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<front>
<journal-meta>
<journal-id journal-id-type="publisher">ACP</journal-id>
<journal-title-group>
<journal-title>Atmospheric Chemistry and Physics</journal-title>
<abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1680-7324</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/acp-12-2409-2012</article-id>
<title-group>
<article-title>Some issues in uncertainty quantification and parameter tuning: a case study of convective parameterization scheme in the WRF regional climate model</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yang</surname>
<given-names>B.</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>Qian</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>Lin</surname>
<given-names>G.</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>Leung</surname>
<given-names>R.</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>Zhang</surname>
<given-names>Y.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Pacific Northwest National Laboratory, Richland, Washington, USA</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>School of Atmospheric Sciences, Nanjing University, Nanjing, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>05</day>
<month>03</month>
<year>2012</year>
</pub-date>
<volume>12</volume>
<issue>5</issue>
<fpage>2409</fpage>
<lpage>2427</lpage>
<permissions>
<license xlink:type="simple">
<license-p>This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
</license>
</permissions>
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<abstract>
<p>The current tuning process of parameters in global climate models is often
performed subjectively or treated as an optimization procedure to minimize
model biases based on observations. While the latter approach may provide
more plausible values for a set of tunable parameters to approximate the
observed climate, the system could be forced to an unrealistic physical
state or improper balance of budgets through compensating errors over
different regions of the globe. In this study, the Weather Research and
Forecasting (WRF) model was used to provide a more flexible framework to
investigate a number of issues related uncertainty quantification (UQ) and
parameter tuning. The WRF model was constrained by reanalysis of data over
the Southern Great Plains (SGP), where abundant observational data from
various sources was available for calibration of the input parameters and
validation of the model results. Focusing on five key input parameters in
the new Kain-Fritsch (KF) convective parameterization scheme used
in WRF as an example, the purpose of this study was to explore the utility
of high-resolution observations for improving simulations of regional
patterns and evaluate the transferability of UQ and parameter tuning across
physical processes, spatial scales, and climatic regimes, which have
important implications to UQ and parameter tuning in global and regional
models. A stochastic importance sampling algorithm, Multiple Very Fast
Simulated Annealing (MVFSA) was employed to efficiently sample the input
parameters in the KF scheme based on a skill score so that the algorithm
progressively moved toward regions of the parameter space that minimize
model errors.
&lt;br&gt;&lt;br&gt;
The results based on the WRF simulations with 25-km grid spacing over the
SGP showed that the precipitation bias in the model could be significantly
reduced when five optimal parameters identified by the MVFSA algorithm were
used. The model performance was found to be sensitive to downdraft- and
entrainment-related parameters and consumption time of Convective Available
Potential Energy (CAPE). Simulated convective precipitation decreased as the
ratio of downdraft to updraft flux increased. Larger CAPE consumption time
resulted in less convective but more stratiform precipitation. The
simulation using optimal parameters obtained by constraining only
precipitation generated positive impact on the other output variables, such
as temperature and wind. By using the optimal parameters obtained at 25-km
simulation, both the magnitude and spatial pattern of simulated
precipitation were improved at 12-km spatial resolution. The optimal
parameters identified from the SGP region also improved the simulation of
precipitation when the model domain was moved to another region with a
different climate regime (i.e. the North America monsoon region). These
results suggest that benefits of optimal parameters determined through
vigorous mathematical procedures such as the MVFSA process are transferable
across processes, spatial scales, and climatic regimes to some extent. This
motivates future studies to further assess the strategies for UQ and
parameter optimization at both global and regional scales.</p>
</abstract>
<counts><page-count count="19"/></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"> % vor jede Referenz Allen, M. R., Stott, P. A., Mitchell, J. F. B., Schnur, R., and Delworth, T. L.: Quantifying the uncertainty in forecasts of anthropogenic climate change, Nature, 407, 617–620, 2000. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple"> Arakawa, A., Jung, J.-H., and Wu, C.-M.: Toward unification of the multiscale modeling of the atmosphere, Atmos. Chem. Phys., 11, 3731–3742, http://dx.doi.org/10.5194/acp-11-3731-2011doi:10.5194/acp-11-3731-2011, 2011. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple"> Barker, H. W., Pincus, R., and Morcrette, J.-J.: The Monte-Carlo Independent Column Approximation: Application within large-scale models. Proceedings of the GCSS/ARM Workshop on the Representation of Cloud Systems in Large-Scale Models, May 2002, Kananaskis, Alberta, Canada, 10 pp., 2003. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple"> Bechtold, P., Bazile, E., Guichard, F., Mascart, P., and Richard, E.: A mass-flux convection scheme for regional and global models, Q. J. Roy. Meteorol. Soc., 127, 869–886, 2001. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple"> Berbery, E. H.: Mesoscale moisture analysis of the North American monsoon, J. Climate, 14, 121–137, 2001. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple"> Boyle, J. S., Williamson, D., Cederwall, R., Fiorino, M., Hnilo, J., Olson, J., Phillips, T., Potter, G., and Xie, S.: Diagnosis of Community Atmospheric Model 2 (CAM2) in numerical weather forecast configuration at Atmospheric Radiation Measurement sites, J. Geophys. Res., 110, D15S15, http://dx.doi.org/10.1029/2004JD005042doi:10.1029/2004JD005042, 2005. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Chen, F. and Dudhia, J.: Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity, Mon. Weather Rev., 129, 569–585, 2001. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple"> Cheng, M. D.: Effects of Downdrafts and Mesoscale Convective Organization on the Heat and Moisture Budgets of Tropical Cloud Clusters. Part II: Effects of Convective-Scale Downdrafts, J. Atmos. Sci., 46, 1540–1564, 1989. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple"> Collins, W. D., Rasch, P. J., Boville, B. A., Hack, J. J., McCaa, J. R., Williamson, D. L., Kiehl, J. T., and Briegleb, B.: Description of the NCAR Community Atmosphere Model (CAM 3.0), NCAR Technical Note, NCAR/TN-464+STR, 226 pp., 2004. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Collins, M., Booth, B. B. B., Bhaskaran, B., Harris, G. R., Murphy, J. M., Sexton, D. M. H., and Webb, M. J.: Climate model errors, feedbacks and forcings: a comparison of perturbed physics and multi-model ensembles, Climate Dyn., 36, 1737–1766, http://dx.doi.org/10.1007/s00382-010-0808-0doi:10.1007/s00382-010-0808-0, 2011. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple"> Colman, R.: A comparison of climate feedbacks in general circulation models, Climate Dyn., 20, 865–873, http://dx.doi.org/10.1007/s00382-003-0310-zdoi:10.1007/s00382-003-0310-z, 2003. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Covey, C., Brandon, S., Bremer, P.-T., Domyancic, D., Garaizar, X., Johannesson, G., Klein, R., Klein, S. A., Lucas, D. D., Tannahill, J., and Zhang, Y.: Quantifying the uncertainties of climate prediction, B. Am. Meteorol. Soc., submitted, 2011. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Emanuel, K. A. and Zivkovic-Rothman, M.: Development and evaluation of a convective scheme for use in climate models, J. Atmos. Sci., 56, 1766–1782, 1999. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple"> Englehart, P. J. and Douglas, A. V.: Defining intraseasonal rainfall variability within the North American monsoon, J. Climate, 19, 4243–4253, 2006. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> Ferrier, B. S., Simpson, J., and Tao, W. K.: Factors responsible for precipitation efficiencies in midlatitude and tropical squall simulations, Mon. Weather Rev., 124, 2100–2125, 1996. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> Gilmore, M. S., Straka, J. M., and Rasmussen, E. N.: Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme, Mon. Weather Rev., 132, 2610–2627, 2004. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> Giorgi, F. and Mearns, L. O.: Calculation of average, uncertainty range, and reliability of regional climate changes from AOGCM simulations via the &quot;reliability ensemble averaging&quot; (REA) method, J. Climate, 15, 1141–1158, 2002. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple"> Grant, A. L. M.: Cloud-base fluxes in the cumulus-capped boundary layer, Q. J. Roy. Meteorol. Soc., 127, 407–421, 2001. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple"> Gregory, D., Morcrette, J. J., Jakob, C., Beljaars, A. C. M., and Stockdale, T.: Revision of convection, radiation and cloud schemes in the ECMWF Integrated Forecasting System, Q. J. Roy. Meteorol. Soc., 126, 1685–1710, 2000. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple"> Grell, G. A. and Devenyi, D.: A generalized approach to parameterizing convection combining ensemble and data assimilation techniques, Geophys. Res. Lett., 29, 1693, http://dx.doi.org/10.1029/2002GL015311doi:10.1029/2002GL015311, 2002. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223–242, 2001. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> Hacker, J. P., Ha, S.-Y., Snyder, C., Berner, J., Eckel, F. A., Pocernich, M., Schramm, J., and Wang, X.: The U.S. Air Force Weather Agency&apos;s mesoscale ensemble: Scientific description and performance results, Tellus, 63, 625–641, http://dx.doi.org/10.1111/j.1600870.2010.00497doi:10.1111/j.1600870.2010.00497, 2011. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> Hawkins, E. and Sutton, R.: The potential to narrow uncertainty in regional climate predictions, B. Am. Meteorol. Soc., 90, 1095–1107, http://dx.doi.org/10.1175/2009BAMS2607.1doi:10.1175/2009BAMS2607.1, 2009. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple"> Hong, S.-Y. and Lim, J.-O. J.: The WRF Single-Moment 6-Class Microphysics Scheme (WSM6), J. Korean Meteor. Soc., 42, 129–151, 2006. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Hurrell, J., Meehl, G., Bader, D., Delworth, T., Kirtman, B., and Wielicki, B.: A unified modeling approach to climate system prediction, B. Am. Meteorol. Soc., 90, 1819–1832, http://dx.doi.org/10.1175/2009BAMS2752.1doi:10.1175/2009BAMS2752.1, 2009. </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Ingber, L.: Very Fast Simulated Re-Annealing, Math. Comput. Model., 12, 967–973, 1989. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple"> Intergovernmental Panel on Climate Change: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge Univ. Press, Cambridge, UK, 2007. </mixed-citation>
</ref>
<ref id="ref28">
<label>28</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., 108, 4583, http://dx.doi.org/10.1029/2002jd002991doi:10.1029/2002jd002991, 2003. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> Jackson, C., Sen, M. K., and Stoffa, P. L.: An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions, J. Climate, 17, 2828–2841, 2004. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> Jackson, C. S., Sen, M. K., Huerta, G., Deng, Y., and Bowman, K. P.: Error Reduction and Convergence in Climate Prediction, J. Climate, 21, 6698–6709, http://dx.doi.org/10.1175/2008jcli2112.1doi:10.1175/2008jcli2112.1, 2008. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> Janjic, Z. I.: The Step-Mountain Eta Coordinate Model - Further Developments of the Convection, Viscous Sublayer, and Turbulence Closure Schemes, Mon. Weather Rev., 122, 927–945, 1994. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> Janjic, Z. I.: Nonsingular Implementation of the Mellor–Yamada Level 2.5 Scheme in the NCEP Meso model, NCEP Office Note, No. 437, 61~pp., 2002. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Johnson, R. H.: The role of convective-scale precipitation downdrafts in cumulus and synoptic-scale interactions, J. Atmos. Sci., 33, 1890–1910, 1976. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Kain, J. S.: The Kain-Fritsch convective parameterization: An update, J. Appl. Meteorol., 43, 170–181, 2004. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Kain, J. S. and Fritsch, J. M.: A One-Dimensional Entraining Detraining Plume Model and Its Application in Convective Parameterization, J. Atmos. Sci., 47, 2784–2802, 1990. </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple"> Kain, J. S. and Fritsch, J. M.: Convective parameterization for mesoscale models: The Kain-Fritcsh scheme, The representation of cumulus convection in numerical models, edited by: Emanuel, K. A. and Raymond, D. J., Amer. Meteor. Soc., Boston, USA, 246 pp., 1993. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple"> Kain, J. S., Baldwin, M. E., Janish, P. R., and Weiss, S. J.: Utilizing the Eta model with two different convective parameterizations to predict convective initiation and evolution at the SPC, Preprints, Ninth Conference on Mesoscale Processes, Ft. Lauderdale, FL, 91–95, 2001. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> Khairoutdinov, M. F. and Randall, D. A.: A cloud resolving model as a cloud parameterization in the NCAR Community Climate System Model: Preliminary results, Geophys. Res. Lett., 28, 3617–3620, 2001. </mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple"> Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P.: Optimization by Simulated Annealing, Science, 220, 671–680, 1983. </mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple"> Knupp, K. R. and Cotton, W. R.: Convective Cloud Downdraft Structure – an Interpretive Survey, Rev. Geophys., 23, 183–215, 1985. </mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple"> Kreitzberg, C. W. and Perkey, D. J.: Release of Potential Instability .1. Sequential Plume Model within a Hydrostatic Primitive Equation Model, J. Atmos. Sci., 33, 456–475, 1976. </mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple"> Liang, F.: Annealing evolutionary stochastic approximation Monte Carlo for global optimization, Stat. Comput., 21, 375–393, http://dx.doi.org/10.1007/s11222-010-9176-1doi:10.1007/s11222-010-9176-1, 2010. </mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple"> Liang, X.-Z., Li, L., Dai, A., and Kunkel, K. E.: Regional climate model simulation of summer precipitation diurnal cycle over the United States, Geophys. Res. Lett., 31, L24208, http://dx.doi.org/10.1029/2004GL021054doi:10.1029/2004GL021054, 2004. </mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple"> Liu, C. H., Moncrieff, M. W., and Grabowski, W. W.: Explicit and parameterized realizations of convective cloud systems in TOGA COARE, Mon. Weather Rev., 129, 1689–1703, 2001. </mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple"> Lopez, A., Tebaldi, C., New, M., Stainforth, D., Allen, M., and Kettleborough, J.: Two approaches to quantifying uncertainty in global temperature changes, J. Climate, 19, 4785–4796, 2006. </mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple"> Maurer, E. P., Wood, A. W., Adam, J. C., Lettenmaier, D. P., and Nijssen, B.: A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States, J. Climate, 15, 3237–3251, 2002. </mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple"> Medeiros, B. and Stevens, B.: Revealing differences in GCM representations of low clouds, Climate Dynam., 36, 385–399, http://dx.doi.org/10.1007/s00382-009-0694-5doi:10.1007/s00382-009-0694-5, 2011. </mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple"> Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E.: Equation of State Calculations by Fast Computing Machines, J. Chem. Phys., 21, 1087–1092, 1953. </mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple"> Min, S. K., Simonis, D., and Hense, A.: Probabilistic climate change predictions applying Bayesian model averaging, Philos. T. Roy. Soc., 365A, 2103–2116, http://dx.doi.org/10.1098/rsta.2007.2070doi:10.1098/rsta.2007.2070, 2007. </mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple"> Molders, N.: Plant- and soil-parameter-caused uncertainty of predicted surface fluxes, Mon. Weather Rev., 133, 3498–3516, 2005. </mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Morrison, H., Curry, J. A., and Khvorostyanov, V. I.: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description, J. Atmos. Sci., 62, 1665–1677, 2005. </mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple"> Murphy, J. M., Sexton, D. M. H., Barnett, D. N., Jones, G. S., Webb, M. J., and Collins, M.: Quantification of modelling uncertainties in a large ensemble of climate change simulations, Nature, 430, 768–772, http://dx.doi.org/10.1038/nature02771doi:10.1038/nature02771, 2004. </mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple"> Murphy, J. M., Booth, B. B. B., Collins, M., Harris, G. R., Sexton, D. M. H., and Webb, M. J.: A methodology for probabilistic predictions of regional climate change from perturbed physics ensembles, Philos. T. Roy Soc., 365A, 1993–2028, http://dx.doi.org/10.1098/rsta.2007.2077doi:10.1098/rsta.2007.2077, 2007. </mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple"> Moskowitz, B. and Caflisch, R. E.: Smoothness and dimension reduction in quasi-Monte Carlo methods, Math Comput. Model, 23, 37–54, 1996. </mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple"> Pincus, R., Barker, H. W., and Morcrette, J. J.: A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields, J. Geophys. Res., 108, 4376, http://dx.doi.org/10.1029/2002JD003322doi:10.1029/2002JD003322, 2003. </mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple"> Sen, M. K. and Stoffa, P. L.: Bayesian inference, Gibbs&apos; sampler and uncertainty estimation in geophysical inversion, Geophys. Prospect., 44, 313–350, 1996. </mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple"> Shepherd, J. M., Ferrier, B. S., and Ray, P. S.: Rainfall morphology in Florida convergence zones: A numerical study, Mon. Weather Rev., 129, 177–197, 2001. </mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple"> Simpson, J. and Wiggert, V.: Models of Precipitating Cumulus Towers, Mon. Weather Rev., 97, 471–489, 1969. </mixed-citation>
</ref>
<ref id="ref59">
<label>59</label><mixed-citation publication-type="other" xlink:type="simple"> Skamarock, W. C., Klemp, J. B., and Dudhia, J.: Prototypes for the WRF (Weather Research and Forecasting) model, Preprints, Ninth Conference on Mesoscale Processes, Amer. Met. Soc., Ft. Lauderdale, FL, J11–J15, 2001. </mixed-citation>
</ref>
<ref id="ref60">
<label>60</label><mixed-citation publication-type="other" xlink:type="simple"> Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Duda, M. G., Huang, X.-Y., Wang, W., and Powers, J. G.: A Description of the Advanced Research WRF Version 3, NCAR Technical Note, NCAR/TN–475+STR, 123 pp., 2008. </mixed-citation>
</ref>
<ref id="ref61">
<label>61</label><mixed-citation publication-type="other" xlink:type="simple"> Stainforth, D. A., Aina, T., Christensen, C., Collins, M., Faull, N., Frame, D. J., Kettleborough, J. A., Knight, S., Martin, A., Murphy, J. M., Piani, C., Sexton, D., Smith, L. A., Spicer, R. A., Thorpe, A. J., and Allen, M. R.: Uncertainty in predictions of the climate response to rising levels of greenhouse gases, Nature, 433, 403–406, http://dx.doi.org/10.1038/nature03301doi:10.1038/nature03301, 2005. </mixed-citation>
</ref>
<ref id="ref62">
<label>62</label><mixed-citation publication-type="other" xlink:type="simple"> Stein, M.: Large Sample Properties of Simulations Using Latin Hypercube Sampling, Technometrics, 29, 143–151, 1987. </mixed-citation>
</ref>
<ref id="ref63">
<label>63</label><mixed-citation publication-type="other" xlink:type="simple"> Tao, W. K., Chern, J. D., Atlas, R., Randall, D., Khairoutdinov, M., Li, J. L., Waliser, D. E., Hou, A., Lin, X., Peters-Lidard, C., Lau, W., Jiang, J., and Simpson, J.: A Multiscale Modeling System Developments, Applications, and Critical Issues, B. Am. Meteorol. Soc., 90, 515–534, http://dx.doi.org/10.1175/2008bams2542.1doi:10.1175/2008bams2542.1, 2009. </mixed-citation>
</ref>
<ref id="ref64">
<label>64</label><mixed-citation publication-type="other" xlink:type="simple"> Taylor, K. E.: Summarizing multiple aspects of model performance in single diagram, J. Geophys. Res., 106, 7183–7192, http://dx.doi.org/10.1029/2000JD900719doi:10.1029/2000JD900719, 2001. </mixed-citation>
</ref>
<ref id="ref65">
<label>65</label><mixed-citation publication-type="other" xlink:type="simple"> Tebaldi, C., Smith, R. L., Nychka, D., and Mearns, L. O.: Quantifying uncertainty in projections of regional climate change: A Bayesian approach to the analysis of multimodel ensembles, J. Climate, 18, 1524–1540, 2005. </mixed-citation>
</ref>
<ref id="ref66">
<label>66</label><mixed-citation publication-type="other" xlink:type="simple"> Tierney, L. and Mira, A.: Some adaptive Monte Carlo methods for Bayesian inference, Stat. Med., 18, 2507–2515, 1999. </mixed-citation>
</ref>
<ref id="ref67">
<label>67</label><mixed-citation publication-type="other" xlink:type="simple"> Villagran, A., Huerta, G., Jackson, C. S., and Sen, M. K.: Computational Methods for Parameter Estimation in Climate Models, Bayesian Analysis, 3, 823–850, http://dx.doi.org/10.1214/08-BA331doi:10.1214/08-BA331, 2008. </mixed-citation>
</ref>
<ref id="ref68">
<label>68</label><mixed-citation publication-type="other" xlink:type="simple"> Warner, T. T. and Hsu, H. M.: Nested-model simulation of moist convection: The impact of coarse-grid parameterized convection on fine-grid resolved convection, Mon. Weather Rev., 128, 2211–2231, 2000. </mixed-citation>
</ref>
<ref id="ref69">
<label>69</label><mixed-citation publication-type="other" xlink:type="simple"> Webb, M. J., Senior, C. A., Sexton, D. M. H., Ingram, W. J., Williams, K. D., Ringer, M. A., McAvaney, B. J., Colman, R., Soden, B. J., Gudgel, R., Knutson, T., Emori, S., Ogura, T., Tsushima, Y., Andronova, N., Li, B., Musat, I., Bony, S., and Taylor, K. E.: On the contribution of local feedback mechanisms to the range of climate sensitivity in two GCM ensembles, Clim. Dynam., 27, 17–38, http://dx.doi.org/10.1007/s00382-006-0111-2doi:10.1007/s00382-006-0111-2, 2006. </mixed-citation>
</ref>
<ref id="ref70">
<label>70</label><mixed-citation publication-type="other" xlink:type="simple"> Zhang, G. J. and McFarlane, N. A.: Sensitivity of Climate Simulations to the Parameterization of Cumulus Convection in the Canadian Climate Center General-Circulation Model, Atmos. Ocean, 33, 407–446, 1995. </mixed-citation>
</ref>
</ref-list>
</back>
</article>