A Scale-Decomposition-Based Radar QPE Ensemble System Incorporating a Statistical Model for VPR Errors

Characterization of the structure of radar Quantitative Precipitation Estimation (QPE) errors is of high importance for applications that use the data quantitatively. This is often overlooked in NWP forecast verification where the forecast rainfall accumulations are usually verified against deterministic radar accumulations, without any consideration for the observation error. In this work we describe an ensemble generator that has been developed primarily to help improve the value of NWP forecast verification at the Met Office but which is general enough to suit a wider range of applications.

To facilitate the representation of the spatial and temporal error correlation structures, we have used a cascade scale decomposition framework that is part of the Short Term Ensemble Prediction System (STEPS); a nowcasting system that was developed jointly at the Met Office and the Bureau of Meteorology. STEPS currently uses a Total Error Model (TEM) approach to enable perturbed QPE fields to be created with spatially correlated errors based on a climatological knowledge of the spatial error correlations of radar minus rain gauge residuals (assuming the gauges to be the ground truth). Conversely, in this work we have used a Source Specific Error Model (SSEM), where the total error variance is the sum of the variances of each of the individual error sources (assumed uncorrelated) which need to quantified individually. The expectation is that, given sufficiently accurate error models, the SSEM will perform better while also having the advantage that the perturbations can adapt to the present weather, rather than being based solely on the climatology.

At long range from the radar, the greatest source of error arises from the extrapolation of measurements aloft to the ground level because the Vertical Profile of Reflectivity (VPR) is not accurately known. The Met Office QPE system, Radarnet, uses a VPR correction scheme to remove VPR bias errors based on one of several parameterized climatological VPRs, selected to match the observations. This leaves a random error, which we choose to model using a stochastic cascade, with the assumption that the horizontal spatial correlation of the VPR error is identical to that of the rain itself. The variance of this stochastic noise is estimated using a model of the vertical correlation (rho) of the reflectivity at the beam height and that at the ground which includes the (NWP) freezing level height as a parameter. This has been calibrated using a large number of pairs of horizontally co-located but vertically separated radar reflectivity observations from the UK radar network. The stochastic noise is scaled to the total variance in the unperturbed analysis (given by an estimate of the spatially varying local variance) and then, at each cascade level, the noise and the analysis are blended. This is achieved by starting at the smallest length scales (bottom of the cascade) and then working upwards, where the unperturbed analysis is replaced with noise until the total noise variance, as a fraction of that in the unperturbed analysis, is equal to the fraction of unexplained variance (1-rho^2) that would be in the reflectivity inferred at the ground.

The presentation includes a description of the ensemble generator, the VPR error model, the results of the VPR error model calibration and the initial results of the evaluation of the SSEM, which at present includes just the VPR error contribution. The results for the SSEM will be compared to an earlier study that was done to evaluate the STEPS TEM.