Improving the rainfall rate estimation in the midstream of the Heihe River Basin using raindrop size distribution

During the intensive observation period of the Watershed Allied Telemetry Experimental Research (WATER), a total of 1074 raindrop size distribution were measured by the Parsivel disdrometer, the latest state-of-the-art optical laser instrument. Because of the limited observation data in Qinghai-Tibet Plateau, the modelling behaviour was not well done. We used raindrop size distributions to improve the rain rate estimator of meteorological radar in order to obtain many accurate rain rate data in this area. We got the relationship between the terminal velocity of the raindrop and the diameter (mm) of a raindrop: <i>v(D)</i> = 4.67<i>D</i><sup>0.53</sup>. Then four types of estimators for X-band polarimetric radar are examined. The simulation results show that the classical estimator <i>R</i> (<i>Z</i><sub>H</sub>) is most sensitive to variations in DSD and the estimator <i>R</i> (<i>K</i><sub>DP</sub>, <i>Z</i><sub>H</sub>, <i>Z</i><sub>DR</sub>) is the best estimator for estimating the rain rate. An X-band polarimetric radar (714XDP) is used for verifying these estimators. The lowest sensitivity of the rain rate estimator <i>R</i> (<i>K</i><sub>DP</sub>, <i>Z</i><sub>H</sub>, <i>Z</i><sub>DR</sub>) to variations in DSD can be explained by the following facts. The difference in the forward-scattering amplitudes at horizontal and vertical polarizations, which contributes <i>K</i><sub>DP</sub>, is proportional to the 3rd power of the drop diameter. On the other hand, the exponent of the backscatter cross-section, which contributes to <i>Z</i><sub>H</sub>, is proportional to the 6th power of the drop diameter. Because the rain rate <i>R</i> is proportional to the 3.57th power of the drop diameter, <i>K</i><sub>DP</sub> is less sensitive to DSD variations than <i>Z</i><sub>H</sub>

Comparing Disdrometer-measured Raindrop Size Distributions from VORTEX-SE with Distributions from Polarimetric Radar Retrievals Using the Constrained Gamma Method

Many aspects of microphysical variations within supercells are not well understood, even though they play a key role in storm dynamics and evolution. Raindrop size distributions (DSDs) provide a lot of insight into a storms microphysics, however, DSDs vary significantly throughout storms. Unfortunately, current radars do not have the capability to directly observe DSDs, making retrieval algorithms based on advanced microphysical models and in-situ disdrometer observations necessary. If these small-scale variations can be better characterized, and differences between convective regimes quantified, it will lead to improved algorithms for retrieving DSD parameters from radars as well as improved microphysical parameterizations within numerical weather prediction models. With better modeling of supercells, tornado predictions and warnings can be improved. While disdrometers can directly measure DSDs, they are severely limited in spatial coverage. In order to improve our understanding of the spatial variation of DSDs across supercells, radar retrieval methods, such as the constrained-gamma method, can be used to retrieve DSD parameters at high spatial resolution across an entire storm. The constrained-gamma method works by finding a relationship between the shape parameter μ and the slope parameter Λ of the underlying gamma distribution. In this study, the constrained gamma method is applied to radar data collected during the 2016 and 2017 VORTEX-SE field program in order to retrieve gamma distributions from polarimetric radar variables. Specifically, new μ-Λ relations will be derived from VORTEX-SE disdrometer data and will be compared to μ-Λ relations found in other studies. The utility of retrievals will then be evaluated using the different relations for characterizing the spatiotemporal variation of DSDs for VORTEX-SE storms. To further improve the μ-Λ relation, the effects of measurement errors will be minimized by using a sorting and averaging technique to group DSDs with similar microphysical properties together

Precipitation Estimation Using C-Band Dual Polarimetric Weather Radar

Radar Quantitative Precipitation Estimation (QPE) plays an important role in weather forecasting, especially nowcasting, and hydrology. This study evaluates the current QPE algorithm implemented by the Canadian Radar Network of Environment Canada, suggests an improved algorithm, and also evaluates the use of polarimetric radars for estimation of Snow Water Equivalent (SWE), solid snowfall, and rainfall rates. Data from the dual polarimetric C-band King City radar (CWKR) near Toronto, Ontario, SWE and solid snowfall rates from Oakville, Ontario, SWE from the CAN-Now project at Pearson International Airport (CYYZ), Toronto, Ontario, and Mount Pearl, Newfoundland were used in this project. The ground observations show that the polarimetric variables could be used to infer a few of the microphysical processes during snowfall. It is suggested that the co-polar correlation coefficient (hv) could be sensitive to the size ranges of different snow habits within the radar sampled volume. Also, higher differential reflectivity (ZDR) values were measured with large aggregates due to the Mie resonance effect, lower fluttering angles, or induced field transverse. Data from the three sites were used to develop S(ZeH)-based algorithms at 1 hr interval SWE, where ZeH is the radar equivalent reflectivity factor. Similarly, two additional algorithms were developed using SWE at 10 min intervals from CYYZ and Mt. Pearl but they were found to have less skill. A modest difference was found between S(ZeH) and the polarimetric algorithm, S(ZeH, ZDR), in estimating SWE. The 1 hr interval SWE accumulation from the three sites were combined to develop an additional S(ZeH) algorithm which had statistically better results. The results show a severe underestimation of SWE and solid snowfall rates by the current Environment Canada algorithm. The similarity of the S(ZeH) algorithms for CYYZ and Mount Pearl suggests that the same algorithm could be used for many sites. A strong correlation was found between radar reflectivity factor and ground solid snowfall measurement. Accordingly, S(ZeH) and S(ZeH, ZDR) algorithms were established to directly estimate solid snowfall rates on the ground. The S(ZeH) was found to have superior results compared to the S(ZeH, ZDR). Finally, the polarimetric variables were found to be useful in estimating rainfall rates. Thus, three rainfall algorithms (R(ZeH), R(ZeH, ZDR), R(KDP)) were established and compared against the current algorithm employed by the Environment Canada and counterpart algorithms established by Bringi et al. (2010). A logic tree was devised with certain polarimetric thresholds to choose the optimal algorithm among the three established ones. It appears that for rain, unlike for snow, the polarimetric parameters are very useful for quantitative precipitation estimation

A Moment-Based Polarimetric Radar Forward Operator for Rain Microphysics

There is growing interest in combining microphysical models and polarimetric radar observations to improve our understanding of storms and precipitation. Mapping model-predicted variables into the radar observational space necessitates a forward operator, which requires assumptions that introduce uncertainties into model-observation comparisons. These include uncertainties arising from the microphysics scheme a priori assumptions of a fixed drop size distribution (DSD) functional form, whereas natural DSDs display far greater variability. To address this concern, this study presents a moment-based polarimetric radar forward operator with no fundamental restrictions on the DSD form by linking radar observables to integrated DSD moments. The forward operator is built upon a dataset of > 200 million realistic DSDs from one-dimensional bin microphysical rain shaft simulations, and surface disdrometer measurements from around the world. This allows for a robust statistical assessment of forward operator uncertainty and quantification of the relationship between polarimetric radar observables and DSD moments. Comparison of "truth" and forward-simulated vertical profiles of the polarimetric radar variables are shown for bin simulations using a variety of moment combinations. Higher-order moments (especially those optimized for use with the polarimetric radar variables: the 6th and 9th) perform better than the lower-order moments (0th and 3rd) typically predicted by many bulk microphysics schemes

Drop Axis Ratio Distributions in Stratiform and Convective Rain

A fully calibrated low profile 2D video disdrometer (2DVD) has been recording many different rainfall events in Northern Alabama (USA) since June 2007. An earlier publication reported drop shapes and axis ratio distributions determined for some of the events. For one of the cases examined, a noticeable shift in the 3.5 - 3.75 mm drop axis ratio distribution was noted. In this paper, we extend the earlier work by separating the 2DVD measurements into stratiform and convective rain. The separation is made possible by using the minute-by-minute drop size distribution (DSD) measured by the 2DVD. The 1-minute DSDs are fitted to a gamma distribution, and using a simple indexing technique which involves two of the fitted parameters, periods of convective and stratiform rain are separated for a given event. The output of the DSD indexing technique is qualitatively confirmed by comparing with simultaneous time series observations from a co-located UHF profiler which continuously records height profiles of reflectivity, Doppler mean and spectral width, all of which enable the identification of bright-band periods and, furthermore, periods of moderate and deep convection. Excellent consistency is found between the output of the DSD-based separation method and the profiler observations. Next, we utilize the output of DSD index-based separation method to flag the periods of severe convection for a given event. Drop axis ratios during the flagged periods are derived and compared with those during stratiform rain periods. Five cases have been considered. Axis ratio distributions do not show appreciable differences between stratiform and convective periods for four of the cases. The fifth case (the same case as reported earlier) shows a shift in the 3.5 - 3.75 mm drop axis ratios during a prolonged period of convection. The contoured shapes for these drops determined from the 2DVD camera data indicate the possibility of non-axisymmetric oscillations, compared with the contoured images for other events which fit well to our reference drop shapes. For all of above cases, observations from a C-band polarimetric radar - situated 15 km away are examined. The variations between the co-polar radar reflectivity and the differential reflectivity as well as the specific differential phase are compared with the 2DVD data based scattering calculations for the 5 events. The implications will be discussed

Retrieval of lower-order moments of the drop size distribution using CSU-CHILL X-band polarimetric radar: a case study

The lower-order moments of the drop size distribution (DSD) have generally been considered difficult to retrieve accurately from polarimetric radar data because these data are related to higher-order moments. For example, the 4.6th moment is associated with a specific differential phase and the 6th moment with reflectivity and ratio of high-order moments with differential reflectivity. Thus, conventionally, the emphasis has been to estimate rain rate (3.67th moment) or parameters of the exponential or gamma distribution for the DSD. Many double-moment “bulk” microphysical schemes predict the total number concentration (the 0th moment of the DSD, or M0) and the mixing ratio (or equivalently, the 3rd moment M3). Thus, it is difficult to compare the model outputs directly with polarimetric radar observations or, given the model outputs, forward model the radar observables. This article describes the use of double-moment normalization of DSDs and the resulting stable intrinsic shape that can be fitted by the generalized gamma (G-G) distribution. The two reference moments are M3 and M6, which are shown to be retrievable using the X-band radar reflectivity, differential reflectivity, and specific attenuation (from the iterative correction of measured reflectivity Zh using the total Φdp constraint, i.e., the iterative ZPHI method). Along with the climatological shape parameters of the G-G fit to the scaled/normalized DSDs, the lower-order moments are then retrieved more accurately than possible hitherto. The importance of measuring the complete DSD from 0.1 mm onwards is emphasized using, in our case, an optical array probe with 50 µm resolution collocated with a two-dimensional video disdrometer with about 170 µm resolution. This avoids small drop truncation and hence the accurate calculation of lower-order moments. A case study of a complex multi-cell storm which traversed an instrumented site near the CSU-CHILL radar is described for which the moments were retrieved from radar and compared with directly computed moments from the complete spectrum measurements using the aforementioned two disdrometers. Our detailed validation analysis of the radar-retrieved moments showed relative bias of the moments M0 through M2 was 0.9. Both radar measurement and parameterization errors were estimated rigorously. We show that the temporal variation of the radar-retrieved mass-weighted mean diameter with M0 resulted in coherent “time tracks” that can potentially lead to studies of precipitation evolution that have not been possible so far

A Bayesian approach for statistical–physical bulk parameterization of rain microphysics. Part II: Idealized Markov chain Monte Carlo experiments

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is presented using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the additional benefit of rigorously quantified uncertainty of these estimates

Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: a self-consistent method with constraints

Includes bibliographical references.Quantitative use of C-band radar measurements of reflectivity (Zh) and differential reflectivity (Zdr) demands the use of accurate attenuation-correction procedures, especially in convective rain events. With the availability of differential phase measurements (Φdp) with a dual-polarized radar, it is now possible to improve and stabilize attenuation-correction schemes over earlier schemes which did not use Φdp. The recent introduction of constraint-based correction schemes using Φdp constitute an important advance [8], [9]. In this paper, a self-consistent, constraint-based algorithm is proposed and evaluated which extends the previous approaches in several important respects. Radar data collected by the C-POL radar during the South China Sea Monsoon Experiment (SCSMEX) are used to illustrate the correction scheme. The corrected radar data are then compared against disdrometer-based scattering simulations, the disdrometer data being acquired during SCSMEX. A new algorithm is used to retrieve the median volume diameter from the corrected Zh, corrected Zdr, and Kdp radar measurements which is relatively immune to the precise drop axis ratio versus drop diameter relation. Histograms of the radar-retrieved Do compared against Do from disdrometer data are in remarkable good agreement lending further validity to the proposed attenuation-correction scheme, as well as to confidence in the use of C-band radar for the remote measurement of rain microphysics.The work of V. N. Bringi and V. Chandrasekar was supported by the NASA/TRMM Grant NAG5-7717 and -7876