Probabilistic precipitation nowcasting based on an extrapolation of radar reflectivity and an ensemble approach

Highlights

• The method of probabilistic precipitation nowcasting is proposed for summer season.

• The probability nowcasting is based on ensemble approach to precipitation forecast.

• The method is based on extrapolation technique.

• The uncertainty in the calculation of trajectories is used to generate ensembles.

Abstract

A new method for the probabilistic nowcasting of instantaneous rain rates (ENS) based on the ensemble technique and extrapolation along Lagrangian trajectories of current radar reflectivity is presented. Assuming inaccurate forecasts of the trajectories, an ensemble of precipitation forecasts is calculated and used to estimate the probability that rain rates will exceed a given threshold in a given grid point. Although the extrapolation neglects the growth and decay of precipitation, their impact on the probability forecast is taken into account by the calibration of forecasts using the reliability component of the Brier score (BS).

ENS forecasts the probability that the rain rates will exceed thresholds of 0.1, 1.0 and 3.0 mm/h in squares of 3 km by 3 km. The lead times were up to 60 min, and the forecast accuracy was measured by the BS. The ENS forecasts were compared with two other methods: combined method (COM) and neighbourhood method (NEI). NEI considered the extrapolated values in the square neighbourhood of 5 by 5 grid points of the point of interest as ensemble members, and the COM ensemble was comprised of united ensemble members of ENS and NEI.

The results showed that the calibration technique significantly improves bias of the probability forecasts by including additional uncertainties that correspond to neglected processes during the extrapolation. In addition, the calibration can also be used for finding the limits of maximum lead times for which the forecasting method is useful. We found that ENS is useful for lead times up to 60 min for thresholds of 0.1 and 1 mm/h and approximately 30 to 40 min for a threshold of 3 mm/h. We also found that a reasonable size of the ensemble is 100 members, which provided better scores than ensembles with 10, 25 and 50 members. In terms of the BS, the best results were obtained by ENS and COM, which are comparable. However, ENS is better calibrated and thus preferable.

Introduction

The nowcasting of rainfall is frequently based on the extrapolation of rain fields observed by weather radars by advection along Lagrangian trajectories. The useful lead time of these forecasts depends on the meteorological situation and on how the forecasts are evaluated. In the case of large precipitation systems, the extrapolation technique is quite successful (Germann and Zawadzki, 2002). However, in cases of small-scale convective systems, the rapid growth or decay of rain cells causes the quality of the forecasts to rapidly decrease with lead time because storm development frequently dominates over advection. In these cases, the useful lead time for rain rate forecasts is limited to only several tens of minutes.

Some currently used numerical weather prediction (NWP) models are able to forecast precipitation with horizontal resolutions comparable to the resolution of radars and are able to simulate the development of storms. However, their forecasts cannot be used operationally for nowcasting because the update-cycle, which is usually 3 or more hours, is insufficient for very short-term forecasts and also the assimilation of radar data is not trivial and computationally expensive task.

At present, extrapolation is probably the only means to nowcast precipitation for the next tens of minutes in real time. This technique can issue forecasts almost immediately after receiving data, but its drawback is that it applies simple advection techniques, instead of sophisticated physical models, which are components of high resolution NWP models.

The inability of extrapolation methods to predict rainfall growth and decay can be partly compensated by applying blending techniques when the forecast is a result of weighted rainfall fields obtained by extrapolation and a forecast of an NWP model. The blending is only useful if NWP exhibits skill in the nowcasting range and if it provides complementary information to the extrapolation nowcast. The blended forecast initially relies on the extrapolation method, and gradually the NWP model forecast is more heavily weighted and drives the forecast. Various lead times (TL) can be found in the literature when an NWP model provides better forecasts than the extrapolation technique alone (Wilks, 2011). For example Lin et al. (2005) found TL = 6 h, Haiden et al. (2011) obtained TL between 2 and 3 h for precipitation and Bližňák et al. (2017) got TL between 1 and 2 h.

Precipitation forecasting is a difficult task and is inevitably connected with uncertainty, which can be quantitatively expressed by a probabilistic formulation of the forecast. Therefore, probabilistic forecasts are frequently used in nowcasting. Usually, the forecast is formulated as the probability that the rain rate of accumulated precipitation will exceed a given threshold for a given area (grid point).

There are methods that take into account the forecast uncertainty that stem from the assumption that small-scale features in rainfall fields do not persist long and are therefore filtered from the forecast (Germann and Zawadzki, 2004). This approach improves the forecast accuracy in terms of root mean square error of the average of ensemble members. However, the improvement of these methods is slight; although they may reduce false alarms, their ability to forecast or at least warn against heavy precipitation is not improved. A similar approach was applied by Seed (2003), who developed the Spectral Prognosis (S-PROG) model that decomposes rainfall fields into spectral scale components using Fourier filters and forecasts each component independently.

A probabilistic technique based on extrapolation and regression models was developed by Kitzmiller (Kitzmiller, 1996, Sokol and Pesice, 2012). Regression models were applied to describe relationships between a yes/no predictand, expressing whether the observed amount of precipitation exceeded a given threshold, and predictors that were derived from forecasted or observed meteorological variables. Precipitation derived from the latest available radar data was the most important predictor.

A straightforward technique that provides a probabilistic forecast considers the forecasted values in the neighbourhood of the point of interest as possible forecasts. Using this assumption, techniques of probabilistic forecasts were developed by Schmid et al. (2000) and Germann and Zawadzki (2004). Further techniques apply stochastic algorithms. Bowler et al. (2006) proposed a stochastic precipitation nowcasting system (Short-Term Ensemble Prediction System (STEPS)), which blended a spatially and temporally correlated cascade of noise fields with the radar extrapolation and NWP cascades. A similar approach was applied by Atencia and Zawadzki (2014), who developed a technique based on the stochastic perturbation, specifically designed to reproduce the spatial and temporal structure of precipitation fields, of a Lagrangian extrapolation of the last observed rainfall field using autoregressive models. They found that the perturbations were able to reproduce the spatial structure of the rainfall field. Berenguer et al. (2011) developed an ensemble nowcasting technique, SBMcast, by Lagrangian extrapolation. The core of the technique is the application of the String of Beads model (Pegram and Clothier, 2001) to generate ensemble members of rainfall forecasts. The utilized model preserves the space and time structure of rainfall fields, which are thus compatible with observations. The results showed that the technique reasonably reproduced the evolution of the rainfall field, but the errors were underestimated. A possible reason was that the uncertainty errors in the motion field were neglected.

The analogue-based approach for precipitation nowcasting finds similar states to the current state in a historical dataset. The main difficulty of this approach is in finding analogues. The ensemble is created using several closest states from the historical data. Panziera et al. (2011) developed a heuristic analogue technique, Nowcasting of Orographic Rainfall by means of Analogues (NORA), for a very short-term forecasting of orographic precipitation. NORA used specific predictors that were selected to have a strong relation with orographic precipitation and characterized the mesoscale conditions. The predictors were derived from radar images and used to find analogues.

The technique was further improved by using principal components analysis to rainfall fields to find analogues (Foresti et al., 2015). Another approach was applied by Atencia and Zawadzki (2015), who were looking for similarities in temporal storm evolutions and synoptic patterns. They concluded that the analogue-based probabilistic forecast had a better forecasting skill than the stochastic Lagrangian ensemble approach.

Ensemble forecasts have become very popular in meteorology. Their basic advantage is that they naturally lead to probabilistic forecasts. In this paper, we propose a two-step method for probabilistic forecasts of instantaneous precipitation. In the first step the method uses Lagrangian extrapolation of radar-derived precipitation, and calculates ensemble forecasts by considering only the errors in advection. The ensemble is generated using historical data and the well-known LU algorithm (e.g., Huynh et al., 2008) to derive the covariance structure of advection errors. In the second step, the error caused by neglecting the growth and decay of precipitation is estimated by applying the calibration making use of the decomposition of Brier Score and historical data. The estimate is included in the probability forecast. The proposed method was applied to data from the warm season of the year, and the forecast was focused on instantaneous rain rates.

This paper comprises 6 Sections. In Section 2, the data and a forecast area are presented. The Lagrangian advection algorithm is described in Section 3, and Section 4 contains a description of the forecasting method, including the ensemble generation. The verification of the method is presented in Section 5. Section 6 presents the summary and conclusions.