Accurate relations between radar reflectivity factor and rainfall rate for attenuating wavelengths

Vertically pointed wind profiling radars can be used to obtain measurements of the underlying drop size distribution (DSD) for a rain event by means of the Doppler velocity spectrum. Precipitation parameters such as rainfall rate, radar reflectivity factor, liquid water content, mass-weighted mean drop diameter, and median volume drop diameter can then be calculated from the retrieved DSD. The DSD retrieval process is complicated by the presence of atmospheric turbulence, vertical ambient air motion, selection of fall speed relationships, and velocity thresholding. In this note, error analysis is presented to quantify the effect of each of those factors on rainfall rate. The error analysis results are then applied to two precipitation events to better interpret the rainfall-rate retrievals. It was found that a large source of error in rain rate is due to unaccounted-for vertical air motion. For example, in stratiform rain with a rainfall rate of R = 10 mm h−1, a mesoscale downdraft of 0.6 m s−1 can result in a 34% underestimation of the estimated value of R. The fall speed relationship selection and source of air density information both caused negligible errors. Errors due to velocity thresholding become more important in the presence of significant contamination near 0 m s−1, such as ground clutter. If particles having an equivalent volume diameter of 0.8 mm and smaller are rejected, rainfall rate errors from −4% to −10% are possible, although these estimates depend on DSD and rainfall rate.

Precipitation plays a crucial role to the global water and energy cycle that governs the weather, climate, and ecological systems. Thorough understanding and accurate forecasting of precipitation is essential to the affairs of humans. The Tropical Rainfall Measuring Mission (TRMM), launched in 1997, is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. The Precipitation Radar (PR) on board the TRMM satellite is the first space borne instrument, capable of providing high-resolution vertical profile of precipitation on a global scale. TRMM-PR operates at a single frequency of Ku- (13.6 GHz) band. The microphysical retrieval algorithms for TRMM-PR rely on the surface-reference technique (SRT) to estimate path attenuation and correct the measured Ku-band reflectivity. With the attenuation-corrected reflectivities, a modified Hitschfeld-Bordan method [1] is then used to retrieve limited drop size distribution (DSD) information, and the rainfall rate [2]. One disadvantage of single-frequency space borne radar such as TRMM-PR is that it is not easy to retrieve the DSD parameters completely. Therefore, k-Z and Z-R relationships, with their inherent assumptions, are used to estimate rainfall rate which is not sufficient to capture the variability of precipitation and has large uncertainty. Global Precipitation Measurement (GPM) mission is poised to be the next generation observations from space after the TRMM mission. GPM is a science mission with integrated applications goals for advancing the knowledge of the global water/energy cycle variability as well as improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM core satellite will be equipped with a dual-frequency precipitation radar (DPR) operating at Ku- (13.6 GHz) and Ka- (35.5 GHz) band [3]. Taking two independent sets of observation, DPR on aboard the GPM is expected to improve our knowledge of precipitation processes relative to the single-frequency (Ku- band) radar used in TRMM by providing greater dynamic range, more detailed information on microphysics. Two parameters of DSDs can be retrieved from dual-frequency observations and better accuracies in rainfall estimation can be achieved. Theoretically, rainfall rate is a function of rain drop size distribution and rain drop terminal velocity, R=0.67π∗10−3∫ v(D)D3N(D)dD. The most critical component in rainfall rate estimation is the time-space variation of drop size distribution. Le and Chandrasekar (2014) [4] developed a hybrid method to retrieve drop size distribution parameters for GPM-DPR. The hybrid method is a profile-based optimization algorithm with the philosophy to combine the attributes of forward method and linear constraints of DSDs in rain. Two of the gamma distribution parameters [5], Do and Nw, at surface are optimized when the deviation between estimates and observations are minimized. The hybrid method can be used to estimate DSDs at each space and temporal resolution of GPM-DPR observation. In this paper, rainfall rate is calculated using DSDs retrieved through the hybrid method [4] based on assumptions of particle terminal velocity. Data collected by GPM-DPR is capability to cover ±65° latitude of the earth with every 2–4 hours. Thus, a global rainfall map can be generated. In polarimetric radar system, rainfall rate can be estimated through dual-polarized radar parameter such as Zdr [6][7]. Zdr is called differential reflectivity and it is a function of particle characteristics itself. Similar of Zdr to the dual-polarization radar retrieval, there is a parameter called dual-frequency ratio (DFR) that plays an important role in the dual-frequency radar retrievals. DFR is defined as the difference of the radar reflectivity at two frequencies in decibels which carries information of single particle characteristics. In this study, we investigate potential relation between rainfall rate, reflectivity at Ku- band and DFR using theoretical simulation [8] and curve fitting. Figure 1 shows a scattergram of rainfall rate estimation from R(Zh, DFR) versus true rainfall rate. Both Zku and DFR are in linear form in this equation. This provides a direct estimation of rainfall rate without prior knowledge of drop size distribution. Since both reflectivity and dual frequency ratio are intrinsic values, attenuation correction is needed before rain rate can be estimated through R(Zh, DFR) equation. The hybrid method [4] described in previous paragraph could be one of the algorithms to perform attenuation correction. The global rainfall map generated through R(Zh, DFR) approach will be cross-compared with DSD approach described in the previous paragraph, as well as other approaches such as attenuation based rainfall rate. The comprehensive analysis of the three techniques are presented.

The rain dropsize distributions measured by a disdrometer in 21 rain events consisting of 1, 640one-minute dropsize spectra have been analyzed for a tropical station, Ile-Ife (geog. lat. 7.5°N, long 4.5°E) in South-Western Nigeria. Empirical power law relations of the form Y = aRb have been obtained between the rainfall rate R, the radar reflectivity factor Z, liquid water content M, optical extinction σ and the median volume diameter D0 for three types of rainfall. A power law relationship was also obtained between the median volume diameter D0 and the liquid water content M. The variability in a and b with rain parameters, rain events and rain types is discussed. The empirical relations have been compared with existing relations for other parts of the world, for their utilization in radar meteorology and radar engineering.

Comparison of the TRMM Precipitation Radar rainfall estimation with ground-based disdrometer and radar measurements in South Greece

Dual‐polarization radar measurements of rain (using horizontal and vertical polarizations with copolar transmit and receive) are compared with simultaneous measurements using a Joss‐Waldvogel distrometer and a rapid response rain gauge. The radar pulse volume was situated 200 m above the ground‐based instruments, at a range of 8 km. The parameters compared are absolute and differential radar reflectivity factors and rainfall rate. A correlation of 0.95 was found between the radar and distrometer measurements of absolute and differential reflectivity factor, with the radar estimate of absolute reflectivity exceeding the distrometer estimate by 1.6 dB on average, and the distrometer estimate of differential reflectivity exceeding the radar estimate (assuming Pruppacher and Pitter drop shapes) by 0.1 dB on average. The latter difference is small but significant and is possibly attributable to drop canting or oscillation. A new relationship between drop shape and drop size is proposed, reducing the mean difference in differential reflectivity to ±0.02 dB. Radar estimates of rainfall rate, assuming an exponential drop‐size distribution, tend to produce significant overestimates compared with the direct measurements of the two ground‐based devices. This is shown to be largely attributable to departure from a strictly exponential distribution of drop sizes, and a correction factor is derived to compensate for this.

In this study, a practical typhoon effective rainfall nowcasting (TERN) model was developed for use in real‐time forecasting. The TERN model was derived from a data‐driven adaptive network‐based fuzzy inference system (ANFIS). The model inputs include meteorological data and radar reflectivity data. The model simulation process begins with an online typhoon warning issued by the Central Weather Bureau (CWB) of Taiwan. It is then determined whether the typhoon approaches the study area according to the typhoon track predicted by the CWB. When a typhoon hits Taiwan, various data are received from sensor instruments, including the ground precipitation data, typhoon climatological data, and radar reflectivity factor by using Weather Surveillance Radar, 1988, Doppler (WSR‐88D) products. The study site was Shihmen Catchment. A maximum of 10 typhoon events from 2000 to 2010 were collected. Regarding the model construction, the input combinations of the ground precipitations and reflectivity factors over the catchment functioned as optimal input variables. To verify the practicability of the ANFIS‐based TERN model, Typhoon Krosa, which hit Taiwan in 2007, was simulated. The results demonstrated that the proposed methodology of real‐time rainfall forecasts during typhoon warning periods yielded favorable performance levels, reliably predicting results regarding 1 h to 6 h forecasting horizons.

A description is given of the effects of variations in the shape or breadth of the drop size distribution (DSD) on rainfall parameters deduced from a measurement technique which employs the differential reflectivity factor ZDR and the reflectivity factor at horizontal polarization ZH. The mathematical form of the DSD used is a gamma distribution. Justification for such a form is given through consideration of varying DSD shape in nature as implied by the results of empirical analyses of other workers. Theoretical expressions are derived for rainfall rate R, liquid water content W, and median volume diameter D0 in terms of ZDR, ZH, and size distribution dependent factors. The latter calculations assume backscattering cross sections for oblate, nonoscillating raindrops falling in still air with equilibrium shapes. These expressions are used to assess quantitatively the effects of changes in DSD breadth on values of R, W, and D0 deduced from ZDR and ZH. They are also used to show the effects of measurement errors in ZDR and ZH on R, W, and D0. The potential improvement in accuracy which is possible when account is taken of DSD shape variations is shown by simulating a (ZDR, ZH) dual‐measurement method using experimental raindrop size spectra. Methods by which DSD shape variations could be detected through the use of a third remote measurable are discussed.

Semi-empirical characteristics of modified lognormal DSD inputs using rain rate distributions for radio links over the African continent

An analysis of drop size distributions (DSDs) measured in four very different precipitation regimes is presented and is compared with polarimetric radar measurements. The DSDs are measured by a 2D video disdrometer, which is designed to measure drop size, shape, and fall speed with unprecedented accuracy. The observations indicate that significant DSD variability exists not only from one event to the next, but also within each system. Also, despite having vastly different storm structures and maximum rain rates, large raindrops with diameters greater than 5 mm occurred with each system. By comparing the occurrence of large drops with rainfall intensity, the authors find that the largest median diameters are not always associated with the heaviest rainfall, but are sometimes located either in advance of convective cores or, occasionally, in stratiform regions where rainfall rates are relatively low. Disdrometer and polarimetric radar measurements of radar reflectivity Z, differential reflectivity ZDR, specific differential phase KDP, and R(Z) and R(KDP) rain-rate estimators are compared in detail. Overall agreement is good, but it is found that both R(Z) and R(KDP) underestimate rain rate when the DSD is dominated by small drops and overestimate rain rate when the DSD is dominated by large drops. The results indicate that a classification of different rain types (associated with different DSDs) should be an essential part of polarimetric rainfall estimation. Furthermore, observations suggest that ZDR is a key parameter for making such a distinction. Last, the authors compute and compare maximum and average of gamma shape, slope, and intercept parameters for all four precipitation events. Potential measurement errors with the 2D video disdrometer are also discussed.

In radio propagation, modelling of rainfall rate, rain attenuation and drop size distribution is highly location-dependent and thus requires availability of reliable data from various locations. Models and mathematical predictions obtained based on data from one location often prove inadequate when applied to another location with either slightly or radically different rainfall pattern. In this paper, the focus is to develop a new rainfall drop size distribution model for equatorial Africa using disdrometer data obtained in Butare, Rwanda (2°35’53.88”S and 29° 44’ 31.5” E). Rainfall data was classified into annual, monthly and rainfall regimes which are drizzle, widespread, shower and thunderstorm, based on their rainfall rates. The maximum likelihood estimation technique was applied to construct estimates of input Drop Size Distribution (DSD) fit parameters of the developed statistical distribution for rainfall DSD in Butare. The newly obtained distribution was compared to the existing rainfall DSD models, namely, Lognormal, Gamma, Marshall-Palmer and Weibull distributions, and found to be an improvement over the existing ones. The Mie Scattering technique is employed to derive the scattering parameters. Thereafter, the derived scattering parameters with DSD models are used for the estimation of rainfall attenuation for the Central African region.

Abstract. In many countries wind turbines are rapidly growing in numbers as the demand for energy from renewable sources increases. The continued deployment of wind turbines can, however, be problematic for many radar systems, which are easily disturbed by turbines located in the radar line of sight. Wind turbines situated in the vicinity of Doppler weather radars can lead to erroneous precipitation estimates as well as to inaccurate wind and turbulence measurements. This paper presents a quantitative analysis of the impact of a wind farm, located in southeastern Sweden, on measurements from a nearby Doppler weather radar. The analysis is based on 6 years of operational radar data. In order to evaluate the impact of the wind farm, average values of all three spectral moments (the radar reflectivity factor, absolute radial velocity, and spectrum width) of the nearby Doppler weather radar were calculated, using data before and after the construction of the wind farm. It is shown that all spectral moments, from a large area at and downrange from the wind farm, were impacted by the wind turbines. It was also found that data from radar cells far above the wind farm (near 3 km altitude) were affected by the wind farm. It is shown that this in part can be explained by detection by the radar sidelobes and by scattering off increased levels of dust and turbulence. In a detailed analysis, using data from a single radar cell, frequency distributions of all spectral moments were used to study the competition between the weather signal and wind turbine clutter. It is shown that, when weather echoes give rise to higher reflectivity values than those of the wind farm, the negative impact of the wind turbines is greatly reduced for all spectral moments.

A phenomenological relationship between vertical air motion and disdrometer derived A-b coefficients

The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter NW, which normalizes the concentrations, and a scaling diameter Dm, which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between NW and Dm, on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the NW–Dm relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (Dm < 1 mm) and large drops (Dm > 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates.

This paper complements an earlier one that demonstrated the bias in the method-of-moments (MM) estimators frequently used to estimate parameters for drop size distribution (DSD) functions being “fitted” to observed raindrop size distributions. Here the authors consider both the bias and the errors in MM estimators applied to samples from known gamma DSDs (of which the exponential DSD treated in the earlier paper is a special case). The samples were generated using a similar Monte Carlo simulation procedure. The skewness in the sampling distributions of the DSD moments that causes this bias is less pronounced for narrower population DSDs, and therefore the bias problems (and also the errors) diminish as the gamma shape parameter increases. However, the bias still increases with the order of the moments used in the MM procedures; thus it is stronger when higher-order moments (such as the radar reflectivity) are used. The simulation results also show that the errors of the estimates of the DSD parameters are usually larger when higher-order moments are employed. As a consequence, only MM estimators using the lowest-order sample moments that are thought to be well determined should be used. The biases and the errors of most of the MM parameter estimates diminish as the sample size increases; with large samples the moment estimators may become sufficiently accurate for some purposes. Nevertheless, even with some fairly large samples, MM estimators involving high-order moments can yield parameter values that are physically implausible or are incompatible with the input observations. Correlations of the sample moments with the size of the largest drop in a sample (Dmax) are weaker than for the case of sampling from an exponential DSD, as are the correlations of the MM-estimated parameters with Dmax first noted in that case. However, correlations between the estimated parameters remain because functions of the same observations are correlated. These correlations generally strengthen as the sample size increases.

Radar measurements are useful for determining rainfall rates because of their ability to cover large areas. Unfortunately, estimating rainfall rates from radar reflectivity data alone is prone to errors resulting from variations in drop size distributions, precipitation types, and other physics that cannot be represented in a simple, one-dimensional Z–R relationship. However, improving estimates is possible by utilizing additional inputs, thereby increasing the dimensionality of the model. The main purpose of this study is to determine the value of surface observations for improving rainfall-rate estimation. This work carefully designed an artificial neural network to fit a model that would relate radar reflectivity, surface temperature, humidity, pressure, and wind to observed rainfall rates. Observations taken over 13 years from the Oklahoma Mesonet and the KTLX WSR-88D radar near Oklahoma City, Oklahoma, were used for the training dataset. While the artificial neural network underestimated rainfall rates for higher reflectivities, it did have an overall better performance than the best-fit Z–R relation. Most importantly, it is shown that the surface data contributed significant value to an unaugmented radar-based rainfall-rate estimation model.