Agronomy Journal 93:1321-1326 (2001)
© 2001 American Society of Agronomy
AGROCLIMATOLOGY
Incorporating Bias Error in Calculating Solar Irradiance
Implications for Crop Yield Simulations
Albert Weiss*,a,
Cynthia J. Haysa,
Qi Hua and
William E. Easterlingb
a School of Nat. Resource Sci., Univ. of Nebraska, Lincoln, NE 68583-0728
b Dep. of Geogr., Pennsylvania State Univ., University Park, PA 16802-5011
* Corresponding author (aweiss1{at}unl.edu)
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ABSTRACT
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Solar irradiance is an important input parameter to many crop simulation models. It is not measured at the same spatial density as air temperature and precipitation, which has lead to the development of algorithms to calculate solar irradiance from air temperature and precipitation data. Fourteen algorithms were evaluated using 10 yr of measured air temperature, precipitation, and solar irradiance data from Mead, NE. All algorithms had similar root mean square errors (RMSE). When the bias error (the difference between measured and simulated values) was plotted against day of year, only one version of the algorithm showed a simple pattern not dependent on fitting a Fourier series to the data. This pattern of the bias error formed the basis for a correction factor that was applied to all calculations of solar irradiance. Using independent meteorological data from nine locations in eastern and western portions of Kansas, Nebraska, and South Dakota, the corrected algorithm developed from the Mead data calculated solar irradiance with RMSE ranging from 3.6 to 4.7 MJ m-2 d-1. Using the Erosion Productivity Impact Calculator, simulated yields of wheat (Triticum aestivum L.), maize (Zea mays L.), and soybean [Glycine max (L.) Merr.] were significantly different when using the measured and uncorrected solar irradiance; however, the yields were not significantly different when using the measured and modified solar irradiance. Using this modification, solar irradiance measured at one location can be used to calculate solar irradiance at locations up to 600 km away in the U.S. Great Plains.
Abbreviations: DOY, day of year • EASN, elevation angles at solar noon • EPIC, Erosion Productivity Impact Calculator • RMSE, root mean square error
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INTRODUCTION
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SOLAR IRRADIANCE is an important weather input parameter in many crop simulation models. It is used primarily to calculate some form of carbohydrate production, e.g., daily dry matter production, and plays an important role in evapotranspiration. As new applications of crop simulation models increase and it becomes necessary to run these models at many locations, it soon becomes apparent that solar irradiance data are not as readily available on an appropriate spatial scale as are air temperature and precipitation data. This situation has led to the development of algorithms that calculate solar irradiance, with reasonable accuracy, from air temperature and precipitation data. Tacit assumptions in using these algorithms are that they be based on physical principles and that their degree of complexity should be less than the crop simulation model in which these data will be used. Since the solar irradiance algorithms tend to be empirical, questions arise about their accuracy in calculating solar irradiance and their applicability to crop simulation models.
Brinsfield et al. (1984) provide a relatively simple, physically based model for calculating solar irradiance. However this model requires hourly cloud cover, which is measured at relatively few locations; thus, for studies across a wide area, this solar irradiance model cannot be used. Hunt et al. (1998) evaluated five solar irradiance models and found that a regression-type relationship based on the difference between the maximum and minimum air temperature squared, the maximum air temperature, the precipitation, and the precipitation squared provided the best fit to measured data based on values of r2 and root mean square error (RMSE) for several locations in Ontario, Canada. Bristow and Campbell (1984) developed a relatively simple relationship to calculate solar irradiance based on the difference of maximum and minimum air temperatures and three empirical coefficients. On rainy days, this temperature relationship was modified to take into account decreased solar irradiance. Variations of the Bristow and Campbell (1984) model have been developed by Ndlovu (1994), Donatelli and Campbell (1998), and Goodin et al. (1999). Bristow and Campbell (1984) suggested using two models, one for high and another for low elevation angles at solar noon (EASN). Goodin et al. (1999) found that a single, annual model worked well. They also found that empirical coefficients developed at Manhattan, KS could be used across a wide range of locations in Kansas. Thornton and Running (1999), following suggestions in Bristow and Campbell (1984), extended this algorithm to apply over a wide range of locations by enhancing the calculation of atmospheric transmissivity. However, this more generalized approach requires vapor pressure as an additional input parameter. The algorithm presented in Thornton and Running (1999) was the basis for a new method to calculate solar irradiance (and humidity) from measured air temperature and precipitation in complex terrain (Thornton et al., 2000). Liu and Scott (2001) evaluated nine algorithms with different data input requirements to calculate solar irradiance for locations across Australia: air temperature data only, precipitation data only, and air temperature and precipitation data. Although the algorithm that required inputs of air temperature and precipitation data was the best predictor, it required the calculation of seven coefficients compared with three for the Bristow and Campbell (1984) model. The latter was almost as good a predictor as the former model.
Richardson (1985) used a mean monthly value in place of daily solar irradiance to calculate wheat yields near Oklahoma City, OK. This result compared favorably with calculations using actual daily solar irradiance. One can interpret this result as implying that daily values of solar irradiance may have little impact on yield calculations or that the cumulative effect of solar irradiance for a month on yield calculations is more important than a specific value for each day. However as Richardson (1985) noted, the major climatic factor determining yield was the lack of precipitation and resulting soil water stress rather than solar irradiance. Under conditions where yields are limited only by air temperature and solar irradiance, obviously daily values of solar irradiance are important inputs into crop simulation models. Under the condition of water stress previously mentioned, it is important to obtain realistic mean monthly values of solar irradiance. Thus, whatever conditions exist, accurate measured or estimated values of solar irradiance on a daily or monthly basis will be required.
The objectives of this research effort were to evaluate (i) different forms of the original Bristow and Campbell algorithm with data from a single location in the central Great Plains of the USA, (ii) the bias error (the difference between simulated and measured values) of solar irradiance calculations using this algorithm and incorporating this error term into a modified method, (iii) this modified algorithm for several locations in the central Great Plains, and (iv) the use of these calculated solar irradiance values in the Erosion Productivity Impact Calculator (EPIC; Williams et al., 1984; Williams et al., 1990) to calculate grain yields of winter wheat, maize, and soybean.
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MATERIALS AND METHODS
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Data used in this study were from Kansas (Tribune, Hesston, and Ottawa), Nebraska (Sidney, Clay Center, and Mead), and South Dakota (Nisland, Brookings, and Redfield) (Fig. 1)
. These daily data are maximum and minimum air temperatures, precipitation, solar irradiance, relative humidity, and wind speed collected by automated weather stations and are available from the High Plains Climate Center Web site (http://hpccsun.unl.edu/online/). The data from Mead, NE for the years 1983–1992 were used as the dependent weather data set to develop all regression coefficients while the data for 1993–1999 were used as the independent data set. The data from the other locations were also used as independent data sets; Clay Center and Sidney, NE and Brookings and Redfield, SD had 17 yr of record; Hesston, Ottawa, and Tribune, KS had 15 yr of record; and Nisland, SD had 12 yr of record. The distances between Mead, NE and the nearest (Clay Center, NE) and farthest (Nisland, SD) locations were about 150 and 700 km, respectively.
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Fig. 1. Locations in Kansas (Tribune, Hesston, and Ottawa), Nebraska (Sidney, Clay Center, and Mead), and South Dakota (Nisland, Brookings, and Redfield) used in this study.
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Fourteen algorithms, variations of the Bristow and Campbell (1984) algorithm, were investigated for calculating transmissivity for use in calculating solar irradiance (Table 1). Solar irradiance is calculated in the Bristow and Campbell (1984) algorithm as the product of the atmospheric transmissivity times the solar irradiance at the top of the atmosphere. It is assumed that solar irradiance at the top of the atmosphere can be readily calculated (Iqbal, 1983) while the atmospheric transmissivity (Tt) is calculated as:
 | [1] |
where A, b, and C are empirical coefficients, and 
T is the temperature term. In the original algorithm, the three coefficients (A, b, and C) must be determined for different seasons (high and low elevation angles at solar noon) and different locations. Ndlovu's (1994) suggestions with respect to these coefficients were followed, i.e., the maximum transmissivity was fixed at 0.75 (the A coefficient), the power coefficient, C, was fixed at 2, and the b coefficient was determined by nonlinear regression. The temperature term, T, is discussed below.
The algorithms in Table 1 can be classified according to seasonal models and an annual model. The seasonal models are divided into periods of high EASN, ±90 d from 21 June, and low EASN for the remaining days of the year. They take into account a temperature term (T), uncorrected and corrected (following Bristow and Campbell, 1984) for days with precipitation. In addition, solar irradiance at the top of the atmosphere, calculated from relationships given in Iqbal (1983), is needed on the current date and 30 d before the current date. Using solar irradiance 30 d before the current date accounts for the time lag between maximum air temperature and solar irradiance, e.g., maximum solar irradiance occurs on 21 June, but maximum air temperatures usually occur at the end of July in the midlatitudes of the northern hemisphere.
The first six algorithms (Table 1) are variations of the Bristow and Campbell (1984) algorithm used by Ndlovu (1994) and Goodin et al. (1999). The remaining algorithms are variations of ideas developed by Donatelli (2000). These algorithms are similar in structure to the first six algorithms except that they take into account average air temperature and minimum temperature functions [f(Tavg) and f(Tmin)]. The purpose of these functions is to account for temperature variations as a function of day of year (DOY) and as a weighting function for nighttime air temperatures that are higher than normal. The empirical coefficients bl, bh, by, and tnc were developed from the dependent data set from Mead, NE, as noted above, using a nonlinear regression procedure with the equations in Table 1.
Crop yields of winter wheat, maize, and soybean were simulated with EPIC using measured and simulated solar irradiance along with the other weather data unique for the nine locations shown in Fig. 1. Extensive tests of EPIC simulations were conducted for more than 150 sites and on more than 10 crops, and the overall results were that EPIC adequately simulated crop yields (Kiniry et al., 1990; Rosenberg et al., 1992). In order to isolate the impact of climate, soil properties were held constant. The soil used in the crop simulation for all locations was a Sharpsburg silty clay loam (fine montmorillonitic, mesic typic). Planting date and cultivar varied according to each location; shorter season cultivars were used in the north and west, and longer season cultivars were used in the south and east. For Sidney, NE and Nisland, SD, soybean is not usually grown. However, for thoroughness, we simulated this crop at these locations. All of the simulations were carried out under nonirrigated conditions.
The RMSE was used to evaluate the different models of solar irradiance and to evaluate the simulated crop yields. PROC MIXED (Littell et al., 1996) was used to analyze the response of simulated yield to the fixed effects of site, crop, and solar irradiance. The random effect is year due to the different climate conditions in each year. The response variable was yield, and the full three-way factorial of site, crop, and solar irradiance was modeled.
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RESULTS AND DISCUSSION
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The 14 different forms of the Bristow and Campbell algorithm (Table 1) were run using the dependent data set from Mead, NE; the resulting solar irradiance calculations were compared with measured values using the RMSE. These RMSE values for the entire year, representing results for all EASN, ranged from 4.0 to 4.6 MJ m-2 d-1 (Table 2). There were better calculations of solar irradiance for the low compared with the high EASN; values of RMSE ranged from 3.1 to 3.7 MJ m-2 d-1 for the low EASN compared with 4.7 to 5.4 MJ m-2 d-1 for the high EASN. Slightly higher RMSE values were obtained when the algorithms were tested against the independent data set. No algorithm was clearly superior to another algorithm. However, when the 10-d weighted average of the bias error for Algorithm 2 was plotted against DOY for the dependent data set (Fig. 2)
, a relatively simple pattern was observed compared with the other algorithms. In general, there was an oscillatory relationship between the bias error and DOY for the other algorithms, which could be fitted with a Fourier series. For the periods of 1 January to 9 April and from 8 October to 31 December (DOY 1–99 and 281–365, respectively), there was an almost uniform bias error of 1.64 MJ m-2 d-1. The bias error for the period from 10 April to 7 October (DOY 100–280) was in the form of a cosine curve, and a correction factor for this period was:
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Table 2. Root mean square error (RMSE) values for calculations of solar irradiance for elevation angles at solar noon (EASN; low, high, and all) for the dependent (1983–1992) and independent (1993–1999) data sets at Mead, NE using the algorithms in Table 1.
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Fig. 2. Bias error of solar irradiance predictions using Algorithm 2 as a function of day of year (DOY) for the dependent data set (1983–1992) for Mead, NE. The solid line represents a 10-d weighted average of the bias error.
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Using Algorithm 2, modified with this correction factor, the RMSE for all EASN decreased from 4.5 to 4.0 MJ m-2 d-1 on the dependent data set and from 4.9 to 4.2 MJ m-2 d-1 for the independent data set from Mead, NE; these represented reductions of 12 and 17%, respectively (Table 3).
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Table 3. Root mean square error (RMSE) values for calculations of solar irradiance for elevation angles at solar noon (EASN; low, high, and all) for the dependent (1983–1992) and independent (1993–1999) data sets at Mead, NE and the other eight locations used in this study using Algorithm 2 and the modified Algorithm 2 (as given in the text).
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When the measured solar irradiance data from the other eight locations in this study were compared with the calculated values using Algorithm 2 without the modification, the RMSE for all EASN ranged from 3.9 to 5.0 MJ m-2 d-1 (Table 3). When the modification was applied, the RMSE for all EASN ranged from 3.6 to 4.7 MJ m-2 d-1, reductions in the RMSE of 3 to 18%. Hunt et al. (1998) evaluated five models of solar irradiance for a single location for an entire year in Ontario and found that the RMSE varied from 4.0 to 7.2 MJ m-2 d-1. Using the best model of these five, they found that the RMSE varied from 3.4 to 4.1 MJ m-2 d-1 at eight locations in Ontario. Using a model similar in structure to Algorithm 3, Goodin et al. (1999) found the RMSE was 3.9 MJ m-2 d-1 for a 30-yr data set at Manhattan, KS. At nine locations out of 10 across Kansas (one location was an outlier), the annual RMSE varied from 2.6 to 3.1 MJ m-2 d-1. A possible reason for their slightly better calculations, in terms of RMSE values, was that the period of record (30 yr) used to calibrate the empirical coefficients in their algorithm was three times the length of the Mead dependent data set, i.e., the 30-yr data set has a better statistical representation of the climatology of solar irradiance. A 30-yr period of solar irradiance data are not available in all states. The longest continuous period of record for solar irradiance in Nebraska is from the automated weather data network. For consistency in this study, data from automated weather stations in South Dakota, Kansas, and Nebraska were used.
Simulated mean maize yields from EPIC using measured solar irradiance (Table 4) ranged from 2.2 to 6.6 t ha-1 at Nisland, SD and Clay Center, NE, respectively. For the same locations using Algorithm 2 and modified Algorithm 2 solar irradiance, yields were 2.2 and 5.8, and 2.0 and 6.4 t ha-1, respectively. For several locations, there was a relatively large difference between the RMSE of the yield calculations using the measured solar irradiance, Algorithm 2, and the modified Algorithm 2. For Clay Center, NE, the RMSE decreased from 1.0 to 0.3 t ha-1.
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Table 4. Simulated maize yields and standard deviations (in parentheses) for locations in Nebraska, Kansas, and South Dakota using measured solar irradiance, Algorithm 2, and modified Algorithm 2. Root mean square error (RMSE) values for simulated yields using Algorithm 2 and modified Algorithm 2.
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Simulated soybean yields and associated RMSE values were similar to the maize results (Table 5). The same locations (Nisland, SD and Clay Center, NE) as in the maize simulations represented the extremes of yield; using the measured solar irradiance, mean yields were 0.7 and 2.4 t ha-1. Using Algorithm 2 and the modified Algorithm 2, simulated soybean yields for these locations were 0.8 and 2.0 and 0.8 and 2.2 t ha-1, respectively. For Clay Center, NE, the RMSE decreased from 0.4 to 0.2 t ha-1.
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Table 5. Simulated soybean yields and standard deviations (in parentheses) for locations in Nebraska, Kansas, and South Dakota using measured solar irradiance, Algorithm 2, and modified Algorithm 2. Root mean square error (RMSE) values for simulated yields using Algorithm 2 and modified Algorithm 2.
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In contrast to the fall-harvested crops of maize and soybean, there were relatively small differences in simulated yields and associated RMSE values for the early summer-harvested crop of winter wheat (Table 6). Using the measured solar irradiance, simulated yields ranged from 2.2 to 2.8 t ha-1 for Redfield, SD (yields for Redfield, SD did not include 1986 because there were some questionable temperature records during the growing season) and Clay Center, NE. Yields simulated using both forms of the modeled solar irradiance show little change (Table 6). In contrast to the changes in RMSE values with the simulations of the fall-harvested crops, generally the changes in RMSE values associated with wheat yields were of a much smaller magnitude. In addition, the simulated wheat yields using the measured solar irradiance, Algorithm 2, and modified Algorithm 2 showed little variation. The reason for these differences are twofold; solar irradiance is better calculated under low compared with high EASN, which is indicated by a smaller RMSE for low EASN (Table 3). Also, magnitude of the solar irradiance is smaller at low rather than high EASN values. When these two factors are combined, the impact on the simulation of dry matter will be relatively small.
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Table 6. Simulated wheat yields and standard deviations (in parentheses) for locations in Nebraska, Kansas, and South Dakota using measured solar irradiance, Algorithm 2, and modified Algorithm 2. Root mean square error (RMSE) values for simulated yields using Algorithm 2 and modified Algorithm 2.
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The statistical analyses of the simulated yields from EPIC using the measured solar irradiance follow. The site x irradiance, crop x irradiance, and site x crop x irradiance interactions were not significant (P > F = 0.9993, P > F = 0.6786, and P > F = 1.0, respectively). The nonsignificance of these interactions mean that yield differences using measured solar irradiance, Algorithm 2, or modified Algorithm 2 do not differ for sites, crops, or both.
The site and crop treatments and site x crop interaction were highly significant (P > F = 0.0001). The significance of the individual terms means that the average simulated yields were different at the sites and for the different crops. The significance of the interaction (site x crop) means that the yield differences of the three crops varied between sites. Whether it be measured or modeled, the type of irradiance used was significant (P > F = 0.0302). This significance means that average simulated yields, using measured solar irradiance, Algorithm 2, and modified Algorithm 2, were different.
When comparing the least squares means for yield (mean values adjusted for the unequal length of meteorological records at each location and the unequal number of harvests), the difference in simulated yields using the measured solar irradiance and the original Algorithm 2 was significant (P > |t| = 0.0109). However, when using the measured solar irradiance and the modified Algorithm 2, the difference in simulated yield was not significant (P > |t| = 0.5143). The simulated yield differences between Algorithm 2 and the modified Algorithm 2 were significant (P > |t| = 0.0579). These results mean that the simulated yields using measured solar irradiance and the modified Algorithm 2 were the same.
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CONCLUSIONS
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Of the 14 algorithms evaluated to calculate solar irradiance, Algorithm 2 was selected because the bias error could be easily taken into account and it involved only one empirical coefficient. When the bias error correction factor was taken into account, solar irradiance calculations were consistently improved, not only at the Mead, NE location where the empirical relationships were developed, but at the wide range of locations in the study area.
The results show that the simulated grain yields from the nine sites and the three crops used in this study were different. Yet, the simulated yield results behave consistently when using measured solar irradiance, Algorithm 2, and modified Algorithm 2. However, simulated yields were not significant when using the measured solar irradiance and the modified Algorithm 2; in contrast, there were significant simulated yield differences when using the measured solar irradiance and the original Algorithm 2.
The results of this study show that statistically significant differences in grain yield simulations can occur when using the original Algorithm 2 calculations of solar irradiance compared with those of the modified Algorithm 2. Earlier studies of climate change effects on crop yields using the EPIC model with generated solar irradiance data (e.g., Easterling et al., 1993) may have provided biased yield estimates. Comparisons of results using the modified Algorithm 2 solar irradiance and results of previous studies are suggested.
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ACKNOWLEDGMENTS
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We want to thank Dr. T.J. Arkebauer and E.A. Walter-Shea for their valuable comments on an earlier version of this paper.
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NOTES
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A contrib. of the Univ. of Nebraska Agric. Res. Div., Lincoln, NE 68583. Journal Ser. no. 13293.
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REFERENCES
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- Brinsfield, R., M. Yaramanoglu, and F. Wheaton. 1984. Ground level solar radiation prediction model including cloud cover effects. Sol. Energy 33:493–499.
- Bristow, K.L., and G.S. Campbell. 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. For. Meteorol. 31:159–166.
- Donatelli, M. 2000. Global solar radiation estimate [Online]. Available at http://www.inea.it/isci/mdon/software/radest/RE_index.htm (verified 21 Aug. 2001).
- Donatelli, M., and G.S. Campbell. 1998. A simple model to estimate global solar radiation. p. 133–134. In Proc. ESA Congr., 5th, Nitra, Slovak Republic. 28 June–2 July 1998. The Slovak Agric. Univ., Nitra, Slovak Republic.
- Easterling, W.E., P.R. Crosson, N.J. Rosenberg, M.S. McKenney, L.A. Katz, and K.M. Lemon. 1993. Towards an integrated impact assessment of climate change: The Mink study: Agricultural impacts of and responses to climate change in the Missouri-Iowa-Nebraska-Kansas (MINK) region. Clim. Change 24:23–61.
- Goodin, D.G., J.M.S. Hutchinson, R.L. Vanderlip, and M.C. Knapp. 1999. Estimating solar irradiance for crop modeling using daily air temperature data. Agron. J. 91:845–851.[Abstract/Free Full Text]
- Hunt, L.A., L. Kuchar, and C.J. Swanton. 1998. Estimation of solar radiation for use in crop modeling. Agric. For. Meteorol. 91:293– 300.
- Iqbal, M. 1983. An introduction to solar radiation. Academic Press, Toronto, Canada.
- Kiniry, J.R., D.A. Spanel, J.R. Williams, and C.A. Jones. 1990. Demonstration and validation of crop grain yield simulation by EPIC. p. 220–234. In A.N. Sharpley and J.R. Williams (ed.) EPIC—Erosion Productivity Impact Calculator: 1. Model Documentation. Tech. Bull. 1768. USDA-ARS, Temple, TX.
- Littell, R.C., G.A. Milliken, W.W. Stroup, and R.D. Wolfinger. 1996. SAS system for mixed models. SAS Inst., Cary, NC.
- Liu, D.L., and B.J. Scott. 2001. Estimation of solar radiation in Australia from rainfall and temperature observations. Agric. For. Meteorol. 106:41–59.
- Ndlovu, L.S. 1994. Generating weather data for crop simulation model. Ph.D diss. Biol. Syst. Eng. Dep., Washington State Univ., Pullman.
- Richardson, C.W. 1985. Weather simulation for crop management models. Trans. ASAE 28:1602–1606.
- Rosenberg, N.J., M.S. McKenney, W.E. Easterling, and K.M. Lemon. 1992. Validation of EPIC model simulations of crop responses to current climate and CO2 conditions: Comparisons with census, expert judgement and experimental plot data. Agric. For. Meteorol. 59:35–51.
- Thornton, P.E., H. Hasenauer, and M.A. White. 2000. Simultaneous estimation of daily solar radiation and humidity from observed temperature and precipitation: An application over complex terrain in Austria. Agric. For. Meteorol. 104:255–271.
- Thornton, P.E., and S.W. Running. 1999. An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity and precipitation. Agric. For. Meteorol. 93:211–228.
- Williams, J.R., C.A. Jones, and P.T. Dyke. 1984. A modeling approach to determining the relationship between erosion and soil productivity. Trans. ASAE 27:129–144.
- Williams, J.R., C.A. Jones, and P.T. Dyke. 1990. The EPIC model. p. 3–92. In A.N. Sharpley and J.R. Williams (ed.) EPIC—Erosion Productivity Impact Calculator: 1. Model Documentation. Tech. Bull. 1768. USDA-ARS, Temple, TX.
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A. Weiss
Comments on "Evaluation of Solar Radiation Prediction Models in North America" (Agron. J. 96:391-397)
Agron. J.,
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L. C. Purcell and R. A. Ball
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TOP
ABSTRACT
INTRODUCTION
