Comment on “Assessing interannual variability of evapotranspiration at the catchment scale using satellite‐based evapotranspiration data sets” by Lei Cheng et al.

[1] Cheng et al. [2011] analyze annual water and energy balance data of 547 watersheds within the United States in a Budyko [1958] framework. Some problems with their water balance equations (equations (1) and (3)) written for the unsaturated zone, should be discussed first. [2] Equation (1) of Cheng et al. [2011] cannot be written for any time period as they claim to obtain the catchment water balance because for longer time periods (e.g., a year, their chosen time period of analysis) the runoff (R) values (i.e., stream discharge) will contain a certain part of the recharge values due to base flow. Therefore, a significant percentage of the groundwater recharge value can and will appear twice in the equation, once as part of recharge and once as runoff. If, indeed, R means only surface runoff (which is not known because the authors do not elaborate on it), then measured discharge at the watershed cannot be decomposed into this R and recharge at an annual basis since not all the recharged water will leave the watershed in the same year at larger catchments. The solution of the problem is to write the water balance for the combined unsaturated-saturated zone of the watershed, with the water storage term (DS) defined for the combined system. This way the recharge term disappears from the equation and evapotranspiration (ET) becomes equal to precipitation (P) less runoff plus the change in water storage, provided net lateral groundwater fluxes are negligible and the watershed is underlain by an impervious layer. [3] The problem with equation (3) of Cheng et al. [2011], in addition to the above, is that irrigation water ought to be included in the equation only if it is from a source outside the catchment. In the Republican River basin in their example, most of the irrigated water comes from center pivot systems, where the water is pumped from within the catchment, thus reducing water storage and runoff (in fact, a serious problem in many prairie states) ; consequently, a certain part of the irrigated water is counted twice in the equation, once as a measured reduced runoff value and once as additional ‘‘precipitation’’, leading to an overestimation of ET. The solution is the same as above, i.e., ET 1⁄4 P – R þ DS (written for the unsaturated-saturated system) is the correct form of the water balance equation for estimating annual ET for center-pivot irrigated catchments, similarly to watersheds without irrigation. [4] Focusing now on the core issue of the present comment, Cheng et al. [2011] found linear relationships between two ratios, ET/P and PET/P (where PET is the Priestley and Taylor [1972] evaporation rate and P is precipitation), for the catchments analyzed. They show that these linear relationships are strong in humid regions while less strong (but still statistically significant) in semiarid ones. However, what the authors overlook is that they see yet another empirical proof of the complementary relationship (CR), originally from Bouchet [1963] and later reformulated by Brutsaert and Stricker [1979] in their advection-aridity (AA) model and by Morton [1983] in his WREVAP model, to name just the two most widely used versions of the CR. Figure 1 displays the AA-estimated 10 year average ET rates plotted against the water balance–derived ET values (ET 1⁄4 P – R) for 23 catchments [Szilagyi and Jozsa, 2009] across the United States that were, supposedly, only minimally affected by human activity for the 1961–1990 period. [5] Szilagyi and Jozsa [2009] demonstrate that by dividing both sides of the AA Formulation of the CR, i.e.,