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- Author or Editor: Qing Cao x
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Abstract
There have been debates and differences of opinion over the validity of using drop size distribution (DSD) models to characterize precipitation microphysics and to retrieve DSD parameters from multiparameter radar measurements. In this paper, simulated and observed rain DSDs are used to evaluate moment estimators. Seven estimators for gamma DSD parameters are evaluated in terms of the biases and fractional errors of five integral parameters: radar reflectivity (ZH ), differential reflectivity (Z DR), rainfall rate (R), mean volume diameter (Dm ), and total number concentration (NT ). It is shown that middle-moment estimators such as M234 (using the second-third-fourth moments) produce smaller errors than lower- and higher-moment estimators if the DSD follows the gamma distribution. However, if there are model errors, the performance of M234 degrades. Even though the DSD parameters can be biased in moment estimators, integral parameters are usually not. Maximum likelihood (ML) and L-moment (LM) estimators perform similarly to low-moment estimators such as M012. They are sensitive to both model error and the measurement errors of the low ends of DSDs. The overall differences among M234, M246, and M346 are not substantial for the five evaluated parameters. This study also shows that the discrepancy between the radar and disdrometer observations cannot be reduced by using these estimators. In addition, the previously found constrained-gamma model is shown not to be exclusively determined by error effects. Rather, it is equivalent to the mean function of normalized DSDs derived through Testud’s approach, and linked to precipitation microphysics.
Abstract
There have been debates and differences of opinion over the validity of using drop size distribution (DSD) models to characterize precipitation microphysics and to retrieve DSD parameters from multiparameter radar measurements. In this paper, simulated and observed rain DSDs are used to evaluate moment estimators. Seven estimators for gamma DSD parameters are evaluated in terms of the biases and fractional errors of five integral parameters: radar reflectivity (ZH ), differential reflectivity (Z DR), rainfall rate (R), mean volume diameter (Dm ), and total number concentration (NT ). It is shown that middle-moment estimators such as M234 (using the second-third-fourth moments) produce smaller errors than lower- and higher-moment estimators if the DSD follows the gamma distribution. However, if there are model errors, the performance of M234 degrades. Even though the DSD parameters can be biased in moment estimators, integral parameters are usually not. Maximum likelihood (ML) and L-moment (LM) estimators perform similarly to low-moment estimators such as M012. They are sensitive to both model error and the measurement errors of the low ends of DSDs. The overall differences among M234, M246, and M346 are not substantial for the five evaluated parameters. This study also shows that the discrepancy between the radar and disdrometer observations cannot be reduced by using these estimators. In addition, the previously found constrained-gamma model is shown not to be exclusively determined by error effects. Rather, it is equivalent to the mean function of normalized DSDs derived through Testud’s approach, and linked to precipitation microphysics.
Abstract
This study presents a two-dimensional variational approach to retrieving raindrop size distributions (DSDs) from polarimetric radar data in the presence of attenuation. A two-parameter DSD model, the constrained-gamma model, is used to represent rain DSDs. Three polarimetric radar measurements—reflectivity ZH , differential reflectivity Z DR, and specific differential phase K DP—are optimally used to correct for the attenuation and retrieve DSDs by taking into account measurement error effects. Retrieval results with simulated data demonstrate that the proposed algorithm performs well. Applications to real data collected by the X-band Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) radars and the C-band University of Oklahoma–Polarimetric Radar for Innovations in Meteorology and Engineering (OU-PRIME) also demonstrate the efficacy of this approach.
Abstract
This study presents a two-dimensional variational approach to retrieving raindrop size distributions (DSDs) from polarimetric radar data in the presence of attenuation. A two-parameter DSD model, the constrained-gamma model, is used to represent rain DSDs. Three polarimetric radar measurements—reflectivity ZH , differential reflectivity Z DR, and specific differential phase K DP—are optimally used to correct for the attenuation and retrieve DSDs by taking into account measurement error effects. Retrieval results with simulated data demonstrate that the proposed algorithm performs well. Applications to real data collected by the X-band Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) radars and the C-band University of Oklahoma–Polarimetric Radar for Innovations in Meteorology and Engineering (OU-PRIME) also demonstrate the efficacy of this approach.
Abstract
The exponential distribution N(D) = N 0 exp(−ΛD) with a fixed intercept parameter N 0 is most commonly used to represent raindrop size distribution (DSD) in rainfall estimation and in single-moment bulk microphysics parameterization schemes. Disdrometer observations show that the intercept parameter is far from constant and systematically depends on the rain type and intensity. In this study, a diagnostic relation of N 0 as a function of rainwater content W is derived based on two-dimensional video disdrometer (2DVD) measurements. The data reveal a clear correlation between N 0 and W in which N 0 increases as W increases. To minimize the effects of sampling error, a relation between two middle moments is used to derive the N 0–W relation. This diagnostic relation has the potential to improve rainfall estimation and bulk microphysics parameterizations. A parameterization scheme for warm rain processes based on the diagnostic N 0 DSD model is formulated and presented. The diagnostic N 0-based parameterization scheme yields less evaporation and accretion for stratiform rain than that using fixed N 0.
Abstract
The exponential distribution N(D) = N 0 exp(−ΛD) with a fixed intercept parameter N 0 is most commonly used to represent raindrop size distribution (DSD) in rainfall estimation and in single-moment bulk microphysics parameterization schemes. Disdrometer observations show that the intercept parameter is far from constant and systematically depends on the rain type and intensity. In this study, a diagnostic relation of N 0 as a function of rainwater content W is derived based on two-dimensional video disdrometer (2DVD) measurements. The data reveal a clear correlation between N 0 and W in which N 0 increases as W increases. To minimize the effects of sampling error, a relation between two middle moments is used to derive the N 0–W relation. This diagnostic relation has the potential to improve rainfall estimation and bulk microphysics parameterizations. A parameterization scheme for warm rain processes based on the diagnostic N 0 DSD model is formulated and presented. The diagnostic N 0-based parameterization scheme yields less evaporation and accretion for stratiform rain than that using fixed N 0.
Abstract
This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization ZH and differential reflectivity Z DR. With this approach, the authors apply a constrained-gamma model with an updated constraining relation to retrieve DSD parameters. Long-term DSD measurements made in central Oklahoma by the two-dimensional video disdrometer (2DVD) are first used to construct a prior probability density function (PDF) of DSD parameters, which are estimated using truncated gamma fits to the second, fourth, and sixth moments of the distributions. The forward models of ZH and Z DR are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of ZH and Z DR is assumed to be a bivariate normal function with appropriate standard deviations. The Bayesian algorithm has a good performance according to the evaluation with simulated ZH and Z DR. The algorithm is also tested on S-band radar data for a mesoscale convective system that passed over central Oklahoma on 13 May 2005. Retrievals of rainfall rates and 1-h rain accumulations are compared with in situ measurements from one 2DVD and six Oklahoma Mesonet rain gauges, located at distances of 28–54 km from Norman, Oklahoma. Results show that the rain estimates from the retrieval agree well with the in situ measurements, demonstrating the validity of the Bayesian retrieval algorithm.
Abstract
This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization ZH and differential reflectivity Z DR. With this approach, the authors apply a constrained-gamma model with an updated constraining relation to retrieve DSD parameters. Long-term DSD measurements made in central Oklahoma by the two-dimensional video disdrometer (2DVD) are first used to construct a prior probability density function (PDF) of DSD parameters, which are estimated using truncated gamma fits to the second, fourth, and sixth moments of the distributions. The forward models of ZH and Z DR are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of ZH and Z DR is assumed to be a bivariate normal function with appropriate standard deviations. The Bayesian algorithm has a good performance according to the evaluation with simulated ZH and Z DR. The algorithm is also tested on S-band radar data for a mesoscale convective system that passed over central Oklahoma on 13 May 2005. Retrievals of rainfall rates and 1-h rain accumulations are compared with in situ measurements from one 2DVD and six Oklahoma Mesonet rain gauges, located at distances of 28–54 km from Norman, Oklahoma. Results show that the rain estimates from the retrieval agree well with the in situ measurements, demonstrating the validity of the Bayesian retrieval algorithm.
Abstract
To obtain internal tidal currents and full-depth tidal currents from limited mooring observations, a method is put forward combining harmonic analysis and modal decomposition. Harmonic analysis is used to separate tidal currents of different constituents, and modal decomposition is used to calculate full-depth tidal currents of each mode. By adding the barotropic tidal currents to all the baroclinic ones, the full-depth tidal currents of each constituent are reconstructed. The feasibility and accuracy of the proposed method is tested by twin experiments. Then, the method is used to extract tidal currents of each mode and to reconstruct full-depth tidal currents for M2 and K1 from a 3-month-long time series of acoustic Doppler current data observed at a station in the northern South China Sea. Results indicate that the total kinetic energy (KE) of M2 is 25% larger than that of K1. For M2, the first baroclinic mode is the dominant one, followed by the barotropic one, and the sum of these modes accounts for more than 90% of the total M2 KE. Tidal constituent K1 is dominated by the barotropic mode, which accounts for more than 90% of the total K1 KE.
Abstract
To obtain internal tidal currents and full-depth tidal currents from limited mooring observations, a method is put forward combining harmonic analysis and modal decomposition. Harmonic analysis is used to separate tidal currents of different constituents, and modal decomposition is used to calculate full-depth tidal currents of each mode. By adding the barotropic tidal currents to all the baroclinic ones, the full-depth tidal currents of each constituent are reconstructed. The feasibility and accuracy of the proposed method is tested by twin experiments. Then, the method is used to extract tidal currents of each mode and to reconstruct full-depth tidal currents for M2 and K1 from a 3-month-long time series of acoustic Doppler current data observed at a station in the northern South China Sea. Results indicate that the total kinetic energy (KE) of M2 is 25% larger than that of K1. For M2, the first baroclinic mode is the dominant one, followed by the barotropic one, and the sum of these modes accounts for more than 90% of the total M2 KE. Tidal constituent K1 is dominated by the barotropic mode, which accounts for more than 90% of the total K1 KE.
Abstract
To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.
Abstract
To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.
On the Equilibration of Numerical Simulation of Internal Tide: A Case Study around the Hawaiian RidgeAbstract
To investigate the equilibration of numerical simulation (ENS) of internal tide, a three-dimensional isopycnic coordinate internal tide model is applied to simulate the M2 internal tide on idealized topography and around the Hawaiian Ridge. An idealized experiment is carried out on a Gaussian topography, and the temporal variations of the baroclinic velocity and the baroclinic energy flux are analyzed, then ENS is studied, and two criteria are presented. Moreover, the impacts of four parameters [horizontal and vertical eddy viscosity coefficients, bottom friction coefficient, and damping coefficient (to parameterize the nonhydrostatic processes in the model)] on ENS during numerical simulations, the baroclinic velocity, the baroclinic tidal energy, and the baroclinic energy flux are investigated. It appears that ENS for the M2 internal tide is more sensitive to the horizontal eddy viscosity coefficient and the damping coefficient. To further examine the criteria of ENS, a numerical experiment is carried out to simulate the M2 internal tidal constituent near the Hawaiian Ridge. The simulated surface tide shows good agreement with results from the Oregon State University tidal model and TOPEX/Poseidon (T/P) observations. The simulation results indicate that a 50 M2 tidal period (25.88 days) run is capable of ensuring ENS for the M2 internal tide in this case. In short, this paper presents a method and two criteria for examining ENS for internal tides for modelers.
Abstract
To investigate the equilibration of numerical simulation (ENS) of internal tide, a three-dimensional isopycnic coordinate internal tide model is applied to simulate the M2 internal tide on idealized topography and around the Hawaiian Ridge. An idealized experiment is carried out on a Gaussian topography, and the temporal variations of the baroclinic velocity and the baroclinic energy flux are analyzed, then ENS is studied, and two criteria are presented. Moreover, the impacts of four parameters [horizontal and vertical eddy viscosity coefficients, bottom friction coefficient, and damping coefficient (to parameterize the nonhydrostatic processes in the model)] on ENS during numerical simulations, the baroclinic velocity, the baroclinic tidal energy, and the baroclinic energy flux are investigated. It appears that ENS for the M2 internal tide is more sensitive to the horizontal eddy viscosity coefficient and the damping coefficient. To further examine the criteria of ENS, a numerical experiment is carried out to simulate the M2 internal tidal constituent near the Hawaiian Ridge. The simulated surface tide shows good agreement with results from the Oregon State University tidal model and TOPEX/Poseidon (T/P) observations. The simulation results indicate that a 50 M2 tidal period (25.88 days) run is capable of ensuring ENS for the M2 internal tide in this case. In short, this paper presents a method and two criteria for examining ENS for internal tides for modelers.
Abstract
Mesoscale convective systems (MCSs) contain both regions of convective and stratiform precipitation, and a bright band (BB) is often found in the stratiform region. Inflated reflectivity intensities in the BB often cause positive biases in radar quantitative precipitation estimation (QPE). A vertical profile of reflectivity (VPR) correction is necessary to reduce such biases. However, existing VPR correction methods for ground-based radars often perform poorly for MCSs owing to their coarse resolution and poor coverage in the vertical direction, especially at far ranges. Spaceborne radars such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), on the other hand, can provide high resolution VPRs. The current study explores a new approach of incorporating the TRMM VPRs into the VPR correction for the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar QPE. High-resolution VPRs derived from the Ku-band TRMM PR data are converted into equivalent S-band VPRs using an empirical technique. The equivalent S-band TRMM VPRs are resampled according to the WSR-88D beam resolution, and the resampled (apparent) VPRs are then used to correct for BB effects in the WSR-88D QPE when the ground radar VPR cannot accurately capture the BB bottom. The new scheme was tested on six MCSs from different regions in the United States and it was shown to provide effective mitigation of the radar QPE errors due to BB contamination.
Abstract
Mesoscale convective systems (MCSs) contain both regions of convective and stratiform precipitation, and a bright band (BB) is often found in the stratiform region. Inflated reflectivity intensities in the BB often cause positive biases in radar quantitative precipitation estimation (QPE). A vertical profile of reflectivity (VPR) correction is necessary to reduce such biases. However, existing VPR correction methods for ground-based radars often perform poorly for MCSs owing to their coarse resolution and poor coverage in the vertical direction, especially at far ranges. Spaceborne radars such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), on the other hand, can provide high resolution VPRs. The current study explores a new approach of incorporating the TRMM VPRs into the VPR correction for the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar QPE. High-resolution VPRs derived from the Ku-band TRMM PR data are converted into equivalent S-band VPRs using an empirical technique. The equivalent S-band TRMM VPRs are resampled according to the WSR-88D beam resolution, and the resampled (apparent) VPRs are then used to correct for BB effects in the WSR-88D QPE when the ground radar VPR cannot accurately capture the BB bottom. The new scheme was tested on six MCSs from different regions in the United States and it was shown to provide effective mitigation of the radar QPE errors due to BB contamination.
Abstract
Complex terrain poses challenges to the ground-based radar quantitative precipitation estimation (QPE) because of partial or total blockages of radar beams in the lower tilts. Reflectivities from higher tilts are often used in the QPE under these circumstances and biases are then introduced due to vertical variations of reflectivity. The spaceborne Precipitation Radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite can provide good measurements of the vertical structure of reflectivity even in complex terrain, but the poor temporal resolution of TRMM PR data limits their usefulness in real-time QPE. This study proposes a novel vertical profile of reflectivity (VPR) correction approach to enhance ground radar–based QPEs in complex terrain by integrating the spaceborne radar observations. In the current study, climatological relationships between VPRs from an S-band Doppler weather radar located on the east coast of Taiwan and the TRMM PR are developed using an artificial neural network (ANN). When a lower tilt of the ground radar is blocked, higher-tilt reflectivity data are corrected with the trained ANN and then applied in the rainfall estimation. The proposed algorithm was evaluated with three typhoon precipitation events, and its preliminary performance was evaluated and analyzed.
Abstract
Complex terrain poses challenges to the ground-based radar quantitative precipitation estimation (QPE) because of partial or total blockages of radar beams in the lower tilts. Reflectivities from higher tilts are often used in the QPE under these circumstances and biases are then introduced due to vertical variations of reflectivity. The spaceborne Precipitation Radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite can provide good measurements of the vertical structure of reflectivity even in complex terrain, but the poor temporal resolution of TRMM PR data limits their usefulness in real-time QPE. This study proposes a novel vertical profile of reflectivity (VPR) correction approach to enhance ground radar–based QPEs in complex terrain by integrating the spaceborne radar observations. In the current study, climatological relationships between VPRs from an S-band Doppler weather radar located on the east coast of Taiwan and the TRMM PR are developed using an artificial neural network (ANN). When a lower tilt of the ground radar is blocked, higher-tilt reflectivity data are corrected with the trained ANN and then applied in the rainfall estimation. The proposed algorithm was evaluated with three typhoon precipitation events, and its preliminary performance was evaluated and analyzed.
Abstract
The study of precipitation in different phases is important to understanding the physical processes that occur in storms, as well as to improving their representation in numerical weather prediction models. A 2D video disdrometer was deployed about 30 km from a polarimetric weather radar in Norman, Oklahoma, (KOUN) to observe winter precipitation events during the 2006/07 winter season. These events contained periods of rain, snow, and mixed-phase precipitation. Five-minute particle size distributions were generated from the disdrometer data and fitted to a gamma distribution; polarimetric radar variables were also calculated for comparison with KOUN data. It is found that snow density adjustment improves the comparison substantially, indicating the importance of accounting for the density variability in representing model microphysics.
Abstract
The study of precipitation in different phases is important to understanding the physical processes that occur in storms, as well as to improving their representation in numerical weather prediction models. A 2D video disdrometer was deployed about 30 km from a polarimetric weather radar in Norman, Oklahoma, (KOUN) to observe winter precipitation events during the 2006/07 winter season. These events contained periods of rain, snow, and mixed-phase precipitation. Five-minute particle size distributions were generated from the disdrometer data and fitted to a gamma distribution; polarimetric radar variables were also calculated for comparison with KOUN data. It is found that snow density adjustment improves the comparison substantially, indicating the importance of accounting for the density variability in representing model microphysics.
