Abraha, Savage_2008_Comparison of Estimates of Daily Solar Radiation From Air Temperature Range for Application in Crop Simulations

7/28/2019 Abraha, Savage_2008_Comparison of Estimates of Daily Solar Radiation From Air Temperature Range for Applicati

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Comparison of estimates of daily solar radiation from airtemperature range for application in crop simulations

M.G. Abraha, M.J. Savage * SoilPlantAtmosphere Continuum Research Unit, Agrometeorology Discipline, School of Environmental Sciences,University of KwaZulu-Natal, Pietermaritzburg, 3201 South Africa

1. Introduction

Crop simulation models have been successfully used toprovide simulations of growth, development and yield of crops ( Jones and Ritchie, 1990 ). Most crop simulation models

require daily solar radiation ( Is), maximum and minimum airtemperatures ( T x and T n ), and precipitation (PP) ( Whisler et al.,1986; Ritchie, 1991; Hunt andBoote, 1998 ). Solar radiationis theprimary input for estimations of reference evaporation andplant biomass accumulation in most crop simulation models.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y 1 4 8 ( 2 0 0 8 ) 4 0 1 4 1 6

a r t i c l e i n f o

Article history:Received 31 January 2007Received in revised form31 August 2007Accepted 1 October 2007

Keywords:Daily solar radiationAir temperature rangeRadiation modelling Model evaluationCrop yield modelling

a b s t r a c t

Daily solar radiation is an input required by most crop growth, development and yieldsimulation models. It is, however, not observed at many locations, preventing the applica-tion of such models. The objective of this work was to (i) evaluate several existing modelsestimating solar radiation based on daily minimum and maximum air temperature and/orprecipitation for seven sites in the world, and (ii) investigate the impact of the estimatedsolar radiation on grass reference evapotranspiration (ETo) and total plant dry biomasssimulations for maize. Comparisons of the solar radiation models was made based on asingle modular indicator, Irad , computed using a fuzzy expert system that aggregated severalstatistical indices, and distribution of mean daily errors over a year. The model estimationswere also evaluated according to their ability to simulate ETo and total dry biomass thatmatches simulations from the observed solar radiation.According to the Irad indicator, therewas no solar radiation model which consistently outperformed all the other models at allthe sites tested, but Irad indicated models that relatively underperformed at all the sites. Thegraphical presentation of the mean uctuation of errors over a year gave a good assessmentof the solar radiation estimation models in investigating the temporal behaviour andmagnitude of the residuals. Performance of the models according to Irad and simulationsof grass ETo and total dry biomass agreed better for models that relatively underperformed.Ranking of the models according to the root mean square error (RMSE) in solar radiationestimation and the RMSE in the grass ETo simulations agreed very well. Comparison of theranking of the models using the Irad (or the individual statistical indices thereof) and totalbiomass simulation was difcult because of the difference in the time scale used incalculation of the statistical indices. The difference in simulations of total dry biomassaccumulated over the years, however, qualitatively agreed with the graphs of the meanuctuation of errors over a year. In general, the Irad indicator demonstrated which solarradiation estimation models should be used for crop simulation modelling.

# 2007 Elsevier B.V. All rights reserved.

* Corresponding author . Tel.: +27 33 2605514; fax: +27 33 2605514.E-mail address: [email protected] (M.J. Savage).

ava i l ab l e a t www.sc i enced i r ec t . com

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0168-1923/$ see front matter # 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.agrformet.2007.10.001
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However, solar radiation data is not as readily available as airtemperature and precipitation data ( Liu and Scott,2001; Weissand Hays, 2004 ). Even at stations where solar radiation isobserved there could be many days when solar radiation dataaremissing or lieoutside the expected range due to equipmentfailure and other problems ( Hunt et al., 1998 ). These problemscould be one of many: calibration problems, problems with

dirt on the sensor, accumulated water, shading of the sensorby masts, etc. The lack of solar radiation data restricts theapplication of crop simulation models ( Hook and McClendon,1992) at locations where recordson past crop experiments andother weathervariables are available. Thishas led researchersto develop a numberof methodsfor estimatingsolarradiation.Some of these methods include estimating solar radiationfrom other available meteorological observations (e.g., Ang-strom, 1924; Cengiz et al., 1981; Bristow and Campbell, 1984;Hargreaves et al., 1985; Hunt et al., 1998; Thornton andRunning, 1999; Liu and Scott, 2001; Mahmood and Hubbard,2002), substitution of data from nearby stations (e.g., Huntet al., 1998; Trnka et al., 2005; Rivington et al., 2006 ), linearinterpolation (e.g., Soltani et al., 2004 ), interpolation in neuralnetworks (e.g., Elizondo et al., 1994; Reddy and Ranjan, 2003 ),satellite-based methods (e.g., Pinker et al., 1995 ) and genera-tion from stochastic weather models (e.g., Richardson andWright, 1984; Hansen, 1999 ).

For accurate crop simulations accurate inputs of theweather variables, including solar radiation, are required.Therefore, in the absence of solar radiation data, accurateestimation techniques have considerable signicance. Theabove techniques for estimating solar radiation have varying degree of complexity, input requirements and accuracy of outputs. Useof solar radiationdata from nearby stations is notalways the best option (e.g., Rivington et al., 2006 ) and theiraccuracy decreaseswith increase in distance ( Hunt et al., 1998;Trnka et al., 2005 ) as they are dependent on climate and/ortopography (e.g., Weiss et al., 2001; Rivington et al., 2006 ).Linear interpolation requires solar radiation data at the site of interest and often fails to reproduce the actual day-to-dayvariation (e.g., Soltani et al., 2004 ). Training neural networksusually requires large data sets and the resulting model maynot be applicable to other locations ( Weiss and Hays, 2004 ).The low sampling frequency and coarse spatial resolution of satellite-based methods ( Pinker et al., 1995 ) renders theminadequate for site-specic application. Satellite-based meth-ods are also relatively new and may not provide long-termhistorical weather data. Generated weather data may be usedfor creating possible scenarios, but cannot be used forcalibration and validation of crop simulation models for aparticular period of time ( Hook and McClendon, 1992; Liu andScott, 2001).

Solar radiation estimation methods from other standardmeteorological observations, however, have the advantagethat the variables used for estimation are commonly observedand available within the site of interest. The most commonapproach of estimating daily solar radiation using thesemethods is to determine the daily extraterrestrial solarradiation ( Iex ) for the site and modify it using the dailyatmospheric transmission coefcient (tt i). The inter-relation-ship between tt i and other meteorological observations suchas air temperature, atmospheric vapour pressure, precipita-

tion and sunshine duration is exploited to estimate daily solarradiation.

Solar radiation can be easily estimated from sunshineduration measurements using several equations with varying degree of complexity following the classic work of Angstrom(1924). In fact, models that estimate solar radiation fromsunshine duration fared better than models involving other

standard meteorological observations involving air tempera-tureand precipitation (e.g., Podesta et al., 2004; Rivingtonet al.,2005; Trnka et al., 2005 ). However, sunshine duration is notcommonly observed in standard meteorological stations asare air temperature and precipitation. In this context, solarradiation estimation models based on daily air temperaturerange and/or precipitation are attractive and viable options.These models are very simplistic, but allow widespreadapplication because air temperature and precipitation areobserved practically in all meteorological stations.

The daily solar radiation that is received at the earthssurface strongly affects the thermal conditions at the surfaceand the immediate atmosphere which in turn can be used asan index of cloudiness andsolar radiation load ( Mahmood andHubbard, 2002 ). Solar radiation estimation models that utilizethese thermalconditions arebased on the assumptions that (i)clear skies will increase the daily maximum air temperaturebecause of the greater short wave radiation input whileresulting in decreased minimum air temperature due toreduced long wave emission from the atmosphere; and (ii)cloudy conditions will decrease the daily maximum airtemperature due to reduced transmissivity while resulting in increased minimum air temperature due to increased long wave emission from theclouds( Donatelli andCampbell, 1998 ).Bristow and Campbell (1984) using this relationship estimateddaily solar radiation using an exponential function of daily airtemperature range ( D T ) and precipitation (see Appendix A fordetails). They were able to account for 7090% of the variationin incoming daily solar radiation data at three northwesternsites in the USA. The Bristow and Campbell (hereafter calledBC) model has been modied by others for specic applica-tions.Forexample, Donatelli and Marletto (1994) and Donatelliand Campbell (1998) included a summer night air temperaturefactor to improve underestimation of predicted values during the summer; Goodin et al. (1999) rened the equation byadding an extra Iex term that is meant to act as a scaling factorallowing D T to accommodatea greater range of solar radiationvalues, although Mahmood and Hubbard (2002) found it toperform worse than the original model for the Northern GreatPlains; Thornton and Running (1999) introduced atmosphericwater vapour pressure to the equation in an attempt toeliminate the need for site-specic calibration of coefcients;and Donatelli and Bellocchi (2001) attemptedto accountfor theeffect of seasonal variation by introducing a trigonometricfunction. Hargreaves et al. (1985) also developed a simplelinear relationship between daily air temperature range andtt i. Hunt et al. (1998) , based on the evaluation of ve solarradiation models, found best estimates in a model withmultiple-linear relationship between daily incoming solarradiation, and air temperature and precipitation. Mahmoodand Hubbard (2002) also found more stable estimations of daily incoming solar radiation from clear-sky solar radiationand daily air temperature range compared with the BC model.



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Most of these models require some observed solar radiationdata for derivation of coefcients, which may inhibit theirapplication at sites where solar radiation has not beenobserved before.

Previous work in this eld has concentrated on evaluating theuncertainty of dailysolar radiationestimation modelsovera localized area (e.g., Hunt et al., 1998; Liu and Scott, 2001;

Mahmood and Hubbard, 2002; Rivington et al., 2005 ). Evalua-tion of most of the existing solar radiation estimation modelsover a wide range of geography and climate in the world islacking. Therefore, the objective of this study was to (i)compare various models that estimate daily global solarradiation from daily maximum and minimum air tempera-tures and/or precipitation over several locations in the world,and (ii) investigate the impact of the estimated solar radiationon simulationsof grass reference evapotranspiration and totalmaize dry biomass using a cropping systems simulationmodel (CropSyst).

2. Materials and methods

2.1. Data

Meteorological data were obtained from seven stations with arange of latitude, longitude and elevation around the world.Information on the sites and period of recorded data ispresentedin Table1 . Thesites includedat leastdailymaximumandminimumairtemperature( T x and T n ),precipitation (PP)andsolar radiation ( Is) data. The data were checked for outliers foreachweathervariable.ForDavis,CAmissingdatawerereplacedby data from another weather station at the same latitude andlongitude. For the other sites, if one or more weather variablewas missing, then all the weather variables for that day werereplaced by that from another year (a year or two of data wereset aside for such purposes for each site) of the same site andday. Precipitation occurrences in that day and two previousdays were taken into account when replacing missing data asthismay affect theestimations.This avoids replacementofdatathrough optimization or other relationships and ensures thatthe data are still from the same site. A year with more than 30days of missing or faultydata was discarded(e.g., the year 1996for Cortez, Colorado).

2.2. Solar radiation estimation formulae

For each site and year of available data, Is was estimated using six solar radiation estimation models presented in Table 2 .

These models were chosen as representative of the existing models that utilize Iex andreadily availableweatherdata of T x ,T n and/or PP. Further information on the models is given inAppendix A .

2.3. Coefcients

All the models require Is (MJ m2) for derivation of thecoefcients for estimation of solar radiation. The BC, CDand DB models are contained within the software RadEst tool(beta v3.00) (SIPEAA, 2006) and iterative optimization utilitiesare provided within the software for determining thecoefcients. The RadEst tool has been used for estimation of solar radiation in previous works (e.g., Bellocchi et al., 2002;Rivington et al., 2006 ). Derivation of the coefcients for theHgvs model involved simple linear regression, and forthe HKSand MH models multiple-linear regression with natural log transformations for the latter ( Genstat, 2006 ). For each site, 3years of daily data of T x, T n , PP, and Is were used for derivationof the coefcients. The data sets used for derivation of coefcients were from consecutive years with no or littlemissing data. The derived coefcients were then used toestimate solar radiation for all the years excluding the onesused for derivation of the coefcients.

2.4. Statistical evaluation

Most studies evaluating the performance of solar radiationmodels have traditionally used coefcient of determination(R2), mean square error (RMSE) and/or model bias to assessmodel suitability and comparison (e.g., Hunt et al., 1998; Liuand Scott, 2001; Mahmood and Hubbard, 2002; Ball et al., 2004;Chen et al., 2004; Weiss and Hays, 2004 ). Evaluation of theperformance of the solar radiation models using a particularsingle or separate multiple statistics not organized in asystematic manner may be inadequate as each statisticevaluates a particular aspect of the model ( Bellocchi et al.,2002; Rivington et al., 2005 ). Bellocchi et al. (2002) argued that amodel may be deemed unsuitable according to one statisticevaluating certain aspects of the model but other features of the model may still be desirable. On the other hand, a modelmay be judged suitable according to one statistic but it may bedecient according to another statistic. To obviate suchproblems, Bellocchi et al. (2002) used a fuzzy-logic basedsystem that simultaneously considers several statisticalindices. The system allows aggregation of several statisticalindices into a single module by assigning an expert weightaccording to the relative importance of the particular

Table 1 Sites of meteorological stations and period of data records used for estimation of solar radiation

Location Latitude Longitude Elevation (m) Period

Cortez, Colorado, USA 37 8 140 (N) 1088 410 (W) 1833 19922005Davis, California, USA 38 8 320 (N) 1218 470 (W) 18 19852005Padova, Italy 44 8 580 (N) 128 110 (W) 0 19902003Rothamsted, UK 51 8 480 (N) 08 240 (E) 128 19802000Wageningen, The Netherlands 51 8 580 (N) 58 380 (E) 7 19852005Pretoria, South Africa 25 8 450 (S) 288 110 (E) 1308 19932003

Grifth, Australia 348

170

(S) 1468

30

(E) 125 19862005

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statistical index. The weight assigned to each statistical indexwas on the basis of the authors experience. The modules arealso aggregated, in the same manner as for the indices, into asingle indicator. The indices and modules considered arepresented in Table 3 . The indices relative root mean squareerror (RRMSE), model efciency (EF) and two-tailed pairedt-test P(t) are aggregated into module Accuracy; correlationcoefcient (R) into module Correlation; and pattern of theresiduals against independent variables of day of year (PI doy )and daily minimum air temperature (PI Tn ) are aggregated intomodule Pattern. Computation of the pattern indices, PI doy andPITn , involves dividing the residuals into four groupsaccording to the independent variables and then calculating pairwisedifferences between the four average residuals. Furtherinformation on patterns of residuals is documented byDonatelli et al. (2004) . The modules Accuracy, Correlationand Pattern are then aggregated into a single modularindicator, Irad , which enabled ranking of the models ( Fig. 1).

Three membership classes (subsets) are dened for allindices: favourable (F), unfavourable (U) and partial (fuzzy)membership. These membership classes, along with decisionrules, are used to calculate a dimensionless module whosevalue ranges between 0 (best model performance) and1 (worstmodelperformance). Membership functions that are S-shapedin transition interval were used ( Bellocchi et al., 2002 ). Therelative importance of the indices, modules and the weightsassigned to them are presented in Fig. 1. Detailed illustrationof aggregation of indices into modules and modules into asingle indicator is presented by Bellocchi et al. (2002).

This study makes use of such an indicator to evaluate thesolar radiation models. The aggregation of indices intomodules and modules into an indicator was performedfollowing the logic in the IRENE_DLL system for modelimplementation ( Fila et al., 2003). Besides, a simple graphicalpresentation of the mean difference between estimated andobserved solar radiation across all years for all the sites wasconsidered for assessment of the solar radiation models.

2.5. ETo and biomass simulations

Observed and estimated solar radiation along with T x, T n andPP, maximum and minimum relative humidity (RH x and RHn )or vapour pressure and wind speed were used to simulategrass reference evapotranspiration (ETo) and total drybiomass of maize at two sites for which the solar radiationestimation was best and worst according to Irad as computedfor all the models. The only variable that kept changing witheach simulation was the solar radiation as observed andestimated from the different models. Daily ETo wascalculatedaccording to the FAO Penman-Monteith procedure as recom-mended by Allen et al. (1998). A soil and plant growthsimulator, CropSysta multi-year multi-crop simulationmodel developed to study the effect of cropping systemsmanagement on productivity and environment ( Sto ckle et al.,2003), was used for biomass simulation purposes. The modelhasbeen tested andvalidated fora wide range of managementconditions and a variety of crops and cropping systems in arange of locations over the world ( Sto ckle, 1996). Default cropparameters formaizewere used. Planting date at each locationwasset to that locally practiced.Thesimulationwasrun forallthe number of available continuous years in rotation along with fallow conditions.

The effect of estimated solar radiation on simulated totaldry biomass of maize was analyzed using the differencebetween cumulative and mean of total dry biomasssimulated from the observed and estimated solar radiationinputs, seasonal means of absolute differences of total drybiomass, R2 during the simulation period, RMSE for indivi-dual seasonal simulations and maximum error between theseasonal dry biomass simulations from the observed andestimated solar radiation inputs. The calculated statisticalmeasures were used in ranking the performance of the solarradiation models on their ability to simulate total drybiomass that matches that simulated using the observedsolar radiation.

Table 2 Models used for estimation of solar radiation

Authors Model abbreviation Model requirements

Bristow and Campbell (1984) BC Iex , T x, T n and PP a

Donatelli and Campbell (1998) CD Iex , T x, T n and PPDonatelli and Bellocchi (2001) DB Iex , T x, T n and PPHargreaves et al. (1985) Hgvs Iex , T x and T nHunt et al. (1998) HKS Iex , T x, T n and PPMahmood and Hubbard (2002) MH Iex , T x and T na The BC, CD and DB models require presence or absence of PP while the HKS model requires the amount (see Appendix A ).

Table 3 Statistical indices and modules used in evaluation of solar radiation models

Index Notation Range Best value Module

Relative root mean square error (%) RRMSE 0 1 0 Accuracy (amount of residuals)Model efciency EF 1 to 1 1Paired Student t-test probability of equal means P(t) 01 1

Correlation coefcient R 11 1 Correlation

Pattern index by day of year (MJ m 2) PIdoy 01 0 Pattern (state of pattern in residuals)

Pattern index by minimum air temperature (MJ m2

) PITn 01 0



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3. Results

All the solar radiation models were calibrated using 3 yearsdata for the specic locations under study. The coefcientsderived for each location and model are presented in Table 4 .Not many works report coefcients for models. Bellocchi et al.

(2002) reported model coefcients for the BC, CD and DBmodels for several locations over the world. For these models,the coefcients derived in our study fall within the range of coefcients they reported. Bechini et al. (2000) for 29locations in northern Italy and Trnka et al. (2005) for 10locations in Czech Republic and Austria also reported model

Fig. 1 The statistical indices, modules and the indicator used for statistical evaluation along with the decision rules andtheir systematic aggregation (indices: RRMSE, relative root mean square error; EF, model efficiency; P ( t ): two-tailed paired t -test; R , correlation coefficient; PI doy and PI Tn pattern of the residuals by day of year and by minimum air temperaturerespectively); modules: Accuracy, Correlation and Pattern, I rad , single modular indicator; F, favourable; U, unfavourable).

Table 4 Calibrated model coefficients for all locations

Model Parameter Location

Cortez,Colorado,

USA

Davis,California,

USA

Padova,Italy

Rothamsted,UK

Wageningen,The Netherlands

Pretoria,SouthAfrica

Grifth,Australia

BC b 0.107 0.137 0.141 0.110 0.100 0.126 0.123c 2 2 2 2 2 2 2

CD b 0.203 0.262 0.396 0.345 0.331 0.39 0.282T nc 104.1 44.5 42.1 106.1 64.1 84.8 100.0

DB b 0.112 0.122 0.131 0.106 0.099 0.134 0.119c1 0.034 0.026 0.040 0.011 0.026 0.053 0.015c2 1.410 1.410 0.008 1.183 0.215 0.041 1.137

Hgvs b1 1.172 0.784 2.041 0.610 0.728 0.258 0.330b2 0.155 0.162 0.190 0.141 0.140 0.173 0.163

HKS b0 1.112 0.301 1.420 0.022 0.235 0.149 2.197b1 0.161 0.164 0.186 0.147 0.132 0.169 0.169b2 0.032 0.050 0.003 0.019 0.039 0.021 0.112b3 0.355 0.264 0.302 0.356 0.305 0.395 0.760b4 0.004 0.004 0.003 0.008 0.008 0.006 0.019

MH b0 0.077 0.067 0.076 0.146 0.099 0.263 0.374b1 0.758 0.796 0.897 0.488 0.721 0.791 0.745b2 1.129 1.172 1.122 1.151 1.088 0.775 0.677

See Appendix A for details of the models.



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coefcients for the CD model. The T nc parameter, in bothcases, appeared to be smaller than presented in this study.This could be because of the localized location they used fortheir studies.

The Hgvs and HKS models predicted quite a few negativesolar radiation values at low daily air temperature rangerecords, especially in the temperate sites during winter. The

estimated solar radiation for such days was set to zero. TheHKS model, because it uses a polynomial function of dailyprecipitation amount for estimation of solar radiation, alsopredicted an unreasonably high solar radiation at highprecipitation records, in two occasions for Pretoria and

Grifth. Assuming these days were overcast, the value of estimated solar radiation was corrected by multiplying the Iexby 0.25 for such days ( Gates, 1980).

3.1. Model evaluation according to the indicator I rad

Mean values of indices and modules are calculated and

presented in Table 5 for each site. Table 6 also presents themean indices and modules for each model over all the sites. Itis apparent from Table 5 that ranking of the solar radiationmodels based on an individual statistic or index is difcult. Amodel may perform well according to one index but may not

Table 5 Performance of the solar radiation models by site according to mean of the indices RRMSE (relative root meansquare error), EF (model efficiency), P( t ) (two-tailed paired t -test), R (correlation coefficient), and PI doy and PI Tn (pattern of residuals by day of year and minimum air temperature respectively); and the modules Accuracy, Correlation and Pattern,and the indicator, IradLocation Model RRMSE

(%)EF P(t) R PIdoy

(MJ m2)PITn

(MJ m2)Accuracy Correlation Pattern Irad

Cortez,Colorado, USA

BC 17.50 0.84 0.14 0.92 1.78 1.55 0.1848 0.0006 0.3799 0.1759CD 17.77 0.83 0.00 0.92 1.74 1.35 0.2286 0.0006 0.3741 0.1962DB 18.42 0.82 0.03 0.92 1.83 1.66 0.2186 0.0016 0.4084 0.1902Hgvs 18.34 0.83 0.17 0.91 1.89 2.08 0.1676 0.0022 0.5606 0.2227HKS 16.88 0.85 0.07 0.93 1.69 1.59 0.1905 0.0000 0.4297 0.1970MH 19.32 0.80 0.04 0.91 2.94 1.79 0.2123 0.0008 0.7147 0.2823

Davis,California, USA


Padova, Italy BC 26.34 0.82 0.24 0.91 2.23 1.86 0.2396 0.0008 0.6632 0.2880CD 25.72 0.83 0.03 0.92 1.70 1.13 0.2141 0.0004 0.2970 0.2126DB 26.32 0.82 0.08 0.91 1.90 1.51 0.2674 0.0004 0.4925 0.2542Hgvs 25.42 0.84 0.00 0.92 1.15 1.34 0.2971 0.0000 0.1628 0.1541HKS 23.54 0.86 0.00 0.93 1.30 1.30 0.2463 0.0000 0.2096 0.1359MH 28.73 0.79 0.00 0.91 2.76 1.13 0.4255 0.0012 0.5154 0.3787

Rothamsted, UK BC 31.51 0.83 0.24 0.91 0.92 0.70 0.3739 0.0003 0.0557 0.1838CD 31.69 0.82 0.19 0.92 0.99 0.79 0.4280 0.0002 0.0555 0.2313DB 31.66 0.82 0.31 0.91 0.81 0.68 0.3579 0.0008 0.0368 0.1611Hgvs 34.30 0.79 0.04 0.90 0.88 0.84 0.5401 0.0028 0.0650 0.3307HKS 32.26 0.82 0.10 0.91 0.81 1.08 0.4491 0.0007 0.0850 0.2470MH 37.43 0.75 0.00 0.89 2.4 0.86 0.6461 0.0097 0.4428 0.5131

Wageningen,The Netherlands


Pretoria,South Africa


Grifth, Australia BC 21.77 0.78 0.06 0.89 1.37 1.60 0.2301 0.0131 0.3721 0.1945CD 21.53 0.79 0.12 0.90 1.82 1.69 0.2105 0.0116 0.4511 0.2157DB 21.62 0.79 0.06 0.89 1.25 2.15 0.2117 0.0101 0.4582 0.2172Hgvs 21.38 0.79 0.23 0.90 1.55 1.64 0.1553 0.0093 0.3969 0.1637HKS 20.74 0.80 0.25 0.90 1.92 1.33 0.1644 0.0197 0.3721 0.1699

MH 22.74 0.77 0.12 0.88 2.19 1.36 0.2502 0.0289 0.5286 0.2682



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do so according to another. Overall, according to Irad , the DB(0.2061) model closely followed by the CD (0.2089) model wasranked top of the group. The DB model had in general bestresults for PI doy while the CD model was best according toRRMSE, EF and PITn . The correlation coefcient, R, had littleeffect on the integrated index, Irad , as the R value for most of the sites and years was close to or greater than 0.9 except forPretoria. The MH model was ranked last of the group with anoverall Irad value of 0.3655, by far larger (less desirable) thanthe other models. The MH model also was often ranked last of the group according to most of the other indices for each site.The mean values of indices and modules over all years for allthe sites may be indicative of model performance for thatindex and module but it should not mean that the modelrankedrst based on that overall mean index or moduleis bestfor all sites. It should also be noted that the aggregation of theindices was performed on a yearly basis and not afteraveraging across all years. In evaluating the models, not onlythe rank but also the difference between the scores of eachrank for each model should be considered.

The BC model, according to Irad , appeared to perform wellfor higher elevation (Cortez (0.1759), Rothamsted (0.1838),Pretoria (0.2143) and Grifth (0.1945)) than for lowerelevation (Padova (0.2880), Davis (0.2738) and Wageningen(0.3063)) sites (Table 5 ). The best result of Irad achieved bythis model was for Cortez. This was also the best Irad valuescored for that site. The BC model had the best overallresults for the paired t-test and in general, it produced smallresiduals compared to the other models with overall meanRMSE of 3.27 MJ m2 (Table 6 ). This enabled it to achieve rstrank according to the overall mean Accuracy ( Table 6 ). It alsoproduced the best Accuracy result at one site and second tobest at ve other sites. Otherwise it produced large PI doy andPITn values which resulted in large Pattern (less desirable)values compared to the other models, especially for thelower elevation sites. The model was also not consistent inthe ranks it achieved according to the module Pattern for theindividual sites.

TheCD model wasranked second with a slightly greater Iradvalue than theDB model ( Table 6 ). The CD model was strong inproducingsmallPI Tn values. According to thisindex,it was thebest model at four sites (Cortez, Davis, Padova and Wagenin-gen), and this led to best Pattern result at three of these sites(Cortez, Davis and Wageningen). But it produced largerresiduals which saw it ranked in the middle of the groupaccording to the module Accuracy ( Table 6 ). It had particularlypoor results for the paired t-test, P(t), for which it was ranked

last at two sites (Cortez and Davis). Otherwise it producedoverall best results for the indices RRMSE (RMSE 3.23 MJ m 2)and EF (0.82) (Table 6 ).

The DB model was the best of all the models according toIrad (Table 6 ). The rank of the model according to most of theindividual indices wasabout average at allthe sites. It resultedin two best Accuracies (Davis and Rothamsted) and two bestPatterns (Rothamsted andPretoria). Itsoverall RMSE value was3.27 MJ m2 (Table 6 ). The DB model generally produced largerPITn at most sites but it produced best results of PI doy at twosites (Rothamsted and Pretoria) that nally enabled it toachieve the best Pattern value at those sites.

The Hgvs model was ranked third in the overall ranking according to Irad (Table 6 ). The model did not showconsistency in the ranks it achieved according to mostmodules and indices. For example, it resulted in bestAccuracy at three sites (Cortez, Wageningen and Grifth)but thenit was atthe tailof the ranks for all the other sites forthe same module. Consequently, it was ranked fth in theoverall ranking forall sitesaccording to the module Accuracy.The model was ranked second according to the modulePattern. This was mainly because it produced about thesmallest PI doy at two sites (Padova and Wageningen) com-pared to the other models.

The HKS model was ranked fth in the overall ranking according to Irad (Table 6 ). This model also did not showconsistency in the ranks it achieved according to Irad as itscored different ranks at different sites, from rst to last(Table 5 ). Its overall ranking according to the modulesAccuracy and Pattern was fourth and third respectively. Itscored the best result for module Pattern at Grifth jointlywith theBC model.This was mainlybecauseof thebest resultinPITn (see Table 5 ). At theothersites, it producedbest resultsof PIdoy (Cortez, Davis and Rothamsted), however, thecorresponding PI Tn values were not as good to result in bestPattern values. The HKS model appeared not to perform wellforthe semi-aridregionswhere thereoccurredinfrequent buthigh rainfall amounts. This was reected in the moduleCorrelation at Pretoriaand Grifth, where theHKS model wasranked last and second to last respectively according to thismodule.

The MH model, which was ranked last according to Irad(Table 6 ), was almost consistently ranked last of the modelsaccording to all the indices and modules ( Table 5 ). The onlytime that it came out of the last ranks was when the modelswere ranked according to the paired t-test, P(t), in which therewas no clear pattern of ranks, and PI Tn .

Table 6 Performance of each model for the indices RMSE (root mean square error), RRMSE (relative root mean squareerror), EF (model efficiency), P( t ) (two-tailed paired t -test), R (correlation coefficient) and PI doy and PI Tn (pattern of residuals by day of year and minimum air temperature respectively); and the modules Accuracy, Correlation and Pattern, and theindicator, Irad as averaged over all the sitesModel RMSE

(MJ m2)RRMSE

(%)EF P(t) R PIdoy

(MJ m2)PITn

(MJ m2)Accuracy Correlation Pattern Irad

BC 3.27 23.16 0.82 0.14 0.91 1.68 1.47 0.2765 0.0126 0.3851 0.2338CD 3.23 22.89 0.82 0.08 0.91 1.53 1.12 0.2948 0.0113 0.2667 0.2089DB 3.30 23.34 0.81 0.11 0.91 1.44 1.32 0.2789 0.0164 0.2963 0.2061Hgvs 3.36 23.74 0.81 0.09 0.91 1.46 1.36 0.3082 0.0249 0.2833 0.2288HKS 3.24 23.31 0.82 0.08 0.90 1.53 1.30 0.3053 0.1240 0.2896 0.2422MH 3.66 25.83 0.78 0.04 0.90 2.61 1.45 0.3767 0.0348 0.5633 0.3653



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3.2. Patterns of observed versus estimated daily meanerrors

A graphicaldistribution of mean daily errorsover a year forthesites considered could indicate a systematic behaviour of themodel and serve as a means of quick visual evaluation of model performance ( Rivington et al., 2005 ). A graph of the

mean daily errors against day of year ( Fig. 2) revealed theexistence of temporal and spatial pattern for most of themodels. The patterns appeared to be different for the northernand southern hemisphere sites, but similar within therespective hemispheres for each model implying that solarradiation estimations are dependent on latitude and season.Cortez, with the highest elevation of all the sites in this study,showeda pattern which is less clearor different from theothersites for some of the models. This also suggests thatestimations may be dependent on elevation as well. Ingeneral, Davis and Padova showed the smallest and largestuctuations of mean daily errors respectively for all sites.

For convenience, the seasons winter, spring, summer andautumn for the northern hemisphere are dened roughly asthe months from December to February, March to May,June toAugust and September to November respectively; and for thesouthern hemisphere June to August, September to Novem-ber, December to February and March to May respectively.

The BC model showedsimilar patterns at Davis andPadovawith an overestimation of solar radiation in winter, earlyspring,late summerandautumnand underestimationof solarradiation in late springandearlysummer.A slight tendencyof overestimation was observed at both Cortez and Rothamstedin summer. For the southern hemisphere sites, the meandailyerrors were well distributed around the observed mean at

Pretoria from autumn through spring but an overestimationwasobserved at Grifth for similar seasons. The best Irad valuefor BC was observed at Cortez (0.1759).

The CD model, for the sites in the northern hemisphere,overestimated (Cortez) and underestimated (Rothamsted andWageningen) in winter. At Davis, underestimation in winter,spring and summer and overestimation in autumn wasobserved. At Padova, errors were evenly distributed with atendency of underestimation in summer. In the southernhemisphere themodel overestimated solar radiation from lateautumnup to late springbutresulted in an evendistribution of errors in spring and summer. The best Irad value for the CDmodel wasobserved at Davis (0.1326) where theuctuations of the mean daily errors were small.

The DB model, for the sites in the northern hemisphere,appeared to overestimate solar radiation in winter, earlyspring and autumn but underestimate it in late autumn andsummer (Cortez, Davis and Padova). The errors were evenly

Fig. 2 Difference between estimated and observed mean daily solar radiation against day of year for all models and sites.



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distributed for Rothamsted with a tendency to underestimateat Wageningen. For the sites in the southern hemisphere, theDB model overestimated solar radiation for most of the year.The best Irad value for the DB model was for Pretoria (0.1349)although the model seemed to overestimate from autumn tolate spring at this site.

The Hgvs model showedthe tendency to overestimate solar

radiationatallofthenorthernhemispheresitesexceptatCortezwhere errors were evenly distributed and at Padova where themodelunderestimatedduringwinterandearlysummer.Forthesouthern hemisphere sites, in spring, the model tended tooverestimateat Pretoriaand underestimateat Grifth.The bestIrad valueobserved for themodel was atDavis (0.1517)where theuctuations of the mean daily errors were small.

For the HKS model, there was no clear pattern of errors forthe northern hemisphere sites. At Wageningen, solar radia-tion was underestimated almost throughout the year. AtRothamsted, the errors seem to be evenly distributed. AtCortez, they appear to be evenly distributed in spring andsummer with underestimations in winter and autumn. AtDavis, the errors uctuated about the mean with a slighttendency to underestimate in spring and summer. Largeunderestimationswere observed at Padovain thesummer.Forthe southern hemisphere, the HKS model overestimated in allthe seasons except in summer. The best Irad value for the HKSmodel was observed at Padova (0.1359). But the modelappeared to underestimate solar radiation in summer and

also the largest uctuations of errors for all models wereobserved at this site.

The existence of patterns was best illustrated by the MHmodel where all the sites produced similar shapes of uctuation of mean daily errors for the respective hemi-spheres. For the rst half of the year, the sites in the northernhemisphere showed a V shaped pattern in which there was

consistent underestimation of solar radiation. This wasfollowed by an even uctuation of errors in the second half of the year. For the sites in the southern hemisphere, themodel produced errors with a W shape in which anoverestimation occurred in the middle of the year. The bestIrad value for the MH model was observed at Grifth where thetemporal distribution of the daily mean errors uctuatedaround the mean throughout the year except in autumn.

3.3. Grass ETo and biomass simulation

Grass ETo and total dry biomass were simulated for Davis andWageningen for which solar radiation estimation modelscollectively produced the smallest and largest Irad valuesrespectively ( Table 5 ). For the grass ETo simulation, the fullweather data set including T x , T n , PP, RHx and RHn or watervapour pressure and wind speed along with the observed andestimated solar radiation were used. For total dry biomasssimulation, all the available years with observed andestimated solar radiation at both sites were used.

Fig. 3 Grass ETo simulated from observed and model-estimated solar radiation for Davis, California.



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For both Davis and Wageningen, the grass ETo simulatedfrom observed and estimated solar radiation appear to be welldistributed along the 1:1 line ( Figs. 3 and 4) with a slightoverestimation of lower and underestimation of higher valuesof grass ETo. Slope, intercept, R2 and RMSE, presented in thegraph, were used to rank the models, although not asrigorously as Irad . Wageningen had a lower slope and larger

RMSE compared with Davis implying that the solar radiationwas not well estimated at Wageningen as it was at Davis. Theranking of the models according to Irad was reected in theranking of the models according to the grass ETosimulationatDavis but not at Wageningen, with only the rst and last ranksmatching at Wageningen. Nevertheless, the RMSE achievedfrom the grass ETo simulations for both sites conrmed theranking of the solar radiation models for Davis and Wagenin-gen according to the index RRMSE ( Table 5 ).

The total dry biomass simulated using the observed solarradiation is taken as a baseline and all simulations frommodel-estimated solar radiation were compared against it(Table 7 ). The smallest and largest mean differences (magni-tude) between the baseline and model-simulated solarradiation simulations were, in tonnes ha 1, 0.02 and 0.71(n = 18), and 0.31 and 1.53 (n = 19) for Davis and Wageningenrespectively. These suggest that the simulations of total drybiomass from model-estimated solar radiation reasonablymatched the baseline simulations. The agreement betweenthe baseline and model-estimated solar radiation simulations

of total dry biomass was better for Davis compared toWageningen ( Fig. 5), as was the solar radiation estimationfrom all the models for these sites. The total and meandifferences presented in Table 7 indicated that, for both Davisand Wageningen, the simulated total dry biomass from allmodel-estimated solar radiation was underestimated exceptfor an overestimation from the DB model at Davis and the

Hgvs model at Wageningen. But the magnitude of theunderestimations was greater at Wageningen than at Davis.Fig. 5 illustrates theextent of theunder andoverestimationsof total dry biomass for each season by all models for both sites.

The total biomass simulation for the BC model at Davis, ingeneral, resulted in a closestmatch to thebaseline simulationscompared with simulations from the other models. Thelargest seasonal under and overestimations by this modelwere (tonnes ha 1) 0.73 and 0.59 respectively (only the largerof the two in magnitude is presented in Table 7 ). Theseindicated that there was compensation of errors from theunder and overestimations in the total biomass simulationsover all the years. As a result, the absolute difference for thismodel was by far larger than that indicated by the meandifference ( Table 7 ). The total and mean differences alsoindicated that the CD model underestimated the total andmean biomass simulations ( Table 7 ). The CD model under-estimated the seasonal total biomass simulations in almostallyears leaving little room for error compensation in the totaldrybiomass accumulated over all the years ( Fig. 5). The largest

Fig. 4 Grass ETo simulated from observed and model-estimated solar radiation for Wageningen, The Netherlands.



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under and overestimations by this model were (tonnes ha 1)0.81 and 0.49 respectively. In contrast, the total and meanbiomass simulations were overestimated by the DB model.The DB model was the only model that overestimated thetotal dry biomass simulations at Davis. The largest underand overestimations by this model were 0.48 and1.77 tonnes ha 1 respectively. The largest overestimation thatoccurred with the simulations using the DB model-estimatedsolar radiationwasan isolated single incidence that happenedin a year when the DB model overestimated the solar radiationfor most of the days during the growing season. Otherwise,the next largest overestimation by the model was0.67 tonnes ha 1. The total and mean difference of totalbiomass simulations from the Hgvs andHKSmodelsproducedsecond and third closest match to the baseline simulationsrespectively. These models also had well distributed underandoverestimations,and simulations with close to zero errors

(Fig. 5). The smallest absolute maximum error in the biomasssimulations (0.66 tonnes ha 1) was observed from the Hgvsmodel. The largest under and overestimations for Hgvs andHKS models were (tonnes ha 1) 0.66 and 0.62, and 0.70 and0.63 respectively. The absolute differences indicated thatthese two models and the BC model simulated seasonal drybiomass that matched well to the baseline compared with theother models ( Table 7 ). The MH model consistently under-estimated the total biomass simulation for all seasons exceptonce implying there was no room for error compensation inthe total dry biomass accumulation. Consequently, it was theworst according to the measures of total, mean and absolutedifferences. The largest under and overestimations by thismodel were (tonnes ha 1) 1.63 and 0.06 respectively.

At Wageningen, the picture was different with most of themodels underestimating the total dry biomass over all theyears and seasons.The BCmodel had three, theCD and DBhad

Fig. 5 Total dry biomass (tonnes ha S 1 ) simulations from using observed and estimated solar radiation from the different models (a) for Davis, California and (b) Wageningen, The Netherlands.

Table 7 Statistical comparison of total dry biomass (tonnes ha S 1 ) simulations for maize at Davis, California andWageningen, The Netherlands using observed and estimated solar radiation

Observed BC CD DB Hgvs HKS MH

Davis, California ( n = 18)Acc. total dry biomass (tonnes ha 1) 177.26 176.88 174.34 180.49 176.74 176.22 164.53Total difference (tonnes ha 1) (0.38) (2.92) 7.51 (0.52) (1.04) (12.74)Mean total dry biomass (tonnes ha 1) 9.85 9.83 9.69 10.03 9.82 9.79 9.14Mean difference (tonnes ha 1) (0.02) (0.16) 0.18 (0.03) (0.06) (0.71)Maximum error (tonnes ha 1) (0.73) (0.81) 1.77 (0.66) (0.70) (1.63)mean absolute error (tonnes ha 1) 0.25 0.29 0.38 0.24 0.25 0.72RMSE (tonnes ha 1) 0.321 0.355 0.531 0.319 0.330 0.848R2 0.99 0.99 0.98 0.99 0.99 0.99

Wageningen, The Netherlands ( n = 19)Acc. total dry biomass (tonnes ha 1) 345.33 331.95 336.15 338.55 351.13 316.33 320.04Total difference (tonnes ha 1) (13.38) (9.19) (6.78) 5.80 (29.00) (23.50)Mean total dry biomass (tonnes ha 1) 18.18 17.47 17.69 17.82 18.48 16.65 16.84Mean difference (tonnes ha 1) (0.70) (0.48) (0.36) 0.31 (1.53) (1.33)Maximum error (tonnes ha 1) (1.77) (1.82) (1.57) 1.76 (2.98) (2.67)Mean absolute error (tonnes ha 1) 0.87 0.61 0.64 0.54 1.66 1.45RMSE (tonnes ha 1) 0.981 0.790 0.743 0.697 1.841 1.610R2 0.90 0.92 0.91 0.91 0.82 0.86

Acc. dry biomass: the total dry biomass accumulated during the simulation period; total and mean difference: the absolute differences in totaland mean dry biomass simulated from estimated and observed solar radiation; maximum error: the largest absolute difference in simulatedtotal dry biomass (negative values indicate the direction of change); RMSE: root mean square error; R2: coefcient of determination.



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four, and the HKS and MH had two seasons in which therewas an overestimation otherwise the total dry biomasssimulations were underestimated in all the seasons. Theoverestimations also appeared to be smaller in magnitudethan the underestimations.This indicated that there was littleroom for compensation of errors in the total dry biomasssimulations accumulated over all the years. The largest under

andoverestimations by these modelswere (tonnes ha 1)1.77and 0.73, 1.82 and 0.59, 1.57 and 1.02, 2.98 and 0.97, and2.67 and 0.62 for the BC, CD, DB, HKS and MH modelsrespectively. The Hgvs model, however, overestimated thetotal dry biomass in more than half of the total simulationyears with underestimation in the rest of the years. Theoverestimations were larger than the underestimations. Thelargest under and overestimations by this model were(tonnes ha 1) 0.54 and 1.76 respectively. The largest andsmallest absolute maximum errors observed in the simula-tions were by the HKS (2.98 tonnes ha 1) and DB(1.57 tonnes ha 1) models respectively. The under and over-estimations observed in the total biomass simulation at thissite were in accordance with the mean daily error graphs of model-estimated solar radiation for Wageningen ( Fig. 2).

According to most of the statistics ( Table 7 ) used in thebiomass simulation the MH model was ranked last at Davis, asit was in the solar radiation estimation according to Irad . Theranking of the CD and BC models seems to have swappedranks according to the statistics used in the biomasssimulation compared with the ranking according to Irad . TheCD and BC models were ranked rst and fth according to Iradrespectively, but the BC model was ranked rst and the CDfourth several times according to the statistics used in thebiomass simulation. But it should be noted that the differencein score among thefour models ranked rst to fourth using thestatistics in the biomass simulation was small. Most of thestatistics used in the biomass simulation were measures of residuals, but the CD model was ranked rst at Davis mainlybecause it produced the best result for the module Patternotherwise it produced similar residuals compared to some of the other models. The ranking of the rest of the modelsaccording to the statistics used in the biomass simulation atthis site was similar to the ranking of the models according toIrad .

At Wageningen, the HKS and MH models were ranked lastand second to last respectively according to Irad , and so werethey in their ranking according to the statistics used in thebiomass simulation. There was little difference in the score of Irad for the other four models and this was reected in theranking according to the statistics used in the biomasssimulation. But, overall, the Hgvs model appeared to beranked rst by most of the statistics used in the biomasssimulations followed by the DB, CD and BC models. Thisranking did not match the ranking of the solar radiationmodels according to the Irad scores, or for that matter any of the modules or conventionally usedstatistical indices thereof.

4. Discussion

Theresults demonstrated that most of themodelstestedwere,in general, able to adequately estimate daily solar radiation

from daily air temperature range and/or precipitation. Theranking of the models, according the indicator, Irad , revealedthat there was no model as such which consistently out-performed all of the other models at all sites. It, however,indicated that the performance of the MH model wasconsistently lower (largest Irad value) at all sites comparedto the other models.

The values of the indices and modules achieved for eachmodel from the calculation indicate the strength and weak-nesses of the model in dealing with the respective index(Table 5 ) (Bellocchi et al., 2002 ). The BC model produced betterresiduals (RRMSE, EF and P(t)) but poor patterns (PI doy and PI Tn ).The CD model was good in handling the indices RRMSE, EF andPITn but was poor in P(t). TheDB model was particularly good inproducing better P(t) and PIdoy . The Hgvs model appears toperform well in allthe indices but PI doy . Theperformanceof theHKSmodelwasabout anaveragein theoverall results ofmostof the indices but lacked consistency at the individual sites. TheMH model showed some strength for the index PI Tn only butotherwise it was poor according to all indices and modules.

The models contained within the RadEst tool (BC, CD andDB)generally performed very well. The BC model wassuperiorin producing smaller residuals than the CD and DB models atmost of the sites. But it was inconsistent in the patterns of residuals it produced. This may be expected as the improve-ment of the CD and DB models over the BC model was in theseaspects. Although correlation had little effect in the sitestested, the CD model appeared to produce better correlations.The DB model had the overall best Irad value, but theCD modelrelatively produced better individual indices at most of thesites. The overall ranks that the DB and CD models achievedand the consistency that they showed in the scores of theindividual indices makes them better options for estimating solar radiation from daily air temperature range and pre-cipitation.

The Hgvs model, considering the simplicity of the formulaeand relative ease of deriving the coefcients for eachgeographic area compared to the other models, performedwell to be ranked third in the overall ranking. But theinconsistency in the results of the statistical indices that ithad showed makes it less desirable as a better option forestimating solar radiation. The largest uctuations that wereobserved from this model were during the rainy seasonimplying the inclusion of precipitation in solar radiationmodels is appropriate.

The HKS model includes the precipitation quantity as PPand (PP)2 in its formulae. The coefcients of these twovariables were negative and positive respectively for all sites.In the case of high rainfall amounts, the estimated solarradiation could be by far greater than that observed. It may beeasy to detect and correct such estimations when they lieoutside the expected range of solar radiation but not whenthey lie within the expected range. The latter can causeundesirable model performance. Moreover, the coefcientsderived for such a model may be erroneous if derived using acalibration dataset with abnormallyhigh precipitation values.Liu and Scott (2001) found that models that use precipitationas a binary input (present or absent) to perform better than theones that use precipitation quantity such as HKS. In general,the HKS model may have less application for semi-arid



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climates where infrequent and high rainfall amounts may beobserved.

The MH model showed clear seasonal and spatial patternsas was illustrated for the northern and southern hemispheresites irrespective of latitude, altitude anddistance to the coast.Mahmood and Hubbard (2002) found similarresults when theycompared the MH with the BC model, leading them to

conclude that the MH model was more stable. But they foundthe BC model to slightly outperform the MH model based onRMSE,d index of agreement ( Willmott, 1981 ) and relative errorfor the Northern Great Plains. Identication of the cause of thepatterns the MH model showed could help in modication of the model to better estimate solar radiation.

Of particular interest is also the uctuation of errors atPadova. Padova showed consistently the largest temporaluctuations of errors compared to the other sites for allmodels. This could be due to, as Padova is located near theAdriatic Sea, a maritime climate inuence. Rivington et al.(2005) have noted similar observations for sites located nearthe coast in the UK.

Rivington et al. (2005) illustrated uctuations of mean dailyerrors for sites in the UK using the CD and DB models. Thesewere similar to the uctuations observed at Rothamsted inthis study, but the values of Irad and other indices calculatedfor Rothamsted in this study were better than theirs. Thedifference in number and type of data setsused for calibrationand validation of the models might be responsible for thesediscrepancies. In general, they achieved Irad values ranging from 0.301 to 0.642 and 0.322 to 0.633 using the CD and DBmodels respectively for several locations in the UK. In otherstudies, involving data from ten locations around the world,Irad values ranging between 0.0086 and 0.5518, 0.0385 and0.5040,and 0.0044 and 0.4704 were reported for the BC, CD andDB models respectively ( Bellocchi et al., 2002 ). The Irad valuescalculated in this study for all the sites fall well between theranges reported in both the above studies. The RMSE has beenwidely used for evaluation of daily solar radiation models andmean or range of this value (in MJ m 2) reported by otherauthors include: for the BC model 3 ( Bristow and Campbell,1984),4.7(Hunt et al., 1998 ), 3.534.78 (Mahmood and Hubbard,2002); for the CD model 2.374.26 (Donatelli and Campbell,1998); for the DB model 2.33.9 (Bechini et al., 2000); forthe Hgvs model 4.24.7 ( Hunt et al., 1998 ); for the HKS model3.44.1 (Hunt et al., 1998 ); and for the MH model 3.904.93(Mahmood andHubbard, 2002 ). The rangeof RMSE achieved inthis study for all models at the individual locations was (inMJ m2) between 2.56 and 4.11 (data not shown) which fallswell within the ranges reported in the other studies.

The statistical results ( Table 7 ) and graphical presentations(Figs. 35) demonstrated that estimates of solar radiation fromdaily air temperature range and/or precipitation could besuccessfully used for grass ETo and total dry biomass simula-tions.Butcareshouldbe exercisedin choosingthebest modeltorepresent the actual solar radiation. At Davis, estimations fromall the models but the MH model could be successfully used inplace of measured data for biomass simulation purposes. AtWageningen, the systematic errors in model-estimated solarradiation maycause a systematic biasin totalplantdrybiomasssimulations. But still, the Hgvs, DB, CD and BC models could beused to give a representative total dry biomass simulation at

this site. The choice of model-estimations may also depend onparticular interest of application. For example, at Wageningenthe Hgvs model should be used if the interest is the smallestabsolutedifferenceandtheDBifthesmallestmaximumerrorisrequired. The statistical results used in the grass ETo using observed and estimated inputs of solar radiation reected theranking of the solar radiation models according to the overall

means of RMSE and to some extent Irad . The ranking of themodels according to the statistics used in the biomasssimulations and Irad , however, agreed well only for modelsthat did notrelativelyperformwell. Therankof themodels thatperformed well with respect to Irad was not reected in thestatistics used in the biomass simulation, but the difference inthe score of the statistics was small. Rivington et al. (2005)suggestedthat the yearly individual indices of RRMSE, EF, Randpatternindicesmaybemoreindicativethantheoverallmeanof Irad since the accuracy and precision of daily weather valuesbecomes more important. But the yearly values of the aboveindices gave little indication of the corresponding errors in thetotal dry biomass simulations. This could be because thestatistical indices used in the evaluation of the solar radiationmodels were calculated for the whole year but the statistics inthe biomass simulations were calculated only from part of theyear which was involved in growing the plant. The response of the solar radiation model during the growing season may bedifferent compared to the whole year. Besides crop growthmodelscontain non-linear functions in which a certain changeininputmayaffecttheoutputdifferently.Ingeneral,themodelswith small Irad produced better simulations (small residuals)and the models with large Irad produced worse simulations(large residuals) although the exact rankof the models was notreected in the biomass simulations for the models thatperformed relatively well. The pattern of the mean dailyerrors(Fig. 2), however, agreed well with the under and overestima-tions of total dry biomass simulations, especially at Wagenin-gen.Graphicalpresentationof thedistributionof themean dailyerrors, along with the Irad , makes the evaluation of the solarradiation models easier. In general, Irad asameansofevaluationof solar radiation models for application in crop simulationmodels was better in discriminating models that did notrelatively perform well. It wasalsohelpfulin indicating sites forwhich the performance of the solar radiation models was goodor poor.

5. Conclusions

In the absence of solar radiation measurement data, reliableestimates can be made from easily available meteorologicalobservationsofair temperatureand/or precipitationalong withextraterrestrial radiation using several existing models. Com-parison of the performance of the models using individualstatisticalindicesprovedtobedifcultbecauseofthenumberof statistical indices considered and the contrasting results theygive. A model could be good according to one statistical indexbut poor according to another index. Aggregation of thestatistical indices into a single modular indicator, Irad , using the fuzzy-logic expert system enabled evaluation and ranking of the solar radiation models performance.According to the Iradindicator, there wasno model which consistentlyoutperformed



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the other models as some models made good estimates at onesite and poor at other sites. But the Irad was good indiscriminating models that relatively underperformed at allsites. Overall, the DB and CD models were found to be bestestimators of solar radiation and the MH model the worst.Graphical presentation of the mean uctuation of the errorsover a year also demonstrated the temporal behaviour of the

models in estimating solar radiation. Sites for which the solarradiationmodelsresultedinrelativelygood Irad valuesproducedbetter simulations of grass ETo and total dry biomass thatmatched the simulations from using inputs of observed solarradiation. Ranking of the models according to the Irad and thegrass ETo and total dry biomass simulations agreed better formodels which relatively did not perform well. The ranking of the models according to the RMSE in the grass ETo simulationsalso agreed very well with the RRMSE (or RMSE) in the solarradiation estimation. Comparison of the solar radiationestimation models according to statistical indices used in thesolar radiation estimation and the total dry biomass simula-tions was difcult because of the difference in the timescaleused in the indices calculation (overall mean or yearly in theformer case and seasonal in the latter). Although the ranks of the relatively good performing models according to the Irad wasnot reected in the grass ETo and total dry biomass simulationexactly, the difference between the statistical indices used inthe grass ETo and total dry biomass simulation was small. Thegraphical presentationof themeanuctuationof theerrorsalsoroughly indicatedthe directionof theerrors ingrass ETo ortotaldry biomass simulation. In general, Irad was able to indicatewhich solar radiation estimation model should be used forapplication in crop simulation models.

Acknowledgements

Weather data for Cortez from Colorado Agricultural Meteor-ological Network (COAGMET); for Davis from University of California, Integrated Pest Management Program (UC IPM); forPadova from University of Basilicata Viale Ateneo Lucano,Potenza, Italy; forRothamsted fromRothamstedResearch, UK;for Wageningen from Wageningen University and ResearchCenter,Meteorology andAir Quality section, Wageningen, TheNetherlands; for Pretoria from South African Weather Service(SAWS) Pretoria, South Africa; and for Grifth from CSIRO,Landand Water,Grifth, Australia is gratefullyacknowledged.The paper beneted from the comments of the anonymousreviewers.

Appendix A. Models for estimating daily solarradiation from daily air temperature range and/orprecipitation

The BC, CD and DB modelsestimate daily solar radiation, Is(MJ m2), at the earths surface as:

Is tt iIex (A1)

where tt i is the daily atmospheric transmissioncoefcientandIex (MJ m2) is the daily extraterrestrialsolar radiationwhich is

calculated based purely on solar geometry and the solar con-stant (e.g., Swift, 1976; Campbell and Norman, 1998 ). The tt ipart of Eq. (A1) is estimated by the BC, CD and DB models asfollows:

BC model (Bristow and Campbell, 1984 ):

tt i t

1 expb D Tic

D Tm ; (A2)

CD model (Donatelli and Campbell, 1998 ):

tt i t 1 exp b0:017exp exp 0:053Tavg i

D Ti2 expTniTnc

0BBBBBB@

1CCCCCCA

26666664

37777775; (A3)

DB model (Donatelli and Bellocchi, 2001 ):

tt i t 1 c1 sinir p180 c2 ir p180 f c2 1 exp b D Ti

2

D Tw !" #;(A4)

f c2 1 1:90c2 int c2 3:83c2 int c22 (A5)

where t is clear-sky atmospheric transmission coefcient, i isday of year, b and c are the daily air temperature range coef-cients, T x(i) and T n( i) (

8 C) are the daily maximum and minimumair temperatures respectively, D T i (

8 C) =T x(i) (T n( i) + T n( i + 1) )/2,D T m (8 C) is the xed monthly mean D T , T nc is the summernightair temperature factor, T avg( i) (8 C) = (T x( i) + T n( i))/2, ir is a reverseoption ( ir = 1 for no reverse; ir = 361 i for reverse), c1 and c2 aregeneralseasonalityfactors, int( c2)istheintegerof c2 and D T w (8 C)is the mobile weekly mean D T . On rainy days D T i is reduced by25%, and if D T on theday before rain occurred, D T (i 1), was lessthan D T (i 2) by 2 8 C it was also reduced by 25% assuming thatcloudy conditions began on day ( i 1) (Bristow and Campbell,1984). Extended rain periods enable equilibration betweenincomingsolar radiation and D T anddo notrequireadjustments(Bristow and Campbell, 1984 ). The T nc factor is meant toprevent underestimation of solar radiation prediction during summer that may be introduced due to higher T n . The BC, CDand DB models are contained within the software RadEst toolwhich is freely available via the website http://www.sipeaa.it/tools .

Hgvs model ( Hargreaves et al., 1985 ):

Is b1 b2 ffiffiffiffiffiffiffiffiffiffiDTiq Iex (A6)where b1 and b2 are empirical coefcients and DT (i) =T x (i) T n( i).

HKS model (Hunt et al., 1998 ):

Is b0 b1Iex DT0:5

i b2Txi b3PPi b4PPi2 (A7)

where b0, b1, b2, b3 and b4 are empirical coefcients, and PP(mm) is the daily total precipitation.

MH model (Mahmood and Hubbard, 2002 ):

http://www.sipeaa.it/toolshttp://www.sipeaa.it/toolshttp://www.sipeaa.it/toolshttp://www.sipeaa.it/tools


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The MH model estimates daily incoming solar radiationbased on clear-sky solar radiation ( Icc )calculated from day of year, maximum daylength for the year for a given latitudefollowing Cengiz et al. (1981):

Is b0 DTb1iIb2cc (A8)

where b0, b1 and b2 are empirical coefcients.

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Abraha, Savage_2008_Comparison of Estimates of Daily Solar Radiation From Air Temperature Range for Application in Crop Simulations