Real-Time Parameter Estimation of a Dual-Pol Radar Rain Rate Estimator Using the Extended Kalman Filter

The extended Kalman filter is an extended version of the Kalman filter for a non-linear problem. This study applies this extended Kalman filter to the real-time estimation of the parameters of the dual-pol radar rain rate estimator. The estimated parameters are also compared with those based on the least squares method. As an application example, this study considers four storm events observed by the Beaslesan radar in Korea. The findings derived include, first, that the parameters of the radar rain rate estimator obtained by the extended Kalman filter are totally different from those by the least squares method. In fact, the parameters obtained by the extended Kalman filter are found to be more reasonable, and are similar to those reported in previous studies. Second, the estimated rain rates based on the parameters obtained by the extended Kalman filter are found to be similar to those observed on the ground. Even though the parameters estimated by applying the least squares method are quite different from previous studies as well as those based on the extended Kalman filter, the resulting radar rain rate is found to be quite similar to that based on the extended Kalman filter. In conclusion, the extended Kalman filter can be a reliable method for real-time estimation of the parameters of the dual-pol radar rain rate estimator. The resulting rain rate is also found to be of sufficiently high quality to be applicable for other purposes, such as various flood warning systems.

Parameter estimation of a dual-pol radar rain rate estimator with truncated paired data

This study proposes a new method for estimating the parameters of a radar rain rate estimator, particularly of the dual-pol radar. The proposed method is similar to the probability matching method (PMM), except for being based on truncated data pairs. A truncation value is introduced to the log-transformed data in order to remove those in the low rain rate zone as well as to introduce Gaussian distribution. The parameters are then estimated by comparing the first- and second-order moments. The proposed method is applied to a total of six rainfall events observed by the Beaslesan Radar in Korea from 2014 to 2017. Summarizing the results, first, the truncation value should be applied to the horizontal reflectivity (dBZh) data. In this case only, the other two data, the rain rate (dBR) and the differential reflectivity (dBZdr), follow the Gaussian distribution well. It is also important to consider rather severe rainfall events for the parameter estimation. The parameters for only the severe rainfall events are all estimated rather reasonably. On the other hand, for the other moderate and light rainfall events, the parameters are estimated as being rather far from their normal ranges. This is mainly due to the relatively small variance of dBR compared to that of dBZh. That is, the variance of dBR is found to be greatly dependent on the peak rain rate, but the variance of dBZh remains almost unchanged, regardless of the peak rain rate. As a result, the peak rain rate plays a dominant role in the reasonable parameter estimation. These findings are also consistent with many previous studies.

Evaluation of GPM-DPR precipitation estimates with WegenerNet gauge data

The core satellite of the Global Precipitation Measurement (GPM) mission provides precipitation observations measured with the Dual-frequency Precipitation Radar (DPR). The precipitation can only be estimated from the radar data, and therefore independent validations using direct precipitation measurements on the ground as a true reference need to be performed. Moreover, the quality and the accuracy of satellite observational data depend on various influencing factors, such as altitude, topography and rainfall type. In this way, a validation may help to minimise those uncertainties. The DPR Level 2 algorithms provide three different sets of radar rain rate estimates: Ku-band-only rain rates, Ka-band-only rain rates, and a product using both the Ku and Ka band. This study presents an evaluation of the three GPM-DPR surface precipitation estimates based on the gridded precipitation data of the WegenerNet, a local-scale terrestrial network of 153 meteorological stations in southeastern Austria. The validation is based on graphical and statistical approaches, using only data where both Ku- and Ka-band measurements are available. The focus lies on the resemblance of the rainfall variability within the whole network and the over- and underestimation of the precipitation through the GPM-DPR. The analysis rests upon 15 rainfall events observed by the GPM-DPR over the WegenerNet in the last 4 years; the meteorological winter is excluded due to technical challenges of snow measurements. The WegenerNet provides between 8 and 12 gauges within each GPM-DPR footprint. Its biases are well studied and corrected; thus, it can be taken as a robust ground reference. This work also includes considerations on the limits of such comparisons between small terrestrial networks with a high density of stations and precipitation observations from a satellite. Our results show that the GPM-DPR estimates basically match with the WegenerNet measurements, but absolute quantities are biased. The three types of radar estimates deliver similar results, where Ku-band and dual-frequency estimates are very close to each other. On a general level, Ka-band precipitation estimates deliver better results due to their greater sensitivity to low rainfall rates.

Evaluation of GPM-DPR precipitation estimates with WegenerNet gauge data

The core satellite of the Global Precipitation Measurement (GPM) mission provides precipitation observations measured with the Dual frequency Precipitation Radar (DPR). The precipitation can only be estimated from the radar data, and therefore, independent validations using direct precipitation observation on the ground as a true reference need to be performed. Moreover, the quality and the accuracy of the measurements depend on various influencing factors. In this way, a validation may help to minimise those uncertainties. The DPR provides three different radar rain rate estimates for the GPM core satellite: Ku-band-only rain rates, Ka-band-only rain rates and a product combining the two frequencies. This study presents an evaluation of the three GPM-DPR surface precipitation estimates based on the gridded precipitation data of the WegenerNet, a local scale terrestrial network of 153 meteorological stations in southeast Austria. The validation is based on a graphical and a statistical approach using only data where both Ku- and Ka-band measurements are available. The data delivered from the WegenerNet are gauge-based gridded rainfall observations; the meteorological winter is excluded due to technical reasons. The focus lies on the resemblance of the variability within the whole network and the over- and underestimation of the precipitation through the GPM-DPR. During the last four years 22 rainfall events were observed by the GPM-DPR over the WegenerNet and the analysis rests upon these rainfall events. The WegenerNet provides a large number of gauges within each GPM-DPR footprint. Its biases are well studied and corrected, thus, it can be taken as a robust ground reference. This work also includes considerations on the limits of such comparisons between small terrestrial networks with a high density of stations and precipitation observations from a satellite. Our results show that the GPM-DPR estimates basically match with the WegenerNet measurements, but absolute quantities are biased. The three types of radar estimates deliver similar results, where Ku-band and dual frequency estimates are very close to each other. On a general level, Ka-band precipitation estimates deliver the best results due to the high number of light rainfall events.

Should radar precipitation depend on incident air temperature? A new estimation algorithm for cold climates

In cold climates, the form of precipitation (snow or rain or mixture of snow and rain) results in uncertainty in radar precipitation estimation. Estimation often proceeds without distinguishing the state of precipitation which can be reliably specified as a function of associated air temperature. In the present study, we hypothesise that incident air temperature is related to the phase of the precipitation and ensuing reflectivity measurement, and therefore could be used in prediction models to improve radar precipitation estimates in cold climates. This is the first study to our knowledge that assesses the dependence of radar precipitation on incident air temperature and presents a procedure that can be used for taking it into consideration. We use a data based nonparametric statistical approach for this assessment. A nonparametric predictive model is constructed with radar rain rate and air temperature as predictor variables and gauge precipitation as observed response using a k-nearest neighbour (k-nn) regression estimator. A partial information theoretic technique is used to ascertain the relative importance of the two predictors. Six years (2011–2017) of hourly radar rain rate from the Norwegian national radar network over the Oslo region, hourly gauged precipitation from 88 raingauges and gridded observational air temperature were used to formulate the predictive model and hence evaluate our hypothesis. The predictive model with temperature as an additional covariate reduces root mean squared error (RMSE) up to 15 % compared to the predictive model with radar rain rate as the sole predictor. More than 80 % of the raingauge locations in the study area showed improvement with the new method. Further, the estimated partial weight for air temperature assumed a zero value for more than 85 % of gauge locations when temperature was above 10 °C, which indicates that the partial dependence of precipitation on air temperature is most important for colder climates.

Measuring and modeling rainfall with terrestrial sensors and radar : implications for rainfall heterogeneity and discharge

Quantitative precipitation estimates are fundamental for hydrometeorological analyses. Radars provide a superior spatiotemporal advantage over terrestrial-based precipitation gauges to provide such measures of rainfall. However, many regions of the Continental US (CONUS) reside outside of the optimal range of weather radar surveillance (i.e., 100 km), with few studies analyzing the performance of radar rain rate estimates beyond this range. Several years' worth of radar rain rate estimates were analyzed from distant S-band Weather Surveillance Radars -- 1988 Doppler (WSR-88D) series, demonstrating poor performance in quantitative precipitation estimates (QPE's) at distances beyond 150 km. Furthermore, these S-band radar rain rates were determined to be significantly (p less than 0.10) less accurate in Quantitative Precipitation Estimates (QPE's) when compared to a locally-sited X-band dual polarimetric radar. In general, S-band radars were best utilized when implementing R(Z,ZDR) algorithms, with the bulk of QPE errors due to missed precipitation, whereas the X-band radar was superior overall with either R(Z,ZDR) or R(ZDR,KDP) with errors primarily due to false alarms. These radar QPE's were then used as input to a physically-based hydrologic model, Vflo, which showed superior performance over spatially-averaged rain gauges, which sometimes missed precipitation events. The results presented demonstrate the importance of choosing the proper radar QPE datasets for hydrometeorological studies.

The Potential Use of the Linear Depolarization Ratio to Distinguish between Convective and Stratiform Rainfall to Improve Radar Rain-Rate Estimates

A major source of errors in radar-derived quantitative precipitation estimates is the inhomogeneous nature of the vertical reflectivity profile (VPR). Operational radars generally scan in azimuth at constant elevation (PPI mode) and provide limited VPR information, so predetermined VPR shapes with limited degrees of freedom are needed to correct for the VPR in real time. Typical stratiform VPRs have a sharp peak below the 0° isotherm, known as the “bright band,” caused by the presence of large melting snowflakes, but this feature is not present in convective cores where the melting ice is in the form of graupel or compact ice. Inappropriate correction assuming a brightband VPR can lead to underestimation of rain rates, with particular impacts in intense convective storms. This paper proposes the use of high values of linear depolarization ratio (LDR) measurements to confirm the presence of large melting snowflakes and lower values for melting graupel or high-density ice as a prerequisite to selecting a suitable profile shape for VPR correction. Using a climatologically representative dataset of short-range, high-resolution C-band vertical profiles, the peak value of the LDR in the melting layer is shown to have robust skill in identifying VPRs without bright band, with the “best” performance at a threshold of −20 dB. Further work is proposed to apply this result to improving corrections for VPR at longer range, where the limited effect of beam broadening on LDR peaks could provide advantages over other available methods.

Radar Rain-Rate Estimators and Their Variability due to Rainfall Type: An Assessment Based on Hydrometeorology Testbed Data from the Southeastern United States

S-band profiling (S-PROF) radar measurements from different southeastern U.S. Hydrometeorology Testbed sites indicated a frequent occurrence of rain that did not exhibit radar bright band (BB) and was observed outside the periods of deep-convective precipitation. This common nonbrightband (NBB) rain contributes ~15%–20% of total accumulation and is not considered as a separate rain type by current precipitation-segregation operational radar-based schemes, which separate rain into stratiform, convective, and, sometimes, tropical types. Collocated with S-PROF, disdrometer measurements showed that drop size distributions (DSDs) of NBB rain have much larger relative fractions of smaller drops when compared with those of BB and convective rains. Data from a year of combined DSD and rain-type observations were used to derive S-band-radar estimators of rain rate R, including those based on traditional reflectivity Ze and ones that also use differential reflectivity ZDR and specific differential phase KDP. Differences among same-type estimators for mostly stratiform BB and deep-convective rain were relatively minor, but estimators derived for the common NBB rain type were distinct. Underestimations in NBB rain-rate retrievals derived using other rain-type estimators (e.g., those for BB or convective rain or default operational radar estimators) for the same values of radar variables can be on average about 40%, although the differential phase-based estimators are somewhat less susceptible to DSD details. No significant differences among the estimators for the same rain type derived using DSDs from different observational sites were present despite significant separation and differing terrain. Identifying areas of common NBB rain could be possible from Ze and ZDR measurements.