST model, as compare to 15% in Yang and 11% in CPCR2 model for predicting direct normal irradiance. The predicted global radiation at horizontal is showing maximum RMSE 7% in REST model, 13.4% in Yang and 25.9% in CPCR2 model. This shows that REST model has good agreement with measured data for these Indian stations as compare to other two models.

Comparison between winter and summer sky-luminance distribution in Central Europe and in the Eastern Mediterranean

This work studies the illuminance levels at a city in Central Europe (Bratislava) and another in the Eastern Mediterranean (Athens) and defines the prevailing sky-luminance distributions for winter and summer. The data used are 5-min values of global and diffuse horizontal irradiance and illuminance along with zenith luminance from the IDMP stations at the two cities for a period of 5 years. The study is based on the new set of the sky types recently adopted by CIE. These sky standards correspond to 15 theoretical diagrams of the ratio of zenith luminance to diffuse horizontal illuminance against solar altitude. The theoretical curves converge above 35 ∘ of solar elevation and in many cases they intersect each other. For this reason, each observation is classified into one of the 15 sky standards, only when the value of the ratio of zenith luminance to diffuse horizontal illuminance lies in a zone of ± 2.5 % around the theoretical curve describing the specific category. If any observation is classified into more than one sky standards, the corresponding ratio of global horizontal illuminance to extraterrestrial horizontal illuminance is compared to the average ratio of the sky types implicated, for the same solar altitude, and the observation is classified in the sky type with the nearest value. It is found that the most frequent sky types for Bratislava are the overcast sky with steep luminance gradation and slight brightening towards the sun (winter) and the white–blue sky with a distinct solar corona (summer), while for Athens the cloudless polluted sky prevails in both seasons. It is also found that during a summer day, a noticeable shift appears in the sky-luminance distribution at both sites.

New Correlation to Estimate Global Solar Radiation on Horizontal Surfaces Using Sunshine Hour and Temperature Data for Indian Sites

Solar radiation data, a prerequisite for the designing and sizing of solar energy systems, are not available in many Indian locations. However, the sunshine hour or temperature data are available for most sites from which solar radiation can be computed. New correlation models have been developed; incorporating the latitude and altitude of a site to estimate the monthly average global solar radiation on horizontal surfaces using the sunshine hour and temperature data. The models are used for computing values of six Indian stations with different geographical locations, based on 10-15years of data. The estimated values are found to be in close agreement with their measured values. The estimated data are also compared with the results using other models to test the accuracy of new models. It has been shown that the estimated values of global radiation using temperature data are also sufficiently accurate and can be utilized for sites for which even sunshine hour data are not measured. This will lead to better inputs for designing and evaluating the performance of solar energy systems including passive solar buildings.

Investigation of the Large-Scale Atmospheric Moisture Field over the Midwestern United States in Relation to Summer Precipitation. Part II: Recycling of Local Evapotranspiration and Association with Soil Moisture and Crop Yields

The relative contributions of locally evapotranspired (i.e., recycled) moisture versus externally advected water vapor for the growing-season precipitation of the U.S. Corn Belt and surrounding areas (1.23 × 106 km2) are estimated in this paper. Four May–August seasons with highly contrasting precipitation and crop yields (1975, 1976, 1979, and 1988) are investigated. A simple recycling equation—developed from the traditional atmospheric moisture budget and involving regional evapotranspiration and atmospheric water vapor inflow—is applied on daily, monthly, and seasonal time scales. Several atmospheric moisture budget components {moisture flux divergence [MFD], storage change [or change in precipitable water (dPW)], and inflow [IF]} are evaluated for 24-h periods using standard finite difference and line integral methods applied to objectively analyzed U.S. and Canadian rawinsonde data (50-hPa vertical resolution, surface to 300 hPa) for 0000 and 1200 UTC. Daily area-averaged precipitation (P) totals are derived from approximately 600 evenly distributed (but ungridded) recording rain gauges. Evapotranspiration (E) is estimated as the residual of the moisture budget equation for 24-h periods; values compare favorably with the few existing observations. Traditional budget results show the following: E is weakly related to P on monthly and seasonal time scales; there is surprising interannual constancy of seasonal E cycles and averages given the large variation in resulting crop yields; and monthly and seasonal variability of the export of the E − P surplus is determined largely by the horizontal velocity divergence component of MFD. New recycling analyses suggest that the contribution of local E to P (i.e., PE/P) is relatively small and remarkably consistent (largely 0.19–0.24) for monthly and seasonal periods, despite large P and crop yield variations. However, the monthly/seasonal averaging process is found to completely mask a striking decrease of daily PE/P (from approximately 0.30 to 0.15) with increasing P from 0 to 8 mm day−1. Unique and detailed analyses of P-stratified daily moisture budget results provide key insights into apparent contradictions between daily and monthly/seasonal recycling and related results and concomitant interannual variability, especially for the very dry 1988 season. Interpretation is facilitated by the use of modeled daily global radiation values, measured (instantaneous) and modeled (monthly) soil moisture, United States Department of Agriculture (USDA) crop yield estimates, and satellite normalized difference vegetation index (NDVI) imagery. This paper shows that land–atmosphere interactions are intimately involved in pronounced seasonal climate anomalies for the world's richest agricultural region, but apparently with considerable complexity that includes plant behavior, solar radiation forcing, and challenging time-scale interrelations.

Analysis of 40 year records of solar radiation data in Shanghai, Nanjing and Hangzhou in Eastern China

In this paper, we analyze global, direct and diffuse solar radiation data on a horizontal surface observed at stations in Shanghai, Nanjing and Hangzhou for the period of 1961 to 2000. The data include monthly averages of the daily clearness index (G/G0: the ratio of global to extraterrestrial solar radiation) and the diffuse fraction (D/G: the ratio of diffuse to global solar radiation. The present study has processed and analyzed the data, including variables or statistics of mean, and annual monthly and daily total, the diurnal variation and the frequency of daily totals of global solar radiation. A correlation between daily values of clearness index and diffuse fraction is obtained and recommended correlation equations were calculated. The annual variations and trend of yearly series are analyzed for daily global, direct and diffuse radiation on a horizontal surface, as well as for daily clearness index and diffuse fraction in Shanghai, Nanjing and Hangzhou. The results show: 1) the east China is characterized by a decrease in global and direct radiation and a little increase in diffuse radiation and a negative linear relationship was obtained between clearness index and diffuse fraction. 2) The annual variations of global, direct and diffuse radiation for Shanghai, Nanjing and Hangzhou are similar with relative low values of global and direct radiation in June due to the Meiyu period. 3) The acceleration of air pollution and decrease of relative sunshine are the possible causes for the decrease of global and direct radiation.

Validation in an Arid Area of an Algorithm for the Estimation of Daily Solar Radiation

Abstract The Thornton–Running algorithm to estimate daily global radiation was tested at a site in a coastal desert of the eastern Mediterranean. In this algorithm three factors are multiplied in order to compute the daily global radiation: the total daily extraterrestrial radiation impinging on a horizontal plane, the maximum daily total atmospheric transmittance possible on days with clear skies (Tt,max), and the realized proportion of Tt,max for days during which the sky is not clear (Tf,max). Estimates of Tt,max compared very well with measured values while this was not the case for Tf,max. A good correlation was, however, obtained between predicted and measured values of daily global radiation with a noticeable underprediction of global radiation when measured values exceeded 20 MJ m−2. A regression analysis showed that errors in the estimated global radiation were linearly related to errors in Tf,max. Analysis of the data used in this study indicated that for the conditions prevailing in the area it...