In hydrologic analysis, net precipitation, or P — ET, is itself a valuable term, and can be readily obtained in the absence of direct surface measurements of the two variables. Consider the moisture budget of an atmospheric column, extending from the surface to a height above which moisture content is negligible (about 300 hPa). The budget can be expressed as where the moisture content of the atmosphere, W, is expressed as precipitable water (the equivalent water depth of the vapor in the column). Time is given by t, ET is the surface evapo-transpiration rate, Q is the vertically integrated water vapor flux (a vector) from the surface to the top of the column, and P is the precipitation rate. The equation hence summarizes the processes by which a column's precipitable water can change. For example, ET from the surface into the column acts to increase precipitable water, while precipitation out of the column has an opposing effect. The last term on the right of Equation (6.2)isthe horizontal divergence (or negative convergence) of the vertically integrated water vapor flux. It follows that horizontal divergence contributes to a decrease in precipitable water, while convergence has the reverse influence.
Rearrangement yields an expression for P - ET:
The convenient aspect of Equation (6.3) is that the terms on the right can be calculated from vertical profiles of specific humidity and winds, which are readily available from the NCEP/NCAR reanalysis or other atmospheric analyses. This circumvents some of the problems with the surface observations of P and ET. Having gridded fields of humidity and winds means that one can obtain gridded fields of P — ET. For long-term annual means (and assuming a stationary climate), the last term of Equation (6.3) is zero and may hence be dropped. The aerological approach neglects the atmospheric flux of water in the liquid and solid phases in clouds. The liquid and solid flux is generally significant only in localized regions and for short time periods, such as over warm ocean currents and in cumulus clouds in the tropics.
The atmospheric and surface branches of the hydrologic cycle can be linked by developing a similar expression for the surface:
where S is the water content of the subsurface column and F represents lateral transports of water. The latter can be a complicated term because it includes both surface runoff and subsurface flows in terrestrial regions and the advection of ice and water in the oceans. Strictly speaking, P — ET is the same in Equations (6.3) and (6.4) only if one assumes that the surface is an atmospheric column's only "source" of ET and its only "sink" of P (Walsh et al, 1994).
Before the advent of atmospheric reanalyses, most studies of P — ET using the aerological approach focused on large areal averages (e.g., the region north of 70° N), based on interpolating rawinsonde data to the domain boundaries and averaging pre-cipitable water over the domain (e.g., Walsh et al., 1994; Serreze et al., 1995a). More recent efforts examining gridded fields of P — ET over the Arctic include Cullather et al. (2000) and Rogers et al. (2001).
While the aerological approach is attractive, it has its drawbacks. The P — ET estimates are prone to error from a variety of sources. Poor instrument performance at low temperatures and humidities introduces errors in rawinsonde moisture profiles. Differences between countries in the types of rawinsondes used, reporting practices and changes in instrumentation and reporting through time introduce further uncertainty. Humidity fields from reanalysis may contain errors related to shortcomings in data assimilation methods (both for rawinsondes and satellite retrievals), and surface ET parameterizations. Regarding the latter, numerical weather prediction models calculate ET, and this calculated value will in turn have some impact on humidity profiles. The flux convergence is also sensitive to errors in the wind fields, which reflect the available density of assimilation data and temporal changes in the reporting network, and the quality of the atmospheric model.
Cullather et al.(2000) compared means of P — ET from NCEP/NCAR and ERA-15 over the Arctic based on the aerological method with those from the six-hour model forecasts of P and ET. These can be termed "aerological" and "forecast" P — ET, respectively. Based on the forecasts, ERA-15 captures the major spatial features of mean annual P — ET as depicted by Gorshkov (1983). By contrast, the mean annual forecasted P — ET from the NCEP/NCAR reanalysis contains a spurious "blotchy" pattern (see Figure 6.9 in Cullather et al., 2000). This is present in the forecast values of P and ET, as well as aerological P — ET. From Serreze and Hurst (2000) and Cullather et al. (2000), it is apparent that the problem is present year-round, and shows a definite association with topographic features. It has been corrected in the NCEP/NCAR operational model as well as in the shorter (1979 to present) NCEP-DOE Reanalysis 2. Consequently, it is necessary to smooth the NCEP/NCAR fields. In addition, the forecast values of annual P — ET from both models are much lower (about 60%) than the aerological values, indicating severe non-closure of the moisture budget. The problem is present in forecasts of both P and ET in the NCEP/NCAR reanaly-sis. These are much too high in summer over land, indicative of an overly vigorous hydrologic cycle.
Despite these shortcomings, the aerological approach applied to atmospheric reanal-ysis seems to work fairly well. This is supported from the study of Cullather et al.
(2000), who compared the annual meridional flux of moisture across 70° N from NCEP/NCAR and ERA-15 against values computed via interpolation of rawinsonde data. Annual average fluxes from both models are significantly higher than the rawinsonde estimates during summer, with better correspondence during winter. Closer examination points to the rawinsonde network being insufficiently dense to capture the major moisture transport "pathways" into the Arctic (Zhu and Newell, 1998). Put differently, the reanalysis seems to provide more realistic depictions of the flux. Aero-logical P — ET averaged for the region north of 70° N from the two models is very similar, with a value of 188 ± 6 mm per year, compared with the rawinsonde-derived estimate of 163 mm per year.
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