<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<front>
<journal-meta>
<journal-id journal-id-type="publisher">HESS</journal-id>
<journal-title-group>
<journal-title>Hydrology and Earth System Sciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">HESS</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Hydrol. Earth Syst. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7938</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/hess-19-2409-2015</article-id>
<title-group>
<article-title>Multi-objective parameter optimization of common land model using adaptive surrogate modeling</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Gong</surname>
<given-names>W.</given-names>
<ext-link>https://orcid.org/0000-0003-3622-7090</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Duan</surname>
<given-names>Q.</given-names>
<ext-link>https://orcid.org/0000-0001-9955-1512</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Li</surname>
<given-names>J.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wang</surname>
<given-names>C.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Di</surname>
<given-names>Z.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Dai</surname>
<given-names>Y.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ye</surname>
<given-names>A.</given-names>
<ext-link>https://orcid.org/0000-0002-5272-134X</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Miao</surname>
<given-names>C.</given-names>
<ext-link>https://orcid.org/0000-0001-6413-7020</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>College of Global Change and Earth System Science (GCESS), Beijing Normal University, Beijing 100875, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Joint Center for Global Change Studies, Beijing 100875, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>21</day>
<month>05</month>
<year>2015</year>
</pub-date>
<volume>19</volume>
<issue>5</issue>
<fpage>2409</fpage>
<lpage>2425</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2015 W. Gong et al.</copyright-statement>
<copyright-year>2015</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://hess.copernicus.org/articles/19/2409/2015/hess-19-2409-2015.html">This article is available from https://hess.copernicus.org/articles/19/2409/2015/hess-19-2409-2015.html</self-uri>
<self-uri xlink:href="https://hess.copernicus.org/articles/19/2409/2015/hess-19-2409-2015.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/19/2409/2015/hess-19-2409-2015.pdf</self-uri>
<abstract>
<p>Parameter specification usually has significant influence on the performance
of land surface models (LSMs). However, estimating the parameters properly
is a challenging task due to the following reasons: (1) LSMs usually have
too many adjustable parameters (20 to 100 or even more), leading to the
curse of dimensionality in the parameter input space; (2) LSMs usually have
many output variables involving water/energy/carbon cycles, so that
calibrating LSMs is actually a multi-objective optimization problem; (3)
Regional LSMs are expensive to run, while conventional multi-objective
optimization methods need a large number of model runs (typically
~10&lt;sup&gt;5&lt;/sup&gt;–10&lt;sup&gt;6&lt;/sup&gt;). It makes parameter optimization
computationally prohibitive. An uncertainty quantification framework was
developed to meet the aforementioned challenges, which include the following
steps: (1) using parameter screening to reduce the number of adjustable
parameters, (2) using surrogate models to emulate the responses of dynamic
models to the variation of adjustable parameters, (3) using an adaptive
strategy to improve the efficiency of surrogate modeling-based optimization;
(4) using a weighting function to transfer multi-objective optimization to
single-objective optimization. In this study, we demonstrate the uncertainty
quantification framework on a single column application of a LSM
– the Common Land Model (CoLM), and evaluate the effectiveness and
efficiency of the proposed framework. The result indicate that this
framework can efficiently achieve optimal parameters in a more effective
way. Moreover, this result implies the possibility of calibrating other
large complex dynamic models, such as regional-scale LSMs,
atmospheric models and climate models.</p>
</abstract>
<counts><page-count count="17"/></counts>
<funding-group>
<award-group id="gs1">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>41075075</award-id>
<award-id>41375139</award-id>
<award-id>51309011</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Ministry of Science and Technology of the People&apos;s Republic of China</funding-source>
<award-id>2010CB428402</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Beijing Normal University</funding-source>
<award-id>2013YB47</award-id>
</award-group>
</funding-group>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Bastidas, L. A., Gupta, H. V., Sorooshian, S., Shuttleworth, W. J., and Yang, Z. L.: Sensitivity analysis of a land surface scheme using multicriteria methods, J. Geophys. Res.-Atmos., 104, 19481–19490, 1999.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Bonan, G. B.: A Land Surface Model (LSM Version 1.0) for Ecological, Hydrological, and Atmospheric Studies: Technical Description and User&apos;s Guide, NCAR, Boulder, CO, USA, 1996.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Boyle, D. P.: Multicriteria calibration of hydrological models, PhD dissertation thesis, University of Arizona, Tucson, USA, 2000.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Boyle, D. P., Gupta, H. V., and Sorooshian, S.: Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods, Water Resour. Res., 36, 3663–3674, 2000.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Breiman, L.: Random forests, Mach. Learn., 45, 5–32, 2001.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Breiman, L., Friedman, J., Stone, C. J., and Olshen, R. A.: Classification and Regression Trees, Chapman and Hall/CRC, Bota Raton, Florida, USA, 1984.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Castelletti, A., Pianosi, F., Soncini-Sessa, R., and Antenucci, J. P.: A multiobjective response surface approach for improved water quality planning in lakes and reservoirs, Water Resour. Res., 46, W6502, &lt;a href=&quot;http://dx.doi.org/10.1029/2009WR008389&quot;&gt;https://doi.org/10.1029/2009WR008389&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Cybenko, G.: Approximation by superpositions of a sigmoidal function, Math. Control. Sig. Syst., 2, 303–314, 1989.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Dai, Y. and Zeng, Q.: A Land Surface Model (IAP94) for Climate Studies Part I: Formulation and Validation in Off-Line Experiments, Adv. Atmos. Sci., 14, 433–460, 1997.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Dai, Y., Xue, F., and Zeng, Q.: A Land Surface Model (IAP94) for Climate Studies Part II:Implementation and Preliminary Results of Coupled Model with IAP GCM, Adv. Atmos. Sci., 15, 47–62, 1998.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Dai, Y. J., Zeng, X. B., Dickinson, R. E., Baker, I., Bonan, G. B., Bosilovich, M. G., Denning, A. S., Dirmeyer, P. A., Houser, P. R., Niu, G. Y., Oleson, K. W., Schlosser, C. A., and Yang, Z. L.: The Common Land Model, B. Am. Meteorol. Soc., 84, 1013–1023, 2003.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Dai, Y. J., Dickinson, R. E., and Wang, Y. P.: A two-big-leaf model for canopy temperature, photosynthesis, and stomatal conductance, J. Climate, 17, 2281–2299, 2004.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Dickinson, R. E., Henderson-Sellers, A., and Kennedy, P. J.: Biosphere-atmosphere Transfer Scheme (BATS) Version 1e as Coupled to the NCAR Community Climate Model, NCAR, Boulder, CO, USA, 1993.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Duan, Q. Y., Sorooshian, S., and Gupta, V. K.: Effective and Efficient Global Optimization for Conceptual Rainfall-Runoff Models, Water Resour. Res., 28, 1015–1031, 1992.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Duan, Q. Y., Gupta, V. K., and Sorooshian, S.: Shuffled Complex Evolution Approach for Effective and Efficient Global Minimization, J. Optimiz. Theory App., 76, 501–521, 1993.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Duan, Q. Y., Sorooshian, S., and Gupta, V. K.: Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models, J. Hydrol., 158, 265–284, 1994.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Friedman, J. H.: Multivariate Adaptive Regression Splines, Ann. Stat., 19, 1–14, 1991.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Gan, Y., Duan, Q., Gong, W., Tong, C., Sun, Y., Chu, W., Ye, A., Miao, C., and Di, Z.: A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model, Environ. Modell. Softw., 51, 269–285, 2014.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Gorissen, D.: Grid-enabled Adaptive Surrogate Modeling for Computer Aided Engineering, PhD thesis, Ghent University, Ghent, Flanders, Belgium, 2010.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information, Water Resour. Res., 34, 751–763, 1998.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Gupta, H. V., Bastidas, L. A., Sorooshian, S., Shuttleworth, W. J., and Yang, Z. L.: Parameter estimation of a land surface scheme using multicriteria methods, J. Geophys. Res., 104, 19491–19503, 1999.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Hastie, T., Tibshirani, R., and Friedman, J.: The Elements of Statistical Learning 2nd, Springer, New York, USA, 2009.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Henderson-Sellers, A., McGuffie, K., and Pitman, A. J.: The Project for Intercomparison of Land-surface Parametrization Schemes (PILPS): 1992 to 1995, Clim. Dynam., 12, 849–859, 1996.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Hu, Z. Y., Ma, M. G., Jin, R., Wang, W. Z., Huang, G. H., Zhang, Z. H., and Tan, J. L.: WATER: dataset of automatic meteorological observations at the A&apos;rou freeze/thaw observation station, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, China, 2003.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Jackson, C., Xia, Y., Sen, M. K., and Stoffa, P. L.: Optimal parameter and uncertainty estimation of a land surface model: A case study using data from Cabauw, Netherlands, J. Geophys. Res.-Atmos., 108, 4583, &lt;a href=&quot;http://dx.doi.org/10.1029/2002JD002991&quot;&gt;https://doi.org/10.1029/2002JD002991&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Jain, A. K., Jianchang, M., and Mohiuddin, K. M.: Artificial neural networks: a tutorial, Computer, 29, 31–44, 1996.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Ji, D. and Dai, Y.: The Common Land Model (CoLM) technical guide, GCESS, Beijing Normal University, Beijing, China, 2010.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Jin, Y.: Surrogate-assisted evolutionary computation: Recent advances and future challenges, Swarm Evolut. Comput., 1, 61–70, 2011.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Jones, D. R.: A Taxonomy of Global Optimization Methods Based on Response Surfaces, J. Global Optim., 21, 345–383, 2001.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Jones, D. R., Schonlau, M., and Welch, W. J.: Efficient global optimization of expensive black-box functions, J. Global Optim., 13, 455–492, 1998.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Koziel, S. and Leifsson, L.: Surrogate-Based Modeling and Optimization, Springer New York, New York, NY, 2013.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Leplastrier, M., Pitman, A. J., Gupta, H., and Xia, Y.: Exploring the relationship between complexity and performance in a land surface model using the multicriteria method, J. Geophys. Res., 107, 4443, &lt;a href=&quot;http://dx.doi.org/10.1029/2001JD000931&quot;&gt;https://doi.org/10.1029/2001JD000931&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Li, J.: Screening and Analysis of Parameters Most Sensitive to CoLM, Master thesis, BNU, Beijing, China, 2012.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Li, J., Duan, Q. Y., Gong, W., Ye, A., Dai, Y., Miao, C., Di, Z., Tong, C., and Sun, Y.: Assessing parameter importance of the Common Land Model based on qualitative and quantitative sensitivity analysis, Hydrol. Earth Syst. Sci., 17, 3279–3293, &lt;a href=&quot;http://dx.doi.org/10.5194/hess-17-3279-2013&quot;&gt;https://doi.org/10.5194/hess-17-3279-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Liang, X., Wood, E. F., Lettenmaier, D. P., Lohmann, D., Boone, A., Chang, S., Chen, F., Dai, Y., Desborough, C., Dickinson, R. E., Duan, Q., Ek, M., Gusev, Y. M., Habets, F., Irannejad, P., Koster, R., Mitchell, K. E., Nasonova, O. N., Noilhan, J., Schaake, J., Schlosser, A., Shao, Y., Shmakin, A. B., Verseghy, D., Warrach, K., Wetzel, P., Xue, Y., Yang, Z., and Zeng, Q.: The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phase 2(c) Red-Arkansas River basin experiment:: 2. Spatial and temporal analysis of energy fluxes, Global Planet. Change, 19, 137–159, 1998.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Liu, Y. Q., Bastidas, L. A., Gupta, H. V., and Sorooshian, S.: Impacts of a parameterization deficiency on offline and coupled land surface model simulations, J. Hydrometeorol., 4, 901–914, 2003.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Liu, Y. Q., Gupta, H. V., Sorooshian, S., Bastidas, L. A., and Shuttleworth, W. J.: Exploring parameter sensitivities of the land surface using a locally coupled land-atmosphere model, J. Geophys. Res., 109, D21101, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JD004730&quot;&gt;https://doi.org/10.1029/2004JD004730&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Liu, Y. Q., Gupta, H. V., Sorooshian, S., Bastidas, L. A., and Shuttleworth, W. J.: Constraining land surface and atmospheric parameters of a locally coupled model using observational data, J. Hydrometeorol., 6, 156–172, 2005.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Lohmann, D., Lettenmaier, D. P., Liang, X., Wood, E. F., Boone, A., Chang, S., Chen, F., Dai, Y., Desborough, C., Dickinson, R. E., Duan, Q., Ek, M., Gusev, Y. M., Habets, F., Irannejad, P., Koster, R., Mitchell, K. E., Nasonova, O. N., Noilhan, J., Schaake, J., Schlosser, A., Shao, Y., Shmakin, A. B., Verseghy, D., Warrach, K., Wetzel, P., Xue, Y., Yang, Z., and Zeng, Q.: The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phase 2(c) Red–Arkansas River basin experiment:: 3. Spatial and temporal analysis of water fluxes, Global Planet. Change, 19, 161–179, 1998.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Loshchilov, I., Schoenauer, M., and Sebag, M. E. L.: Comparison-based Optimizers Need Comparison-based Surrogates, in Proceedings of the 11th International Conference on Parallel Problem Solving from Nature: Part I, 364–373, Berlin, Heidelberg, 2010.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Marler, R. T. and Arora, J.: The weighted sum method for multi-objective optimization: new insights, Struct Multidiscip O., 41, 853–862, 2010.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Marquardt, D. W.: An Algorithm for Least-Squares Estimation of Nonlinear Parameters, J. Soc. Indust. Appl. Math., 11, 431–441, 1963.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">McKay, M. D., Beckman, R. J., and Conover, W. J.: A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, 21, 239–245, 1979.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Minsky, M. and Papert, S. A.: Perceptrons: An Introduction to Computational Geometry, MIT Press, Cambridge, Massachusetts, USA, 1969.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Ong, Y., Nair, P. B., Keane, A. J., and Wong, K. W.: Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems, in: Studies in Fuzziness and Soft Computing, edited by: Jin, Y., 307–331, Springer Berlin Heidelberg, 2005.</mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Pilát, M. and Neruda, R.:, Surrogate model selection for evolutionary multiobjective optimization, paper presented at Evolutionary Computation (CEC), 2013 IEEE Congress on 1 January, 2013.</mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Pollacco, J. A. P., Mohanty, B. P., and Efstratiadis, A.: Weighted objective function selector algorithm for parameter estimation of SVAT models with remote sensing data, Water Resour. Res., 49, 6959–6978, 2013.</mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple">Rasmussen, C. E. and Williams, C. K. I.: Gaussian Processes for Machine Learning, MIT Press, Massachusetts, USA, 2006.</mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple">Razavi, S., Tolson, B. A., and Burn, D. H.: Review of surrogate modeling in water resources, Water Resour. Res., 48, W7401, &lt;a href=&quot;http://dx.doi.org/10.1029/2011WR011527&quot;&gt;https://doi.org/10.1029/2011WR011527&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple">Shahsavani, D., Tarantola, S., and Ratto, M.: Evaluation of MARS modeling technique for sensitivity analysis of model output, Procedia – Social and Behavioral Sciences, 2, 7737–7738, 2010.</mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Shangguan, W., Dai, Y., Liu, B., Zhu, A., Duan, Q., Wu, L., Ji, D., Ye, A., Yuan, H., Zhang, Q., Chen, D., Chen, M., Chu, J., Dou, Y., Guo, J., Li, H., Li, J., Liang, L., Liang, X., Liu, H., Liu, S., Miao, C., and Zhang, Y.: A China data set of soil properties for land surface modeling, J. Adv. Model. Earth Syst., 5, 212–224, 2013.</mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple">Song, X., Zhan, C., and Xia, J.: Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model, Chinese Sci. Bull., 57, 3397–3403, 2012.</mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple">Taylor, K. E.: Summarizing multiple aspects of model performance in a single diagram, J. Geophys. Res.-Atmos., 106, 7183–7192, 2001.</mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple">van Griensven, A. and Meixner, T.: A global and efficient multi-objective auto-calibration and uncertainty estimation method for water quality catchment models, J. Hydroinform., 9, 277–291, 2007.</mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple">Vapnik, V. N.: Statistical Learning Theory, John Wiley &amp; Sons, NewYork, USA, 1998.</mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple">Vapnik, V. N.: The Nature of Statistical Learning Theory, 2nd Edn., Springer, New York, 2002.</mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple">Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39, 1201, &lt;a href=&quot;http://dx.doi.org/10.1029/2002WR001642&quot;&gt;https://doi.org/10.1029/2002WR001642&lt;/a&gt;, 2003a.</mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple">Vrugt, J. A., Gupta, H. V., Bastidas, L. A., Bouten, W., and Sorooshian, S.: Effective and efficient algorithm for multiobjective optimization of hydrologic models, Water Resour. Res., 39, 1214, &lt;a href=&quot;http://dx.doi.org/10.1029/2002WR001746&quot;&gt;https://doi.org/10.1029/2002WR001746&lt;/a&gt;, 2003b.</mixed-citation>
</ref>
<ref id="ref59">
<label>59</label><mixed-citation publication-type="other" xlink:type="simple">Wang, C., Duan, Q., Gong, W., Ye, A., Di, Z., and Miao, C.: An evaluation of adaptive surrogate modeling based optimization with two benchmark problems, Environ. Modell. Softw., 60, 167–179, 2014.</mixed-citation>
</ref>
<ref id="ref60">
<label>60</label><mixed-citation publication-type="other" xlink:type="simple">Wang, Q. J.: The Genetic Algorithm and Its Application to Calibrating Conceptual Rainfall-Runoff Models, Water Resour. Res., 27, 2467–2471, 1991.</mixed-citation>
</ref>
<ref id="ref61">
<label>61</label><mixed-citation publication-type="other" xlink:type="simple">Wood, E. F., Lettenmaier, D. P., Liang, X., Lohmann, D., Boone, A., Chang, S., Chen, F., Dai, Y., Dickinson, R. E., Duan, Q., Ek, M., Gusev, Y. M., Habets, F., Irannejad, P., Koster, R., Mitchel, K. E., Nasonova, O. N., Noilhan, J., Schaake, J., Schlosser, A., Shao, Y., Shmakin, A. B., Verseghy, D., Warrach, K., Wetzel, P., Xue, Y., Yang, Z., and Zeng, Q.: The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) Phase 2(c) Red–Arkansas River basin experiment:: 1. Experiment description and summary intercomparisons, Global Planet. Change, 19, 115–135, 1998.</mixed-citation>
</ref>
<ref id="ref62">
<label>62</label><mixed-citation publication-type="other" xlink:type="simple">Xia, Y., Pittman, A. J., Gupta, H. V., Leplastrier,, M., Henderson-Sellers, A., and Bastidas, L. A.: Calibrating a land surface model of varying complexity using multicriteria methods and the Cabauw dataset, J. Hydrometeorol., 3, 181–194, 2002.</mixed-citation>
</ref>
<ref id="ref63">
<label>63</label><mixed-citation publication-type="other" xlink:type="simple">Yapo, P. O., Gupta, H. V., and Sorooshia, S.: Multi-objective global optimization for hydrologic models, J. Hydrol., 204, 83–97, 1998.</mixed-citation>
</ref>
<ref id="ref64">
<label>64</label><mixed-citation publication-type="other" xlink:type="simple">Zhan, C., Song, X., Xia, J., and Tong, C.: An efficient integrated approach for global sensitivity analysis of hydrological model parameters, Environ. Modell. Softw., 41, 39–52, 2013.</mixed-citation>
</ref>
</ref-list>
</back>
</article>