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AGROCLIMATOLOGY

Estimating Solar Irradiance for Crop Modeling Using Daily Air Temperature Data

^a Dep. of Geography, Dickens Hall, Kansas State University, Manhattan, KS 66506-0801 USA
^b Weather Data Library and Dep. of Communications, Kansas State University, Manhattan, KS 66506 USA

dgoodin{at}ksu.edu

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 
Crop growth models require solar irradiance as input data, yet there are few places where such data are routinely measured. For locations where measured values are not available, solar irradiance can be estimated using empirical models such as the Bristow–Campbell (B–C) model. This study was conducted to assess the spatial and seasonal accuracy of the B–C model for midcontinental locations in Kansas. A 30-year data set from Manhattan, KS, was used to calibrate and evaluate unmodified and modified forms of the B–C model. The effect of seasonality was investigated by subdividing the yearly data into two subsets, a high noontime solar elevation angle period, ranging from DOY 121 to 273, and a low noontime elevation angle period comprising the remainder of the year. The B–C model was also evaluated without seasonal division of the year. The calibrated models were then tested against measured solar irradiance values for 10 sites distributed across the state of Kansas. Results indicate that, for the calibration site at Manhattan, irradiance was more accurately estimated using a modified form of the B–C model. For the yearly data, root mean square error (RMSE) was 3.9 MJ m^-2 d^-1 (25% error), compared with 5.2 MJ m^-2 d^-1 (24% error) for the high solar elevation angle period and 3.6 MJ m^-2 d^-1 (32% error) for the low solar elevation angle period. The RMSE for the 10 test sites ranged from 2.0 to 6.2 MJ m^-2 d^-1; percentage error ranged from 26 to 47%. Neither latitude nor distance from the calibration site significantly affected the accuracy of irradiance estimates at the evaluation sites. Results suggest that the modified B–C model provides reasonably accurate estimates of irradiance at noninstrumented sites and that the model can successfully be used at sites away from the calibration site. Seasonal subdivision of the data adds little to the accuracy of estimates.

Abbreviations: DOY, day of year • NWS, National Weather Service • RMSE, root mean square error

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 
CROP MODELS are increasingly being used to forecast yields, determine risk, and/or provide support for management decisions (Hammer and Muchow, 1991; McCown et al., 1996; Heiniger et al., 1997). While these models require solar irradiance data as input, there are few places where solar irradiance data are measured, especially for longer time periods. Between 1950 and 1965, only 93 permanent solar irradiance measurement sites existed in the United States (Hook and McClendon, 1992). While the number of stations has increased, the network of measurement sites is still sparse. The period of record of the newer sites is also short, restricting their application in retrospective or validation studies (Hutchinson, 1991).

The need for solar irradiance data for crop models has led researchers to develop a number of methods for simulating such data. For example, some crop modelers (e.g., Rosenthal et al., 1989) have incorporated stochastic weather generators into their simulations. These weather generators simulate irradiance and other meteorological and climatological inputs based on probabilistic criteria. This approach eliminates the need for measured solar irradiance; however, it seems reasonable that estimated, rather than randomly generated, solar irradiance values would also result in improved yield estimates.

A number of techniques are available for estimating solar irradiance. These vary in sophistication from simple empirical formulations based on common weather or climate data to complex radiative transfer schemes that explicitly model the absorption and scattering of the solar beam as it passes through the atmosphere. These more complex models are capable of highly accurate estimates of incoming solar irradiance. However, they tend to be too complex and data-intensive for operational use, or are limited by requirements for site-specific data which are unavailable outside of a few locations (Liu and Jordan, 1963; Goldberg et al., 1979; Reddy, 1971; Barbaro et al., 1978).

Other methods for estimating historical solar irradiance are much simpler in operation and in data requirements. Bristow and Campbell (1984) developed a method with simple data requirements (i.e., latitude and daily air temperature range). The Bristow–Campbell (B–C) model calculates daily incoming solar irradiance by estimating the daily transmissivity coefficient (T_t), defined as

(1)

where R_s is daily irradiance at the surface (MJ d^-1) and Q_o is daily irradiance at the top of the atmosphere (see Eq. [5]).

The transmissivity coefficient is estimated from the daily air temperature range (T, which is calculated from instantaneous observations) using an exponential equation:

(2)

where A, B, and C are empirical coefficients. Although empirically derived and conceptually simple, the B–C model is founded on theoretical concepts for energy exchange in the surface boundary layer. The B–C model exploits the relationship between diurnal air temperature range and irradiance load to estimate the daily flux of incoming solar irradiance. Using this technique along with refinements for rain days and seasonality, Bristow and Campbell (1984) found that they could account for 70 to 90% of the variation in daily incoming solar irradiance from three sites: Tacoma and Pullman, WA, and Great Falls, MT. The accuracy and simplicity of data requirements appear to make the B–C model an ideal tool for estimating solar irradiance at sites where measured values are unavailable. Before the B–C model can be used as an operational technique, however, its suitability at other sites should be evaluated. One potential limitation is the assumption that radiation loading is the predominant mechanism forcing diurnal air temperature range. While this may be a valid assumption in some areas, in other locations frontal activity and regional advection may also contribute substantially to daily air temperature extremes. This is particularly true in central North America, where the regional climate is characterized by great daily contrasts in air temperature, due in part to radiation loading but also influenced by synoptic meteorological patterns. The effect of this continental climatic regime on the accuracy of the B–C model is not well understood.

Another consideration in applying the B–C model is the spatial and seasonal generality of the empirical coefficients. These coefficients must be derived at a site where both air temperature and solar irradiance measurements are available. In effect, this must be done at one of the permanent solar irradiance monitoring stations (which are dispersed and few—hence the necessity for estimating solar irradiance). The accuracy and precision of these coefficients at other sites is open to question. Researchers need some idea of how reliable they are at sites away from the calibration site. Seasonal effects on model accuracy are also not well understood. In light of these questions, our objectives for this study were twofold: first, to evaluate the ability of the B–C model to calculate solar irradiance at a midcontinent site (Manhattan, KS); second, to evaluate the spatial and temporal generality of the model coefficients by comparing solar irradiance values estimated using the B–C model calibrated at Manhattan to measured solar irradiance values at 10 sites located throughout the state of Kansas.

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 
Data used for model calibration were from the 1961–1990 30-year normal observations collected at the National Weather Service (NWS) cooperative observer station on the campus of Kansas State University at Manhattan, KS (39°11'N, 96°34'W; see Fig. 1) . Air temperatures were measured at screen height (1.5 m) using maximum and minimum thermometers housed in a Stevenson screen shelter. Solar irradiance was measured using an Eppley Precision Spectral Pyranometer.¹ Quality control measures applied to these data are similar to those at NWS first-order stations, and include visual checks for outliers, calibration against NWS standard instruments, and comparison against nearby stations to spot anomalous measurements or shifts in instrument calibration.

View larger version (32K): [in this window] [in a new window]   Fig. 1 Location of measurement sites in Kansas. Circles indicate automated stations

(3)

where T_MAX is daily maximum air temperature (°C), T_MIN is daily minimum air temperature (°C), and J is the day in question. Use of daily minimum air temperatures from the measurements surrounding the daily maximum is suggested by Bristow and Campbell (1984) as a method for reducing the effects of large-scale advection of warm or cold air masses. Once the daily air temperature range was calculated, measured T_t values for parameterizing the model were calculated from Eq. [1], using values of R_S measured with the Eppley pyranometer. Each day's Q_o was determined as a function of site latitude using the equation given by Gates (1980):

(4)

where d' is the mean earth–sun distance, d is the earth–sun distance, is the latitude of the location of interest, is solar declination, h_s is half day length (measured in degrees), and S_o is the solar constant (1367 W m^-2; Clark, 1982).

In this research we evaluated two forms of the B–C model. The first of these was the basic B–C equation given in Eq. [2]. Following the suggestions of Bristow and Campbell (1984) and Donatelli and Marletto (1994), we also used a modified version of the B–C equation formed by inserting daily exoatmospheric incoming solar irradiance Q_o (see Eq. [4]) as an extra term in the equation for estimating T_t:

(5)

The Q_o term acts as a seasonal scaling factor, allowing T to accommodate a greater range of solar irradiance values. Despite the addition of the Q_o term, Bristow and Campbell (1984) noted that seasonality affected model coefficient values. Following their example, we divided our dataset into two subdivisions: a period characterized by high noontime solar elevation angles (DOY 121–273) and a low noontime solar elevation period (the rest of the year; i.e., DOY 1–120 and 274–365). This division of the year was suggested by the annual behavior of T, which shows a more narrow range in the high elevation angle period (Fig. 2) . Three separate sets of model coefficients were developed, one for each subdivision and one for the entire year. In their original formulation, Bristow and Campbell used an adjustment for rain days, reasoning that cloudy conditions associated with rain would greatly affect transmissivity relative to daily air temperature differences. This adjustment is quite reasonable for the Pacific Northwest, given the tendency for long-duration, low-intensity precipitation events accompanied by constant cloud cover that are characteristic of the marine-influenced climate. However, preliminary results for our location indicated that correction for rain days did little to improve model accuracy relative to measured values. In Kansas, precipitation events tend to be short and of higher intensity, often occurring in the late evening or at night (Trewartha, 1981; Balling, 1985). Precipitation is therefore not as closely associated with variation in daily transmissivity.

View larger version (63K): [in this window] [in a new window]   Fig. 2 The daily air temperature range T for the 30-year data period at Manhattan, KS. Note the narrower ranges in the high-sun season. DOY, day of year

Model coefficients were tested in two ways. First, estimated solar irradiance values were compared with measured values for the entire 30-year normalizing period at Manhattan. This comparison not only established baseline values for accuracy of the B–C model at a midlatitude continental site, it also provided a standard by which the accuracy of the model at other locations could be evaluated. The second phase of evaluation consisted of testing the geographic generality of the model coefficients by comparing solar irradiance estimates made using the coefficients derived at Manhattan to measured values at 10 automated measurement stations located throughout the state of Kansas (Fig. 1). These automated stations were equipped with Li-Cor silicon-cell pyranometers for measuring solar irradiance and Fenwell thermistor–thermometers for minimum and maximum air temperature measurement. Pyranometers at the automated stations are calibrated annually, by the manufacturer, and are cleaned and leveled twice annually. The procedure for estimating solar irradiance at each automated station was identical to that used at Manhattan. Daily T and Q_o values from each station were inserted into Eq. [2] and [5] along with the appropriate seasonal values of A, B, and C for each of the two forms of the B–C equation derived from the Manhattan data. The resulting T_t values were used to estimate R_S. These estimated values of R_S were then compared with measured values. The automated stations used for validation have been in operation only since 1986; thus, only 10 years of data were available for verification.

	Results

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 
The seasonal A, B, and C coefficients resulting from calibration of the model at Manhattan are summarized in Table 1 . Since the modified B–C equation (Eq. [5]) resulted in better solar irradiance estimates compared with measured values than the unmodified version (Eq. [2]), most of the subsequent discussion will be confined to the results obtained using this form of the model. Overall, the scatterplots resulting from plotting T_t against T/Q_o for each season (Fig. 3–5) show a curvilinear pattern similar to those reported by other users of the B–C technique (e.g., Bristow and Campbell, 1984; Donatelli and Marletto, 1994). The distribution of points for the high sun season (Fig. 3) is more compact than for the low sun season, with a smaller range of T/Q_o values. The constraints on T/Q_o range during the high sun season reflects both the smaller range of T and the larger Q_o values. In contrast, the low sun season is characterized by a less distinct distribution of points, with a larger number of outliers distributed over a greater range of T/Q_o values. For both seasons, the average maximum values of T_t range from about 0.70 to 0.72, indicating that mean maximum atmospheric transmissivity for both seasons is roughly equal. The equality of mean maximum T_t is even clearer on the yearly plot (Fig. 5). Notice that the distribution of points in Fig. 5 maintains the same basic curvilinear shape as each of the seasonal plots, suggesting that accuracy of a single model fitted to all data would differ little from the accuracy of the individual seasonal models.

View larger version (32K): [in this window] [in a new window]   Fig. 3 Scatterplot for high noontime solar elevation period data at Manhattan, KS

View larger version (53K): [in this window] [in a new window]   Fig. 4 Scatterplot for low noontime solar elevation period data at Manhattan, KS

View larger version (50K): [in this window] [in a new window]   Fig. 5 Scatterplot for full-year data at Manhattan, KS

View larger version (28K): [in this window] [in a new window]   Fig. 6 Measured vs. modeled solar irradiance at Manhattan, KS: (a) high noontime solar elevation angle; (b) low noontime-time solar elevation angle; (c) full year

Seasonal RMSE values for the 10 automated stations used to evaluate the geographic generality of the model coefficients, together with their distances from the Manhattan station, are presented in Table 3 . In general, the seasonal pattern of error resembles that of the Manhattan station, with the high solar elevation period showing the larger RMSE. The pattern of percentage error also generally corresponds to Manhattan, although this does not hold for each individual station. The RMSE for each automated station differed only slightly from the RMSE for Manhattan. In fact, for several cases the model performance was better for the validation stations than for the station where the coefficients were derived. Given the empirical nature of the model, this is somewhat surprising. The accuracy of the empirically derived model coefficients would be expected to decay with distance from the calibration stations, yet the associated RMSE values do not bear out this expectation (Table 3). Apart from the station at Parsons, which is a substantial outlier showing very large error in all seasons, there is no discernible relationship between distance from Manhattan and model accuracy. Clearly, simple distance from the site of model calibration is not a major factor in determining accuracy. We also note that several of the automated stations are located at sites in the western part of Kansas, where drier climatic conditions dominate. Estimated solar irradiance values from these sites were no less accurate than those of the more humid eastern part of the state. Apparently, climatic differences between the calibration and test sites are not particularly relevant to model performance. This suggests that some factor other than regional climatic variation must influence model coefficient values.

View larger version (11K): [in this window] [in a new window]   Fig. 7 Seasonal root mean square error (RMSE) for each automated station as a function of latitude difference between the automated station and Manhattan, KS. The outlying Parsons station is represented by the open symbol. The dashed line represents the trend with Parsons included; the solid line is the trend with Parsons deleted

	Discussion and conclusions

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

Another significant result from this study concerns the spatial robustness of the model coefficients. We found that the coefficients calibrated using data from Manhattan were able to estimate irradiance at 10 sites throughout the state with accuracy approaching (and sometimes exceeding) that of the calibration site itself. This suggests that coefficients for the model are more widely applicable than would typically be expected from empirically derived values. Latitudinal deviation between the calibration site and the model test sites may play a slight role in the accuracy of the solar irradiance estimates, but simple distance from the calibration site appears not to be relevant. This further suggests that either overall climatic setting is not critical in determining coefficient values, or that climate does not vary sufficiently throughout Kansas to greatly affect accuracy.

The modified Bristow–Campbell model has shown itself to be a robust and reasonably accurate method for estimating solar irradiance. The quality of these estimates varies somewhat with date and location, yet the estimates are generally within 2 to 5 MJ m^-2 d^-1 of measured values. The error in our results exceeds that reported by other users of forms of the Bristow–Campbell model (e.g., Bristow and Campbell, 1984; Donatelli and Marletto, 1994); however, it should be noted that our model coefficients are derived from a longer time series of solar irradiance data. Over the 30-year normalizing period, there have been notable changes in air temperature climatology (Wagner, 1996; Williams and Parker, 1997). These climatic changes inevitably affect the observed relationship between T and daily irradiance. Although our versions of the B–C model are generally less accurate than some others, incorporation of a long series of calibration data may help explain their spatial and seasonal robustness.

While the overall percentage of error associated with these simulated irradiance values is at times somewhat high, one must keep in mind the intended application of the model. We are evaluating the Bristow–Campbell model as a simple tool for estimating solar irradiance at noninstrumented sites, with the intention of incorporating these estimates into crop yield and risk assessment models. While other options for modeling or generating solar irradiance values are available, these approaches have substantial drawbacks. Use of stochastic weather generators is completely nondeterministic and thus unable to reliably estimate irradiance for any given day. Rather, stochastic generators can simulate only generic, average days. Clearly, this is a less desirable approach for researchers wishing to realistically model irradiance at specific dates and locations. Complex radiative transfer models produce much more accurate solar irradiance values, but only if their extensive data requirements are met. There are few places where these data are available; however, there are numerous sites at which daily minimum and maximum air temperature are observed. Preliminary evaluation indicates that the performance of the modified B–C model is suitable for crop yield simulation (R.W. Heiniger, personal communication). Use of the modified B–C model may not provide adequate irradiance estimates for other applications.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 
Contribution no. 97-165-J, Kansas Agric. Exp. Stn., Manhattan, KS.

¹ Use of brand names is for informational purposes only and does not imply endorsement by Kansas State University.

Received for publication November 4, 1998.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion and conclusions REFERENCES

 

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This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Web of Science (22) Citing Articles via Google Scholar Google Scholar Articles by Goodin, D. G. Articles by Knapp, M.C. Search for Related Content PubMed Articles by Goodin, D. G. Articles by Knapp, M.C. Agricola Articles by Goodin, D. G. Articles by Knapp, M.C. Related Collections Agroclimatology Crop Growth and Development Crop Models