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

2001 ◽  
Vol 39 (9) ◽  
pp. 1906-1915 ◽  
Author(s):  
V.N. Bringi ◽  
T.D. Keenan ◽  
V. Chandrasekar
Keyword(s):  
Rain Attenuation ◽  
Radar Reflectivity ◽  
Self Consistent ◽  
Consistent Method ◽  
Reflectivity Data ◽  
Differential Reflectivity

scholarly journals Correction of Radar Reflectivity and Differential Reflectivity for Rain Attenuation at X Band. Part I: Theoretical and Empirical Basis

2005 ◽  
Vol 22 (11) ◽  
pp. 1621-1632 ◽  
Author(s):  
S-G. Park ◽  
V. N. Bringi ◽  
V. Chandrasekar ◽  
M. Maki ◽  
K. Iwanami
Keyword(s):  
Rain Attenuation ◽  
Mean Value ◽  
Radar Reflectivity ◽  
The Self ◽  
Band Frequency ◽  
X Band ◽  
Wide Range ◽  
Self Consistent ◽  
Consistent Method ◽  
Differential Reflectivity

Abstract In this two-part paper, a correction for rain attenuation of radar reflectivity (ZH) and differential reflectivity (ZDR) at the X-band wavelength is presented. The correction algorithm that is used is based on the self-consistent method with constraints proposed by Bringi et al., which was originally developed and evaluated for C-band polarimetric radar data. The self-consistent method is modified for the X-band frequency and is applied to radar measurements made with the multiparameter radar at the X-band wavelength (MP-X) operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan. In this paper, characteristic properties of relations among polarimetric variables, such as AH–KDP, ADP–AH, AH–ZH, and ZDR–ZH, that are required in the correction methodology are presented for the frequency of the MP-X radar (9.375 GHz), based on scattering simulations using drop spectra measured by disdrometers at the surface. The scattering simulations were performed under conditions of three different temperatures and three different relations for drop shapes, in order to consider variability of polarimetric variables for these conditions. For the X-band wavelength, the AH–KDP and ADP–AH relations can be assumed to be nearly linear. The coefficient α of the AH–KDP relation varies over a wide range from 0.139 to 0.335 dB (°)−1 with a mean value of 0.254 dB (°)−1. The coefficient γ of the ADP–AH relation varies from 0.114 to 0.174, with a mean value of 0.139. The exponent b of the AH–ZH relation does not depend on drop shapes and is almost constant for a given temperature (about 0.78 at the temperature of 15°C). The ZDR–ZH relation depends primarily on drop shape, and does not vary with temperature.

The Utility of X-Band Polarimetric Radar for Quantitative Estimates of Rainfall Parameters

2005 ◽  
Vol 6 (3) ◽  
pp. 248-262 ◽  
Author(s):  
Sergey Y. Matrosov ◽  
David E. Kingsmill ◽  
Brooks E. Martner ◽  
F. Martin Ralph
Keyword(s):  
Rain Attenuation ◽  
Polarimetric Radar ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Drop Size Distributions ◽  
Russian River ◽  
Phase Shift Data ◽  
Reflectivity Data ◽  
Differential Reflectivity

Abstract The utility of X-band polarimetric radar for quantitative retrievals of rainfall parameters is analyzed using observations collected along the U.S. west coast near the mouth of the Russian River during the Hydrometeorological Testbed project conducted by NOAA’s Environmental Technology and National Severe Storms Laboratories in December 2003 through March 2004. It is demonstrated that the rain attenuation effects in measurements of reflectivity (Ze) and differential attenuation effects in measurements of differential reflectivity (ZDR) can be efficiently corrected in near–real time using differential phase shift data. A scheme for correcting gaseous attenuation effects that are important at longer ranges is introduced. The use of polarimetric rainfall estimators that utilize specific differential phase and differential reflectivity data often provides results that are superior to estimators that use fixed reflectivity-based relations, even if these relations were derived from the ensemble of drop size distributions collected in a given geographical region. Comparisons of polarimetrically derived rainfall accumulations with data from the high-resolution rain gauges located along the coast indicated deviation between radar and gauge estimates of about 25%. The ZDR measurements corrected for differential attenuation were also used to retrieve median raindrop sizes, D0. Because of uncertainties in differential reflectivity measurements, these retrievals are typically performed only for D0 > 0.75 mm. The D0 estimates from an impact disdrometer located at 25 km from the radar were in good agreement with the radar retrievals. The experience of operating the transportable polarimetric X-band radar in the coastal area that does not have good coverage by the National Weather Service radar network showed the value of such radar in filling the gaps in the network coverage. The NOAA X-band radar was effective in covering an area up to 40–50 km in radius offshore adjacent to a region that is prone to flooding during wintertime landfalling Pacific storms.

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

scholarly journals Estimating Rain Rates from Tipping-Bucket Rain Gauge Measurements

2008 ◽  
Vol 25 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Jianxin Wang ◽  
Brad L. Fisher ◽  
David B. Wolff
Keyword(s):  
Rain Rate ◽  
Tropical Rainfall Measuring Mission ◽  
Rain Gauge ◽  
Radar Reflectivity ◽  
Time Shift ◽  
Estimation Errors ◽  
Rate Estimation ◽  
Reflectivity Data ◽  
Rain Rates ◽  
Event Definition

Abstract This paper describes the cubic spline–based operational system for the generation of the Tropical Rainfall Measuring Mission (TRMM) 1-min rain-rate product 2A-56 from tipping-bucket (TB) gauge measurements. A simulated TB gauge from a Joss–Waldvogel disdrometer is employed to evaluate the errors of the TB rain-rate estimation. These errors are very sensitive to the time scale of rain rates. One-minute rain rates suffer substantial errors, especially at low rain rates. When 1-min rain rates are averaged over 4–7-min intervals or longer, the errors dramatically reduce. Estimated lower rain rates are sensitive to the event definition whereas the higher rates are not. The median relative absolute errors are about 22% and 32% for 1-min rain rates higher and lower than 3 mm h−1, respectively. These errors decrease to 5% and 14% when rain rates are used at the 7-min scale. The radar reflectivity–rain-rate distributions drawn from the large amount of 7-min rain rates and radar reflectivity data are mostly insensitive to the event definition. The time shift due to inaccurate clocks can also cause rain-rate estimation errors, which increase with the shifted time length. Finally, some recommendations are proposed for possible improvements of rainfall measurements and rain-rate estimations.

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