Estimating net radiation at surface using artificial neural networks: a new approach

This study describes the results of artificial neural network (ANN) models to estimate net radiation (R _n), at surface. Three ANN models were developed based on meteorological data such as wind velocity and direction, surface and air temperature, relative humidity, and soil moisture and temperature. A comparison has been made between the R _n estimates provided by the neural models and two linear models (LM) that need solar incoming shortwave radiation measurements as input parameter. Both ANN and LM results were tested against in situ measured R _n. For the LM ones, the estimations showed a root mean square error (RMSE) between 34.10 and 39.48?W?m^?2 and correlation coefficient (R ²) between 0.96 and 0.97 considering both the developing and the testing phases of calculations. The estimates obtained by the ANN models showed RMSEs between 6.54 and 48.75?W?m^?2 and R ² between 0.92 and 0.98 considering both the training and the testing phases. The ANN estimates are shown to be similar or even better, in some cases, than those given by the LMs. According to the authors?? knowledge, the use of ANNs to estimate R _n has not been discussed earlier, and based on the results obtained, it represents a formidable potential tool for R _n prediction using commonly measured meteorological parameters.     

Estimation of evapotranspiration based on only air temperature data using artificial neural networks for a subtropical climate in Iran

This paper examines the potential for the use of artificial neural networks (ANNs) to estimate the reference crop evapotranspiration (ET₀) based on air temperature data under humid subtropical conditions on the southern coast of the Caspian Sea situated in the north of Iran. The input variables for the networks were the maximum and minimum air temperature and extraterrestrial radiation. The temperature data were obtained from eight meteorological stations with a range of latitude, longitude, and elevation throughout the study area. A comparison of the estimates provided by the ANNs and by Hargreaves equation was also conducted. The FAO-56 Penman–Monteith model was used as a reference model for assessing the performance of the two approaches. The results of this study showed that ANNs using air temperature data successfully estimated the daily ET₀ and that the ANNs with an R ² of 0.95 and a root mean square error (RMSE) of 0.41 mm day^?1 simulated ET₀ better than the Hargreaves equation, which had an R ² of 0.91 and a RMSE of 0.51 mm day^?1.     

Single and dual crop coefficients and crop evapotranspiration for wheat and maize in a semi-arid region

In this study, weighing lysimeters were used to investigate the daily crop coefficient and evapotranspiration of wheat and maize in the Fars province, Iran. The locally calibrated Food and Agriculture Organization (FAO) Penman–Monteith equation was used to calculate the reference crop evapotranspiration (ET_o). Micro-lysimetry was used to measure soil evaporation (E). Transpiration (T) was estimated by the difference between crop evapotranspiration (ET_c) and E. The single crop coefficient (K _c) was calculated by the ratio of ET_c to ET_o. Furthermore, the dual crop coefficient is composed of the soil evaporation coefficient (K _e) and the basal crop coefficients (K _cb) calculated from the ratio of E and T to ET_o, respectively. The maximum measured evapotranspiration rate for wheat was 9.9 mm?day^?1 and for maize was 10 mm?day^?1. The total evaporation from the soil surface was about 30 % of the total wheat ET_c and 29.8 % of total maize ET_c. The single crop coefficient (K _c) values for the initial, mid-, and end-season growth stages of maize were 0.48, 1.40, and 0.31 and those of wheat were 0.77, 1.35, and 0.26, respectively. The measured K _c values for the initial and mid-season stages were different from the FAO recommended values. Therefore, the FAO standard equation for K _c-_mid was calibrated locally for wheat and maize. The K _cb values for the initial, mid-, and end-season growth stages were 0.23, 1.14, and 0.13 for wheat and 0.10, 1.07, and 0.06 for maize, respectively. Furthermore, the FAO procedure for single crop coefficient showed better predictions on a daily basis, although the dual crop coefficient method was more accurate on seasonal scale.     

A comparison of different methods of estimating energy‐limited evapotranspiration in the peace river region of British Columbia

Abstract

The performances of eight methods for estimating daily energy‐limited evapotranspiration (E_e) were compared with reliable values for the Peace River region of British Columbia. They included the methods of Priestley and Taylor (PT), Jensen and Haise (JH), Hargreaves (H) and Makkink (M), the first and second equations of Baier and Robertson (BR1 and BR2), and the modified methods of Blaney and Criddle (BC) and Thornthwaite (T). The reference data were obtained from previous workers, who in 1977 and 1979 made micrometeorological measurements of E_e using the Bowen ratio method.

The relationships between estimated and measured E_e values excluding the T method in 1977 had correlation coefficients (R) ranging from 0.65 to 0.84. These were not significantly different at the 5% level. The Standard Errors of the Estimate (SEE) ranged from 0.43 to 1.69 mm d^?1. The PT, JH, BR1 and T methods had low SEE values, whereas the BR2, H, BC and M methods had high SEE values. Six of the eight methods (PT, JH, H, M, BR2 and BC) were calibrated for local conditions using 1979 data. After calibration, the methods were tested with the 1977 data. The results indicated significant improvement in the fit of four of the methods (H, M, BR2 and BC). Overall, it was concluded that after calibration, six of the eight methods had predictive power and fit that were not significantly different at the 5% level.     

Utility of coactive neuro-fuzzy inference system for pan evaporation modeling in comparison with multilayer perceptron

Estimation of pan evaporation (E _pan) using black-box models has received a great deal of attention in developing countries where measurements of E _pan are spatially and temporally limited. Multilayer perceptron (MLP) and coactive neuro-fuzzy inference system (CANFIS) models were used to predict daily E _pan for a semi-arid region of Iran. Six MLP and CANFIS models comprising various combinations of daily meteorological parameters were developed. The performances of the models were tested using correlation coefficient (r), root mean square error (RMSE), mean absolute error (MAE) and percentage error of estimate (PE). It was found that the MLP6 model with the Momentum learning algorithm and the Tanh activation function, which requires all input parameters, presented the most accurate E _pan predictions (r?=?0.97, RMSE?=?0.81?mm?day^?1, MAE?=?0.63?mm?day^?1 and PE?=?0.58?%). The results also showed that the most accurate E _pan predictions with a CANFIS model can be achieved with the Takagi–Sugeno–Kang (TSK) fuzzy model and the Gaussian membership function. Overall performances revealed that the MLP method was better suited than CANFIS method for modeling the E _pan process.     

Hourly air temperature driven using multi-layer perceptron and radial basis function networks in arid and semi-arid regions

This study employed two artificial neural network (ANN) models, including multi-layer perceptron (MLP) and radial basis function (RBF), as data-driven methods of hourly air temperature at three meteorological stations in Fars province, Iran. MLP was optimized using the Levenberg–Marquardt (MLP_LM) training algorithm with a tangent sigmoid transfer function. Both time series (TS) and randomized (RZ) data were used for training and testing of ANNs. Daily maximum and minimum air temperatures (MM) and antecedent daily maximum and minimum air temperatures (AMM) constituted the input for ANNs. The ANN models were evaluated using the root mean square error (RMSE), the coefficient of determination (R ²) and the mean absolute error. The use of AMM led to a more accurate estimation of hourly temperature compared with the use of MM. The MLP-ANN seemed to have a higher estimation efficiency than the RBF ANN. Furthermore, the ANN testing using randomized data showed more accurate estimation. The RMSE values for MLP with RZ data using daily maximum and minimum air temperatures for testing phase were equal to 1.2°C, 1.8°C, and 1.7°C, respectively, at Arsanjan, Bajgah, and Kooshkak stations. The results of this study showed that hourly air temperature driven using ANNs (proposed models) had less error than the empirical equation.     

Estimation of dew point temperature using neuro-fuzzy and neural network techniques

This study investigates the ability of two different artificial neural network (ANN) models, generalized regression neural networks model (GRNNM) and Kohonen self-organizing feature maps neural networks model (KSOFM), and two different adaptive neural fuzzy inference system (ANFIS) models, ANFIS model with sub-clustering identification (ANFIS-SC) and ANFIS model with grid partitioning identification (ANFIS-GP), for estimating daily dew point temperature. The climatic data that consisted of 8 years of daily records of air temperature, sunshine hours, wind speed, saturation vapor pressure, relative humidity, and dew point temperature from three weather stations, Daego, Pohang, and Ulsan, in South Korea were used in the study. The estimates of ANN and ANFIS models were compared according to the three different statistics, root mean square errors, mean absolute errors, and determination coefficient. Comparison results revealed that the ANFIS-SC, ANFIS-GP, and GRNNM models showed almost the same accuracy and they performed better than the KSOFM model. Results also indicated that the sunshine hours, wind speed, and saturation vapor pressure have little effect on dew point temperature. It was found that the dew point temperature could be successfully estimated by using T _mean and R _H variables.     

Modeling daily reference evapotranspiration (ET0) in the north of Algeria using generalized regression neural networks (GRNN) and radial basis function neural networks (RBFNN): a comparative study

Estimation of reference evapotranspiration (ET₀) is needed to support irrigation design and scheduling, and watershed hydrology studies. There are many available methods to estimate evapotranspiration from a water surface, comprising both direct and indirect methods. In the first part of this study, the generalized regression neural networks model (GRNN) and radial basis function neural network (RBFNN) are developed and compared in order to estimate the reference ET₀ for the first time in Algeria. Various daily climatic data, that is, daily mean relative humidity, sunshine duration, maximum, minimum and mean air temperature, and wind speed from Dar El Beida, Algiers, Algeria, are used as inputs to the GRNN and RBFNN models to estimate the ET₀ obtained using the FAO-56 Penman-Monteith equation (PM56). The performances of the models are evaluated using root mean square errors (RMSE), mean absolute error (MAE), Willmott index of agreement (d) and correlation coefficient (CC) statistics. In the second part of the study, the empirical Hargreaves-Samani (HG) and Priestley-Taylor (PT) equations are also considered for the comparison. Based on the comparisons, the GRNN was found to perform better than the RBFNN, Priestley-Taylor and Hargreaves-Samani models. The RBFNN model is ranked as the second best model.     

Comparison of artificial neural network and multivariate linear regression methods for estimation of daily soil temperature in an arid region

Soil temperature (T _S) strongly influences a wide range of biotic and abiotic processes. As an alternative to direct measurement, indirect determination of T _S from meteorological parameters has been the focus of attention of environmental researchers. The main purpose of this study was to estimate daily T _S at six depths (5, 10, 20, 30, 50 and 100?cm) by using a multilayer perceptron (MLP) artificial neural network (ANN) model and a multivariate linear regression (MLR) method in an arid region of Iran. Mean daily meteorological parameters including air temperature (T _a), solar radiation (R _S), relative humidity (RH) and precipitation (P) were used as input data to the ANN and MLR models. The model results of the MLR model were compared to those of ANN. The accuracy of the predictions was evaluated by the correlation coefficient (r), the root mean-square error (RMSE) and the mean absolute error (MAE) between the measured and predicted T _S values. The results showed that the ANN method forecasts were superior to the corresponding values obtained by the MLR model. The regression analysis indicated that T _a, RH, R _S and P were reasonably correlated with T _S at various depths, but the most effective parameters influencing T _S at different depths were T _a and RH.     

Evaluation of solar radiation estimation methods for reference evapotranspiration estimation in Canada

The accuracy of nine solar radiation (R _s ) estimation models and their effects on reference evapotranspiration (ET _o ) were evaluated using data from eight meteorological stations in Canada. The R _s estimation models were FAO recommended Angstrom-Prescott (A-P) coefficients, locally calibrated A-P coefficients, Hargreaves and Samani (H-S) (1982), Annandale et al., (2002), Allen (1995), Self-Calibrating (S-C, Allen, 1997), Samani (2000), Mahmood and Hubbard (M-H) (2002), and Bristow and Campbell (B-C) (1984). The estimated R _s values were then compared to measured R _s to check the appropriateness of these models at the study locations. Based on root mean square error (RMSE), mean bias error (MBE) and modelling efficiency (ME) ranking, calibrated A-P coefficients performed better than all other methods. The calibrated H-S method (using new K _RS 0.15) estimated R _s more accurately than FAO-56 recommended A-P in Elora, and Winnipeg. The RMSE of the calibrated H-S method ranged between 1-6% and the RMSE of the calibrated and FAO recommended Angstrom-Prescott (A-P) methods ranged between 1-9%. The models with the least accuracy at the eight locations are the Mahmood & Hubbard (2002) and Self-Calibrating models. The percent deviation in ET _o calculated with estimated R _s was reduced by about 50% as compared to deviation in measured versus estimated R _s .     

Retrieving daily global solar radiation from routine climate variables

Solar radiation is an important variable for studies related to solar energy applications, meteorology, climatology, hydrology, and agricultural meteorology. However, solar radiation is not routinely measured at meteorological stations; therefore, it is often required to estimate it using other techniques such as retrieving from satellite data or estimating using other geophysical variables. Over the years, many models have been developed to estimate solar radiation from other geophysical variables such as temperature, rainfall, and sunshine duration. The aim of this study was to evaluate six of these models using data measured at four independent worldwide networks. The dataset included 13 stations from Australia, 25 stations from Germany, 12 stations from Saudi Arabia, and 48 stations from the USA. The models require either sunshine duration hours (Ångstrom) or daily range of air temperature (Bristow and Campbell, Donatelli and Bellocchi, Donatelli and Campbell, Hargreaves, and Hargreaves and Samani) as input. According to the statistical parameters, Ångstrom and Bristow and Campbell indicated a better performance than the other models. The bias and root mean square error for the Ångstrom model were less than 0.25 MJ m² day^?1 and 2.25 MJ m² day^?1, respectively, and the correlation coefficient was always greater than 95 %. Statistical analysis using Student’s t test indicated that the residuals for Ångstrom, Bristow and Campbell, Hargreaves, and Hargreaves and Samani are not statistically significant at the 5 % level. In other words, the estimated values by these models are statistically consistent with the measured data. Overall, given the simplicity and performance, the Ångstrom model is the best choice for estimating solar radiation when sunshine duration measurements are available; otherwise, Bristow and Campbell can be used to estimate solar radiation using daily range of air temperature.     

Annual precipitation forecast for west, southwest, and south provinces of Iran using artificial neural networks

Rainfed agriculture plays an important role in the agricultural production of the southern and western provinces of Iran. In rainfed agriculture, the adequacy of annual precipitation is considered as an important factor for dryland field and supplemental irrigation management. Different methods can be used for predicting the annual precipitation based on climatic and non-climatic inputs. Among which artificial neural networks (ANN) is one of these methods. The purpose of this research was to predict the annual precipitation amount (millimeters) in the west, southwest, and south of Islamic Republic of Iran with the total area of 394,259?km², by applying non-climatic inputs according to the long-time average precipitation in each station (millimeters), 47.5?mm precipitation since the first of autumn (day), t _47.5, and other effective parameters like coordinate and altitude of the stations, by using the artificial neural networks. In order to intelligently estimate the annual amount of precipitation in the study regions (ten provinces), feedforward backpropagation artificial neural network model has been used (method I). To predict the annual precipitation amount more accurately, the region under study was divided into three sub-regions, according to the precipitation mapping, and for each sub-region, the neural networks were developed using t _47.5 and long-time average annual precipitation in each station (method II). It is concluded that neural networks did not significantly increase the prediction accuracy in the study area compared with multiple regression model proposed by other investigators. However, in case of ANN, it is better to use a structure of 2–6–6–10–1 and Levenberg–Marquardt learning algorithm and sigmoid logistic activation function for prediction of annual precipitation.     

Available energy and energy balance closure at four coniferous forest sites across Europe

The available energy (AE), driving the turbulent fluxes of sensible heat and latent heat at the earth surface, was estimated at four partly complex coniferous forest sites across Europe (Tharandt, Germany; Ritten/Renon, Italy; Wetzstein, Germany; Norunda, Sweden). Existing data of net radiation were used as well as storage change rates calculated from temperature and humidity measurements to finally calculate the AE of all forest sites with uncertainty bounds. Data of the advection experiments MORE II (Tharandt) and ADVEX (Renon, Wetzstein, Norunda) served as the main basis. On-site data for referencing and cross-checking of the available energy were limited. Applied cross checks for net radiation (modelling, referencing to nearby stations and ratio of net radiation to global radiation) did not reveal relevant uncertainties. Heat storage of sensible heat J _H, latent heat J _E, heat storage of biomass J _veg and heat storage due to photosynthesis J _C were of minor importance during day but of some importance during night, where J _veg turned out to be the most important one. Comparisons of calculated storage terms (J _E, J _H) at different towers of one site showed good agreement indicating that storage change calculated at a single point is representative for the whole canopy at sites with moderate heterogeneity. The uncertainty in AE was assessed on the basis of literature values and the results of the applied cross checks for net radiation. The absolute mean uncertainty of AE was estimated to be between 41 and 52 W m^?2 (10–11 W m^?2 for the sum of the storage terms J and soil heat flux G) during mid-day (approximately 12% of AE). At night, the absolute mean uncertainty of AE varied from 20 to about 30 W m^?2 (approximately 6 W m^?2 for J plus G) resulting in large relative uncertainties as AE itself is small. An inspection of the energy balance showed an improvement of closure when storage terms were included and that the imbalance cannot be attributed to the uncertainties in AE alone.     

Spectral investigation of the diffuse-to-direct solar beam irradiances ratio (UV–VIS) in the urban Athens atmosphere

This study explores the influence of air gaseous pollutants–aerosols and solar zenith angle (SZA) on the spectral diffuse-to-direct beam E _dλ/E _bλ irradiances ratio. It does so using ground-based spectroradiometric measurements taken over the Athens atmosphere during May 1995. It was found that the spectral E _dλ/E _bλ ratio decreases rapidly with increasing wavelength and regression curves of the form E _dλ/E _bλ = aλ^?b fitted the experimental data. These curves are strongly modified by aerosols–air pollutants, aerosol optical properties, and SZA. The log–log plot of E _dλ/E _bλ versus λ reveals a significant departure from linearity, which is likely to be associated with aerosol physical properties and SZA effects. The effect of atmospheric turbidity, as expressed through the aerosol optical at 500 nm and SZA on the spectral E _dλ/E _bλ ratio, is investigated in detail for two discernible atmospheric conditions observed in the urban Athens atmosphere. The first case includes different atmospheric turbidity levels under the same SZA, while the second corresponds to different SZA values under the same turbidity levels. It was found that the correlation between E _dλ/E _bλ and spectral aerosol optical depth can be a useful tool in determining the aerosol optical properties and aerosol types composition.     

GANN models for reference evapotranspiration estimation developed with weather data from different climatic regions

Accurate estimation of reference evapotranspiration (ET₀) becomes imperative for better managing the more and more limited agricultural water resources. This study examined the feasibility of developing generalized artificial neural network (GANN) models for ET₀ estimation using weather data from four locations representing different climatic patterns. Four GANN models with different combinations of meteorological variables as inputs were examined. The developed models were directly tested with climatic data from other four distinct stations. The results showed that the GANN model with five inputs, maximum temperature, minimum temperature, relative humidity, solar radiation, and wind speed, performed the best, while that considering only maximum temperature and minimum temperature resulted in the lowest accuracy. All the GANN models exhibited high accuracy under both arid and humid conditions. The GANN models were also compared with multivariate linear regression (MLR) models and three conventional methods: Hargreaves, Priestley–Taylor, and Penman equations. All the GANN models showed better performance than the corresponding MLR models. Although Hargreaves and Priestley–Taylor equations performed slightly better than the GANN models considering the same inputs at arid and semiarid stations, they showed worse performance at humid and subhumid stations, and GANN models performed better on average. The results of this study demonstrated the great generalization potential of artificial neural techniques in ET₀ modeling.     

Least squares support vector machine for short-term prediction of meteorological time series

The prediction of meteorological time series plays very important role in several fields. In this paper, an application of least squares support vector machine (LS-SVM) for short-term prediction of meteorological time series (e.g. solar irradiation, air temperature, relative humidity, wind speed, wind direction and pressure) is presented. In order to check the generalization capability of the LS-SVM approach, a K-fold cross-validation and Kolmogorov–Smirnov test have been carried out. A comparison between LS-SVM and different artificial neural network (ANN) architectures (recurrent neural network, multi-layered perceptron, radial basis function and probabilistic neural network) is presented and discussed. The comparison showed that the LS-SVM produced significantly better results than ANN architectures. It also indicates that LS-SVM provides promising results for short-term prediction of meteorological data.     

Estimating sunshine duration from other climatic data by artificial neural network for ET0 estimation in an arid environment

Sunshine duration data are desirable for calculating daily solar radiation (R _s) and subsequent reference evapotranspiration (ET₀) using the Penman–Monteith (PM) method. In the absence of measured R _s data, the Ångström equation has been recommended by the Food and Agriculture Organization (FAO) of the United Nations. This equation requires actual sunshine duration that is not commonly observed at many weather stations. This paper examines the potential for the use of artificial neural networks (ANNs) to estimate sunshine duration based on air temperature and humidity data under arid environment. This is important because these data are commonly available parameters. The impact of the estimated sunshine duration on estimation of R _s and ET₀ was also conducted. The four weather stations selected for this study are located in Sistan and Baluchestan Province (southeast of Iran). The study demonstrated that modelling of sunshine duration through the use of ANN technique made acceptable estimates. Models were compared using the determination coefficient (R ²), the root mean square error (RMSE) and the mean bias error (MBE). Average R ², RMSE and MBE for the comparison between measured and estimated sunshine duration were calculated resulting 0.81, 6.3 % and 0.1 %, respectively. Our analyses also demonstrate that the difference between the measured and estimated sunshine duration has less effect on the estimated R _s and ET₀ by using Ångström and FAO-PM equations, respectively.     

Estimation of daytime downward longwave radiation under clear and cloudy skies conditions over a sub-humid region

Downward longwave radiation (LW _↓ ) is a relevant variable for meteorological and climatic studies. Good estimates of this term are vitally important in correct determining of the net radiation, which, in turn, modulates the magnitude of the terms in the surface energy budget (e.g., evaporation). In remote sensing applications, the determination of daytime LW_↓ is required for estimation of the net radiation using satellite data. LW_↓ is not directly measured in weather stations and then is estimated using models with surface air temperature and humidity as input. In this paper, we identify the best models to estimate daytime downward longwave radiation from meteorological data in the sub-humid Pampean region. Several well-known models to estimate LW_↓ under clear and cloudy skies were tested. We use downward radiation components and meteorological data registered at Tandil (Argentina) from 2006 to 2010 (840 days). In addition, we propose two multiple linear regression models (MLRM-1 and MLRM-2) to estimate LW_↓ at the surface for all sky conditions. The new equations show better performance than the others models tested with root mean square errors between 12 and 16 W m^?2, bias close to zero and best agreements with measured data (r ²?≥?0.85).     

Calibration of radar reflectivity measurements from the KMA operational radar network

A systematic procedure for calibrating system gain bias (so-called “calibration error”) of radar reflectivity measurements from the Korea Meteorological Administration (KMA) operational radar network is presented. First, the RJNI radar located at Jindo Island is calibrated by comparing with radar reflectivities simulated theoretically by a scattering algorithm using drop spectra collected by a disdrometer from June 19 to 29, 2009. Once the RJNI radar is calibrated, the reflectivity measurements from nearby radars are compared with the RJNI radar reflectivities to determine existing gain biases of nearby radars. This radar-radar calibration procedure was repeated with the other radars within the network. For isolating a system gain bias, echoes affected by partial beam blockage due to ground clutter and by attenuation due to precipitation were removed. The system gain biases of the RJNI and RPSN radars were ?3 and ?4.2 dB, respectively, during the experimental period. The RBRI and RDNH radars revealed relatively large biases, above ?8 dB. The other radars (RKSN, RGSN, RSSP, RKWK, RGDK, RIIA, and RMYN) revealed biases from ?6 to ?7 dB. Thus, the reflectivity measurements from all of the KMA radars were severely biased. New R-Z relations of R = 3.350 × 10^?2Z^0.624 (Z = 231.1R ^1.6) for stratiform and R=1.546 × 10^?2 Z ^0.714 (Z = 342.4R ^1.4) for convective precipitations were derived using disdrometer data. Using these R-Z relations, the radar-derived total rainfall amounts from the reflectivity measurements without calibration produced significant underestimations, compared to gauge measurements at about 80 sites, with a normalized bias of about ?56%. On the other hand, after calibrating the above system biases, the radar-derived rainfall amounts corresponded well with the gauge measurements, with a normalized bias of about ?3%. In conclusions, the radar reflectivity measurements from the KMA radar network are severely biased and the procedure presented in this study can be used to resolve the system gain biases.     

Retrieving air humidity,global solar radiation,and reference evapotranspiration from daily temperatures: development and validation of new methods for Mexico. Part II: radiation

We propose a new model to estimate daily global radiation from daily temperature range measurements. This model combines that of Majumdar et al. (Sol Energy 13(4):383–394, 1972) to estimate clear sky radiation with a Gompertz function to estimate the relation between temperature range and cloud transmittance. Model parameters are estimated from historical weather data: maximum and minimum temperatures and, if available, relative humidity; no other calibration is required. The model was parametrized and validated using 788 weather stations in Mexico. When calibrated using historical humidity data, daily global radiation was estimated with a mean root mean square error of 3.06 MJ m^?2 day^?1. The model performed well in all situations, except for a few stations around the Gulf of Mexico and in mountain areas. When using estimated humidity, the root mean square error of prediction was only slightly degraded (3.07 MJ m^?2 day^?1). Possible theoretical basis and applicability of this model to other environments are discussed.