1. Motivation

Many standard users of high-resolution weather forecasts are especially interested in the small-scale information of the forecast field (view slide). Mesoscale phenomena, however, are often induced by dynamical instabilities whose time scale is very small compared to the lead time of the forecast. Therefore, those phenomena might not be deterministically predictable especially with respect to their exact position in space and time. Thus, the direct model output of the LM might contain a significant amount of noise and needs careful interpretation (view slide).

One example of a potentially problematic way of forecast interpretation is the meteogram, an operational forecast product which isolates the direct model output at each grid point without complementing the forecast by any estimate of uncertainty (view slide). In case of a convective precipitation event, for example, the meteogram pretends that the forecaster is 100% certain about the event's exact position on the model grid. This obviously contradicts any forecaster's best judgment.

2. Objectives

Our aim is the development of automatic methods for the detection of limited predictability and for the optimal interpretation of the direct model output in cases of limited predictability (view slide). We have to distinguish deterministically predictable features from random information (noise). In the context of high-resolution models it is especially important to estimate the intrinsic uncertainty of small-scale features. In order to accomplish this, we are (a) conducting experimental ensemble predictions and (b) developing methods to statistically postprocess the direct model output (view slide).

3. Experimental Ensemble

We have produced several experimental ensembles (view slide) with the Lokal-Modell (version 2.4 with filtered orography) by perturbing the parametrized tendencies (i.e. tendencies due to convection, radiation, cloud microphysics) and by perturbing surface parameters (i.e. roughness length, orography) . Thus, the ensemble simulates part of the model random error. An ensemble has been produced for a situation with strong convection and heavy precipitation (04.07.1994, start: 00UTC, shown: accumulated precipitation 11-12UTC) (view slide). The ensemble currently consists of 10 members. The results reveal that the direct model output contains a significant amount of noise (view slide). The noise prevails in the small scales (view slide1, slide2) and becomes most evident in the hourly sum of precipitation at the ground, cloud cover and the solar net flux of radation at the ground. The impact of the perturbations on 2m-temperature is only moderate and the impact on the 10m-wind is almost negligible.

4. Statistical Postprocessing

Due to lack of computer capacities an operational version of this kind of ensemble prediction is not within reach, though. As a temporary solution, we are developing statistical postprocessing methods which require the data of one model simulation only. The postprocessed forecast is a de-noised or a probabilistic forecast (view slide). It is supposed to resemble the results of an ensemble prediction system without actually having processed the data of an ensemble. Thus, the postprocessing method may be optimized by comparing its results with the experimental ensemble. We are currently working on two different postprocessing methods: the neighbourhood method and the wavelet method. In both methods the main obstacle is the lack of several forecast realisations at a specific grid point. Both methods consist in a spatio-temporal aggregation of the direct model output.

4.1. Neighbourhood Method

The neighbourhood method defines a spatio-temporal neighbourhood around each grid point (view slide). The forecast values within such a neighbourhood are assumed to form a sample of the forecast at the corresponding grid point in the center of the neighbourhood. Thus, the spatio-temporal variation within each neighbourhood is assumed to be random. Methods are included which aim at preserving orographically induced variation.

The neighbourhood method estimates several statistical  parameters at each grid point: the expected value and a range of quantiles, for example the 25%- , the 50%- , and the 75%-quantile (view slide). The 50%-quantile (the median) and the expected value represent a de-noised forecast, similar to the ensemble mean in ensemble forecasting (view slide). The difference between the 25%- and the 75%-quantile is an estimate of forecast uncertainty, similar to the standard deviation between the ensemble members in ensemble forecasting. There should be a probability of 50% that the correct forecast will be within the interval between the 25%- and the 75%-quantile. The neighbourhood method can be applied to the hourly sum of precipitation at the ground, 2m-temperature, cloud cover, wind in 10m height and the solar and thermal net flux of radiation at the ground. As an example, the results for one specific grid point are shown (view slide).

4.2. Wavelet Method

The wavelet method is based on a spatial wavelet transformation. First, the direct model output is transformed into the wavelet domain. Then the method curtails those wavelet coefficients which are believed to be associated with noise. Finally, the data is transformed back to the grid point domain. As a result, we obtain a de-noised forecast in the grid point domain (view slide).

5. Verification

Whereas the wavelet method is still in its infancy, the neighbourhood method is already undergoing a pre-operational test phase. Currently, the expected value and the 50%-quantile (median) of hourly precipitation and 2m-temperature are being verified against observations at the ground. First results show that the postprocessed forecast outperforms the direct model output in all respects (view slide).

6. Summary