References

HESS

Hydrology and Earth System Sciences

HESS

Hydrol. Earth Syst. Sci.

1607-7938

Copernicus Publications

Göttingen, Germany

10.5194/hess-16-1863-2012

An analytical model for soil-atmosphere feedback

Schaefli

¹ ² van der Ent

R. J.

² Woods

³ Savenije

H. H. G.

Laboratory of Ecohydrology (ECHO), School of Architecture, Civil and Environmental Engineering (ENAC), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

Water Resources Section, Delft University of Technology (TU Delft), Delft, The Netherlands

National Institute for Water and Atmospheric Research (NIWA), Christchurch, New Zealand

05 07 2012

16 7 1863 1878

2012

This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/

This article is available from https://hess.copernicus.org/articles/16/1863/2012/hess-16-1863-2012.html

The full text article is available as a PDF file from https://hess.copernicus.org/articles/16/1863/2012/hess-16-1863-2012.pdf

Soil-atmosphere feedback is a key for understanding the hydrological cycle and the direction of potential system changes. This paper presents an analytical framework to study the interplay between soil and atmospheric moisture, using as input only the boundary conditions at the upstream end of trajectory, assuming advective moisture transport with average wind speed along this trajectory and vertical moisture exchange with the soil compartment of uniform vertical properties. Precipitation, evaporation from interception and runoff are assumed to depend through simple functional relationships on the soil moisture or the atmospheric moisture. Evaporation from soil moisture (including transpiration) depends on both state variables, which introduces a nonlinear relationship between the two compartments. This nonlinear relationship can explain some apparently paradoxical phenomena such as a local decrease of precipitation accompanied by a runoff increase. <br><br> The solutions of the resulting water balance equations correspond to two different spatial moisture regimes showing either an increasing or a decreasing atmospheric moisture content along a trajectory starting at the coast, depending on boundary conditions and parameters. The paper discusses how different model parameters (e.g. time scales of precipitation, evaporation or runoff) influence these regimes and how they can create regime switches. Such an analysis has potential to anticipate the range of possible land use and climate changes or to interpret the results of complex land-atmosphere interaction models. Based on derived analytical expressions for the Horton index, the Budyko curve and a precipitation recycling ratio, the analytical framework opens new perspectives for the classification of hydrological systems.

References 1

Bierkens, M. P. and van den Hurk, B. J. J. M.: Groundwater convergence as a possible mechanism for multi-year persistence in rainfall, Geophys. Res. Lett., 34, L02402, <a href="http://dx.doi.org/10.1029/2006GL028396">https://doi.org/10.1029/2006GL028396</a>, 2007.

Bretherton, C. S., Peters, M. E., and Back, L. E.: Relationships between water vapor path and precipitation over the tropical oceans, J. Climate, 17, 1517–1528, <a href="http://dx.doi.org/10.1175/1520-0442(2004)017<1517:rbwvpa>2.0.co;2">https://doi.org/10.1175/1520-0442(2004)017<1517:rbwvpa>2.0.co;2</a>, 2004.

Brutsaert, W.: Hydrology, an introduction, Cambridge Univeristy Press, Cambridge, 2005.

Budyko, M. I.: Evaporation Under Natural Conditions, Gidrometeorizdat, St. Petersburg, Russia, 1984.

Burde, G. I. and Zangvil, A.: The estimation of regional precipitation recycling, \textsc{P}art \textsc{I}: \textsc{R}eview of recycling models, J. Climate, 14, 2497–2508, <a href="http://dx.doi.org/10.1175/1520-0442(2001)014<2497:TEORPR>2.0.CO;2">https://doi.org/10.1175/1520-0442(2001)014<2497:TEORPR>2.0.CO;2</a>, 2001.

Clark, M. P., Slater, A. G., Rupp, D. E., Woods, R. A., Vrugt, J. A., Gupta, H. V., Wagener, T., and Hay, L. E.: \textsc{F}ramework for \textsc{U}nderstanding \textsc{S}tructural \textsc{E}rrors (FUSE): A modular framework to diagnose differences between hydrological models, Water Resour. Res., 44, W00b02, <a href="http://dx.doi.org/10.1029/2007wr006735">https://doi.org/10.1029/2007wr006735</a>, 2008.

DeAngelis, A., Dominguez, F., Fan, Y., Robock, A., Kustu, M. D., and Robinson, D.: Evidence of enhanced precipitation due to irrigation over the \textsc{G}reat \textsc{P}lains of the \textsc{U}nited \textsc{S}tates, J. Geophys. Res., 115, D15115, <a href="http://dx.doi.org/10.1029/2010JD013892">https://doi.org/10.1029/2010JD013892</a>, 2010.

de Groen, M. M. and Savenije, H. H. G.: A monthly interception equation based on the statistical characteristics of daily rainfall, Water Resour. Res., 42, W12417, <a href="http://dx.doi.org/10.1029/2006WR005013">https://doi.org/10.1029/2006WR005013</a>, 2006.

Dirmeyer, P. A., Koster, R. D., and Guo, Z. C.: Do global models properly represent the feedback between land and atmosphere?, J. Hydrometeorol., 7, 1177–1198, <a href="http://dx.doi.org/10.1175/JHM532.1">https://doi.org/10.1175/JHM532.1</a>, 2006.

Dirmeyer, P. A., Brubaker, K. L., and DelSole, T.: Import and export of atmospheric water vapor between nations, J. Hydrol., 365, 11–22, <a href="http://dx.doi.org/10.1016/j.jhydrol.2008.11.016">https://doi.org/10.1016/j.jhydrol.2008.11.016</a>, 2009.

Dominguez, F. and Kumar, P.: Precipitation Recycling Variability and Ecoclimatological Stability – A Study Using \textsc{NARR} Data, \textsc{P}art \textsc{II}: \textsc{N}orth \textsc{A}merican Monsoon Region, J.  Climate, 21, 5165–5186, <a href="http://dx.doi.org/10.1175/2008JCLI1760.1">https://doi.org/10.1175/2008JCLI1760.1</a>, 2008.

Dominguez, F., Kumar, P., Liang, X. Z., and Ting, M. F.: Impact of atmospheric moisture storage on precipitation recycling, J. Climate, 19, 1513–1530, <a href="http://dx.doi.org/10.1175/JCLI3691.1">https://doi.org/10.1175/JCLI3691.1</a>, 2006.

Eltahir, E. A. B.: A soil moisture-rainfall feedback mechanism. 1. \textsc{T}heory and observations, Water Resour. Res., 34, 765–776, <a href="http://dx.doi.org/10.1029/97WR03499">https://doi.org/10.1029/97WR03499</a>, 1998.

Eltahir, E. A. B. and Bras, R. L.: Precipitation recycling in the \textsc{A}mazon \textsc{B}asin, Q. J. Roy. Meteorol. Soc., 120, 861–880, <a href="http://dx.doi.org/10.1002/qj.49712051806">https://doi.org/10.1002/qj.49712051806</a>, 1994.

Fenicia, F., Savenije, H. H. G., Matgen, P., and Pfister, L.: Is the groundwater reservoir linear? Learning from data in hydrological modelling, Hydrol. Earth Syst. Sci., 10, 139–150, <a href="http://dx.doi.org/10.5194/hess-10-139-2006">https://doi.org/10.5194/hess-10-139-2006</a>, 2006.

Gerrits, A. M. J., Savenije, H. H. G., Veling, E. J. M., and Pfister, L.: Analytical derivation of the \textsc{B}udyko curve based on rainfall characteristics and a simple evaporation model, Water Resour. Res., 45, W04403, <a href="http://dx.doi.org/10.1029/2008wr007308">https://doi.org/10.1029/2008wr007308</a>, 2009.

Gerrits, A. M. J., Pfister, L., and Savenije, H. H. G.: Spatial and temporal variability of canopy and forest floor interception in a beech forest, Hydrol. Process., 24, 3011–3025, <a href="http://dx.doi.org/10.1002/hyp.7712">https://doi.org/10.1002/hyp.7712</a>, 2010.

Goessling, H. F. and Reick, C. H.: What do moisture recycling estimates tell us? Exploring the extreme case of non-evaporating continents, Hydrol. Earth Syst. Sci., 15, 3217–3235, <a href="http://dx.doi.org/10.5194/hess-15-3217-2011">https://doi.org/10.5194/hess-15-3217-2011</a>, 2011.

Higgins, R. W., Yao, Y., and Wang, X. L.: Influence of the \textsc{N}orth \textsc{A}merican monsoon system on the \textsc{U}\textsc{S} summer precipitation regime, J. Climate, 10, 2600–2622, \href{http://dx.doi.org/10.1175/1520-0442(1997)010<2600:iotnam>2.0.co;2} https://doi.org/10.1175/1520-0442(1997)010<2600:iotnam>2.0.co;2, 1997.

Howell, T. A. and Evett, S. R.: The Penman-Monteith method, in: Evapotranspiration: Determination of Consumptive Use in Water Rights Proceedings, Continuing Legal Education in Colorado, Inc. Denver, Colorado, 2004.

Koster, R. D., Dirmeyer, P. A., Guo, Z., Bonan, G., Chan, E., Cox, P., Gordon, C. T., Kanae, S., Kowalczyk, E., Lawrence, D., Liu, P., Lu, C. H., Malyshev, S., McAvaney, B., Mitchell, K., Mocko, D., Oki, T., Oleson, K., Pitman, A., Sud, Y. C., Taylor, C. M., Verseghy, D., Vasic, R., Xue, Y., and Yamada, T.: Regions of strong coupling between soil moisture and precipitation, Science, 305, 1138–1140, <a href="http://dx.doi.org/10.1126/science.1100217">https://doi.org/10.1126/science.1100217</a>, 2004.

Kunstmann, H. and Jung, G.: Influence of soil-moisture and land use change on precipitation in the \textsc{V}olta \textsc{B}asin of \textsc{W}est \textsc{A}frica, International Journal of River Basin Management, 5, 9–16, <a href="http://dx.doi.org/10.1080/15715124.2007.9635301">https://doi.org/10.1080/15715124.2007.9635301</a>, 2007.

Langmuir, I.: The constitution and fundamental properties of solids and liquids. \textsc{P}art \textsc{I}. \textsc{S}olids, J. Am. Chem. Soc., 38, 2221–2295, <a href="http://dx.doi.org/10.1021/ja02268a002">https://doi.org/10.1021/ja02268a002</a>, 1916.

Lintner, B. R., Gentine, P., Findell, K. L., D'Andrea, F., and Sobel, A. H.: An idealized prototype for large-scale land-atmosphere coupling, J. Climate, pending with minor revisions, 2012.

Matsoukas, C., Benas, N., Hatzianastassiou, N., Pavlakis, K. G., Kanakidou, M., and Vardavas, I.: Potential evaporation trends over land between 1983–2008: driven by radiative fluxes or vapour-pressure deficit?, Atmos. Chem. Phys., 11, 7601–7616, <a href="http://dx.doi.org/10.5194/acp-11-7601-2011">https://doi.org/10.5194/acp-11-7601-2011</a>, 2011.

Monteith, J. L.: Evaporation and environment, Proc. Symp. Soc. Exp. Biol., 19, 205–234, 1965.

Pisso, I., Real, E., Law, K. S., Legras, B., Bousserez, N., Attié, J. L., and Schlager, H.: Estimation of mixing in the troposphere from \textsc{L}agrangian trace gas reconstructions during long-range pollution plume transport, J. Geophys. Res., 114, D19301, <a href="http://dx.doi.org/10.1029/2008JD011289">https://doi.org/10.1029/2008JD011289</a>, 2009.

Pitman, A. J., de Noblet-Ducoudre, N., Cruz, F. T., Davin, E. L. , Bonan, G. B., Brovkin, V., Claussen, M., Delire, C., Ganzeveld, L., Gayler, V., van den Hurk, B. J. J. M., Lawrence, P. J., van der Molen, M. K., Muller, C., Reick, C. H., Seneviratne, S. I., Strengers, B. J., and Voldoire, A.: Uncertainties in climate responses to past land cover change: First results from the \textsc{LUCID} intercomparison study, Geophys. Res. Lett., 36, L14814, <a href="http://dx.doi.org/10.1029/2009GL039076">https://doi.org/10.1029/2009GL039076</a>, 2009

Priestley, C. H. B. and Taylor, R. J.: On the assessment of surface heat flux and evaporation using large-scale parameters, Mon. Weather Rev., 100, 81–92, <a href="http://dx.doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2">https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2</a>, 1972.

Randel, D. L., Vonder Haar, T. H., Ringerud, M. A., Stephens, G. L., Greenwald, T. J., and Combs, C. L.: A New Global Water Vapor Dataset, B. Am. Meteorol. Soc., 77, 1233–1246, <a href="http://dx.doi.org/10.1175/1520-0477(1996)077<1233:ANGWVD>2.0.CO;2">https://doi.org/10.1175/1520-0477(1996)077<1233:ANGWVD>2.0.CO;2</a>, 1996.

Savenije, H. H. G.: New definitions for moisture recycling and the relationship with land-use changes in the \textsc{S}ahel, J. Hydrol., 167, 57–78, <a href="http://dx.doi.org/10.1016/0022-1694(94)02632-L">https://doi.org/10.1016/0022-1694(94)02632-L</a>, 1995{a}.

Savenije, H. H. G.: Does moisture feedback affect rainfall significantly?, Phys. Chem. Earth, 20, 507–513, <a href="http://dx.doi.org/10.1016/S0079-1946(96)00014-6">https://doi.org/10.1016/S0079-1946(96)00014-6</a>, 1995{b}.

Savenije, H. H. G.: The Runoff Coefficient as the Key to Moisture Recycling, J. Hydrol., 176, 219–225, <a href="http://dx.doi.org/10.1016/0022-1694(95)02776-9">https://doi.org/10.1016/0022-1694(95)02776-9</a>, 1996.

Savenije, H. H. G.: The importance of interception and why we should delete the term evapotranspiration from our vocabulary, Hydrol. Process., 18, 1507–1511, <a href="http://dx.doi.org/10.1002/hyp.5563">https://doi.org/10.1002/hyp.5563</a>, 2004.

Schär, C., Lüthi, D., and Beyerle, U.: The soil-precipitaiton feedback: a process study with a regional climate model, J. Climate, 12, 722–741, <a href="http://dx.doi.org/10.1175/1520-0442(1999)012<0722:TSPFAP>2.0.CO;2">https://doi.org/10.1175/1520-0442(1999)012<0722:TSPFAP>2.0.CO;2</a>, 1999.

Schreiber, P.: Über die \textsc{B}eziehungen zwischen dem \textsc{N}iederschlag und der \textsc{W}asserführung der \textsc{F}lüsse in \textsc{M}itteleuropa, \textsc{Z}. \textsc{M}eteorol., 21, 441–452, 1904.

Seneviratne, S. I., Corti, T., Davin, E. L., Hirschi, M., Jaeger, E. B., Lehner, I., Orlowsky, B., and Teuling, A. J.: Investigating soil moisture-climate interactions in a changing climate: A review, Earth-Sci. Rev., 99, 125–161, <a href="http://dx.doi.org/10.1016/j.earscirev.2010.02.004">https://doi.org/10.1016/j.earscirev.2010.02.004</a>, 2010.

Sultan, B. and Janicot, S.: The \textsc{W}est \textsc{A}frican monsoon dynamics. Part II: The "preonset" and "onset" of the summer monsoon, J. Climate, 16, 3407–3427, \href{http://dx.doi.org/10.1175/1520-0442(2003)016<3407:TWAMDP>2.0.CO;2} https://doi.org/10.1175/1520-0442(2003)016<3407:TWAMDP>2.0.CO;2, 2003.

Tian, L., Yao, T., MacClune, K., White, J. W. C., Schilla, A., Vaughn, B., Vachon, R., and Ichiyanagi, K.: Stable isotopic variations in west \textsc{C}hina: \textsc{A} consideration of moisture sources, J. Geophys. Res.-Atmos., 112, D10112, <a href="http://dx.doi.org/10.1029/2006jd007718">https://doi.org/10.1029/2006jd007718</a>, 2007.

Trenberth, K. E.: Atmospheric moisture residence times and cycling: implications for rainfall rates and climate change, Climatic Change, 39, 667–694, 1998.

Trenberth, K. E.: Climate system modeling, Cambridge University Press, Cambridge, 2009.

Trenberth, K. E., Dai, A., Rasmussen, R. M., and Parsons, D. B.: The changing character of precipitation, B. Am. Meteorol. Soc., 84, 1205–1217, <a href="http://dx.doi.org/10.1175/BAMS-84-9-1205">https://doi.org/10.1175/BAMS-84-9-1205</a>, 2003.

Troch, P. A., Martinez, G. F., Pauwels, V. R. N., Durcik, M., Sivapalan, M., Harman, C., Brooks, P. D., Gupta, H. V., and Huxman, T.: Climate and vegetation water use efficiency at catchment scales, Hydrol. Process., 23, 2409–2414, <a href="http://dx.doi.org/10.1002/hyp.7358">https://doi.org/10.1002/hyp.7358</a>, 2009.

Tuinenburg, O. A., Hutjes, R. W. A., Jacobs, C. M. J., and Kabat, P.: Diagnosis of local land-atmosphere feedbacks in \textsc{I}ndia, J. Climate, 24, 251–266, <a href="http://dx.doi.org/10.1175/2010JCLI3779.1">https://doi.org/10.1175/2010JCLI3779.1</a>, 2011.

van der Ent, R. J. and Savenije, H. H. G.: Length and time scales of atmospheric moisture recycling, Atmos. Chem. Phys., 11, 1853–1863, <a href="http://dx.doi.org/10.5194/acp-11-1853-2011">https://doi.org/10.5194/acp-11-1853-2011</a>, 2011.

Van der Ent, R. J., Savenije, H. H. G., Schaefli, B., and Steele-Dunne, S. C.: The origin and fate of atmospheric moisture over continents, Water Resour. Res., 46, W09525, <a href="http://dx.doi.org/10.1029/2010WR009127">https://doi.org/10.1029/2010WR009127</a>, 2010.

Voepel, H., Ruddell, B., Schumer, R., Troch, P. A., Brooks, P. D., Neal, A., Durcik, M., and Sivapalan, M.: Quantifying the role of climate and landscape characteristics on hydrologic partitioning and vegetation response, Water Resour. Res., 47, W00J09, <a href="http://dx.doi.org/10.1029/2010wr009944">https://doi.org/10.1029/2010wr009944</a>, 2011.

Wagener, T., Sivapalan, M., Troch, P. A., and Woods, R.: Catchment classification and hydrologic similarity, Geography Compass, 1, 901–931, <a href="http://dx.doi.org/10.1111/j.1749-8198.2007.00039.x">https://doi.org/10.1111/j.1749-8198.2007.00039.x</a>, 2007.

Woods, R. A.: Analytical model of seasonal climate impacts on snow hydrology: Continuous snowpacks, Adv. Water Resour., 32, 1465–1481, <a href="http://dx.doi.org/10.1016/j.advwatres.2009.06.011">https://doi.org/10.1016/j.advwatres.2009.06.011</a>, 2009.

Worden, J., Noone, D., and Bowman, K.: Importance of rain evaporation and continental convection in the tropical water cycle, Nature, 445, 528–532, <a href="http://dx.doi.org/10.1038/nature05508">https://doi.org/10.1038/nature05508</a>, 2007.