Weather Simulation Uncertainty Estimation Using Bayesian Hierarchical Models

Jianfeng Wang Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden

Search for other papers by Jianfeng Wang in
Current site
Google Scholar
PubMed
Close
,
Ricardo M. Fonseca Group of Atmospheric Science, Division of Space Technology, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology, Luleå, Sweden

Search for other papers by Ricardo M. Fonseca in
Current site
Google Scholar
PubMed
Close
,
Kendall Rutledge Novia University of Applied Sciences, Vaasa, Finland

Search for other papers by Kendall Rutledge in
Current site
Google Scholar
PubMed
Close
,
Javier Martín-Torres Group of Atmospheric Science, Division of Space Technology, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology, Luleå, Sweden, and Instituto Andaluz de Ciencias de la Tierra (CSIC-UGR), Granada, Spain

Search for other papers by Javier Martín-Torres in
Current site
Google Scholar
PubMed
Close
, and
Jun Yu Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden

Search for other papers by Jun Yu in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Estimates of the uncertainty of model output fields (e.g., 2-m temperature, surface radiation fluxes, or wind speed) are of great value to the weather and climate communities. The traditional approach for the uncertainty estimation is to conduct an ensemble of simulations where the model configuration is perturbed and/or different models are considered. This procedure is very computationally expensive and may not be feasible, in particular for higher-resolution experiments. In this paper, a new method based on Bayesian hierarchical models (BHMs) that requires just one model run is proposed. It is applied to the Weather Research and Forecasting (WRF) Model’s 2-m temperature in the Botnia–Atlantica region in Scandinavia for a 10-day period in the winter and summer seasons. For both seasons, the estimated uncertainty using the BHM is found to be comparable to that obtained from an ensemble of experiments in which different planetary boundary layer (PBL) schemes are employed. While WRF-BHM is not capable of generating the full set of products obtained from an ensemble of simulations, it can be used to extract commonly used diagnostics including the uncertainty estimation that is the focus of this work. The methodology proposed here is fully general and can easily be extended to any other output variable and numerical model.

© 2019 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: Jianfeng Wang, jianfeng.wang@umu.se

Abstract

Estimates of the uncertainty of model output fields (e.g., 2-m temperature, surface radiation fluxes, or wind speed) are of great value to the weather and climate communities. The traditional approach for the uncertainty estimation is to conduct an ensemble of simulations where the model configuration is perturbed and/or different models are considered. This procedure is very computationally expensive and may not be feasible, in particular for higher-resolution experiments. In this paper, a new method based on Bayesian hierarchical models (BHMs) that requires just one model run is proposed. It is applied to the Weather Research and Forecasting (WRF) Model’s 2-m temperature in the Botnia–Atlantica region in Scandinavia for a 10-day period in the winter and summer seasons. For both seasons, the estimated uncertainty using the BHM is found to be comparable to that obtained from an ensemble of experiments in which different planetary boundary layer (PBL) schemes are employed. While WRF-BHM is not capable of generating the full set of products obtained from an ensemble of simulations, it can be used to extract commonly used diagnostics including the uncertainty estimation that is the focus of this work. The methodology proposed here is fully general and can easily be extended to any other output variable and numerical model.

© 2019 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: Jianfeng Wang, jianfeng.wang@umu.se
Save
  • Banks, R. F., J. Tiana-Alsina, J. M. Baldasano, F. Rocadenbosch, A. Papayannis, S. Solomos, and C. G. Tzanis, 2016: Sensitivity of boundary-layer variables to PBL schemes in the WRF Model based on surface meteorological observations, lidar, and radiosondes during the HygrA-CD campaign. Atmos. Res., 176–177, 185201, https://doi.org/10.1016/j.atmosres.2016.02.024.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berger, J., 2006: The case for objective Bayesian analysis. Bayesian Anal., 1, 385402, https://doi.org/10.1214/06-BA115.

  • Bitner-Gregersen, E. M., and Coauthors, 2014: Recent developments of ocean environmental description with focus on uncertainties. Ocean Eng., 86, 2646, https://doi.org/10.1016/j.oceaneng.2014.03.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blangiardo, M., M. Cameletti, G. Baio, and H. Rue, 2013: Spatial and spatio-temporal models with R-INLA. Spat. Spatio-Temporal Epidemiol., 7, 3955, https://doi.org/10.1016/j.sste.2013.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bougeault, P., and P. Lacarrère, 1989: Parameterization of orography-induced turbulence in mesobeta-scale model. Mon. Wea. Rev., 117, 18721890, https://doi.org/10.1175/1520-0493(1989)117<1872:POOITI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., and S. Park, 2009: A new moist turbulence parameterization in the community atmosphere model. J. Climate, 22, 34223448, https://doi.org/10.1175/2008JCLI2556.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, F., and J. Dudhia, 2001: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, https://doi.org/10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cohen, A. E., S. M. Cavallo, M. C. Coniglio, and H. E. Brooks, 2015: A review of planetary boundary layer parameterization schemes and their sensitivity in simulating Southeastern U.S. cold season severe weather environments. Wea. Forecasting, 30, 591612, https://doi.org/10.1175/WAF-D-14-00105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cressie, N., and C. K. Wikle, 2011: Statistics for Spatio-Temporal Data. Wiley, 624 pp.

  • DeMaria, M., and J. Kaplan, 1994: A Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic basin. Wea. Forecasting, 9, 209220, https://doi.org/10.1175/1520-0434(1994)009<0209:ASHIPS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DeMaria, M., M. Mainelli, L. K. Shay, J. A. Knaff, and J. Kaplan, 2005: Further improvements to the Statistical Hurricane Intensity Prediction Scheme (SHIPS). Wea. Forecasting, 20, 531543, https://doi.org/10.1175/WAF862.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • De Smedt, T., K. Simons, A. Van Nieuwenhuyse, and G. Molenberghs, 2015: Comparing MCMC and INLA for disease mapping with Bayesian hierarchical models. Arch. Public Health, 73 (Suppl.), O2, https://doi.org/10.1186/2049-3258-73-S1-O2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dormann, C. F., 2007: Effects of incorporating spatial autocorrelation into the analysis of species distribution data. Global Ecol. Biogeogr., 16, 129138, https://doi.org/10.1111/j.1466-8238.2006.00279.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duynkerke, P. G., 1991: Radiation fog: A comparison of model simulations with detailed observations. Mon. Wea. Rev., 119, 324341, https://doi.org/10.1175/1520-0493(1991)119<0324:RFACOM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Evans, J. P., M. Ekström, and F. Ji, 2012: Evaluating the performance of a WRF physics ensemble over South-East Australia. Climate Dyn., 39, 12411258, https://doi.org/10.1007/s00382-011-1244-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fox, N. I., and C. K. Wikle, 2005: A Bayesian quantitative precipitation nowcast scheme. Wea. Forecasting, 20, 264275, https://doi.org/10.1175/WAF845.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • García-Díez, M., J. Fernández, L. Fita, and C. Yagüe, 2013: Seasonal dependence of WRF Model biases and sensitivity to PBL schemes over Europe. Quart. J. Roy. Meteor. Soc., 139, 501514, https://doi.org/10.1002/qj.1976.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grenier, H., and C. S. Bretherton, 2001: A moist PBL parameterization for large-scale models and its application to subtropical cloud-topped marine boundary layers. Mon. Wea. Rev., 129, 357377, https://doi.org/10.1175/1520-0493(2001)129<0357:AMPPFL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haining, R., J. Law, R. Maheswaran, T. Pearson, and P. Brindley, 2007: Bayesian modelling of environmental risk: A small area ecological study of coronary heart disease mortality in relation to modelled outdoor nitrogen oxide levels. Stochastic Environ. Res. Risk Assess., 21, 501509, https://doi.org/10.1007/s00477-007-0134-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hines, K. M., and D. H. Bromwich, 2008: Development and testing of polar WRF. Part I: Greenland Ice Sheet meteorology. Mon. Wea. Rev., 136, 19711989, https://doi.org/10.1175/2007MWR2112.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Janjić, Z. I., 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer and turbulence closure schemes. Mon. Wea. Rev., 122, 927945, https://doi.org/10.1175/1520-0493(1994)122<0927:TSMECM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Katata, G., M. Kajino, T. Hiraki, M. Aikawa, T. Kobayashi, and H. Nagai, 2011: A method for simple and accurate estimation of fog deposition in a mountain forest using a meteorological model. J. Geophys. Res., 116, D20102, https://doi.org/10.1029/2010JD015552.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Koh, T.-Y., and R. Fonseca, 2016: Subgrid-scale cloud-radiation feedback for the Betts-Miller-Janjić convection scheme. Quart. J. Roy. Meteor. Soc., 142, 9891006, https://doi.org/10.1002/qj.2702.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuligowski, R. J., and A. P. Barros, 1998: Localized precipitation forecasts from a numerical weather prediction model using artificial neural networks. Wea. Forecasting, 13, 11941204, https://doi.org/10.1175/1520-0434(1998)013<1194:LPFFAN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comput. Phys., 227, 35153539, https://doi.org/10.1016/j.jcp.2007.02.014.

  • Lindgren, F., H. Rue, and J. Lindström, 2011: An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. J. Roy. Stat. Soc., 73B, 423498, https://doi.org/10.1111/j.1467-9868.2011.00777.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lo, J. C.-F., Z.-L. Yang, and R. A. Pielke Sr., 2008: Assessment of three dynamical downscaling methods using the Weather Research and Forecasting (WRF) Model. J. Geophys. Res., 113, D09112, https://doi.org/10.1029/2007JD009216.

    • Search Google Scholar
    • Export Citation
  • MacKay, D. J., 2003: Information Theory, Inference and Learning Algorithms. Cambridge University Press, 640 pp.

  • Malmberg, A., A. Arellano, D. P. Edwards, N. Flyer, D. Nychka, and C. Wikle, 2008: Interpolating fields of carbon monoxide data using a hybrid statistical-physical model. Ann. Appl. Stat., 2, 12311248, https://doi.org/10.1214/08-AOAS168.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martino, S., and H. Rue, 2010: Implementing Approximate Bayesian Inference using Integrated Nested Laplace Approximation: A manual for the INLA program. Department of Mathematical Sciences, Norwegian University of Science and Technology, 72 pp.

  • Massey, F. J., Jr., 1951: The Kolmogorov-Smirnov test for goodness of fit. J. Amer. Stat. Assoc., 46, 6878, https://doi.org/10.1080/01621459.1951.10500769.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matérn, B., 1960: Spatial variation: Stochastic models and their application to some problems in forest surveys and other sampling investigations. Ph.D. dissertation, Stockholm University, 144 pp.

  • Mills, C. M., 2011: On the Weather Research Forecasting model’s treatment of sea ice albedo over the Arctic Ocean. 10th Annual School of Earth, Society, and Environmental Research Review, Urbana, Illinois, University of Illinois at Urbana-Champaign.

  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the ground layer of the atmosphere. Trans. Geophys. Inst. Akad. Nauk USSR, 151, 163187.

    • Search Google Scholar
    • Export Citation
  • Nakanishi, M., 2000: Large-eddy simulation of radiation fog. Bound.-Layer Meteor., 94, 461493, https://doi.org/10.1023/A:1002490423389.

  • Nakanishi, M., and H. Niino, 2006: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog. Bound.-Layer Meteor., 119, 397407, https://doi.org/10.1007/s10546-005-9030-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Overland, J. E., and Coauthors, 2016: Nonlinear response of mid-latitude weather to the changing Arctic. Nat. Climate Change, 6, 992999, https://doi.org/10.1038/nclimate3121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pepin, N., M. Schaefer, and L. D. Riddy, 2009: Quantification of the cold air pool in Kevo Valley, Finish Lapland. Weather, 64, 6067, https://doi.org/10.1002/wea.260.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pleim, J. E., 2007: A combined local and nonlocal closure model for the atmospheric boundary layer. Part I: Model description and testing. J. Appl. Meteor. Climatol., 46, 13831395, https://doi.org/10.1175/JAM2539.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Prein, A. F., and Coauthors, 2015: A review on regional convection-permitting climate modelling: Demonstrations, prospects and challenges. Rev. Geophys., 53, 323361, https://doi.org/10.1002/2014RG000475.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raftery, A. E., T. Gneiting, F. Balabdaoui, and M. Polakowski, 2005: Using Bayesian model averaging to calibrate forecast ensembles. Mon. Wea. Rev., 133, 11551174, https://doi.org/10.1175/MWR2906.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rue, H., S. Martino, and N. Chopin, 2009: Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations. J. Roy. Stat. Soc., 71B, 319392, https://doi.org/10.1111/j.1467-9868.2008.00700.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 10151057, https://doi.org/10.1175/2010BAMS3001.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salazar, E., D. Hammerling, X. Wang, B. Sansó, A. O. Finley, and L. O. Means, 2016: Observation-based blended projections from ensembles of regional climate models. Climatic Change, 138, 5569, https://doi.org/10.1007/s10584-016-1722-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shin, H. H., and S.-Y. Hong, 2015: Representation of the subgrid-scale turbulent transport in convective boundary layers at gray-zone resolutions. Mon. Wea. Rev., 143, 250271, https://doi.org/10.1175/MWR-D-14-00116.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sideratos, G., and N. D. Hatziargyriou, 2007: An advanced statistical method for wind power forecasting. IEEE Trans. Power Syst., 22, 258265, https://doi.org/10.1109/TPWRS.2006.889078.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, D. P., H. Rue, T. G. Martins, A. Riebler, and S. H. Sørbye, 2015: Penalising model component complexity: A principled, practical approach to constructing priors. arXiv.org, https://arxiv.org/abs/1403.4630.

  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Slingo, J. M., and T. Palmer, 2011: Uncertainty in weather and climate prediction. Philos. Trans. Roy. Soc., 369A, 47514767, https://doi.org/10.1098/rsta.2011.0161.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smedman, A.-S., H. Bergström, and U. Högström, 1995: Spectra, variances and length scales in a marine stable boundary layer dominated by a low level jet. Bound.-Layer Meteor., 76, 211232, https://doi.org/10.1007/BF00709352.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steele, C. J., S. R. Dorling, R. von Glasow, and J. Bacon, 2013: Idealized WRF Model sensitivity simulations of sea breeze types and their effects on offshore wind fields. Atmos. Chem. Phys., 13, 443461, https://doi.org/10.5194/acp-13-443-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steele, C. J., S. R. Dorling, R. von Glasow, and J. Bacon, 2015: Modelling sea-breeze climatologies and interactions on coasts in the southern North Sea: Implications for offshore wind energy. Quart. J. Roy. Meteor. Soc., 141, 18211835, https://doi.org/10.1002/qj.2484.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steeneveld, G.-J., 2014: Current challenges in understanding and forecasting stable boundary layers over land and ice. Front. Environ. Sci., 2, 41, https://doi.org/10.3389/fenvs.2014.00041.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stein, M. L., 1999: Interpolation of Spatial Data: Some Theory for Kriging. Springer-Verlag, 228 pp.

    • Crossref
    • Export Citation
  • Steinsland, I., and H. Jensen, 2010: Utilizing Gaussian Markov random field properties of Bayesian animal models. Biometrics, 66, 763771, https://doi.org/10.1111/j.1541-0420.2009.01336.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., B. Galperin, and V. Perov, 2005: Application of a new spectral model of stratified turbulence to the atmospheric boundary layer over sea ice. Bound.-Layer Meteor., 117, 231257, https://doi.org/10.1007/s10546-004-6848-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W.-K., J. Simpson, and M. McCumber, 1989: An ice-water saturation adjustment. Mon. Wea. Rev., 117, 231235, https://doi.org/10.1175/1520-0493(1989)117<0231:AIWSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tegen, I., P. Hollrig, M. Chin, I. Fung, D. Jacob, and J. Penner, 1997: Contribution of different aerosol species to the global aerosol extinction optical thickness: Estimates from model results. J. Geophys. Res., 102, 23 89523 915, https://doi.org/10.1029/97JD01864.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Torn, R. D., and G. J. Hakim, 2009: Initial condition sensitivity of western Pacific extratropical transitions determined using ensemble-based sensitivity analysis. Mon. Wea. Rev., 137, 33883406, https://doi.org/10.1175/2009MWR2879.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Toth, E., A. Brath, and A. Montanari, 2000: Comparison of short-term rainfall prediction models for real-time flood forecasting. J. Hydrol., 239, 134147, https://doi.org/10.1016/S0022-1694(00)00344-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vislocky, R. L., and J. M. Fritsch, 1995: Improved model output statistics forecast through model consensus. Bull. Amer. Meteor. Soc., 76, 11571164, https://doi.org/10.1175/1520-0477(1995)076<1157:IMOSFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vislocky, R. L., and J. M. Fritsch, 1997: Performance of an advanced MOS system in the 1996–97 National Collegiate Weather Forecasting Contest. Bull. Amer. Meteor. Soc., 78, 28512857, https://doi.org/10.1175/1520-0477(1997)078<2851:POAAMS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, M., Y. Kamarianakis, A. Mahalov, M. Wagner, M. Georgescu, G. Miguez-Macho, and M. Moustaoui, 2016: Spatio-temporal modeling for regional climate model comparison: Application on perennial bioenergy crop impacts. Joint Statistical Meeting 2016, Chicago, Illinois, Section on Statistics and the Environment, 2886–2898.

  • Zeng, X., and A. Beljaars, 2005: A prognostic scheme of sea surface skin temperature for modeling and data assimilation. Geophys. Res. Lett., 32, L14605, https://doi.org/10.1029/2005GL023030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, H., Z. Pu, and X. Zhang, 2013: Examination of errors in near-surface temperature and wind from WRF numerical simulations in regions of complex terrain. Wea. Forecasting, 28, 893914, https://doi.org/10.1175/WAF-D-12-00109.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1066 414 39
PDF Downloads 705 263 26