Agronomy Journal 95:323-328 (2003)
© 2003 American Society of Agronomy
MODELING
Estimating Daily Dew Point Temperature for the Northern Great Plains Using Maximum and Minimum Temperature
Kenneth G. Hubbarda,
Rezaul Mahmood*,b and
Christy Carlsona
a High Plains Regional Clim. Cent., 242 L.W. Chase Hall, Univ. of Nebraska, Lincoln, NE 68583-0728
b Dep. of Geogr. and Geol. and Kentucky Clim. Cent., Western Kentucky Univ., Bowling Green, KY 42101
* Corresponding author (rezaul.mahmood{at}wku.edu)
Received for publication June 15, 2001.
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ABSTRACT
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Dew point temperature (Td) is a precise measure of atmospheric moisture. A significant number of models for studying crop–climate interactions and earth processes require daily Td as an input. However, limited availability of Td data is a major barrier for applications of these models. In this paper, we present a daily Td estimation method for the northern Great Plains (NGP). The daily Td estimation method presented here requires daily maximum, minimum, and mean temperature data. Data from six sites in the NGP were used for the study. These sites record hourly Td data from relative humidity. Length of the time series is 14 yr (1986–1999). Four different regression-based approaches were adopted and applied to all sites. Eventually, the best method was adopted based on its performance. The model evaluation statistics show that the selected model performs satisfactorily for these six sites. For example, root mean square error (RMSE), mean absolute error (MAE), and d index (ranges between 0 and 1, where 1 indicates no model error) values for North Platte, NE, application are 3.23, 2.55, and 0.97, respectively. The selected method was further applied to five additional locations in the NGP, and again it performed satisfactorily. For example, RMSE, MAE, and d index values for McCook, NE, application are 2.6, 2.0, and 0.98, respectively. From the model evaluation, we conclude that the model performed satisfactorily and will be quite useful in estimating Td.
Abbreviations: MAE, mean absolute error • NGP, northern Great Plains • PET, potential evapotranspiration • QC, quality control • RH, relative humidity • RMSE, root mean square error • Td, dew point temperature
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INTRODUCTION
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DEW POINT TEMPERATURE is an important geophysical parameter that indicates the state of moisture content in the air under given conditions. It is vital for estimating various agrometeorological parameters, including evapotranspiration. As a result, numerous agronomic, hydrological, ecological, and climatological and meteorological models require Td data. However, few surface weather-observing sites measure and record Td. Often data for a particular location is composed of relatively shorter length of the time series. This presents a significant hurdle for conducting long-term historical studies. One approach to overcoming this problem is to estimate Td by using readily available meteorological data.
In this paper, we present a temperature-based (daily maximum, minimum, and mean) daily Td estimation method for historical studies in the NGP. It is well known that almost all of the weather-monitoring sites under cooperative networks in the USA and other countries collect temperature data. The guidelines followed during model development were that the method should be simple, input data should be readily available, and the model should lend itself to physical explanation. We believe that this method is applicable for estimating historical Td and subsequently will be used for various studies at numerous locations. During the application phase, it would require readily available input data sets at the multidecadal time scale. As noted above, daily air temperature, including maximum and minimum temperature, is generally available at the multidecadal scale for a large number of sites.
It is suggested by several authors that Td remains relatively constant during the day (Dyer and Brown, 1977; Glassy and Running, 1994; and Running et al., 1987) and equal to nightly minimum temperature (Dyer and Brown, 1977; Running et al., 1987). As a result, managerial and operational level decision-makers tend to use minimum temperature as a surrogate for Td. However, Butler (1992) noted that these assumptions are not correct. It is reported that the strength of the relationship between minimum temperature and Td depends on the climatic characteristics and the season (Running et al., 1987; Butler, 1992; Kimball et al., 1997). Kimball et al. (1997) indicated that the assumption of equivalency is not applicable in the absence of nighttime condensation.
To overcome the unreliability of using daily minimum temperature as a surrogate for Td, several methods have been developed in the past (e.g., Butler, 1992; Kimball et al., 1997). Butler (1992) used dry- and wet-bulb temperature from an experimental site to determine and archive hourly Td in a semiarid region of India. These data show a clear seasonal and diurnal pattern in daily Td. For example, normalized Td for February was fairly stable at night and decreased to a minimum at 1600 h local time. On the other hand, Td remained fairly stable for a 24-h period in August during the rainy monsoon season. It is also reported that the amplitude of Td is smallest during the monsoon season. To simulate these characteristics of diurnal and seasonal variations, Butler (1992) proposed a Td estimation method that includes a cosine function, daily maximum and minimum temperature, daylength, and time of sunrise. Generally, this method performed realistically. Daily Td estimated by Kimball et al. (1997) is a function of daily maximum and minimum temperature, annual precipitation, and potential evapotranspiration (PET). Kimball et al. (1997) developed their method by using data from 52 locations in conterminous United States and Alaska. They used the Priestly–Taylor method (Priestly and Taylor, 1972) to estimate PET. Unfortunately, daily maximum and minimum Td, wet-bulb temperature data (Butler, 1992), and input data for the Priestly–Taylor method (Priestly and Taylor, 1972) are not readily available. Thus, application of these methods (Butler, 1992; Kimball et al., 1997) is not always an option. Moreover, the cooperative weather network does not record input data for the above methods. As a result, we may not be able to apply models that require multidecadal humidity data across an increased number of sites to better understand spatio-temporal variations of different phenomena of the earth system. The method presented in this paper has considered these issues during its development. This method is simple and requires widely available input data so that it can be applied at multidecadal timescale and at many locations.
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MATERIALS AND METHODS
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Observed daily maximum and minimum air temperature data from six automated weather stations were used for model development (Fig. 1)
. Length of the time series (14 yr, 1986–1999) was the primary reason for selection of these sites. This was the longest data set available for this study. The stations are part of the Automated Weather Data Network of the NGP (Hubbard et al., 1983). This network is a collaborative effort between the state climate offices of the region and the High Plains Regional Climate Center. The Automated Weather Data Network records and archives hourly data and maintains a midnight-to-midnight (2400–2400 h) reporting time. The network programs calculated Td from relative humidity (RH) data. Saturation vapor pressure (es) was obtained from Teten's (Murray 1967) method; the actual vapor pressure (ea) was obtained from the relation [RH = (ea/es) x 100]. Subsequently, Td was calculated from the method presented by Allen et al. (1994). Daily Td was calculated as the average of hourly Td estimates. The RH207 (Campbell Sci., Logan, UT) and Vaisala (Campbell Sci., Logan, UT) temperature probes were used to record air temperature before and after 1991, respectively. These two instruments agree to within 1°C. The RH measuring sensors are part of the air temperature sensing instrument package and are mounted with the thermometers. The sensors have been calibrated once a year between spring and summer. A quality control (QC) procedure notifies data managers when there is any data problem. The QC program has been applied once a day for this purpose. Site visits (repair and maintenance) occurred when the QC program indicated a problem with the data. The data used in this study can be acquired online from the High Plains Regional Climate Center.
We developed four regression-based methods (Eq. [1] to [4]) and adopted an existing method (Eq. [5] to [6]) developed by Kimball et al. (1997) for estimating Td. All five methods were tested for performance evaluation before the selection of one approach for the whole region. Conceptually, the first four methods can be expressed as follows:
 | [1] |
 | [2] |
 | [3] |
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where 
, ß, 
, and 
are coefficients of the regression equations and Td, Tx, Tn, Tm, and Pdaily are daily dew point temperature; maximum, minimum, and mean air temperature; and daily precipitation, respectively. These equations will be referred to as Methods 1 through 4, respectively, in the rest of this paper. In all equations, the inclusion of Tn represents its well-known relationships with Td. The difference between Tx and Tn indicates moistness of an air mass (cf., Baier and Robertson, 1965). Generally, in the NGP and elsewhere, large differences between Tx and Tn indicate a high radiative condition, and low Tn is associated with cloudless skies. In Methods 3 and 4, mean temperature and daily precipitation, respectively, were added to represent overall local climatic conditions. Precipitation also indicates the moisture content of the atmosphere. Method 2 was tested to determine whether a nonlinear approach improves the fit between variables, improves accuracy of estimates, and explains the variations better. The following method was used by Kimball et al. (1997) to estimate Td.
 | [5] |
 | [6] |
where EF is an index of evaporative demand, 
w is density of water (kg m-3), tday is daylength (s), Ep is PET (kg m-2 s-1), and lP, ann is annual precipitation in meters. In this study, we replaced the Priestly–Taylor method (Priestly and Taylor, 1972) with the Penman (1948) method to estimate PET. The notable reasons for selecting the Penman (1948) method include its availability, reliability, and comparable physical basis.
Seven sets of coefficients were derived for each method (Method 1–4). Each method applied at each location (Fig. 1) resulted in a total of six sets. An additional set of coefficients for a method was derived from the applications to a combined data set of these six sites. Therefore, a total of 28 equations were developed. Coefficients for each site and the combined data set were derived, applied, and their performance compared to determine whether a method using coefficients from one location represents the whole region. After selection of one method and coefficients, it was applied to five additional locations to demonstrate its applicability. It is to be noted that, in the past, Mahmood and Hubbard (2002) successfully developed a method for estimating solar radiation in the NGP by using coefficients derived from one site representing the whole region.
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MODEL SELECTION, PERFORMANCE EVALUATION, AND DISCUSSIONS
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A summary of the performance of Methods 1 through 5 is presented in Tables 1 through 5. Coefficient of efficiency (E), MAE, d index, r2, and RMSE statistics were used for performance evaluation of these methods. A review of these statistics for model evaluation can be found in Legates and McCabe (1999). Coefficient of efficiency (E) is defined as follows:
 | [7] |
where O and P are observed and predicted values. It ranges from minus infinity to 1.0, where higher values indicate better performance. The d index can be expressed as follows:
 | [8] |
where d index ranges between 0 and 1.0 and higher index values represent superior performance. Model evaluation statistics show all four methods performed nearly equally satisfactorily at all sites (Tables 1–4). These statistics also suggest that all four methods performed consistently better for all locations when coefficients were derived from a merged data set, developed from combining data from six sites.
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Table 1. Performance of Method 1 for estimation of dew point temperature. Evaluation statistics are computed for each application, and the average is presented here. Coefficients were derived for each site and then applied to all sites including point of origin. Thus, there are six applications for each set of coefficients derived from any location. The leftmost column lists the sites that provided data. Combined indicates when the data from all six stations are merged and coefficients subsequently developed.
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This led us to select a method with coefficients derived from the combined data set. According to the d index, all four methods performed nearly equally well. The r2 indicates that Methods 1 through 3 performed equally satisfactorily, and Method 4 showed slight (1%) improvement. Root mean square error and E also indicated similar types of agreement in model performance evaluation. Overall, the performance of all four methods with coefficients derived from the merged data set was satisfactory and the differences in their performances negligible. However, a careful assessment indicated that Method 3 performed slightly better than the others. Four of the model evaluation statistics (E, MAE, d index, and RMSE) produced best estimates for Method 3 (Fig. 2a, 2b, and 2c) . It is noted that MAE, r2, and RMSE indicate that Kimball et al.'s (1997) method performed comparatively more satisfactorily for the NGP than Method 3 based on combined data set (Tables 3 and 5). Nevertheless, we selected Method 3 for estimating Td in the NGP because it performed satisfactorily, it is simple, and input data for further applications are available. Moreover, in some cases, even infrastructure for applying these methods to estimate PET is nonexistent. In other words, the proposed model will provide the necessary accuracy without complications associated with data availability. The model based on Method 3 can be expressed as follows:
 | [9] |
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Fig. 2. Examples of model application at three sites: (a) Akron, CO; (b) North Platte, NE; and (c) Mead, NE.
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The model showed a strong relationship between Tn and Td. Diurnal temperature range and Tm also contributed to improve the accuracy of Td. Because diurnal temperature range indicates moisture condition of a given air mass, lower range generally indicates that the air mass is moist. The range also indicates availability of solar energy and vapor pressure deficit (Baier and Robertson, 1965). These two parameters affect direction of mass and energy transfer (away from the surface vs. toward the surface) and thus, Td. Therefore, physically, diurnal temperature range is providing additional information on local moistness and radiative characteristics. Again, both of these parameters influence attainment of a given Td. Moist conditions can moderate daily Tx and thus modify Tm. Daily mean temperature reflects overall thermal condition and influences Td. The inclusion of Tm and its subsequent contribution to accuracy of Td supports above observation. Kimball et al. (1997) have shown in their analysis that Tn at the arid sites is warmer than the humid subtropical and coastal–maritime locations. In addition, Td and Tn agree best at coastal–maritime locations and least at arid sites. Intuitively, Td is related to overall thermal condition represented by Tm. Therefore, inclusion of this parameter made the model more realistic. It can be stated that despite the empirical structure, adequate physical explanation was embedded in the model, which captured thermodynamic environment of a given Td.
To further demonstrate the performance of the selected model (Eq. [9]), it was applied to five additional sites (Fig. 3)
. These applications and model evaluation statistics suggested that the proposed model's estimates of Td were satisfactory (Table 6 and Fig. 4a and 4b)
. It was found that Td estimates using independent data were superior compared with estimates from trained data. Statistical nature of our method was primarily responsible for this result.
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Fig. 4. Examples of model application at two sites for further assessment of its performance: (a) McCook, NE and (b) Silver Lake, KS.
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Results indicated that the model performance did not vary notably with the changes of seasons. Figure 4a and 4b show scatter distribution of estimated and recorded Td. The scatter included Td data from various seasons and varied conditions. It was sufficiently clear that the modeled estimates did not show systematic bias as the Td varied from high to low. In other words, as Td varied with the seasons, our model estimates did not show any bias. Thus, it is possible to conclude that Td estimation by our model is robust over various seasons. Note that the results were obtained by using 14 yr of data compared with Kimball et al.'s (1997) 2 to 8 yr of data.
We surmise that the model would estimate Td with sufficient accuracy under varied climatic conditions. This suggestion is formulated based on the satisfactory performance of this model under wide variety conditions. The climatic conditions observed within the NGP are representative of many other regions of the world. These include, for example, conditions ranging from the subhumid to semiarid and extreme to moderately cold winter conditions. Thus, the Td model is sufficiently robust for application in other parts of the world. However, we suggest that a recalibration of the model with local data would potentially provide more suitable coefficients and subsequently, more accurate estimation of Td. Further application and analyses is needed to determine the performance of the model in the coastal areas or areas under maritime climate or at the higher elevation.
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SUMMARY
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This study presents a simple Td estimation method for the NGP. Numerous models for simulating crop growth, crop–climate interactions, and environmental processes require Td to estimate other agrometeorological parameters. Unfortunately, these data are not readily available, and estimation of Td can resolve this problem. It was envisioned at the developmental phase that this model would be simple and physically sound and that input data requirements would be easy to meet. This would allow the model to be readily available to researchers, managerial decision-makers, and the operational community. As a result, the model we developed can be used for long-term retrospective agroclimatological, hydrological, and ecological process studies. The input data for the model are maximum, minimum, and mean daily temperature. The length of the time series we used to develop the model was 14 yr (1986–1999). Four different approaches of model formulation were developed and tested. Each approach was applied to six selected sites and to a combined data set developed from merging the data from these sites to derive model coefficients. Finally, one particular method was selected (Eq. [9]) based on its superior performance. Coefficients of the model were derived from the combined data set. Model evaluation statistics show that the Td estimation method performed satisfactorily. For applications of the model to six sites, E, MAE, d index, r2, and RMSE report values of 0.88, 2.52, 0.97, 0.89, and 3.29, respectively. These values are averages, calculated from six applications
Kimball et al.'s (1997) method performed slightly better than the model presented here (Eq. [9]). However, complex data requirements for this model pose a significant barrier for its widespread application. Our model was further applied to an additional five sites to demonstrate its accuracy in Td estimation. Model evaluation statistics E, MAE, d index, r2, and RMSE report average values of 0.92, 2.20, 0.98, 0.92, and 3.0, respectively. Thus, performance of the Td estimation method (Eq. [9]) is satisfactory. Based on the performance, we conclude that the model fulfills the underlying requirements for providing satisfactory estimates of daily Td.
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ACKNOWLEDGMENTS
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The authors thank Professors Blaine L. Blad and Donald A. Wilhite for their comments and suggestions during preparation of this manuscript. Technical assistance provided by Sebastien O. Korner during preparation of the maps is much appreciated. This paper has a University of Nebraska Agricultural Research Division Journal Series no. 13314.
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REFERENCES
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ABSTRACT
INTRODUCTION
