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Understanding Model Uncertainty – An Application of Uncertainty Quantification to Wind Energy
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Wind resource characterization and short-term wind power forecasts often utilize mesoscale meteorological models such as the Weather Research and Forecasting (WRF) model. Because of the finite nature of the model grid, parameterizations must be used to represent processes that are sub-grid scale, such as those associated with planetary boundary layer (PBL) turbulence. Few published studies have attempted to rigorously define the uncertainty in the simulated wind speed, wind shear, and wind power associated with the assumed constants applied in the PBL and surface layer parameterizations. Likewise, the design of most field studies with the goal of improving PBL parameterizations are based on the intuition of the investigator, rather than an explicit analysis of the causes of uncertainty within the parameterization. In this study we use uncertainty quantification (UQ) to address these shortcomings and provide guidance for the instrument deployments that will be part of the second Department of Energy Wind Forecast Improvement Project (WFIP 2). The most widely used sensitivity analysis (SA) approach is to conduct "one-at-a-time" (OAT) sensitivity tests that systematically investigate departures of model behavior from the baseline simulation by varying one parameter at a time. However, OAT tests can only evaluate a limited number of parameters at the same time, consider only a small fraction of the total parameter uncertainty space, and are computationally expensive. Another critical limitation of the OAT approach is that it does not allow for the quantification of the effects of interaction among parameters. A more comprehensive method is to populate the statistical distribution of model outputs by simultaneously sampling hundreds or thousands of possible configurations of multiple parameters. The SA, such as analysis of variance and variance decomposition, then use the output distributions to understand the contribution of each parameter (along with any interaction effects it has with other parameters) to the overall variance. The UQ analysis will be used to document the uncertainty in hub-height wind, wind shear across the rotor diameter, and wind power for WRF simulations completed using the Mellor-Yamada-Nakanishi-Niino (MYNN) PBL parameterization and the recently revised Mesoscale Model 5 (MM5) surface layer scheme for a location in the Pacific Northwest. The UQ results will be used to develop recommendations for the WFIP 2 instrument deployment. An example WRF time series of simulated 80 m wind speed and wind power is shown in the figure below, with each time series resulting from one of 256 individual WRF simulations completed using combinations of different values for 12 PBL parameters. The figure highlights how the uncertainty in the wind speed gives rise to large variations in the wind power that can range from approximately the rated power of 1.6 MW to less than 0.4 MW for a given point in time. Our analysis shows that the WRF simulations of hub-height wind speed are ultimately sensitive to a relatively small number of parameters, including surface roughness length (z0), the von Karman constant, the turbulence kinetic energy (TKE) dissipation rate, the Prandlt Number, parameters associated with the length scales applied in the MYNN PBL parameterization, and to a lesser extent Monin-Obukhov similarity functions during nighttime. These results argue for the measurement of TKE and TKE dissipation rates over the depth of the PBL (or deeper in stable conditions during which the PBL might be quite thin) at a number of locations over the WFIP 2 domain. The day-night changes in the sensitivity point to the need for measurements of the surface sensible heat flux to help determine the static stability at any given time. The relative importance of the various parameters also changes as a function of terrain slope. For example, the relative contribution of the variance associated with changes of a parameter related to the TKE dissipation rate, ranges from 30% in daytime conditions for gentle slopes to nearly 50% during daytime conditions and steep slopes. Overall, the results presented in this work quantify the uncertainty in WRF simulations of hub-height wind speed and wind power in a region of complex terrain, and point to key measurements that should be included as part of WFIP 2.