Complementary Relationship Of Evaporation Research Articles

What is the Priestley–Taylor wet-surface evaporation parameter? Testing four hypotheses

Abstract. This study compares four different hypotheses regarding the nature of the Priestley–Taylor parameter α. They are as follows: α is a universal constant. The Bowen ratio (H/LE, where H is the sensible heat flux, and LE is the latent heat flux) for equilibrium (i.e., saturated air column near the surface) evaporation is a constant times the Bowen ratio at minimal advection (Andreas et al., 2013). Minimal advection over a wet surface corresponds to a particular relative humidity value. α is a constant fraction of the difference from the minimum value of 1 to the maximum value of α proposed by Priestley and Taylor (1972). Formulas for α are developed for the last three hypotheses. Weather, radiation, and surface energy flux data from 171 FLUXNET eddy covariance stations were used. The condition LEref/LEp> 0.90 was taken as the criterion for nearly saturated conditions (where LEref is the reference, and LEp is the apparent potential evaporation rate from the equation by Penman, 1948). Daily and monthly average data from the sites were obtained. All formulations for α include one model parameter which is optimized such that the root mean square error of the target variable was minimized. For each model, separate optimizations were done for predictions of the target variables α, wet-surface evaporation (α multiplied by equilibrium evaporation rate) and actual evaporation (the latter using a highly successful version of the complementary relationship of evaporation). Overall, the second and fourth hypotheses received the best support from the data.

Dynamic Scaling of the Generalized Complementary Relationship Improves Long-term Tendency Estimates in Land Evaporation

Most large-scale evapotranspiration (ET) estimation methods require detailed information of land use, land cover, and/or soil type on top of various atmospheric measurements. The complementary relationship of evaporation (CR) takes advantage of the inherent dynamic feedback mechanisms found in the soil-vegetation-atmosphere interface for its estimation of ET rates without the need of such biogeophysical data. ET estimates over the conterminous United States by a new, globally calibrated, static scaling (GCR-stat) of the generalized complementary relationship (GCR) of evaporation were compared to similar estimates of an existing, calibration-free version (GCR-dyn) of the GCR that employs a temporally varying dynamic scaling. Simplified annual water balances of 327 medium and 18 large watersheds served as ground-truth ET values. With long-term monthly mean forcing, GCR-stat (also utilizing precipitation measurements) outperforms GCR-dyn as the latter cannot fully take advantage of its dynamic scaling with such data of reduced temporal variability. However, in a continuous monthly simulation, GCR-dyn is on a par with GCR-stat, and especially excels in reproducing long-term tendencies in annual catchment ET rates even though it does not require precipitation information. The same GCR-dyn estimates were also compared to similar estimates of eight other popular ET products and they generally outperform all of them. For this reason, a dynamic scaling of the GCR is recommended over a static one for modeling long-term behavior of terrestrial ET.

MODIS‐Aided Statewide Net Groundwater‐Recharge Estimation in Nebraska

Monthly evapotranspiration (ET) rates (2000 to 2009) across Nebraska at about 1-km resolution were obtained by linear transformations of the MODIS (MODerate resolution Imaging Spectroradiometer) daytime surface temperature values with the help of the Priestley-Taylor equation and the complementary relationship of evaporation. For positive values of the mean annual precipitation and ET differences, the mean annual net recharge was found by an additional multiplication of the power-function-transformed groundwater vulnerability DRASTIC-code values. Statewide mean annual net recharge became about 29 mm (i.e., 5% of mean annual precipitation) with the largest recharge rates (in excess of 100 mm/year) found in the eastern Sand Hills and eastern Nebraska. Areas with the largest negative net recharge rates caused by declining groundwater levels due to large-scale irrigation are found in the south-western region of the state. Error bounds of the estimated values are within 10% to 15% of the corresponding precipitation rates and the estimated net recharge rates are sensitive to errors in the precipitation and ET values. This study largely confirms earlier base-flow analysis-based statewide groundwater recharge estimates when considerations are made for differences in the recharge definitions. The current approach not only provides better spatial resolution than available earlier studies for the region but also quantifies negative net recharge rates that become especially important in numerical modeling of shallow groundwater systems.

Estimating spatially distributed monthly evapotranspiration rates by linear transformations of MODIS daytime land surface temperature data

Abstract. Under simplifying conditions catchment-scale vapor pressure at the drying land surface can be calculated as a function of its watershed-representative temperature (<Ts>) by the wet-surface equation (WSE, similar to the wet-bulb equation in meteorology for calculating the dry-bulb thermometer vapor pressure) of the Complementary Relationship of evaporation. The corresponding watershed ET rate, <ET>, is obtained from the Bowen ratio with the help of air temperature, humidity and percent possible sunshine data. The resulting (<Ts>,<ET>) pair together with the wet-environment surface temperature (<Tws>) and ET rate (ETw), obtained by the Priestley-Taylor equation, define a linear transformation on a monthly basis by which spatially distributed ET rates can be estimated as a sole function of MODIS daytime land surface temperature, Ts, values within the watershed. The linear transformation preserves the mean which is highly desirable. <Tws>, in the lack of significant open water surfaces within the study watershed (Elkhorn, Nebraska), was obtained as the mean of the smallest MODIS Ts values each month. The resulting period-averaged (2000–2007) catchment-scale ET rate of 624 mm/yr is very close to the water-balance derived ET rate of about 617 mm/yr. The latter is a somewhat uncertain value due to the effects of (a) observed groundwater depletion of about 1m over the study period caused by extensive irrigation, and; (b) the uncertain rate of net regional groundwater supply toward the watershed. The spatially distributed ET rates correspond well with soil/aquifer properties and the resulting land use type (i.e. rangeland versus center-pivot irrigated crops).

Analytical solution of the coupled 2-D turbulent heat and vapor transport equations and the complementary relationship of evaporation

The existence of a symmetrical complementary relationship (CR) in evaporation has been hypothesized in the hydrologic literature but the conditions required have not been investigated in much detail. In this study it is shown that under near-neutral atmospheric conditions and a constant energy term at the evaporating surface, the analytical solution of the coupled turbulent diffusion equations of heat and vapor transport across a moisture discontinuity of the surface yields a symmetrical CR between the evaporation rate of the uniform drying land upwind of the discontinuity and the mean evaporation rate of the wet area provided, the latter has a proper fetch (i.e., along-the-wind extent). This fetch is a function of the air stability parameter and the assumed uniform surface roughness value, and it is in the order of a 100 m for a smooth surface under near-neutral atmospheric conditions. The analytically derived mean evaporation rates of such a smooth wet surface compare well, i.e., within 10%, to the Penman equation estimates, most frequently employed within the CR framework.