Abstract
Abstract. In this study we propose and demonstrate a data-driven approach in an “information-theoretic” framework to quantitatively estimate precipitation. In this context, predictive relations are expressed by empirical discrete probability distributions directly derived from data instead of fitting and applying deterministic functions, as is standard operational practice. Applying a probabilistic relation has the benefit of providing joint statements about rain rate and the related estimation uncertainty. The information-theoretic framework furthermore allows for the integration of any kind of data considered useful and explicitly considers the uncertain nature of quantitative precipitation estimation (QPE). With this framework we investigate the information gains and losses associated with various data and practices typically applied in QPE. To this end, we conduct six experiments using 4 years of data from six laser optical disdrometers, two micro rain radars (MRRs), regular rain gauges, weather radar reflectivity and other operationally available meteorological data from existing stations. Each experiment addresses a typical question related to QPE. First, we measure the information about ground rainfall contained in various operationally available predictors. Here weather radar proves to be the single most important source of information, which can be further improved when distinguishing radar reflectivity–ground rainfall relationships (Z–R relations) by season and prevailing synoptic circulation pattern. Second, we investigate the effect of data sample size on QPE uncertainty using different data-based predictive models. This shows that the combination of reflectivity and month of the year as a two-predictor model is the best trade-off between robustness of the model and information gain. Third, we investigate the information content in spatial position by learning and applying site-specific Z–R relations. The related information gains are only moderate; specifically, they are lower than when distinguishing Z–R relations according to time of the year or synoptic circulation pattern. Fourth, we measure the information loss when fitting and using a deterministic Z–R relation, as is standard practice in operational radar-based QPE applying, e.g., the standard Marshall–Palmer relation, instead of using the empirical relation derived directly from the data. It shows that while the deterministic function captures the overall shape of the empirical relation quite well, it introduces an additional 60 % uncertainty when estimating rain rate. Fifth, we investigate how much information is gained along the radar observation path, starting with reflectivity measured by radar at height, continuing with the reflectivity measured by a MRR along a vertical profile in the atmosphere and ending with the reflectivity observed by a disdrometer directly at the ground. The results reveal that considerable additional information is gained by using observations from lower elevations due to the avoidance of information losses caused by ongoing microphysical precipitation processes from cloud height to ground. This emphasizes both the importance of vertical corrections for accurate QPE and of the required MRR observations. In the sixth experiment we evaluate the information content of radar data only, rain gauge data only and a combination of both as a function of the distance between the target and predictor rain gauge. The results show that station-only QPE outperforms radar-only QPE up to a distance of 7 to 8 km from the nearest station and that radar–gauge QPE performs best, even compared with radar-based models applying season or circulation pattern.
Highlights
1.1 Approaches to quantitative precipitation estimation (QPE)Quantitative precipitation estimation at high temporal and spatial resolution and in high quality are important prerequisites for many hydrometeorological design and management purposes
We selected the predictors with the constraint that they are operationally available at any potential point of interest, which applies most importantly to reflectivity measured by weather radar, and to the predictors we assumed to be spatially invariant within the test domain: convective available potential energy, circulation pattern, air temperature and humidity, wind, and season
With the goal in mind of providing guidance for the layout of future QPE sensor networks, we addressed the following questions: “are micro rain radars (MRRs) observations at 1500 m more informative than weather radar observations taken at the same height?”; “how much information is gained if we use near-surface instead of elevated MRR observations, omitting the influence of the vertical profile of reflectivity?”; and “how much information is lost if we measure reflectivity instead of rainfall at ground level?”
Summary
1.1 Approaches to quantitative precipitation estimation (QPE)Quantitative precipitation estimation at high temporal and spatial resolution and in high quality are important prerequisites for many hydrometeorological design and management purposes. While the advantage of weather radar is that it provides 3-D observations at a high spatial and temporal resolution and with large coverage, its use relies on some assumptions, which are sometimes justified and sometimes not. It is further hampered by considerable error and uncertainty arising from measuring the radar reflectivity factor Z (hereinafter referred to as reflectivity) instead of rain rate R, measuring at height instead of at the ground, and many other factors such as ground clutter, beam blockage, attenuation, second-trip echoes, anomalous beam propagation and brightband effects. For a good overview on sources of errors, see Zawadzki (1984) or Villarini and Krajewski (2010)
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