Hydrology and Land Surface Studies
Indications of increasing land surface evaporation during the second half of the 20th century
 It is generally agreed that the evaporation from pans has been decreasing for the past half century over many regions of the Earth. However, the significance of this negative trend, as regards terrestrial evaporation, is still somewhat controversial, and its implications for the global hydrologic cycle remain unclear. The controversy stems from the alternative views that these evaporative changes resulted, either from global radiative dimming, or from the complementary relationship between pan and terrestrial evaporation. Actually, these factors are not mutually exclusive but act concurrently. It is shown quantitatively that, if the presently available data records are taken at face value, despite global dimming, the observed decreases in pan evaporation are generally evidence of increased terrestrial evaporation in those regions. This is consistent with independent hydrologic budget calculations for several large river basins in the USA, and likely further evidence of an accelerating hydrologic cycle in many areas.
 Observations of decreasing pan evaporation over the past 50 years or so have been reported for many regions throughout the world with widely different climates. Such negative trends were first documented a little more than a decade ago with measurements in European Russia, Siberia and the United States [Peterson et al., 1995], and they were soon confirmed by reports of decreasing pan evaporation in India [Chattopadhyay and Hulme, 1997], and Venezuela [Quintana-Gomez, 1998]. Meanwhile, many more analyses have been published indicating similar negative trends for pan evaporation in other parts of the world, namely in China [Liu et al., 2004; Liu and Zeng, 2004; Xu et al., 2005], Japan [Asanuma et al., 2004], Australia [Roderick and Farquhar, 2004]; and in Thailand [Tebakari et al., 2005]. These decreases in pan evaporation were not universal, and at some local pan stations positive trends were recorded; in some cases positive trends were observed over larger areas, for instance in the Southeast of the U.S.A. [Lawrimore and Peterson, 2000], the Pacific Northwest of the U.S.A., parts of arid Central Asia and Kazakhstan [Golubev et al., 2001], Israel [Cohen et al., 2002], and central parts of China [Liu and Zeng, 2004; Xu et al., 2005]. Nevertheless, by and large the observed decreases in pan evaporation over the second half of the twentieth century appear to have been widespread and broadly consistent enough to have led to the present consensus of their general validity. However, the interpretation of the negative trend has been controversial, and so far agreement on its significance regarding terrestrial evaporation has remained elusive.
 The negative pan evaporation trends were, at first, thought to be an indication of a general negative trend in terrestrial evaporation in those areas. But such an interpretation seemed incompatible with the reported general increases in global precipitation in the same period [e.g., Dai et al., 1997; Karl and Knight, 1998]; except in wetlands and swamps this would normally suggest an increasing rate of evaporation.
 This apparent incongruity was initially dubbed the evaporation paradox [Brutsaert and Parlange, 1998], and it was suggested that, on the contrary, the observed decreases in pan evaporation may well be an indication of increased terrestrial evaporation, on account of the complementary relationship between apparent potential evaporation and actual evaporation. The explanation by Brutsaert and Parlange  was concluded to be plausible and generally consistent with other evidence by Lawrimore and Peterson , Golubev et al.  and Hobbins et al. ; on the other hand, it was also the subject of some skepticism, if not rejection, in the studies by Cohen et al. , Roderick and Farquhar , Ohmura and Wild , and Liu et al. , on the grounds that the decreasing pan evaporation must be caused by decreasing solar irradiance, or global dimming, and thus evidence of decreasing landscape evaporation.
 But global dimming and the complementary principle need not be mutually incompatible. In fact, it will be shown next that both effects can be combined, and that the conjunction of the available measurements of decreasing net radiation with those of decreasing pan evaporation results in a positive trend in terrestrial evaporation during the second half of the 20th century.
2. Terrestrial Evaporation as Related to Pan Evaporation and Radiation
 The complementary principle of latent heat transfer, probably first formally advanced by Bouchet , states that for given radiative input conditions, as the aridity of the environment intensifies in the absence of precipitation, terrestrial evaporation will decrease, whereas the apparent potential evaporation will increase; the apparent potential evaporation can be defined as the potential evaporation estimated on the basis of measurements under non-potential conditions, and the evaporation from a pan or from some other type of small wet surface can be considered a good measure of it. However, in Bouchet's original description, the physical meaning and spatial scale of the two types of potential evaporation, namely the true potential evaporation and the apparent potential evaporation, were not clearly articulated; moreover, the true potential evaporation was somehow connected with the global short-wave radiation, further confounding its meaning. Consequently, it took several years before the basic idea gained some degree of acceptance; also, although meanwhile numerous attempts have been made, there is still no unanimity on how the concept should be used in practice, or how the effect of radiation should be included. This may explain in part the controversy mentioned above. To remove some of the uncertainties, the specific application of the concept with evaporation pans was recently subjected to a critical experimental analysis [Kahler and Brutsaert, 2006], so that it can now be considered a more reliable tool in the present context. The resulting formulation can be found elsewhere [Brutsaert and Parlange, 1998; Brutsaert, 2005; Kahler and Brutsaert, 2006], and only the final result need be presented here.
 In the case of pan evaporation in a drying environment, the complementary relationship can be formulated as follows,
in which Epa is the evaporation from a pan and E is the actual terrestrial evaporation from the surrounding environment; the symbol Epo denotes the true potential evaporation, that is the evaporation, when the surface is amply supplied with water, so that it satisfies E = Epo = CpEpa under those special conditions. The parameter Cp is a coefficient of proportionality which relates the pan evaporation to the actual evaporation under potential conditions, and the parameter b represents a measure of the effectiveness, with which heat transfer takes place between the pan and its surroundings, in response to changes in environmental aridity. In the application of (1) to relate the terrestrial evaporation E with the pan evaporation Epa, the required constant parameters Cp and b can be determined readily by calibration or from past experience. However, the determination of the potential evaporation Epo and its dependency on radiation are more problematic. The reason is that under drying conditions, Epo is the hypothetical evaporation rate which would take place, if conditions were potential, given the same external forcing conditions, namely the same solar radiation and the same general mesoscale circulation pattern; whenever the available surface moisture is inadequate to maintain potential conditions, it is hard to infer the atmospheric and surface conditions that would prevail if water were not lacking, not to mention the evaporation under those hypothetical conditions.
 For the present purpose, this difficulty can be sidestepped by means of two considerations. The first, following Brutsaert and Stricker , is that Priestley and Taylor's [1972; Brutsaert, 2005] empirical extension of equilibrium evaporation to describe evaporation from a wet surface under conditions of minimal advection, depends mainly on the solar radiation input and is relatively insensitive to changing surface moisture conditions. The second consideration is that the heat flux into the ground G, which is difficult to estimate in practice, can generally be assumed to be proportional to the net radiation. With these two assumptions the potential evaporation Epo assumes the form
in which Δ ≡ de*/dT is the slope of the saturation water vapor pressure at the temperature of the air T, γ is the psychrometric constant, Rne = Rn/Le is the net radiation expressed in units of evaporation, Le is the latent heat of vaporization, and ae is an empirical constant which is to be determined by calibration for any given surface, and which combines the Priestley-Taylor constant and the ground-heat-flux proportionality [Kahler and Brutsaert, 2006].
 Substitution of (2) into (1) yields
which can be used in practice to estimate actual evaporation with data of air temperature, net radiation, and pan evaporation, provided the parameters ae, Cp and b are known. Equation (3) was tested and calibrated [Kahler and Brutsaert, 2006] with data from two experimental sites and nearby Class A pan stations, namely one in the Konza Prairie in northeastern Kansas, and one in the Little Washita River basin in Oklahoma. Equation (3) was found to give a good description of the experimental data. The parameters vary with location, but when no other information is available, they can be assigned typical values of the order of Cp = 1.0, ae = 1.0(±0.12), and b = 5.0(±0.15).
 Since (3) has been validated experimentally to give a reliable description of terrestrial evaporation of natural terrain, it can similarly be used to estimate evaporation trends. When air temperature, net radiation, and pan evaporation are time-dependent, one obtains for the rate of change of the actual evaporation
in which the apostrophe mark indicates the partial time derivative, and T is the near-surface air temperature. For a global average temperature of, say T = 15°C, for an assumed average net radiation on land of Rne = 793 mm y−1 (=62 W m−2), and with the above typical values of the parameters, (4) can be simplified to the following “working” equation
which should be adequate for order of magnitude estimates.
 The temporal trends of the variables appearing on the right hand side of (5) have been determined experimentally in many studies and typical values for the past half century can be derived from that literature. The least well-known among the three is probably the trend in net radiation R′n. Wild et al.  have summarized the available data records from 66 stations deposited in the Global Energy Balance Archive (GEBA) data base, with at least a decade of measurements; 16 stations were located in Europe, 21 in Canada, 28 in the former Soviet Union, and 1 in Australia. The weighted average linear trend in these measurements indicates a dimming, of the order of R′n = −0.05 W m−2y−1, or R′ne = −0.64 mm y−2; this is also roughly the average trend observed at the 28 stations in the former Soviet Union, which include some of the longer and more reliable records. The global average trend in the near-surface air temperature from 1950 to 2000 is generally [Jones et al., 1999] accepted to be of the order of T′ = +0.01°C y−1. As noted, pan evaporation trends over the same period vary widely, and values as high as −11.4 mm y−2 have been reported [Chattopadhyay and Hulme, 1997] for India. However, values around −3 mm y−2 appear to be more typical for stations where it is measured only during the warm season; if one assumes that the pan evaporation equivalent drying in the cold season is about 1/3 of the warm season value, this gives E′pa = −4 mm y−2. With these typical average values of the global trends of net radiation, of temperature and of pan evaporation, (5) yields the trend of terrestrial evaporation as E′ = +0.44 mm y−2.
 This value is of the same order as the increases, ranging between 0.39 and 1.86 mm y−2, derived independently and calculated from the difference between precipitation and river flow for some large river basins in the U.S.A. Indeed, Milly and Dunne  obtained E′ = +0.69 mm y−2 for the Mississippi River basin, and Walter et al.  derived similar values, with an average (±σ) of E′ = + 1.03(±0.54) mm y−2 for 7 other basins.
 While the agreement is excellent, admittedly the data trends used here and also the underlying theory of (4) and (5) are subject to some uncertainty. For example, although (3) has been validated experimentally, one assumption is that Epo can be represented by (2), which is the source of the temperature trend dependency term in (4) and (5); nevertheless, if this term were omitted, the evaporation trend would still remain of the same order and decrease only to E′ = +0.32 mm y−2. Another point is that the radiation dimming is not well understood; satellite measurements indicate that globally it was probably different from what the ground-based record suggests [e.g., Pinker et al., 2005]. Use of a different value of R′n would also result in a different terrestrial evaporation trend. For the present, however, this issue is largely moot; radiative dimming has apparently ceased [Wild et al., 2005] and global surface insolation has been increasing for the past 15 years at many locations in the world, thus strengthening the positive evaporation trend, calculated here.
 The implementation of the complementary concept presented herein leads to the following result. If the presently available records of net radiative dimming are taken at face value, the observed decreases in pan evaporation are an indication of increased terrestrial evaporation during the second half of the twentieth century in those regions. With typical values of the parameters and of the global trends of net radiation, of temperature and of pan evaporation, this increase in terrestrial evaporation was found to be around E′ = +0.44 mm y−2. This is of the same order as the increases, ranging between 0.39 and 1.86 mm y−2, obtained independently using hydrologic budget calculations for a number of large river basins in the United States. Taken together with observed positive trends in precipitation and in soil moisture, this is one more indication of an accelerating hydrologic cycle over large regions of the Earth during the same period.
 Part of this work was carried out while on leave at the Graduate School of Life and Environmental Sciences, University of Tsukuba with support from the Japan Society for the Promotion of Science; helpful discussions with Michiaki Sugita and Jun Asanuma are gratefully acknowledged.