The estimation of agricultural water demand is very important in long-term water resources planning, because agricultural water use accounts for the largest portion of total freshwater use. Globally, about 70% of freshwater is consumed by agricultural production [1
], and agriculture will use more water in the future [2
]. In order to estimate agricultural water demand, the reference crop evapotranspiration (
) needs to be calculated. The Food and Agriculture Organization (FAO) Penman–Monteith (P-M) equation, which combines both energy and mass balances based on physical principles, is recommended as the standard method for estimating
in a variety of climate types [3
]. The equation, however, can be restricted in use, since it requires a number of meteorological inputs which may not be available everywhere [4
Global solar radiation is one of the essential inputs of the P-M equation. The Ångström–Prescott (A-P) formula is recommended for the estimation of the global solar radiation if it is not measured [3
]. Parameters in the formula (i.e., a and b) vary depending on atmospheric conditions and solar declination [3
]. Accordingly, there have been many studies on their estimation in different regions having different climates [6
]. For South Korea, Choi et al. [12
] calibrated A-P coefficients by using 25 years (1983–2007) of observed daily global solar radiation and sunshine duration data at 18 meteorological stations. The calibrated coefficients were validated by comparing the estimates of daily solar radiation, using the locally extracted coefficients from the spatially interpolated map of the calibrated coefficients, with the observed solar radiation for a one-year period (September 2008 to August 2009) at eight locations. In the case that no measured solar radiation data are available and no calibration has been carried out for the parameters, the values of 0.25 and 0.50 are recommended for a and b, respectively [3
Despite the many studies on estimating the A-P coefficients for a specific region, only a few studies have evaluated the effects of A-P coefficients on the estimation of
. Moreover, previous studies on the effects have suggested that the recommended A-P coefficients may call into question the accuracy of the P-M equation [7
]. Sabziparvar et al. [10
] showed that daily
estimates in a humid subtropical climate could be improved up to 72.7% when the calibrated A-P coefficients were used instead of the recommended A-P coefficients. For these reasons, Liu et al. [7
] argued that there is a need for further exploration into the variation in
caused by the A-P coefficients in different climates.
In addition to the
, the estimation of irrigation water requirements (IWRs) and design water requirements (DWRs), which is an essential part of the design and operation of agricultural water resources systems [13
], is also affected by the use of A-P coefficients when the estimation uses the P-M equation. The IWR is the net depth of water that is required to be applied to a crop to fully satisfy its specific crop water requirement for achieving full production potential [14
]. The estimation of IWR, explained in the following section in detail, generally requires the estimation of
and crop coefficients for a given crop, but also involves other factors such as effective rainfall and deep percolation, which altogether influence the effects of A-P coefficients on the estimation. When it comes to the DWR for a certain return period in paddy irrigation in South Korea, this is determined from the frequency analysis of IWRs for a given location [13
]. Considering the proportion of agricultural water in total water use and the frequent use of the P-M equation in the estimation of agricultural water demand, it is necessary to study whether the use of recommended A-P coefficients overestimates or underestimates the IWRs and DWRs; this question has not been comprehensively explored so far.
The objective of this study, therefore, is to bridge these gaps by exploring how the A-P coefficients alter the estimation of
, IWR, and DWR in South Korea. South Korea provides a good testing ground to further study the effects of A-P coefficients on the estimation, because in South Korea, the P-M equation is used as the standard for calculating evapotranspiration when agricultural water demand is estimated [15
] and about 80% of agricultural water is used for the production of one single crop: paddy rice [16
]. In this study, therefore, IWRs and DWRs are calculated for paddy rice production.
4. Discussion and Conclusions
The FAO P-M equation is recognized as the standard method for the estimation of and has been widely used in a variety of climates. The A-P formula is recommended to determine (global) solar radiation, one of the essential meteorological inputs of the P-M equation. However, A-P coefficients used in the equation could have a considerable impact on the estimation of , and thus influence the estimation of IWR and DWR in agricultural water resources planning. In this study, we explored the impact of A-P coefficients on the estimation of , IWR, and DWR by analyzing and comparing their estimates using the recommended and locally calibrated A-P coefficients in 16 locations of South Korea.
Based on our results, considerable overestimation from using the recommend A-P coefficients (i.e., a = 0.25 and b = 0.50) was verified in the estimation of
across all 16 study sites in South Korea. The overestimation ranged from 3.8% to 14.0% as compared to the estimates using the locally calibrated A-P coefficients and the average was 10.0%. All study sites were significantly different (
) on a daily basis, and 15 out of 16 sites showed a significant difference (
) on an annual basis. In contrast to other studies [7
], which presented possibilities of both the over- and underestimation of
, the use of the recommended A-P coefficients in this study only resulted in
overestimation. This is presumably because of the climate region. The study sites included in the current study are located in the humid subtropical and continental climate regions, according to the Köppen–Geiger climate classification [17
], while the other studies covered more various climate regions such as tundra and tropical and subtropical desert. Nevertheless, the study sites of Liu et al. [7
] and Sabziparvar et al. [10
], which are located in the same climate region as this study, also presented overestimated results for
estimation. The estimation of
is the basis for predicting the demand for agricultural water use in water resources planning and many other applications, which require water partitioning (e.g., hydrological modeling) or the estimation of crop water consumption (e.g., crop modeling). Given the important role and frequent use of the P-M equation in the
estimation, the accurate estimation of evapotranspiration using the locally calibrated A-P coefficients should be recommended when available.
The 10% overestimation in the
estimation during the growing season of paddy rice resulted in a 5.1% overestimation of the IWR, on average. A variation of 3.8% to 14.0% in the overestimation of the mean annual
estimation during the growing season corresponded to a variation of 1.7% to 7.2% in the overestimation of the mean annual IWR estimation. This suggests that the use of the recommend A-P coefficients can have a level of uncertainty similar to the impact of future climate change in predicting the agricultural water demand for paddy rice production in South Korea. Yoo et al. [28
] predicted that climate change could lead to a change of −2.7% to 2.7% in agricultural water demand for paddy rice production in South Korea for this century. Although only one out of 16 study sites presented a significant difference (
) in the IWR estimation, the possible overestimation for paddy irrigation would reach about 625 million tons (5% of 12.5 billion tons), considering the amount of agricultural water used for paddy rice cultivation [14
]. It reaches about 12.5 billion tons a year, which accounts for almost 30% of the industrial water use (2.1 billion tons a year) in South Korea [16
]. The effect of the A-P coefficients on the IWR estimation showed a tendency to decrease as the IWR increased. Therefore, the effect of A-P coefficients on the DWR estimation was slightly reduced, and it was about 4.8% on average. The DRDY, which is defined by the DWR, was determined differently by the use of A-P coefficients at four sites out of the 16 study sites. Therefore, it is necessary to examine the impact of the use of A-P coefficients more closely in terms of engineering and economics perspectives, in that the DWR estimates and the resulting DRDY directly affect the design of irrigation facilities.
There can be many uncertainties associated with the use of the P-M equation other than those concerning the A-P coefficients [29
]. However, as shown in the results of this study, the use of A-P coefficients can cause considerable uncertainty in estimating
using the P-M equation and its applications. As such, this study underscores the need for the accurate consideration of the A-P coefficients in agricultural water management. As the FAO recommends [3
], if the A-P coefficients can be locally calibrated, then the use of the calibrated coefficients should be considered when using the P-M equation. Estimates of other variables (e.g., the crop coefficient) being used in the process of calculating the actual evapotranspiration from
should be reestablished in order to properly use the calibrated A-P coefficients.
We have also identified some directions for future studies. The effects of climate change and calibration method on the estimation of A-P coefficients need to be explored. Climate change is expected to make a significant difference in the various meteorological factors associated with the estimation of
. Therefore, it is necessary to see how A-P coefficients will affect changes in future
driven by climate change. In addition, since the A-P coefficients can differ depending on the data and method used in their estimates [7
], it is necessary to further examine the effect of the method on
estimation. Last but not least, as argued by Liu et al. [7
], in the estimation of
, a similar argument can be raised. The effects of A-P coefficients on the estimation of agricultural water demand and the design of agricultural water resources system should be explored in a variety of climates.