Wavelet-based methodology for the verification of stochastic submeso and meso-gamma fluctuations

Numerical weather prediction model skill is difficult to assess for transient, nonstationary, nondeterministic, or stochastic motions, like submeso and small meso-gamma motions. New approaches are needed to complement traditional methods and to quantify and evaluate the variability and the errors for these high-frequency, nondeterministic modes. A new verification technique that uses the wavelet transform as a bandpass filter to obtain scale-dependent frequency distributions of fluctuations is proposed for assessing model performance or accuracy. This new approach quantifies the nondeterministic variability independent of time while accounting for the time scale and amplitude of each fluctuation. The efficacy of this wavelet decomposition technique for the verification of submeso and meso-gamma motions is first illustrated for a single case before the analysis is extended to six cases. The sensitivity of subkilometer grid-length Weather Research and Forecasting Model forecasts to the choice of three initialization strategies is assessed for both deterministic and stochastic motions using observations from a special network located at Rock Springs, Pennsylvania. It is demonstrated that the use of data assimilation in a preforecast period results in improved temperature and wind speed statistics for deterministic motions and for nondeterministic fluctuations with periods greater than ~20 min. As expected, there is little-to-no accuracy forecasting the occurrence of variability for temperature and wind in the smaller-submeso range and greater accuracy in the larger-submeso and meso-gamma ranges. Nonetheless, the model has some difficulty reproducing the observed variability with the correct amplitude. It underestimates the amplitude of observed fluctuations even for larger time scales, where better model performance could be expected.