Priestley-Taylor Parameter Over Inland Water, Snow, and Ice: Bowen Ratio-Dependent Variations and Implications for Estimating the Latent Heat Flux

The Priestley-Taylor evaporation model is extensively adopted in attempts to estimate the terrestrial evaporation and latent heat flux, largely because of its relatively simple form, and hence limited data requirements (e.g. the available energy and surface temperature). When applying this model in moisture-saturated areas (e.g. inland water bodies and irrigated agricultural crops), previous studies typically assume the Priestley-Taylor parameter (α) as a constant value, most frequently as 1.26. Based on measurements over a reservoir in central Mississippi (i.e. inland water surface) and a glacier on the Tibetan Plateau (i.e. snow and ice surfaces), we strive to extend the applicability of the original Priestley-Taylor model, primarily by taking account of the Bowen ratio-dependence of α. With α expressed as a function of the Bowen ratio (β), the extended model is found to produce fairly accurate estimates of the latent heat flux in different heat-flux regimes. Specific methods and findings are summarized in the follows.

(1) According to the signs of eddy-covariance fluxes of sensible heat (H) and latent heat (LE), observational data over each surface are organized into four heat-flux regimes: I (H > 0; LE > 0), II (H < 0; LE > 0), III (H > 0; LE < 0), and IV (H < 0; LE < 0). Relevant constraints on the Bowen ratio (i.e. β = H / LE) are then incorporated into the data screening, so that supersaturation in the air (e.g. fog and mist) is forbidden over saturated surfaces (i.e. water, snow, and ice herein). Following examinations of ‘Bowen-ratio similarity', we introduce auxiliary measures for data screening in regime II, given the original constraint of β < 0 can be naturally satisfied and is practically ineffective. Quality-controlled measurements suggest that regimes I and II are dominant over inland water, and regimes II and IV are dominant over snow and ice.

(2) Over inland water, α differs significantly between regimes I (β > 0) and II (β < 0, indicative of advective effects mostly in the afternoon). For instance, linear regressions of LE versus the ‘equilibrium evaporation' result in α values of 1.13 and 1.33 for regimes I and II, respectively. Deviations from the commonly used constant value of 1.26 imply that it is indeed inappropriate to assume α as a fixed parameter. Over snow and ice, we also find fundamentally different ranges of α between regimes II (β < 0) and IV (β > 0) – both representing stable boundary layers over snow and ice: α in regime II (absolute values) varies wildly between 0 and infinitive, while α in regime IV falls into a much narrower range of 0 to 1. Despite the wide variations as observed, a simple function of the Bowen ratio is found to reproduce the behavior of α fairly well.

(3) To assess the significance of taking account of the Bowen ratio-dependence of α, we compare estimates of the latent heat flux from the Priestley–Taylor formulae (using different approaches of α) against the eddy-covariance measurements (LE). Over inland water, the original α value of 1.26 leads to overestimated and underestimated latent heat fluxes for regimes I and II, respectively, though the relative differences are within 10% overall. In comparison, when α is taken as a function of the Bowen ratio, the estimated latent heat fluxes have a perfect match with the measurements. Furthermore, over snow and ice, assuming α as locally determined constant values (e.g. -3.09 and -1.19) leads to significant errors in the flux estimates for regime II (sublimation over the glacier), often with incorrect directions of water vapor transfer. To remedy this deficiency, the Bowen ratio-dependence of α is incorporated, leading to notably improved flux estimates. Similarly, for regime IV (deposition), α has to be expressed as a function of the Bowen ratio, so as to derive accurate flux estimates from the Priestley–Taylor formulae. To sum, the original Priestley-Taylor model is extended in this work to a wider variety of heat-flux regimes – irrespective of the presence of advective effects, direction of water vapor transfer, and boundary-layer stability.