<?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-11-793-2007</article-id>
<title-group>
<article-title>Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Tang</surname>
<given-names>Y.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Reed</surname>
<given-names>P.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wagener</surname>
<given-names>T.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>van Werkhoven</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, Pennsylvania, USA</addr-line>
</aff>
<pub-date pub-type="epub">
<day>05</day>
<month>02</month>
<year>2007</year>
</pub-date>
<volume>11</volume>
<issue>2</issue>
<fpage>793</fpage>
<lpage>817</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2007 Y. Tang et al.</copyright-statement>
<copyright-year>2007</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by-nc-sa/2.5/">https://creativecommons.org/licenses/by-nc-sa/2.5/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://hess.copernicus.org/articles/11/793/2007/hess-11-793-2007.html">This article is available from https://hess.copernicus.org/articles/11/793/2007/hess-11-793-2007.html</self-uri>
<self-uri xlink:href="https://hess.copernicus.org/articles/11/793/2007/hess-11-793-2007.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/11/793/2007/hess-11-793-2007.pdf</self-uri>
<abstract>
<p>This study seeks to identify sensitivity tools that will advance our
understanding of lumped hydrologic models for the purposes of model
improvement, calibration efficiency and improved measurement
schemes. Four sensitivity analysis methods were tested: (1) local
analysis using parameter estimation software (PEST), (2) regional
sensitivity analysis (RSA), (3) analysis of variance (ANOVA), and
(4) Sobol&apos;s method. The methods&apos; relative efficiencies and
effectiveness have been analyzed and compared. These four
sensitivity methods were applied to the lumped Sacramento soil
moisture accounting model (SAC-SMA) coupled with SNOW-17. Results
from this study characterize model sensitivities for two medium
sized watersheds within the Juniata River Basin in Pennsylvania,
USA. Comparative results for the 4 sensitivity methods are presented
for a 3-year time series with 1 h, 6 h, and 24 h time
intervals. The results of this study show that model parameter
sensitivities are heavily impacted by the choice of analysis method
as well as the model time interval. Differences between the two
adjacent watersheds also suggest strong influences of local physical
characteristics on the sensitivity methods&apos; results. This study also
contributes a comprehensive assessment of the repeatability,
robustness, efficiency, and ease-of-implementation of the four
sensitivity methods. Overall ANOVA and Sobol&apos;s method were shown to
be superior to RSA and PEST. Relative to one another, ANOVA has
reduced computational requirements and Sobol&apos;s method yielded more
robust sensitivity rankings.</p>
</abstract>
<counts><page-count count="25"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple"> Abbaspour, K C., Schulin, R., and van Genuchten M Th.: Estimating unsaturated soil hydraulic parameters using ant colony optimization, Adv. Water Resour., 24, 827&amp;ndash;841, 2001. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple"> Anderson, E A.: National Weather Service River Forecast System - Snow Accumulation and Ablation Model, Tech. rep., NOAA Technical Memorandum NWS Hydro-17, Dept. of Commerce, Silver Spring, Maryland, USA, 1973. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple"> Anderson, E A.: Calibration of Conceptual Hydrologic Models for Use in River Forecasting, Tech. rep., NOAA Technical Report, NWS 45, Hydrology Laboratory,Silver Spring, Maryland, USA, 2002. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple"> Andres, T H.: Sampling method and sensitivity analysis for large parameter sets, J. Statist. Comput. Simul., 57, 77&amp;ndash;110, 1997. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple"> Andres, T H. and Wayne, C H.: Using Iterated Fractional Factorial Design to Screen Parameters in Sensitivity analysis of a Probabilistic Risk Assessment Model, in: Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications, edited by: Kusters, H., Stein, E., and Werner, W., vol 2, pp 328&amp;ndash;337, 1993. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple"> Archer, G. E B., Saltelli, A., and Sobol&apos;, I M.: Sensitivity measures, ANOVA-like techniques and the use of bootstrap, J. Statist. Comput. Simul., 58, 99&amp;ndash;120, 1997. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Beven, K.: Uniqueness of place and process representations in hydrological modeling, Hydrol. Earth Syst. Sci., 4, 203&amp;ndash;214, 2000. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple"> Beven, K. and Freer, J.: Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11&amp;ndash;29, 2001. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple"> Box, G. E P., Hunter, W G., and Hunter, J S.: Statistics for Experiments: An Introduction to Design, Data Analysis, and Modeling Building, Wiley, New York, 1978. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple"> Boyle, D., Gupta, H., and Sorooshian, S.: Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods, Water Resour. Res., 36, 3663&amp;ndash;3674, 2000. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple"> Bratley, P. and Fox, B L.: Implement Sobol&apos;s Quasirandom Sequence Generator, ACM Transactions on Mathematical Software, 14, 88&amp;ndash;100, 1988. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Burnash, R. J C.: The NWS river forecast system-Catchment model, in: Computer Models of Watershed Hydrology, edited by Singh, V P., Water Resour. Publ., Highlands Ranch, CO, 1995. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Christiaens, K. and Feyen, J.: Use of sensitivity and uncertainty measures in distributed hydrological modeling with an application to the MIKE SHE model, Water Resour. Res., 38, 1169, https://doi.org/10.1029/2001WR000 478, 2002. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple"> Demaria, E., Nijssen, B., and Wagener, T.: Monte Carlo sensitivity analysis of land surface parameters using the variable infiltration capacity model, J. Geophys. Res. &amp;ndash; Atmos., in press, 2007. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> Doherty, J.: Groundwater model calibration using pilot points and regularization, Ground Water, 41, 170&amp;ndash;177, 2003. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> Doherty, J.: PEST-Model Independent Parameter Estimation User Manual: 5th Edition, Watermark Numerical Computing, Brisbane, Australia, 2004. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> Doherty, J. and Johnston, J M.: Methodologies for calibration and predictive analysis of a watershed model, J. Amer. Water Resour. Assoc., 39, 251&amp;ndash;265, 2003. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple"> Duan, Q., Gupta, V K., and Sorooshian, S.: Effective and efficient global optimization for conceptual rainfall-runoff models, Water Resour. Res., 28, 1015&amp;ndash;1031, 1992. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple"> Duffy, C J.: A two-state integral-balance model for soil moisture and groundwater dynamics in complex terrain, Water Resour. Res., 32, 2421&amp;ndash;2434, 1996. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple"> Duffy, C. J.: Semi-Discrete Dynamical Model for Mountain-Front Recharge and Water Balance Estimation (Rio Grande of Southern Colorado and New Mexico), in: Groundwater Recharge in a Desert Environment: The Southwestern United States, edited by: Hogan, J., Phillips, F., and Scanlon, B., Water Science and Application Monograph, 9, American Geophysical Union, pp 236&amp;ndash;255, 2004. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Efron, B. and Tibshirani, R.: An introduction to the bootstrap, Chapman Hall, New York, USA, 1993. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> Fieberg, J. and Jenkins, K J.: Assessing uncertainty in ecological systems using global sensitivity analyses: a case example of simulated wolf reintroduction effects on elk, Ecological Modelling, 187, 259&amp;ndash;280, 2005. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> Freer, J., Beven, K J., and Ambroise, B.: Bayesian estimation of uncertainty in runoff prediction and the value of data: An application of the GLUE approach, Water Resour. Res., 32, 2161&amp;ndash;2173, 1996. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple"> Frey, H. and Patil, S.: Identification and Review of Sensitivity Analysis Methods, Risk Analysis, 22, 553&amp;ndash;578, 2002. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Hall, J., Tarantola, S., P.D.Bates, and M.S.Horritt: Distributed sensitivity analysis of flood inumdation model calibration, J. Hydraulic Eng., https://doi.org/10.1061/(ASCE)0733-9429(2005)131:2(117), 2005. </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Hamby, D.: A review of techniques for sensitivity analysis of environmental models, Environmental Modelling and Assessment, 32, 135&amp;ndash;154, 1994. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple"> Helton, J. and Davis, F.: Illustration of sampling-based methods for uncertainty and sensitivity analysis, Risk Analysis, 22, 622&amp;ndash;691, 2002. </mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple"> Helton, J. and Davis, F.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliability Engineering and System Safty, 81, 23&amp;ndash;69, 2003. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> Henderson-Sellers, A., Yang, Z.-L., and Dickinson, R.: The project of intercomparison of land-surface parameterization schemes, Bull. Am. Meteorol. Soc., 74, 1335&amp;ndash;1349, 1993. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> Hornberger, G. and Spear, R.: An approach to the preliminary analysis of environmental systems, J. Environ. Manage., 12, 7&amp;ndash;18, 1981. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> Koren, V., S., R., Smith, M., Zhang, Z., and Seo, D J.: Hydrology laboratory research modeling system (HL-RMS) of the US national weather service, J. Hydrol., 291, 297&amp;ndash;318, 2004. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> Kottegoda, N. and Rosso, R.: Statistics, Probability and Reliability for Civil and Environmental Engineering, McGraw-Hill, New York, 1997. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Langbein, W B.: Overview of Conference on Hydrologic Data Networks, Water Resour. Res., 15, 1867&amp;ndash;1871, 1979. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Lence, B. and Takyi, A.: Data requirements for seasonal discharge programs: an application of a regionalized sensitivity analysis, Water Resour. Res., 28, 1781&amp;ndash;1789, 1992. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple"> Levenberg, K.: A method for the solution of certain non-linear problems in least squares, Q. Appl. Math., 2, 164&amp;ndash;168, 1944. </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple"> Liang, X. and Guo, J.: Intercomparison of land-surface parameterization schemes: sensitivity of surface energy and water fluxes to model parameters, J. Hydrol., 279, 182&amp;ndash;209, 2003. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple"> Marquardt, D W.: An algorithm for least-squares estimation of nonlinear parameters, Journal of the Society of Industrial and Applied Mathematics, 11, 431&amp;ndash;441, 1963. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> Mckay, M., Beckman, R., and Conover, W.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239&amp;ndash;245, 1979. </mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple"> Misirli, F., Gupta, H V., Sorooshian, S., and Thiemann, M.: Bayesian recursive estimation of parameter and output uncertainty for watershed models, in: Calibration of Watershed Models, edited by: Duan, Q. and Gupta, H. V., Vol 6, pp 113&amp;ndash;124, American Geophysical Union, Washington, D.C., 2003. </mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple"> Mokhtari, A. and Frey, H C.: Sensitivity Analysis of a Two-Dimensional Probabilistic Risk Assessment Model Using Analysis of Variance, Risk Analysis, 25, 1511&amp;ndash;1529, 2005. </mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple"> Moore, C. and Doherty, J.: Role of the calibration process in reducing model predictive error, Water Resour. Res., 41, W05020, https://doi.org/10.1029/2004WR003 501, 2005. </mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple"> Moreda, F., Koren, V., Zhang, Z., Reed, S., and Smith, M.: Parameterization of distributed hydrological models: learning from the experiences of lumped modeling, J. Hydrol., 320, 218&amp;ndash;237, 2006. </mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple"> Moss, M E.: Space, Time, and the Third Dimension (Model Error), Water Resour. Res., 15, 1797&amp;ndash;1800, 1979. </mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple"> Muleta, M. and Nicklow, J W.: Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model, J. Hydrol., 306, 1&amp;ndash;4, 127&amp;ndash;145, 2005. </mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple"> Neter, J., Kutner, M., Nachtsheim, C., and Wasserman, W.: Applied Linear Statitical Models, 4th ed., McGraw-Hill, Chicago, IL, 1996. </mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple"> Oakley, J. and O&apos;Hagan, A.: Probabilistic sensitivity analysis of complex models: a Bayesian approach, Journal of Royal Statistical Society Series B - statistical Methodology, 66, 751&amp;ndash;769, 2004. </mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple"> Osidele, O. and Beck, M B.: Identification of model structure for aquatic ecosystems using regionalized sensitivity analysis, Water Sci. Technol., 43, 271&amp;ndash;278, 2001. </mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple"> Panday, S. and Huyakorn, P.: A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow, Adv.  Water Resour., 27, 361&amp;ndash;382, 2004. </mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple"> Pappenberger, F., Iorgulescu, I., and Beven, K J.: Sensitivity analysis based on regional splits and regression trees (SARS-RT), Environmental Modelling and Software, 21, 976&amp;ndash;990, 2005. </mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple"> Pappenberger, F., Iorgulescu, I., and Beven, K.: Sensitivity analysis based on regional splits and regression trees (SARS-RT), Environmental Modelling &amp; Software, 21, 976&amp;ndash;990, 2006. </mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple"> Patil, S. and Frey, H.: Comparison of sensitivity analysis methods based upon applications to a food safety risk model, Risk Analysis, 23, 135&amp;ndash;154, 2004. </mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple"> Peck, E L.: Catchment modeling and initial parameter estimation for the Natioanl Weather Service river forecast system, Tech. rep., Tech. Memo, NWS Hydro-31, Natl. Oceanic and Atmos. Admin., Silver Spring, Maryland, USA, 1976. </mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple"> Ratto, M., Young, P C., Romanowicz2, R., Pappenberge, F., Saltelli1, A., and Pagano1, A.: Uncertainty, sensitivity analysis and the role of data based mechanistic modeling in hydrology, Hydrol. Earth Syst. Sci., 3, 3099&amp;ndash;3146, 2006. </mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple"> Reed, P., Brooks, R., Davis, K., DeWalle, D R., Dressler, K A., Duffy, C J., Lin, H S., Milller, D., Najjar, R., Salvage, K M., Wagener, T., and Yarnal, B.: Bridging River Basin Scales and Processes to Assess Human-Climate Impacts and the Terrestrial Hydrologic System, Water Resour. Res., 42, W07418, https://doi.org/10.1029/2005WR004 153, 2006. </mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple"> Reed, S., Koren, V., Smith, M., Zhang, Z., Moreda, F., Seo, D., and Participants, D.: Overall distributed model intercomparison project results, J. Hydrol., 298, 27&amp;ndash;60, 2004. </mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple"> Saltelli, A.: Making best use of model evaluations to compute sensitivity indices, Computer Physics Communications, 145, 280&amp;ndash;297, 2002. </mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple"> Saltelli, A., Andres, T H., and Homma, T.: Sensitivity analysis of model output. Performance of the iterated fractional factorial design method, Computational Statistics $&amp;$ Data Analysis, 20, 387&amp;ndash;407, 1995. </mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple"> Saltelli, A., Tarantola, S., and Chan, K. P.-S.: A quantitative model-independent method for global sensitivity analysis of model output, Technometrics, 41, 39&amp;ndash;56, 1999. </mixed-citation>
</ref>
<ref id="ref59">
<label>59</label><mixed-citation publication-type="other" xlink:type="simple"> Saltelli, A., Tarantola, S., and Campolongo, F.: Sensitivity Analysis as an Ingredient of Modeling, Statistical Science, 15, 377&amp;ndash;395, 2000. </mixed-citation>
</ref>
<ref id="ref60">
<label>60</label><mixed-citation publication-type="other" xlink:type="simple"> Saltelli, A., Tarantola, A., Campolongo, F., and Ratto, M.: Sensitivity Analysis in Practice-A Guide to Assessing Scientific Models, John Wiley and Sons, Chichester, 2004. </mixed-citation>
</ref>
<ref id="ref61">
<label>61</label><mixed-citation publication-type="other" xlink:type="simple"> Sieber, A. and Uhlenbrook, S.: Sensitivity analyses of a distributed catchment model to verify the model structure, J. Hydrol., 310, 216&amp;ndash;235, 2005. </mixed-citation>
</ref>
<ref id="ref62">
<label>62</label><mixed-citation publication-type="other" xlink:type="simple"> Singh, V. and Woolhiser, D.: Mathematical modeling of watershed hydrology, J. Hydrol. Eng., 7, 270&amp;ndash;292, 2002. </mixed-citation>
</ref>
<ref id="ref63">
<label>63</label><mixed-citation publication-type="other" xlink:type="simple"> Smith, M., Seo, D., Koren, V., Reed, S., Zhang, Z., Duan, Q., Moreda, F., and Cong, S.: The distributed model intercomparison project (DMIP): motivation and experiment design, J. Hydrol., 298, 4&amp;ndash;26, 2004. </mixed-citation>
</ref>
<ref id="ref64">
<label>64</label><mixed-citation publication-type="other" xlink:type="simple"> Sobol&apos;, I.: Sensitivity estimates for nonlinear mathematical models, Math Model Comput. Exp., 1, 407&amp;ndash;417, 1993. </mixed-citation>
</ref>
<ref id="ref65">
<label>65</label><mixed-citation publication-type="other" xlink:type="simple"> Sobol&apos;, I.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, 55, 271&amp;ndash;280, 2001. </mixed-citation>
</ref>
<ref id="ref66">
<label>66</label><mixed-citation publication-type="other" xlink:type="simple"> Sobol&apos;, I M.: On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. Math. Phys., 7, 86&amp;ndash;112, 1967. </mixed-citation>
</ref>
<ref id="ref67">
<label>67</label><mixed-citation publication-type="other" xlink:type="simple"> Sobol&apos;, I M.: A primer for the Monte Carlo method, CRC Press, Boca Raton, Fla., 1994. </mixed-citation>
</ref>
<ref id="ref68">
<label>68</label><mixed-citation publication-type="other" xlink:type="simple"> Spear, R., Grieb, T M., and Shang, N.: Parameter uncertainty and interaction in complex environmental models, Water Resour. Res., 30, 3159&amp;ndash;3169, 1994. </mixed-citation>
</ref>
<ref id="ref69">
<label>69</label><mixed-citation publication-type="other" xlink:type="simple"> Tang, Y., Reed, P., and Kollat, J.: Parallelization Strategies for Rapid and Robust Evolutionary Multiobjective Optimization in Water Resources Applications, Adv. Water Resour., 30(3), 335&amp;ndash;353, 2007. </mixed-citation>
</ref>
<ref id="ref70">
<label>70</label><mixed-citation publication-type="other" xlink:type="simple"> Tang, Y., Reed, P., and Wagener, T.: How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration, Hydrol. Earth Syst. Sci., 10, 289&amp;ndash;307, 2006. </mixed-citation>
</ref>
<ref id="ref71">
<label>71</label><mixed-citation publication-type="other" xlink:type="simple"> Tonkin, M J. and Doherty, J.: A hybrid regularized inversion methodology for highly parameterized environmental models, Water Resour. Res., 41, W10412, https://doi.org/10.1029/2005WR003 995, 2005. </mixed-citation>
</ref>
<ref id="ref72">
<label>72</label><mixed-citation publication-type="other" xlink:type="simple"> Vandeberghe, V., Bauwens, W., and Vanrolleghem, P.: Evaluation of uncertainty propagation into river water quality predictions to guide future monitoring campaigns, Environmental Modelling &amp; Software, 22(5), 725&amp;ndash;732, 2007. </mixed-citation>
</ref>
<ref id="ref73">
<label>73</label><mixed-citation publication-type="other" xlink:type="simple"> Vrugt, J., 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, https://doi.org/10.1029/2002WR001 746, 2003. </mixed-citation>
</ref>
<ref id="ref74">
<label>74</label><mixed-citation publication-type="other" xlink:type="simple"> Wagener, T. and Kollat, J.: Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox, Environmental Modeling and Software, in press, 2007. </mixed-citation>
</ref>
<ref id="ref75">
<label>75</label><mixed-citation publication-type="other" xlink:type="simple"> Wagener, T., Boyle, D., Lees, M J., Wheater, Gupta, H S., and H V Sorooshian, S.: A framework for development and application of hydrological models, Hydrol. Earth Syst. Sci., 5, 13&amp;ndash;26, 2001. </mixed-citation>
</ref>
<ref id="ref76">
<label>76</label><mixed-citation publication-type="other" xlink:type="simple"> Wagener, T., McIntyre, N., Lees, M J., Wheater, H S., and Gupta, H V.: Towards reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic identifiability analysis, Hydrol. Processes, 17, 455&amp;ndash;476, 2003. </mixed-citation>
</ref>
<ref id="ref77">
<label>77</label><mixed-citation publication-type="other" xlink:type="simple"> Wagener, T., Wheater, H S., and Gupta, H V.: Rainfall-runoff modeling in gauged and ungauged catchments, Imperial College Press, London, UK, 2004. </mixed-citation>
</ref>
<ref id="ref78">
<label>78</label><mixed-citation publication-type="other" xlink:type="simple"> Wagener, T., Liu, Y., Gupta, H., Springer, E., and Brookshire, D.: Multi-resolution integrated assessment modeling for water resources management in arid and semi-arid regions, in: Regional hydrologic impacts of climate change - Impact assessment and decision making, edited by: Wagener, T., Franks, S., Bøgh, E., Gupta, H., Bastidas, L., Nobre, C., and Oliveira~Galväo, C., IAHS Redbook Publ., 295, pp 265&amp;ndash;272, 2005. </mixed-citation>
</ref>
<ref id="ref79">
<label>79</label><mixed-citation publication-type="other" xlink:type="simple"> William, H., Teukolsky, S A., William, T V., and Brian, P F.: Numerical recipes in C (2nd edition), Cambridge University Press, New York, USA, 1999. </mixed-citation>
</ref>
<ref id="ref80">
<label>80</label><mixed-citation publication-type="other" xlink:type="simple"> Young, P C.: A general theory of modelling for badly defined dynamic systems, in: Modeling, Identification and Control in Environmental Systems, edited by: Vansteenkiste, G C., North Holland, Amsterdam, pp 103&amp;ndash;135, 1978. </mixed-citation>
</ref>
</ref-list>
</back>
</article>