Environmental Modelling & Software 21 (2006) 411e416 www.elsevier.com/locate/envsoft
Short communication
A software component for estimating solar radiation M. Donatelli*, L. Carlini, G. Bellocchi Agriculture Research Council e Research Institute for Industrial Crops, via di Corticella 133, 40128 Bologna, Italy Received 16 August 2004; received in revised form 22 April 2005; accepted 26 April 2005 Available online 27 July 2005
Abstract GSRad (global solar radiation) is a software component containing models to estimate extra-terrestrial and ground-level solar radiation (global and photosynthetically active; direct, diffuse, and reflected components) from alternative methods. Radiation data are estimated as either 1-h or 24-h values. Moreover, GSRad provides methods to compute clear sky transmissivity, slope and aspect angles of tilted terrains from a grid of elevation points, and geometric factors to convert radiation estimates from horizontal to nonhorizontal surfaces. The component is released as .NET assemblies, allowing the development of clients under Windows operating systems using one of the .NET languages. The component design allows extending the computing capabilities of GSRad without requiring its re-compilation. Examples of clients developed in C# are provided as source code. The component is available for free download, along with an extensive hypertext help. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Component architecture; GSRad; Solar radiation fractions; Atmospheric transmissivity; Model extensibility
Software availability Name of software: GSRad Developers: Marcello Donatelli, Laura Carlini, Gianni Bellocchi Contact address: CRA-ISCI, Bologna, Italy Telephone: C39 051 6316811 Fax: C39 051 374857 E-mail:
[email protected] Availability: http://www.sipeaa.it/tools
1. Introduction In the last decade there has been an increasing demand for modularity and interchangeability in biophysical model development (e.g. Jones et al., 2001; David et al., 2002; Donatelli et al., 2003b, 2004b), aiming both at * Corresponding author. Tel.: C39 051 6316811; fax: C39 051 374857. E-mail address:
[email protected] (M. Donatelli). 1364-8152/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2005.04.002
improving the efficiency of use of resources and at fostering higher quality of modelling units via specialization. The modular approach developed in the software industry is based on the concept of encapsulating the solution of a modelling problem in a discrete, replaceable, and interchangeable software unit. Such discrete units are called components. A software component can be defined as ‘‘a unit of composition with contractually specified interfaces and explicit context dependencies only. A software component can be deployed independently and is subject by composition by third parties’’ (Szypersky et al., 2002). Component-oriented designs actually represent a natural choice for building scalable, robust, large-scale applications, and to maximize the ease of maintenance in a variety of domains, including agro-ecological modelling (Argent, 2004). The concept of developing modular systems for biophysical simulation has lead to the development of several modelling frameworks (e.g. Simile, ModCom, IMA, TIME, OpenMI, SME, OMS, as listed in Argent and Rizzoli, 2004; Rizzoli et al., 2004), which allow making use of components by linking them either together or to a simulation engine. In spite of the
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wide acceptance of the concepts above, an extensive search in literature and on internet has not yielded references to available, ready-to-use, modelling framework independent components in the domain of biophysical modelling. Preliminary experiences made at CRA-ISCI by making available quite rudimentary components in terms of software design (Donatelli et al., 2003c; Fila et al., 2003; Donatelli et al., 2004a) have led to large numbers of downloads, indicating at least some interest of the scientific community in components developed with no specific dependency to a modelling framework. In this paper we describe a component which allows estimating solar radiation and related variables for use in modelling studies. Estimation of solar radiation has been explored in several surveys that are based on empirical or semi-empirical deterministic approaches, even implemented in dedicated software (e.g., RadEst, Donatelli et al., 2003a). Other methods to obtain solar radiation are through a stochastic process that is capable of producing one or more weather variables with the same statistical properties as naturally occurs for a given location (Wilks and Wilby, 1999). These methods are implemented into software tools usually called weather generators (WGEN, Richardson and Wright, 1984; ClimGen, Sto¨ckle et al., 2001, etc.). Some weather generators have been developed to estimate a specific weather variable, such as WGENR, an adaptation of the solar radiation model developed by Hodges et al. (1985). All such approaches illustrate from different perspectives that there is actually a wealth of well-developed solutions to the basic problem of estimating or generating radiation data. At the same time, the need to evaluate alternative approaches in a comparative fashion has suggested to make available such estimation methods in a component. The component global solar radiation (GSRad) supplies a collection of alternative, either deterministic or stochastic methods, to estimate/ generate synthetic daily and hourly radiation data and related outputs for use within agro-ecological modelling projects. The objective of this paper is to describe the scientific implementation and the software design of GSRad, focusing on the features of reusability and extensibility.
2.1. Extra-terrestrial solar radiation Solar radiation outside earth’s atmosphere is calculated at any hour based on routines derived from the solar geometry (e.g. Stine and Harrigan, 1985). Daily values are an integration of hourly values from sunrise to sunset. 2.2. Clear sky transmissivity The upper bound for the transmission of global radiation through the earth’s atmosphere (i.e., under conditions of cloudless sky), can be set to a sitespecific constant or estimated daily by diverse methods (Table 1). 2.3. Global solar radiation at ground level Broadband global solar radiation (about 0.3e3.0 mm wave-band) striking daily horizontal earth’s surfaces is estimated from alternative sets of weather inputs (Table 2) according to strategies based on either physical relationships or stochastic procedures. A sine-curve assumption is used to prescribe the hourly distribution of solar radiation from its daily value, assuming changes with solar elevation angle (Chen et al., 1999). The most simplified models (Bristow and Campbell, 1984; Donatelli and Campbell, 1998; Donatelli and Bellocchi, 2001) relate diurnal temperature range to solar energy transmission through the earth’s atmosphere. As one of the most important phenomena limiting solar radiation at the earth’s surface are clouds, a cloud cover measure is incorporated in the model from Supit and van Kappel (1998) to estimate transmissivity. The radiation model from Winslow et al. (2001) uses saturation vapour pressures at minimum and maximum air temperatures as a measure of the atmospheric transmission of incident solar radiation. The model from A˚ngstro¨m (1924) and Prescott (1940) is the most common choice to estimate global solar radiation when sunshine measurements are
Table 1 Alternative approaches for estimating clear sky transmissivity and relevant inputs Clear sky transmissivity models Source
Site features
2. Background The procedures implemented in the component, the scientific background, and some principles of usage are illustrated in a fully documented hypertext help file. A summary description of models and procedures implemented in GSRad follows.
Type of input
Thornton and Running (1999) Winslow et al. (2001) Woodward et al. (2001)
Air temperature
Solar geometry
Atmosphere features
X
X
X
X X
X
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M. Donatelli et al. / Environmental Modelling & Software 21 (2006) 411e416 Table 2 Alternative methods for estimating global solar radiation and relevant inputs Global solar radiation models Source
Bristow and Campbell (1984) Donatelli and Campbell (1998) Donatelli and Bellocchi (2001) Winslow et al. (2001) A˚ngstro¨m (1924), Prescott (1940) Johnson et al. (1995), Woodward et al. (2001) Supit and van Kappel (1998) Richardson (1981) Garcia y Garcia and Hoogenboom (submitted for publication) a
Nature
Physically-based Physically-based Physically-based Physically-based Physically-based
Type of inputs Extra-terrestrial radiation
Air temperature
X X X X X
X X X X
Cloud cover
Solar radiation
Precipitation occurrence
X X
(X)a X
X
Physically-based Physically-based Stochastically-based Stochastically-based
Sunshine
X X
X X X
X
Optional.
available. As an alternative, an implementation of the model from Johnson et al. (1995) and Woodward et al. (2001) is given. Stochastic generation is based on the dependence structure of daily maximum and minimum temperature, and solar radiation (Richardson, 1981). Such variables are reduced to time series of normally distributed residual elements with mean zero and variance of one. An autoregressive, weakly stationary multivariate process is used to generate the residuals series. Daily values of global solar radiation are generated for dry and wet days as daily deviations above and below the monthly average value. An implementation by Garcia y Garcia and Hoogenboom (submitted for publication) is given as well.
2.4. Radiation fractions The flux density at the earth’s surface, on a horizontal plane, is comprised of a fraction of direct beam, coming directly from the direction of the sun, and a diffuse radiation coming from many directions simultaneously. The irradiance on a tilted surface even includes ground reflected fraction. The current implementation derives from the general approach from Liu and Jordan (1960). The estimation of diffuse radiation on a horizontal surface depends on the extra-terrestrial irradiance and a transmission function. Hourly transmission relies on the anisotropic assumption for estimation on inclined surfaces and is further divided into the isotropic, circumsolar and horizontal ribbon sub-fractions. These sub-fractions are calculated separately and then summed to provide the diffuse irradiance. Ground reflected irradiance is estimated from a slope-dependent factor (Section 2.6). Direct fraction of solar radiation is the complement to global solar radiation.
2.5. Photosynthetically active radiation (PAR) The visible band (0.38e0.71 mm wavelength) is estimated daily by the diffuse/direct radiation ratio (Ross, 1975), and hourly by the solar elevation course (Supit and van der Goot, 2003). PAR amount can also be disaggregated into direct and diffuse fractions. 2.6. Slope and aspect angles Slope is the angle the surface makes with the horizontal plane, and aspect is the clockwise orientation to south. One or both are required to compute geometric factors that convert radiation estimates from horizontal to non-horizontal surfaces. An ESRI-based approach (http://www.esri.com) is implemented to derive slope and aspect from digital elevation data grids.
3. Software features 3.1. Inputs and outputs The outputs that may be produced by GSRad are listed in Table 3. The inputs required by the component are listed in Table 4 (variables) and Table 5 (method specific parameters). 3.2. Sample applications The source code of two Windows applications which show how to use the component is provided. The first one shows how to call some of the public methods available, whereas the second sample application shows
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Table 3 GSRad output variables and their identification number (ID) Outputs
Unit
t, clear sky transmissivity S(t), hourly (t Z hr) or daily (t Z d) extra-terrestrial solar Gx(t), hourly (t Z hr) or daily (t Z d) ground-level global solar radiation on a horizontal (x Z h) or inclined (x Z i) surface Bx(t), hourly (t Z hr) or daily (t Z d) ground-level direct solar radiation on a horizontal (x Z h) or inclined (x Z i) surface Dx(t), hourly (t Z hr) or daily (t Z d) ground-level diffuse solar radiation on a horizontal (x Z h) or inclined (x Z i) surface Ri(t), hourly (t Z hr) or daily (t Z d) ground reflected solar radiation from an inclined surface a#, slope (from a digital elevation model) g#, aspect (from a digital elevation model) Hb(t), hourly (t Z hr) or daily (t Z d) slope-aspect factor PAR(t), hourly (t Z hr) or daily (t Z d) ground-level photosynthetically active radiation PARb(t), hourly (t Z hr) or daily (t Z d) ground-level direct photosynthetically active radiation PARd(t), hourly (t Z hr) or daily (t Z d) ground-level diffuse photosynthetically active radiation DL(d), astronomical day length sr(d), sunrise hour of the day ss(d), sunset hour of the day d(d), daily solar declination b(hr) hourly solar elevation u(hr), hour angle cki;pd ;k ð3Þ; daily solar radiation residual
e MJ m2 h1, MJ m2 d1 MJ m2 h1, MJ m2 d1
1 2 3
MJ m2 h1, MJ m2 d1
4
MJ m2 h1, MJ m2 d1
5
MJ m2 h1, MJ m2 d1
6
how to extend models. As further examples of component use, a web service and a web application are developed and the relevant code made available at http://www.sipeaa.it/tools. 3.3. Extending models The developer of an application which uses the component GSRad may wish to make available to end users one or more further approaches for estimating solar radiation and related outputs. This can be done taking advantage of the GSRad component architecture, using the design pattern ‘‘strategy’’ (Mesketer, 2004). This software design allows adding further modelling capabilities to estimate global solar radiation, clear sky transmissivity, and the partitioning of radiation into beam, diffuse and reflected fractions. The key feature is that such added models can be implemented by clients without the need of recompiling the component and still using the services provided (test of preand post-conditions, see below).
Output ID
e MJ m2 h1, MJ m2 d1
7 8 9 10
MJ m2 h1, MJ m2 d1
11
MJ m2 h1, MJ m2 d1
12
h h h rad rad
13 14 15 16 17 18 19
e
contract approach has an impact on quality aspects and speed of software development, it also makes available explicit knowledge to both the system being modelled and the models implemented. Also, setting pre-conditions allows an easier development of ‘‘unit tests’’, that is, numerical tests performed on each methods implemented (the tests performed during model development are also reported in the help file) by narrowing the range of the tests. GSRad implements options to deal with input data violating pre-conditions, and to check post-conditions by making use of the component Preconditions (http:// www.sipeaa.it/tools). The output of pre- and postconditions tests can be directed to screen, to a TXT file, to an XML file, or to a custom developed output (via an implementation of the design pattern strategy in the component Preconditions). If pre-conditions are violated, exceptions may occur. GSRad includes exception handling, both preventing the application from crashing, and providing the user with information about the type and location of the exception.
3.4. The design-by-contract approach
4. Concluding remarks
The design-by-contract approach (Meyer, 1997) requires pre-conditions (in this case input values within a given range, e.g. 0 ! clear sky transmissivity ! 0.85) to be respected. Whether implementing the design-by-
The component for the computation of solar radiation data serves as a convenient means to support collaborative projects among scientists involved in creating applications implementing models for agronomy and
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M. Donatelli et al. / Environmental Modelling & Software 21 (2006) 411e416 Table 4 GSRad input variables, and the outputs calculated using each input listed as ID (see Table 3)
Table 5 GSRad input parameters, and the outputs calculated using each input listed as ID (see Table 3)
Input variables
Unit
Output ID
Input parameters
Unit
i, current Julian day number into year l, latitude
e
1, 2, 5, 13, 14, 15, 1, 2, 13, 14, 15, 16, 1, 5 7, 8 7, 8 9 3, 5 5, 6, 9 9 3, 4, 5 3 3
Output ID
A, Woodward average clear sky transmissivity B, Woodward amplitude factor ta, aerosol/ozone transmittance t0, transmittance at the sea level at nadir ea, actual vapour pressure y, clear sky transmissivity-actual vapour pressure slope b, temperature range coefficient Tnc, summer night temperature factor c1, amplitude factor of the seasonality c2, frequency factor of the seasonality ir, reverse option FF, cloud-blue factor Aa, minimum transmissivity for overcast sky Ba, transmissivity angular coefficient As, temperature range multiplicator Bs, cloud cover coefficient Cs, radiation adjustment factor a, first parameter of daily PAR b, second parameter of daily PAR TLK, Linke turbidity factor N, number of days in the month Nw, number of wet days in the month bR, scaling factor ko, wet/dry days separation option k, precipitation occurrence F k, adjustment factor for annual curve of solar radiation FPP, adjustment factor for radiation noise GkM, annual mean solar radiation for dry (k Z 0) or wet (k Z 1) days GkA, mean amplitude of solar radiation for dry (k Z 0) or wet (k Z 1) k ;k G 0 ; function of daily average global solar radiation in a month sGk0 ;k ; standard deviation of daily global solar radiation in a month o ckp;i1 ðjÞ; 3 ! 1 matrix of solar radiation, minimum and maximum air temperature residuals one day before current day Ako , 3 ! 3 matrix, function of the correlation matrix among solar radiation, minimum and maximum air temperature residuals B ko , 3 ! 3 matrix, function of the lag-1 correlation matrix among solar radiation, minimum and maximum air temperature residuals
e
1
e e e
1 1 1
Pa Pa1
1 1
C1 C1 e e e e e
3 3 3 3 3 3 3
e 0$5 C e MJ m2 d1 e e e e e e e e e
3 3 3 3 10 10 5 3 3 3 3, 19 3, 19 3
e MJ m2 d1
3 3
MJ m2 d1
3
MJ m2 d1
3
MJ m2 d1
3
e
3, 19
e
3, 19
e
3, 19
z, elevation above sea level Zi,j, elevation matrix from a DEM s, grid cell dimension d(d), daily solar declination t, clear sky transmissivity a#, slope g#, aspect Hb(t), slope-aspect factor DT(d), daily air temperature range DT(m), monthly mean air temperature range DT(w), weekly mean air temperature range DT(y), yearly mean air temperature range Tmax(d), daily maximum air temperature Tmin(d), daily minimum air temperature Tavg(d), daily average air temperature Tavg(y), yearly average air temperature SSD(d), daily sunshine duration DL(d), astronomical day length of the day b(12:00), solar elevation at noon b(hr), hourly solar elevation S(d), daily extra-terrestrial solar radiation Cw(d), daily cloud cover Gx(d), daily ground-level global solar radiation on a horizontal (x Z h) or inclined (x Z i) surface Bx(d), daily ground-level direct solar radiation on a horizontal (x Z h) or inclined (x Z i) surface Dx(d), daily ground-level diffuse solar radiation on a horizontal (x Z h) or inclined (x Z i) surface
rad m m m rad e
e C C
C
3
C
3
C
3
C
3
C
3
C
1, 3
h h
3 3
rad rad MJ m2 d1
3 10 3, 5
okta MJ m2 d1
3 10
MJ m2 d1
10
MJ m2 d1
10, 12
agro-meteorology. GSRad is a concrete and available example of a modular implementation of biophysical models. Its design, rather than being targeted to a use in a specific modelling framework, intrinsically promotes reusability by limiting dependencies, by specifying interfaces and by encapsulating the solution of a modelling problem in a discrete software unit. By providing the capability of extending its models in a simple and straightforward way, it also allows updates and model comparison. The GSRad design is being used as a template in the development of other components to estimate meteorological variables.
Acknowledgements Work jointly supported by the integrated project SEAMLESS (EU contract no. 010036-2, FP6) and the project SIPEAA (paper no. 28).
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References A˚ngstro¨m, A., 1924. Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society 50, 121e125. Argent, R.M., 2004. An overview of model integration for environmental applications e components, frameworks and semantics. Environmental Modelling and Software 19, 219e234. Argent, R.M., Rizzoli, A.E., 2004. Development of multi-framework model components. In: Pahl-Wostl, C., Schmidt, S., Rizzoli, A.E., Jakeman, A.J. (Eds.), Transactions of the Second Biennial Meeting of the International Environmental Modelling and Software Society, Osnabru¨ck, Germany, vol. 1, pp. 365e370. Bristow, K.L., Campbell, G.S., 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agricultural and Forest Meteorology 31, 159e166. Chen, J.M., Liu, J., Cihlar, J., Goulden, M.L., 1999. Daily canopy photosynthesis model through temporal and spatial scaling for remote sensing applications. Ecological Modelling 124, 99e119. David, O., Markstrom, S.L., Rojas, K.W., Ahuja, L.R., Schneider, W., 2002. The object modelling system. In: Ahuja, L.R., Ma, L., Howell, T.A. (Eds.), Agricultural System Models in Field Research and Technology Transfer. Lewis Publishers, Boca Raton, FL, USA, pp. 317e344. Donatelli, M., Bellocchi, G., 2001. Estimate of daily global solar radiation: new developments in the software RadEst3.00. In: Bindi, M., Donatelli, M., Porter, J.R., van Ittersum, M.K. (Eds.), Proceedings of the Second International Symposium on Modelling Cropping Systems. Florence, Italy, pp. 213e214. Donatelli, M., Bellocchi, G., Fontana, F., 2003a. RadEst3.00: software to estimate daily radiation data from commonly available meteorological variables. European Journal of Agronomy 18, 363e367. Donatelli, M., Bolte, J., van Evert, F., Wang, W., 2003b. Which software designs for evolution. In: van Ittersum, M.K., Donatelli, M. (Eds.), Modelling cropping systems: science, software and applications. European Journal of Agronomy 18, 193e195. Donatelli, M., Campbell, G.A., 1998. A simple model to estimate global solar radiation. In: Zima, M., Bartosˇ ova´, M.L. (Eds.), Proceedings of the Fifth European Society for Agronomy Congress, Nitra, The Slovak Republic, pp. 133e134. Donatelli, M., Carlini, L., Bellocchi, G., 2004a. GSRad: un componente software per la stima della radiazione solare. Rivista Italiana di Agrometeorologia 1, 24e30. Donatelli, M., Omicini, A., Fila, G., Monti, C., 2004b. Targeting reusability and replaceability of simulation models for agricultural systems. In: Jacobsen, S.E., Jensen, C.R., Porter, J.R. (Eds.), Proceedings of the Eighth European Society for Agronomy Congress, 11e15 July, Copenhagen, Denmark, pp. 237e238. Donatelli, M., Sto¨ckle, C.O., Nelson, R.L., Bellocchi, G., 2003c. ET_CSDLL: a dynamic link library for the computation of reference and crop evapotranspiration. Agronomy Journal 95, 1334e1336. Fila, G., Bellocchi, G., Donatelli, M., Acutis, M., 2003. IRENE_DLL: a class library for evaluating numerical estimates. Agronomy Journal 95, 1330e1333. Garcia y Garcia, A., Hoogenboom, G. Evaluation of an improved daily solar radiation generator for the southeastern USA. Climate Research, submitted for publication. Hodges, T., French, V., LeDuc, S.K., 1985. Estimating solar radiation for plant simulation, models. AgRISTARS Tech. Rep. JSC-20239; YM-15e00403, Columbia, MO, USA.
Johnson, I.R., Riha, S.J., Wilks, D.S., 1995. Modelling daily net canopy photosynthesis and its adaptation to irradiance and atmospheric CO2 concentration. Agricultural Systems 50, 1e35. Jones, J.W., Keating, B.A., Porter, C.H., 2001. Approaches to modular model development. Agricultural Systems 70, 421e443. Liu, B.Y.H., Jordan, R.C., 1960. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4, 1e19. Mesketer, S.J., 2004. Design Patterns in C#. Addison-Wesley, Boston, MT, USA. Meyer, B., 1997. Object-Oriented Software Construction, second ed. Prentice Hall, Upper Saddle River, NJ, USA. Prescott, J.A., 1940. Evaporation from a water surface in relation to solar radiation. Transactions of the Royal Society of South Australia 64, 114e118. Richardson, C.W., 1981. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research 17, 182e190. Richardson, C.W., Wright, D.A., 1984. WGEN: A Model for Generating Daily Weather Variables. U.S. Department of Agriculture, Agricultural Research Service, ARS-8. Rizzoli, A.E., Donatelli, M., Muetzelfeldt, R., Otjens, T., Svennson, M.G.E., van Evert, F., Villa, F., Bolte, J., 2004. SEAMFRAME, a proposal for an integrated modelling framework for agricultural systems. In: Jacobsen, S.E., Jensen, C.R., Porter, J.R. (Eds.), Proceedings of the Eighth European Society for Agronomy Congress, 11e15 July. Copenhagen, Denmark, pp. 331e332. Ross, J., 1975. Radiative transfer in plant communities. In: Monteith, J.L. (Ed.), Principles. Vegetation and the Atmosphere, vol. I. Academy Press, London, United Kingdom, pp. 13e55. Stine, W.B., Harrigan, R.W., 1985. Solar Energy Systems Design. John Wiley and Sons, Inc, New York, USA. Sto¨ckle, C.O., Nelson, R.L., Donatelli, M., Castellvı` , F., 2001. ClimGen: a flexible weather generation program. In: Bindi, M., Donatelli, M., Porter, J.R., Van Ittersum, M.K. (Eds.), Proceedings of the Second International Symposium on Modelling Cropping Systems, Florence, Italy, pp. 229e230. Supit, I., van Kappel, R.R., 1998. A simple method to estimate solar radiation. Solar Energy 63, 147e160. Supit, I., van der Goot, E., 2003. Updated system description of the Wofost crop growth simulation model as implemented in the crop growth monitoring system applied by the European Commission. Treemail, Heelsum, The Netherlands. Szypersky, C., Gruntz, D., Murer, S., 2002. Component Software e Beyond Object-Oriented Programming, second ed. AddisonWesley, London, United Kingdom. Thornton, P.E., Running, S.W., 1999. An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity and precipitation. Agricultural and Forest Meteorology 93, 211e228. Wilks, D.S., Wilby, R.L., 1999. The weather generation game: a review of stochastic weather models. Progress in Physical Geography 23, 329e357. Winslow, J.C., Hunt, E.R., Piper, S.C., 2001. A globally applicable model of daily solar irradiance estimated from air temperature and precipitation data. Ecological Modelling 143, 227e243. Woodward, S.J.R., Barker, D.J., Zyskowski, R.F., 2001. A practical model for predicting soil water deficit in New Zealand pastures. New Zealand Journal of Agricultural Research 44, 91e109.
