New analytical derivation of the mean annual water‐energy balance equation

Water Resources Research - Tập 44 Số 3 - 2008
Hanbo Yang1, Dawen Yang1, Zhidong Lei1, Fubao Sun1
1State Key Laboratory of Hydro-Science and Engineering and Department of Hydraulic Engineering, Tsinghua University, Beijing, China

Tóm tắt

The coupled water‐energy balance on long‐term time and catchment scales can be expressed as a set of partial differential equations, and these are proven to have a general solution as E/P = F(E0/P, c), where c is a parameter. The state‐space of (P, E0, E) is a set of curved faces in P − E0 − E three‐dimensional space, whose projection into E/P − E0/P two‐dimensional space is a Budyko‐type curve. The analytical solution to the partial differential equations has been obtained as E = E0P/(Pn + E0n)1/n (parameter n representing catchment characteristics) using dimensional analysis and mathematic reasoning, which is different from that found in a previous study. This analytical solution is a useful theoretical tool to evaluate the effect of climate and land use changes on the hydrologic cycle. Mathematical comparisons between the two analytical equations showed that they were approximately equivalent, and their parameters had a perfectly significant linear correlation relationship, while the small difference may be a result of the assumption about derivatives in the previous study.

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Tài liệu tham khảo

10.1016/S0022-1694(02)00101-4

Bagrov N. A., 1953, Mean long‐term evaporation from land surface, Meteorol. Gidrol., 10, 20

Bouchet R. J., 1963, Evapotranspiration reelle evapotranspiration potentielle, signification climatique, Int. Assoc. Sci. Hydrol. Proc., 62, 134

10.1007/s00703-003-0616-8

10.1029/2006GL027532

10.1038/23845

10.1029/WR015i002p00443

Budyko M. I., 1958, The heat balance of the Earth's surface, 144

Budyko M. I., 1974, Climate and Life

10.1016/S0022-1694(98)00293-5

10.1016/S0309-1708(99)00019-6

10.1029/WR014i005p00749

10.1017/CBO9780511535680

Fu B. P., 1981, On the calculation of the evaporation from land surface (in Chinese), Sci. Atmos. Sin., 5, 23

Intergovernmental Panel on Climate Change, 2001, Climate Change 2001: The Scientific Basis

10.1029/2005WR004541

10.1175/1520-0442(1999)012<1911:ASFFET>2.0.CO;2

10.1016/S0309-1708(01)00005-7

Mezentsev V. S., 1955, More on the calculation of average total evaporation, Meteorol. Gidrol., 5, 24

10.1029/94WR00586

Ol'dekop E. M., 1911, On evaporation from the surface of river basins, Trans. Meteorol. Obs. Univ. Tartu, 4, 200

10.1029/91WR02482

Pike J. G., 1964, The estimation of annual runoff from meteorological data in a tropical climate, J. Hydrol., 12, 2116

10.1029/2004WR003697

10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2

Schaake J. C., 1990, Climate Change and U. S. Water Resources, 177

Schreiber P., 1904, Ueber die Beziehungen zwischen dem Niederschlag und der Wasserfvhrung der flvsse in Mitteleuropa, Meteorol. Z., 21, 441

Shuttleworth W. J., 1993, Handbook of Hydrology, 4.1

10.3354/cr011149

10.1029/2006WR005224

10.1029/2000WR900325

10.1029/2003WR002710

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Water Resources Research

Tập 44 Số 3

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