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Wentao Li, Quan J. Wang, and Qingyun Duan


Statistical postprocessing methods can be used to correct bias and dispersion error in raw ensemble forecasts from numerical weather prediction models. Existing postprocessing models generally perform well when they are assessed on all events, but their performance for extreme events still needs to be investigated. Commonly used joint probability postprocessing models are based on the correlation between forecasts and observations. Because the correlation may be lower for extreme events as a result of larger forecast uncertainty, the dependence between forecasts and observations can be asymmetric with respect to the magnitude of the precipitation. However, the constant correlation coefficient in the traditional joint probability model lacks the flexibility to model asymmetric dependence. In this study, we formulated a new postprocessing model with a decreasing correlation coefficient to characterize asymmetric dependence. We carried out experiments using Global Ensemble Forecast System reforecasts for daily precipitation in the Huai River basin in China. The results show that, although it performs well in terms of continuous ranked probability score or reliability for all events, the traditional joint probability model suffers from overestimation for extreme events defined by the largest 2.5% or 5% of raw forecasts. On the contrary, the proposed variable-correlation model is able to alleviate the overestimation and achieves better reliability for extreme events than the traditional model. The proposed variable-correlation model can be seen as a flexible extension of the traditional joint probability model to improve the performance for extreme events.

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Wentao Li, Qingyun Duan, and Quan J. Wang


Statistical postprocessing models can be used to correct bias and dispersion errors in raw precipitation forecasts from numerical weather prediction models. In this study, we conducted experiments to investigate four factors that influence the performance of regression-based postprocessing models with normalization transformations for short-term precipitation forecasts. The factors are 1) normalization transformations, 2) incorporation of ensemble spread as a predictor in the model, 3) objective function for parameter inference, and 4) two postprocessing schemes, including distributional regression and joint probability models. The experiments on the first three factors are based on variants of a censored regression model with conditional heteroscedasticity (CRCH). For the fourth factor, we compared CRCH as an example of the distributional regression with a joint probability model. The results show that the CRCH with normal quantile transformation (NQT) or power transformation performs better than the CRCH with log–sinh transformation for most of the subbasins in Huai River basin with a subhumid climate. The incorporation of ensemble spread as a predictor in CRCH models can improve forecast skill in our research region at short lead times. The influence of different objective functions (minimum continuous ranked probability score or maximum likelihood) on postprocessed results is limited to a few relatively dry subbasins in the research region. Both the distributional regression and the joint probability models have their advantages, and they are both able to achieve reliable and skillful forecasts.

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Yulin Pan, Brian K. Arbic, Arin D. Nelson, Dimitris Menemenlis, W. R. Peltier, Wentao Xu, and Ye Li


We consider the power-law spectra of internal gravity waves in a rotating and stratified ocean. Field measurements have shown considerable variability of spectral slopes compared to the high-wavenumber, high-frequency portion of the Garrett–Munk (GM) spectrum. Theoretical explanations have been developed through wave turbulence theory (WTT), where different power-law solutions of the kinetic equation can be found depending on the mechanisms underlying the nonlinear interactions. Mathematically, these are reflected by the convergence properties of the so-called collision integral (CL) at low- and high-frequency limits. In this work, we study the mechanisms in the formation of the power-law spectra of internal gravity waves, utilizing numerical data from the high-resolution modeling of internal waves (HRMIW) in a region northwest of Hawaii. The model captures the power-law spectra in broad ranges of space and time scales, with scalings ω −2.05±0.2 in frequency and m −2.58±0.4 in vertical wavenumber. The latter clearly deviates from the GM76 spectrum but is closer to a family of induced-diffusion-dominated solutions predicted by WTT. Our analysis of nonlinear interactions is performed directly on these model outputs, which is fundamentally different from previous work assuming a GM76 spectrum. By applying a bicoherence analysis and evaluations of modal energy transfer, we show that the CL is dominated by nonlocal interactions between modes in the power-law range and low-frequency inertial motions. We further identify induced diffusion and the near-resonances at its spectral vicinity as dominating the formation of power-law spectrum.

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