Simple $\mathit{E}{\mathit{T}}_{\mathbf{0}}$ Forms of Penman’s Equation without Wind and/or Humidity Data. I: Theoretical Development

In this paper, new algebraic expressions are derived for estimating reference evapotranspiration ($E{T}_0$) from limited meteorological data. Reference evapotranspiration is commonly computed from readily available measured data at weather stations; e.g., solar radiation, $R_S$ ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{d}$); relative humidity, $RH$ (%); wind speed, $u$ ($\mathrm{m}/\mathrm{s}$); and average temperature, $T$ (°C). Recently, a simple algebraic formula, equivalent in accuracy to the Penman equation, was derived by Valiantzas for computing $E{T}_0$ from readily available measured data. The derivation of the formula is based on simplifications made to the standardized form of the Penman equation. In a first place, an improved and more simplified form of Penman’s equation is proposed, requiring a full set of data. The new full set of data formula is obtained by calibration using meteorological data obtained from the CLIMWAT global database. For many places where reliable wind speed data are not available, an expression is also suggested that does not require wind data. Further simplifications were applied in the proposed formula to derive the following new formula based on $R_S$ and $T$ measurements alone: $E{T}_0\approx 0.0393R_S\sqrt{T+9.5}-0.19R_S^{0.6}{\phi }^{0.15}+0.0061(T+20){(1.12T-T_{\min }-2)}^{0.7}$ where $T_{\min }$ = minimum temperature; and $\phi$ (rad) = latitude of the station. The proposed formula, which requires limited data, can be also applied when taking the local long-term average wind speed value into account. Evaluation of the formulas and comparisons with other methods using daily meteorological data are given in the companion paper.