## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 12, Number 1 (2018), 432-458.

### Stochastic simulation of predictive space–time scenarios of wind speed using observations and physical model outputs

Julie Bessac, Emil Constantinescu, and Mihai Anitescu

**Full-text: Access denied (no subscription detected) **

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

#### Abstract

We propose a statistical space–time model for predicting atmospheric wind speed based on deterministic numerical weather predictions and historical measurements. We consider a Gaussian multivariate space–time framework that combines multiple sources of past physical model outputs and measurements in order to produce a probabilistic wind speed forecast within the prediction window. We illustrate this strategy on wind speed forecasts during several months in 2012 for a region near the Great Lakes in the United States. The results show that the prediction is improved in the mean-squared sense relative to the numerical forecasts as well as in probabilistic scores. Moreover, the samples are shown to produce realistic wind scenarios based on sample spectra and space–time correlation structure.

#### Article information

**Source**

Ann. Appl. Stat., Volume 12, Number 1 (2018), 432-458.

**Dates**

Received: October 2016

Revised: September 2017

First available in Project Euclid: 9 March 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1520564479

**Digital Object Identifier**

doi:10.1214/17-AOAS1099

**Mathematical Reviews number (MathSciNet)**

MR3773400

**Zentralblatt MATH identifier**

06894713

**Keywords**

Hierarchical Gaussian model multiple data sources predictive scenarios spatio-temporal wind speed

#### Citation

Bessac, Julie; Constantinescu, Emil; Anitescu, Mihai. Stochastic simulation of predictive space–time scenarios of wind speed using observations and physical model outputs. Ann. Appl. Stat. 12 (2018), no. 1, 432--458. doi:10.1214/17-AOAS1099. https://projecteuclid.org/euclid.aoas/1520564479

#### References

- Ailliot, P., Frénod, E. and Monbet, V. (2006). Long term object drift forecast in the ocean with tide and wind.
*Multiscale Model. Simul.***5**514–531. - Anderson, J. L. (1996). A method for producing and evaluating probabilistic forecasts from ensemble model integrations.
*J. Climate***9**1518–1530. - Anitescu, M., Chen, J. and Wang, L. (2012). A matrix-free approach for solving the parametric Gaussian process maximum likelihood problem.
*SIAM J. Sci. Comput.***34**A240–A262. - Apanasovich, T. and Genton, M. G. (2010). Cross-covariance functions for multivariate random fields based on latent dimensions.
*Biometrika***97**15–30. - Bao, L., Gneiting, T., Grimit, E. P., Guttorp, P. and Raftery, A. E. (2010). Bias correction and Bayesian model averaging for ensemble forecasts of surface wind direction.
*Mon. Weather Rev.***138**1811–1821. - Baran, S. (2014). Probabilistic wind speed forecasting using Bayesian model averaging with truncated normal components.
*Comput. Statist. Data Anal.***75**227–238. - Baran, S. and Lerch, S. (2015). Log-normal distribution based Ensemble Model Output Statistics models for probabilistic wind-speed forecasting.
*Q. J. R. Meteorol. Soc.***141**2289–2299. - Baran, S. and Lerch, S. (2016). Mixture EMOS model for calibrating ensemble forecasts of wind speed.
*Environmetrics***27**116–130. - Berliner, M. (2000). Hierarchical Bayesian modeling in the environmental sciences.
*AStA Adv. Stat. Anal.***84**141–153. - Berrocal, V. J., Gelfand, A. E. and Holland, D. M. (2012). Space–time data fusion under error in computer model output: An application to modeling air quality.
*Biometrics***68**837–848. - Bouallegue, Z. B., Heppelmann, T., Theis, S. E. and Pinson, P. (2016). Generation of scenarios from calibrated ensemble forecasts with a dual-ensemble copula-coupling approach.
*Mon. Weather Rev.***144**4737–4750. - Bourotte, M., Allard, D. and Porcu, E. (2016). A flexible class of non-separable cross-covariance functions for multivariate space–time data.
*Spat. Stat.***18**125–146. - Brisson, N., Gary, C., Justes, E., Roche, R., Mary, B., Ripoche, D., Zimmer, D., Sierra, J., Bertuzzi, P. and Burger, P. (2003). An overview of the crop model STICS.
*Eur. J. Agron.***18**309–332. - Brown, B. G., Katz, R. W. and Murphy, A. H. (1984). Time series models to simulate and forecast wind speed and wind power.
*J. Clim. Appl. Meteorol.***23**1184–1195. - Clark, M., Gangopadhyay, S., Hay, L., Rajagopalan, B. and Wilby, R. (2004). The Schaake shuffle: A method for reconstructing space–time variability in forecasted precipitation and temperature fields.
*J. Hydrometeorol.***5**243–262. - Constantinescu, E. M. and Anitescu, M. (2013). Physics-based covariance models for Gaussian processes with multiple outputs.
*Int. J. Uncertain. Quantif.***3**47–71. - Constantinescu, E., Zavala, V., Rocklin, M., Lee, S. and Anitescu, M. (2011). A computational framework for uncertainty quantification and stochastic optimization in unit commitment with wind power generation.
*IEEE Trans. Power Syst.***26**431–441. - Cowles, M. K., Zimmerman, D. L., Christ, A. and McGinnis, D. L. (2002). Combining snow water equivalent data from multiple sources to estimate spatio-temporal trends and compare measurement systems.
*J. Agric. Biol. Environ. Stat.***7**536–557. - Cressie, N. and Wikle, C. K. (2011).
*Statistics for Spatio-Temporal Data*. Wiley, Hoboken, NJ. - Dawid, A. P. and Sebastiani, P. (1999). Coherent dispersion criteria for optimal experimental design.
*Ann. Statist.***27**65–81. - Fanshawe, T. R. and Diggle, P. J. (2012). Bivariate geostatistical modelling: A review and an application to spatial variation in Radon concentrations.
*Environ. Ecol. Stat.***19**139–160. - Feldmann, K., Scheuerer, M. and Thorarinsdottir, T. L. (2015). Spatial postprocessing of ensemble forecasts for temperature using nonhomogeneous Gaussian regression.
*Monthly Weather Rev.***143**955–971. - Fuentes, M. and Raftery, A. E. (2005). Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models.
*Biometrics***61**36–45. - Fuentes, M., Chen, L., Davis, J. M. and Lackmann, G. M. (2005). Modeling and predicting complex space–time structures and patterns of coastal wind fields.
*Environmetrics***16**449–464. - Gel, Y., Raftery, A. E. and Gneiting, T. (2004). Calibrated probabilistic mesoscale weather field forecasting: The geostatistical output perturbation method.
*J. Amer. Statist. Assoc.***99**575–583. - Genton, M. G. and Kleiber, W. (2015). Cross-covariance functions for multivariate geostatistics.
*Statist. Sci.***30**147–163.Mathematical Reviews (MathSciNet): MR3353096

Digital Object Identifier: doi:10.1214/14-STS487

Project Euclid: euclid.ss/1433341471 - Glahn, H. R. and Lowry, D. A. (1972). The use of model output statistics (MOS) in objective weather forecasting.
*J. Appl. Meteorol.***11**1203–1211. - Gneiting, T., Raftery, A. E., Westveld, A. H. III and Goldman, T. (2005). Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation.
*Mon. Weather Rev.***133**1098–1118. - Gneiting, T., Larson, K., Westrick, K., Genton, M. G. and Aldrich, E. (2006). Calibrated probabilistic forecasting at the stateline wind energy center: The regime-switching space–time method.
*J. Amer. Statist. Assoc.***101**968–979. - Gneiting, T., Stanberry, L. I., Grimit, E. P., Held, L. and Johnson, N. A. (2008). Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds.
*TEST***17**211–235. - Hamill, T. M. (2001). Interpretation of rank histograms for verifying ensemble forecasts.
*Mon. Weather Rev.***129**550–560. - Hering, A. S. and Genton, M. G. (2010). Powering up with space–time wind forecasting.
*J. Amer. Statist. Assoc.***105**92–104. - Kang, E. L., Cressie, N. and Sain, S. R. (2012). Combining outputs from the North American regional climate change assessment program by using a Bayesian hierarchical model.
*J. R. Stat. Soc. Ser. C. Appl. Stat.***61**291–313. - Kazor, K. and Hering, A. S. (2015). The role of regimes in short-term wind speed forecasting at multiple wind farms.
*Stat***4**271–290. - Lerch, S. and Thorarinsdottir, T. L. (2013). Comparison of non-homogeneous regression models for probabilistic wind speed forecasting.
*Tellus A***65**21206. - Li, N., Uckun, C., Constantinescu, E., Birge, J., Hedman, K. and Botterud, A. (2015). Flexible operation of batteries in power system scheduling with renewable energy.
*IEEE Trans. Sustain. Energy***7**685–696. - Palmer, T. (2014). More reliable forecasts with less precise computations: A fast-track route to cloud-resolved weather and climate simulators?
*Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.***372**20130391. - Papavasiliou, A., Oren, S. S. and Rountree, B. (2015). Applying high performance computing to transmission-constrained stochastic unit commitment for renewable energy integration.
*IEEE Trans. Power Syst.***30**1109–1120. - Pinson, P. (2013). Wind energy: Forecasting challenges for its operational management.
*Statist. Sci.***28**564–585. - Pinson, P. and Girard, R. (2012). Evaluating the quality of scenarios of short-term wind power generation.
*Appl. Energy***96**12–20. - Pinson, P. and Tastu, J. (2013). Discrimination ability of the energy score. Technical University of Denmark. Tech. rep.
- Pinson, P., Christensen, L. E. A., Madsen, H., Sorensen, P. E., Donovan, M. H. and Jensen, L. E. (2008). Regime-switching modelling of the fluctuations of offshore wind generation.
*J. Wind Eng. Ind. Aerodyn.***96**2327–2347. - Pinson, P., Madsen, H., Nielsen, H., Papaefthymiou, G. and Klöckl, B. (2009). From probabilistic forecasts to statistical scenarios of short-term wind power production.
*Wind Energy***12**51–62. - Raftery, A. E., Gneiting, T., Balabdaoui, F. and Polakowski, M. (2005). Using Bayesian model averaging to calibrate forecast ensembles.
*Mon. Weather Rev.***133**1155–1174. - Royle, J. A. and Berliner, L. M. (1999). A hierarchical approach to multivariate spatial modeling and prediction.
*J. Agric. Biol. Environ. Stat.***4**29–56. - Royle, J., Berliner, L., Wikle, C. and Milliff, R. (1999). A hierarchical spatial model for constructing wind fields from scatterometer data in the Labrador Sea. In
*Case Studies in Bayesian Statistics*367–382. Springer, Berlin. - Schefzik, R., Thorarinsdottir, T. L. and Gneiting, T. (2013). Uncertainty quantification in complex simulation models using ensemble copula coupling.
*Statist. Sci.***28**616–640. - Scheuerer, M. and Hamill, T. M. (2015). Variogram-based proper scoring rules for probabilistic forecasts of multivariate quantities.
*Mon. Weather Rev.***143**1321–1334. - Scheuerer, M. and Möller, D. (2015). Probabilistic wind speed forecasting on a grid based on ensemble model output statistics.
*Ann. Appl. Stat.***9**1328–1349. - Schuhen, N., Thorarinsdottir, T. L. and Gneiting, T. (2012). Ensemble model output statistics for wind vectors.
*Mon. Weather Rev.***140**3204–3219. - Shumway, R. and Stoffer, D. (2010).
*Time Series Analysis and Its Applications*:*With R Examples*. Springer Science & Business Media. - Skamarock, W., Klemp, J., Dudhia, J., Gill, D., Barker, D., Duda, M., Huang, X.-Y., Wang, W. and Powers, J. (2008). A description of the Advanced Research WRF Version 3 Tech. Rep. Tech Notes-475+ STR, NCAR.
- Sloughter, J. M. L., Gneiting, T. and Raftery, A. E. (2010). Probabilistic wind speed forecasting using ensembles and Bayesian model averaging.
*J. Amer. Statist. Assoc.***105**25–35. - Sloughter, J. M. L., Gneiting, T. and Raftery, A. E. (2013). Probabilistic wind vector forecasting using ensembles and Bayesian model averaging.
*Mon. Weather Rev.***141**2107–2119. - Smith, L. A. and Hansen, J. A. (2004). Extending the limits of ensemble forecast verification with the minimum spanning tree.
*Mon. Weather Rev.***132**1522–1528. - Stein, M. L. (1999).
*Interpolation of Spatial Data*:*Some Theory for Kriging*. Springer, New York. - Stein, M., Chen, J. and Anitescu, M. (2012). Difference filter preconditioning for large covariance matrices.
*SIAM J. Matrix Anal. Appl.***33**52–72. - Thorarinsdottir, T. L. and Gneiting, T. (2010). Probabilistic forecasts of wind speed: Ensemble model output statistics by using heteroscedastic censored regression.
*J. Roy. Statist. Soc. Ser. A***173**371–388. - Thorarinsdottir, T. L. and Johnson, M. S. (2012). Probabilistic wind gust forecasting using non-homogeneous Gaussian regression.
*Mon. Weather Rev.***140**889–897. - Thorarinsdottir, T. L., Scheuerer, M. and Heinz, C. (2016). Assessing the calibration of high-dimensional ensemble forecasts using rank histograms.
*J. Comput. Graph. Statist.***25**105–122. - Wilks, D. S. (2015). Multivariate ensemble Model Output Statistics using empirical copulas.
*Q. J. R. Meteorol. Soc.***141**945–952.

### More like this

- Probabilistic wind speed forecasting on a grid based on ensemble model output statistics

Scheuerer, Michael and Möller, David, The Annals of Applied Statistics, 2015 - Incorporating geostrophic wind information for improved space–time short-term wind speed forecasting

Zhu, Xinxin, Bowman, Kenneth P., and Genton, Marc G., The Annals of Applied Statistics, 2014 - Downscaling Global Weather Forecast Outputs Using ANN for Flood Prediction

Do Hoai, Nam, Udo, Keiko, and Mano, Akira, Journal of Applied Mathematics, 2011

- Probabilistic wind speed forecasting on a grid based on ensemble model output statistics

Scheuerer, Michael and Möller, David, The Annals of Applied Statistics, 2015 - Incorporating geostrophic wind information for improved space–time short-term wind speed forecasting

Zhu, Xinxin, Bowman, Kenneth P., and Genton, Marc G., The Annals of Applied Statistics, 2014 - Downscaling Global Weather Forecast Outputs Using ANN for Flood Prediction

Do Hoai, Nam, Udo, Keiko, and Mano, Akira, Journal of Applied Mathematics, 2011 - A dynamic nonstationary spatio-temporal model
for short term prediction of precipitation

Sigrist, Fabio, Künsch, Hans R., and Stahel, Werner A., The Annals of Applied Statistics, 2012 - Hybrid Wind Speed Forecasting Model Study Based on SSA and Intelligent Optimized Algorithm

Zhang, Wenyu, Su, Zhongyue, Zhang, Hongli, Zhao, Yanru, and Zhao, Zhiyuan, Abstract and Applied Analysis, 2014 - Wind Energy: Forecasting Challenges for Its Operational Management

Pinson, Pierre, Statistical Science, 2013 - Wind Power Assessment Based on a WRF Wind Simulation with Developed Power Curve Modeling Methods

Guo, Zhenhai and Xiao, Xia, Abstract and Applied Analysis, 2014 - Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling

Schefzik, Roman, Thorarinsdottir, Thordis L., and Gneiting, Tilmann, Statistical Science, 2013 - Probabilistic quantitative precipitation field
forecasting using a two-stage spatial model

Berrocal, Veronica J., Raftery, Adrian E., and Gneiting, Tilmann, The Annals of Applied Statistics, 2008 - A multivariate semiparametric Bayesian spatial
modeling framework for hurricane surface wind fields

Reich, Brian J. and Fuentes, Montserrat, The Annals of Applied Statistics, 2007