Xingqin Fang

The authors revisit the issue regarding the predictability of a flow that possesses many scales of motion raised by Lorenz in 1969 and apply the general systems theory developed by Selvam in 1990 to error diagnostics and the predictability of the fractal atmosphere. They then introduce a new generic method to quantify the scale predictability of the fractal atmosphere following the assumptions of the intrinsic inverse power law and the upscale cascade of error. The eddies (of all scales) are extracted against the instant zonal mean, and the ratio of noise (i.e., the domain-averaged square of error amplitudes) to signal (i.e., the domain-averaged square of total eddy amplitudes), referred to as noise-to-signal ratio (NSR), is defined as a measure of forecast skill. The time limit of predictability for any wavenumber can be determined by the criterion or by the criterion , where is the golden ratio and m is a scale index. The NSR is flow adaptive, bias aware, and stable in variation (in a logarithm transformation), and it offers unique advantages for model verification, allowing evaluation of different model variables, regimes, and scales in a consistent manner. In particular, an important advantage of this NSR method over the widely used anomaly correlation coefficient (ACC) method is that it could detect the successive scale predictability of different wavenumbers without the need to explicitly perform scale decomposition. As a demonstration, this new NSR method is used to examine the scale predictability of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) 500-hPa geopotential height.

In this paper, a modified probability-matching technique is developed for ensemble-based quantitative precipitation forecasts (QPFs) associated with landfalling typhoons over Taiwan. The main features of this technique include a resampling of the ensemble realizations, a rainfall pattern adjustment, and a bias correction. Using this technique, a synthetic ensemble is created for the purpose of rainfall prediction from a large-size (32 members), low-resolution (36 km) ensemble and a small-size (8 members), high-resolution (4 km) ensemble. The rainfall pattern is adjusted based on the precipitation distribution of the 36- and 4-km ensembles. A bias-correction scheme is then applied to remove the known systematic bias from the resampled 4-km ensemble realizations as part of the probability-matching procedure. The modified probability-matching scheme is shown to substantially reduce or eliminate the intrinsic model rainfall bias and to provide better QPF guidance. The encouraging results suggest that this modified probability-matching technique is a useful tool for the QPF of the topography-enhanced typhoon heavy rainfall over Taiwan using ensemble forecasts at dual resolutions.

In this study, the impacts of Taiwan topography on the extreme rainfall of Typhoon Morakot and the predictability of this rainfall are examined with a high-resolution (4 km) ensemble simulation using the Advanced Research core of the Weather Research and Forecasting Model (WRF-ARW). Ensemble prediction with realistic topography reproduces salient features of orographic precipitation. The 24- and 96-h accumulated rainfall amount and distribution from the ensemble mean compare reasonably well with the observed precipitation. When the terrain of Taiwan is removed, the rainfall distribution is markedly changed, suggesting the importance of the orography in determining the rainfall structure. Moreover, the peak 96-h rainfall amount is reduced to less than 20%, and the total rainfall amount over southern Taiwan is reduced to less than 60% of the experiments with Taiwan topography. Further analysis indicates that Taiwan’s topography substantially increases the variability of rainfall prediction. Analysis uncertainties as reflected in the perturbed initial state of the ensemble are amplified due to orographic influences on the typhoon circulation. As a result, significant variability occurs in the storm track, timing, and location of landfall, and storm intensities, which in turn, increases the rainfall variability. These results suggest that accurate prediction of heavy precipitation at a specific location and at high temporal resolution for an event such as Typhoon Morakot over Taiwan is extremely challenging. The forecasting of such an event would benefit from probabilistic prediction provided by a high-resolution mesoscale ensemble forecast system.