Sensitivity Analyses and Sensitivity Coefficients of Standardized Daily ASCE-Penman-Monteith Equation

The sensitivity of the standardized ASCE grass-reference Penman-Monteith evapotranspiration (ASCE-PM $E{T}_o$ ) equation to climate variables in different regions has not yet been studied. Sensitivity analyses for the standardized daily form of the ASCE-PM equation were conducted on wind speed at $2\mathrm{m}$ height $\left(U_2\right)$ , maximum and minimum air temperatures ( $T_{\max }$ and $T_{\min }$ ), vapor pressure deficit (VPD), and solar radiation $\left(R_s\right)$ in the following regions of the United States: semiarid (Scottsbluff, Nebraska, and Bushland, Texas), a Mediterranean-type climate (Santa Barbara, California), coastal humid (Fort Pierce, Florida), inland humid and semihumid (Rockport, Missouri, and Clay Center, Nebraska), and an island (Twitchell Island, California). The sensitivity coefficients were derived for each variable on a daily basis. In general, $E{T}_o$ was most sensitive to VPD at all locations, while sensitivity of $E{T}_o$ to the same variable showed significant variation from one location to another and at the same location within the year. After VPD, $E{T}_o$ was most sensitive to $U_2$ in semiarid regions (Scottsbluff, Clay Center, and Bushland) during the summer months. The $R_s$ was the dominant driving force of $E{T}_o$ at humid locations (Fort Pierce and Rockport) during the summer months. At Santa Barbara, the sensitivity of $E{T}_o$ to $U_2$ was minimal during the summer months. At Bushland, Scottsbluff, and Twitchell Island, $E{T}_o$ was more sensitive to $T_{\max }$ than $R_s$ in summer months, whereas it was equally sensitive to $T_{\max }$ and $R_s$ at Clay Center. The $E{T}_o$ was not sensitive to $T_{\min }$ at any of the locations. The change in $E{T}_o$ was linearly related to change in climate variables (with $r^2⩾0.96$ in most cases), with the exception of $T_{\min }$ , at all sites. Increase in $E{T}_o$ with respect to increase in climate variable changed considerably by month. On an annual average, a $1°\mathrm{C}$ increase in $T_{\max }$ resulted in 0.11, 0.06, 0.16, 0.07, 0.11, 0.08, and $0.10\mathrm{mm}$ increases in $E{T}_o$ at Scottsbluff, Santa Barbara, Bushland, Fort Pierce, Twitchell Island, Rockport, and Clay Center. A $1\mathrm{m}\bullet {\mathrm{s}}^{-1}$ increase in $U_2$ resulted in 0.42, 0.18, 0.37, 0.28, 0.31, 0.20, and $0.26\mathrm{mm}$ increases in $E{T}_o$ at the same locations. A unit increase in $T_{\max }$ resulted in the largest increase in $E{T}_o$ at Bushland, and a unit increase in $R_s$ caused the largest increases in $E{T}_o$ at Fort Pierce. A $1\mathrm{MJ}{\mathrm{m}}^{-2}\bullet {\mathrm{d}}^{-1}$ increase in $R_s$ resulted in 0.05, 0.08, 0.06, 0.11, 0.05, 0.06, and $0.06\mathrm{mm}$ increases in $E{T}_o$ at the same locations. A $0.4\mathrm{kPa}$ increase in VPD resulted in 1.13, 0.54, 1.29, 0.57, 1.04, 1.10, and $1.22\mathrm{mm}$ increases in $E{T}_o$ at the same locations. The $U_2$ had the most effect on $E{T}_o$ at Scottsbluff and Bushland, the two locations where dry and strong winds are common during the growing season. The sensitivity coefficient for $R_s$ was higher during the summer months and lower during the winter months, and the opposite was observed for VPD (except for Twitchell Island). The decrease of the sensitivity coefficients for $R_s$ corresponding to an increase in the sensitivity coefficient for VPD is due to a decrease in the energy term in favor of the increase in significance of the aerodynamic term of the standardized ASCE-PM equation in summer versus winter months. Because the ASCE-PM and the Food and Agriculture Organization paper number 56 Penman-Monteith (FAO56-PM) equations are identical when applied on a daily time step, the results of the sensitivity analyses and sensitivity coefficients of this study should be directly applicable to the FAO56-PM equation.