Application of the Maximum Entropy Production Model of Evapotranspiration over Partially Vegetated Water-Limited Land Surfaces

Islem Hajji Department of Civil and Water Engineering, Université Laval, Quebec, Quebec, Canada

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Daniel F. Nadeau Department of Civil and Water Engineering, Université Laval, Quebec, Quebec, Canada

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Biljana Music Ouranos–Consortium on Regional Climatology and Adaptation to Climate Change, Montreal, and Department of Civil and Water Engineering, Université Laval, Quebec, Quebec, Canada

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François Anctil Department of Civil and Water Engineering, Université Laval, Quebec, Quebec, Canada

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Jingfeng Wang Georgia Institute of Technology, Atlanta, Georgia

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Abstract

The maximum entropy production (MEP) model based on nonequilibrium thermodynamics and the theory of Bayesian probabilities was recently developed to model land surface fluxes, including soil evaporation and vegetation transpiration. This model requires few input data and ensures the closure of the surface energy balance. This study aims to test the capability of such a model to realistically simulate evapotranspiration (ET) over a wide range of climates and vegetation covers. A weighting coefficient is introduced to calculate total ET from soil evaporation and vegetation transpiration over partially vegetated land surfaces, resulting in the MEP-ET model. Using this coefficient, the model outputs are compared with in situ observations of ET at eight FLUXNET sites across the continental United States. Results confirm the close agreement between the MEP-ET predicted daily ET and the corresponding observations at sites characterized by moderately limited water availability. Poor ET results were obtained under high water stress conditions. A regulation parameter was therefore introduced in the MEP-ET model to properly take into account the effects of soil water stress on stomata, yielding the generalized MEP-ET model. This parameter considerably reduced model biases under water stress conditions for various heterogeneous land surface sites. The generalized MEP-ET model outperforms several popular ET models, including Penman–Monteith (PM), modified Priestley–Taylor–Jet Propulsion Laboratory (PT-JPL), and air-relative-humidity-based two-source model (ARTS) at all test sites.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Islem Hajji, islem.hajji.1@ulaval.ca

Abstract

The maximum entropy production (MEP) model based on nonequilibrium thermodynamics and the theory of Bayesian probabilities was recently developed to model land surface fluxes, including soil evaporation and vegetation transpiration. This model requires few input data and ensures the closure of the surface energy balance. This study aims to test the capability of such a model to realistically simulate evapotranspiration (ET) over a wide range of climates and vegetation covers. A weighting coefficient is introduced to calculate total ET from soil evaporation and vegetation transpiration over partially vegetated land surfaces, resulting in the MEP-ET model. Using this coefficient, the model outputs are compared with in situ observations of ET at eight FLUXNET sites across the continental United States. Results confirm the close agreement between the MEP-ET predicted daily ET and the corresponding observations at sites characterized by moderately limited water availability. Poor ET results were obtained under high water stress conditions. A regulation parameter was therefore introduced in the MEP-ET model to properly take into account the effects of soil water stress on stomata, yielding the generalized MEP-ET model. This parameter considerably reduced model biases under water stress conditions for various heterogeneous land surface sites. The generalized MEP-ET model outperforms several popular ET models, including Penman–Monteith (PM), modified Priestley–Taylor–Jet Propulsion Laboratory (PT-JPL), and air-relative-humidity-based two-source model (ARTS) at all test sites.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Islem Hajji, islem.hajji.1@ulaval.ca
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  • Agarwal, D. A., M. Humphrey, N. F. Beekwilder, K. R. Jackson, M. M. Goode, and C. van Ingen, 2010: A data-centered collaboration portal to support global carbon-flux analysis. Concurrency Comput. Pract. Exper., 22, 23232334, https://doi.org/10.1002/cpe.1600.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aubinet, M., T. Vesala, and D. Papale, 2012: Eddy Covariance: A Practical Guide to Measurement and Data Analysis. Springer, 424 pp.

    • Crossref
    • Export Citation
  • Baldocchi, D. D., B. B. Hincks, and T. P. Meyers, 1988: Measuring biosphere-atmosphere exchanges of biologically related gases with micrometeorological methods. Ecology, 69, 13311340, https://doi.org/10.2307/1941631.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baldocchi, D. D., E. Falge, L. Gu, and R. Olson, 2001: FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull. Amer. Meteor. Soc., 82, 24152434, https://doi.org/10.1175/1520-0477(2001)082<2415:FANTTS>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, J. A., D. J. Beerling, and P. J. Franks, 2010: Stomata: Key players in the earth system, past and present. Curr. Opin. Plant Biol., 13, 232239, https://doi.org/10.1016/j.pbi.2010.04.013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brutsaert, W., 2005: Hydrology: An Introduction. Cambridge University Press, 618 pp.

    • Crossref
    • Export Citation
  • Budyko, M. I., 1974: Climate and Life. D. H. Miller, Ed., International Geophysics Series, Vol. 18, Academic Press, 508 pp.

  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181189, https://doi.org/10.1175/1520-0469(1971)028<0181:FPRITA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Calvet, J., J. Noilhan, and P. Bessemoulin, 1998: Retrieving the root-zone soil moisture from surface soil moisture or temperature estimates: A feasibility study based on field measurements. J. Appl. Meteor., 37, 371386, https://doi.org/10.1175/1520-0450(1998)037<0371:RTRZSM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duan, Z., and W. Bastiaanssen, 2017: Evaluation of three energy balance-based evaporation models for estimating monthly evaporation for five lakes using derived heat storage changes from a hysteresis model. Environ. Res. Lett., 12, 024005, https://doi.org/10.1088/1748-9326/aa568e.

    • Search Google Scholar
    • Export Citation
  • Edlefsen, N., and A. Anderson, 1943: Thermodynamics of soil moisture. Hilgardia, 15 (2), 31298, https://doi.org/10.3733/hilg.v15n02p031.

  • Ershadi, A., M. F. McCabe, J. P. Evans, G. Mariethoz, and D. Kavetski, 2013: A Bayesian analysis of sensible heat flux estimation: Quantifying uncertainty in meteorological forcing to improve model prediction. Water Resour. Res., 49, 23432358, https://doi.org/10.1002/wrcr.20231.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ershadi, A., M. McCabe, J. P. Evans, N. W. Chaney, and E. F. Wood, 2014: Multi-site evaluation of terrestrial evaporation models using FLUXNET data. Agric. For. Meteor., 187, 4661, https://doi.org/10.1016/j.agrformet.2013.11.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ershadi, A., M. McCabe, J. P. Evans, and E. Wood, 2015: Impact of model structure and parameterization on Penman–Monteith type evaporation models. J. Hydrol., 525, 521535, https://doi.org/10.1016/j.jhydrol.2015.04.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fisher, J. B., K. P. Tu, and D. D. Baldocchi, 2008: Global estimates of the land–atmosphere water flux based on monthly AVHRR and ISLSCP-II data, validated at 16 FLUXNET sites. Remote Sens. Environ., 112, 901919, https://doi.org/10.1016/j.rse.2007.06.025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fritschen, L. J., 1966: Evapotranspiration rates of field crops determined by the Bowen ratio method. Agron. J., 58, 339342, https://doi.org/10.2134/agronj1966.00021962005800030028x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gibbs, J. W., 1902: Elementary Principles in Statistical Mechanics. Yale University Press, 207 pp.

  • Gollan, T., R. Richards, H. Rawson, J. Passioura, D. Johnson, and R. Munns, 1986: Soil water status affects the stomata. Funct. Plant Biol., 13, 459464, https://doi.org/10.1071/PP9860459.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gu, L., and Coauthors, 2006: Direct and indirect effects of atmospheric conditions and soil moisture on surface energy partitioning revealed by a prolonged drought at a temperate forest site. J. Geophys. Res., 111, D16102, https://doi.org/10.1029/2006JD007161.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harbeck, G. E., 1962: A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory. Geological Survey Prof. Paper 272-E, 9 pp., https://pubs.usgs.gov/pp/0272e/report.pdf.

    • Crossref
    • Export Citation
  • Hari, P., and L. Kulmala, 2008: Boreal Forest and Climate Change. Springer, 532 pp.

    • Crossref
    • Export Citation
  • Isabelle, P.-E., D. F. Nadeau, A. N. Rousseau, C. Coursolle, and H. A. Margolis, 2015: Applicability of the bulk-transfer approach to estimate evapotranspiration from boreal peatlands. J. Hydrometeor., 16, 15211539, https://doi.org/10.1175/JHM-D-14-0171.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jacquemin, B., and J. Noilhan, 1990: Sensitivity study and validation of a land surface parameterization using the HAPEX-MOBILHY data set. Bound.-Layer Meteor., 52, 93134, https://doi.org/10.1007/BF00123180.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaynes, E. T., 1957: Information theory and statistical mechanics. Phys. Rev., 106, 620, https://doi.org/10.1103/PhysRev.106.620.

  • Jaynes, E. T., 2003: Probability Theory: The Logic of Science. Cambridge University Press, 650 pp.

    • Crossref
    • Export Citation
  • Ji, S., and Coauthors, 2017: A modified optimal stomatal conductance model under water-stressed condition. Int. J. Plant Prod., 11, 295314.

    • Search Google Scholar
    • Export Citation
  • Kleidon, A., 2009: Nonequilibrium thermodynamics and maximum entropy production in the Earth system. Naturwissenschaften, 96, 125, https://doi.org/10.1007/s00114-009-0509-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kleidon, A., and R. D. Lorenz, 2004: Non-Equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond. Springer, 264 pp.

    • Crossref
    • Export Citation
  • Kohler, M. A., T. J. Nordenson, and W. Fox, 1955: Evaporation from pans and lakes. NOAA Weather Bureau Research Paper 38, 21 pp.

  • Kustas, W., and J. Norman, 1996: Use of remote sensing for evapotranspiration monitoring over land surfaces. Hydrol. Sci. J., 41, 495516, https://doi.org/10.1080/02626669609491522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martyushev, L., and V. Seleznev, 2006: Maximum entropy production principle in physics, chemistry and biology. Phys. Rep., 426, 145, https://doi.org/10.1016/j.physrep.2005.12.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Massman, W., and X. Lee, 2002: Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges. Agric. For. Meteor., 113, 121144, https://doi.org/10.1016/S0168-1923(02)00105-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Misson, L., J. A. Panek, and A. H. Goldstein, 2004: A comparison of three approaches to modeling leaf gas exchange in annually drought-stressed ponderosa pine forests. Tree Physiol., 24, 529541, https://doi.org/10.1093/treephys/24.5.529.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monteith, J., and M. Unsworth, 1990: The radiation environment. Principles of Environmental Physics, 2nd ed., Edward Arnold, 36–57.

  • Müller, J., A. Eschenröder, and O. Christen, 2014: LEAFC3-N photosynthesis, stomatal conductance, transpiration and energy balance model: Finite mesophyll conductance, drought stress, stomata ratio, optimized solution algorithms, and code. Ecol. Modell., 290, 134145, https://doi.org/10.1016/j.ecolmodel.2013.10.036.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noilhan, J., and S. Planton, 1989: A simple parameterization of land surface processes for meteorological models. Mon. Wea. Rev., 117, 536549, https://doi.org/10.1175/1520-0493(1989)117<0536:ASPOLS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ozawa, H., A. Ohmura, R. D. Lorenz, and T. Pujol, 2003: The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle. Rev. Geophys., 41, 1018, https://doi.org/10.1029/2002RG000113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Penman, H. L., 1948: Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London, 193A, 120145, https://doi.org/10.1098/rspa.1948.0037.

    • Search Google Scholar
    • Export Citation
  • Pereira, L. S., P. Paredes, G. C. Rodrigues, and M. Neves, 2015: Modeling malt barley water use and evapotranspiration partitioning in two contrasting rainfall years. Assessing AquaCrop and SIMDualKc models. Agric. Water Manage., 159, 239254, https://doi.org/10.1016/j.agwat.2015.06.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pontailler, J.-Y., G. J. Hymus, and B. G. Drake, 2003: Estimation of leaf area index using ground-based remote sensed NDVI measurements: Validation and comparison with two indirect techniques. Can. J. Remote Sens., 29, 381387, https://doi.org/10.5589/m03-009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Priestley, C. H. B., and R. J. Taylor, 1972: On the assessment of surface heat flux and evaporation using large scale parameters. Mon. Wea. Rev., 100, 8192, https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Qi, J., and Coauthors, 2000: Spatial and temporal dynamics of vegetation in the San Pedro River basin area. Agric. For. Meteor., 105, 5568, https://doi.org/10.1016/S0168-1923(00)00195-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sala, A., and J. Tenhunen, 1996: Simulations of canopy net photosynthesis and transpiration in Quercus ilex L. under the influence of seasonal drought. Agric. For. Meteor., 78, 203222, https://doi.org/10.1016/0168-1923(95)02250-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shanafield, M., P. G. Cook, H. A. Gutiérrez-Jurado, R. Faux, J. Cleverly, and D. Eamus, 2015: Field comparison of methods for estimating groundwater discharge by evaporation and evapotranspiration in an arid-zone playa. J. Hydrol., 527, 10731083, https://doi.org/10.1016/j.jhydrol.2015.06.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shannon, C. E., 1948: A mathematical theory of communication. Bell Syst. Tech. J., 27, 379423, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shi, T., D. Guan, A. Wang, J. Wu, C. Jin, and S. Han, 2008: Comparison of three models to estimate evapotranspiration for a temperate mixed forest. Hydrol. Processes, 22, 34313443, https://doi.org/10.1002/hyp.6922.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Spanner, M. A., L. L. Pierce, S. W. Running, and D. L. Peterson, 1990: The seasonality of AVHRR data of temperate coniferous forests: Relationship with leaf area index. Remote Sens. Environ., 33, 97112, https://doi.org/10.1016/0034-4257(90)90036-L.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stewart, J., 1988: Modelling surface conductance of pine forest. Agric. For. Meteor., 43, 1935, https://doi.org/10.1016/0168-1923(88)90003-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thom, A. S., 1975: Momentum, mass, and heat exchange of plant communities. Vegetation and the Atmosphere, J. L. Monteith, Ed., Academic Press, 57109.

    • Search Google Scholar
    • Export Citation
  • Tuzet, A., A. Perrier, and R. Leuning, 2003: A coupled model of stomatal conductance, photosynthesis and transpiration. Plant Cell Environ., 26, 10971116, https://doi.org/10.1046/j.1365-3040.2003.01035.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Uddling, J., M. Hall, G. Wallin, and P. E. Karlsson, 2005: Measuring and modelling stomatal conductance and photosynthesis in mature birch in Sweden. Agric. For. Meteor., 132, 115131, https://doi.org/10.1016/j.agrformet.2005.07.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Van Wijk, M., S. Dekker, W. Bouten, F. Bosveld, W. Kohsiek, K. Kramer, and G. Mohren, 2000: Modeling daily gas exchange of a Douglas-fir forest: Comparison of three stomatal conductance models with and without a soil water stress function. Tree Physiol., 20, 115122, https://doi.org/10.1093/treephys/20.2.115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., D. Tetzlaff, and C. Soulsby, 2017: Testing the maximum entropy production approach for estimating evapotranspiration from closed canopy shrub land in a low-energy humid environment. Hydrol. Processes, 31, 46134621, https://doi.org/10.1002/hyp.11363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., and R. L. Bras, 2009: A model of surface heat fluxes based on the theory of maximum entropy production. Water Resour. Res., 45, W11422, https://doi.org/10.1029/2009WR007900.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., and R. L. Bras, 2010: An extremum solution of the Monin–Obukhov similarity equations. J. Atmos. Sci., 67, 485499, https://doi.org/10.1175/2009JAS3117.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., and R. L. Bras, 2011: A model of evapotranspiration based on the theory of maximum entropy production. Water Resour. Res., 47, W03521, https://doi.org/10.1029/2010WR009392.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., R. L. Bras, G. Sivandran, and R. Knox, 2010: A simple method for the estimation of thermal inertia. Geophys. Res. Lett., 37, L05404, https://doi.org/10.1029/2009GL041851.

    • Search Google Scholar
    • Export Citation
  • Wang, J., R. L. Bras, P. Goyal, A. Giffin, K. H. Knuth, and E. Vrscay, 2012: An application of the maximum entropy production principle in modeling heat fluxes over land surfaces. AIP Conf. Proc., 1443, 282289, https://doi.org/10.1063/1.3703645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., V. Nieves, and R. L. Bras, 2013: MaxEnt and MaxEP in modeling fractal topography and atmospheric turbulence. Beyond the Second Law: Entropy Production and Non-Equilibrium Systems, R. Dewar et al., Eds., Springer, 309–322, https://doi.org/10.1007/978-3-642-40154-1_16.

    • Crossref
    • Export Citation
  • Wang, Y.-P., and R. Leuning, 1998: A two-leaf model for canopy conductance, photosynthesis and partitioning of available energy I: Model description and comparison with a multi-layered model. Agric. For. Meteor., 91, 89111, https://doi.org/10.1016/S0168-1923(98)00061-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, C. A., and Coauthors, 2012: Climate and vegetation controls on the surface water balance: Synthesis of evapotranspiration measured across a global network of flux towers. Water Resour. Res., 48, W06523, https://doi.org/10.1029/2011WR011586.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, M., and Coauthors, 2009: Improving land surface models with FLUXNET data. Biogeosciences, 6, 13411359, https://doi.org/10.5194/bg-6-1341-2009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wilson, K., and Coauthors, 2002: Energy balance closure at FLUXNET sites. Agric. For. Meteor., 113, 223243, https://doi.org/10.1016/S0168-1923(02)00109-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wittich, K., and O. Hansing, 1995: Area-averaged vegetative cover fraction estimated from satellite data. Int. J. Biometeor., 38, 209215, https://doi.org/10.1007/BF01245391.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yan, H., and H. H. Shugart, 2010: An air relative-humidity based evapotranspiration model from eddy covariance data. J. Geophys. Res., 115, D16106, https://doi.org/10.1029/2009JD013598.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yan, H., and Coauthors, 2012: Global estimation of evapotranspiration using a leaf area index-based surface energy and water balance model. Remote Sens. Environ., 124, 581595, https://doi.org/10.1016/j.rse.2012.06.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, L., J. Xia, C.-y. Xu, Z. Wang, L. Sobkowiak, and C. Long, 2013: Evapotranspiration estimation methods in hydrological models. J. Geogr. Sci., 23, 359369, https://doi.org/10.1007/s11442-013-1015-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zotarelli, L., M. Dukes, and K. Morgan, 2010: Interpretation of soil moisture content to determine soil field capacity and avoid over-irrigating sandy soils using soil moisture sensors. IFAS Publ. AE460, University of Florida, 4 pp., http://edis.ifas.ufl.edu/ae460.

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