• Anagnostou, E. N., , Anagnostou M. N. , , Krajewski W. F. , , Kruger A. , , and Miriovsky B. J. , 2004: High-resolution rainfall estimation from X-band polarimetric radar measurements. J. Hydrometeor., 5 , 110128.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andsager, K., , Beard K. V. , , and Laird N. F. , 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56 , 26732683.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beard, K. V., , and Chuang C. , 1987: A new model for the equilibrium shape of raindrops. J. Atmos. Sci., 44 , 15091524.

  • Bringi, V. N., , and Chandrasekar V. , 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Chandrasekar V. , , Balakrishnan N. , , and Zrnić D. S. , 1990: An examination of propagation effects in rainfall on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol., 7 , 829840.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Huang G. J. , , Chandrasekar V. , , and Gorgucci E. , 2002: A methodology for estimating the parameters of a gamma raindrop size distribution model from polarimetric radar data: Application to a squall-line event from the TRMM/Brazil campaign. J. Atmos. Oceanic Technol., 19 , 633645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Chandrasekar V. , , Hubbert J. , , Gorgucci E. , , Randeu W. L. , , and Schoenhuber M. , 2003: Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci., 60 , 354365.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., , Gorgucci E. , , and Baldini L. , 2002: Evaluation of polarimetric radar rainfall algorithms at X-band. Proc. ERAD 2002, Delft, Netherlands, ERAD, 277–281.

  • Chandrasekar, V., , Fukatsu H. , , and Mubarak K. , 2003: Global mapping of attenuation at Ku- and Ka-band. IEEE Trans. Geosci. Remote Sens., 41 , 21662176.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., , Gorgucci E. , , Lim S. , , and Baldini L. , 2004a: Simulation of X-band radar observation of precipitation from S-band measurements. Proc. IGARSS 2004, Anchorage, AK, IEEE, 2752–2755.

  • Chandrasekar, V., , Lim S. , , Bharadwaj N. , , Li W. , , McLaughlin D. , , Bringi V. N. , , and Gorgucci E. , 2004b: Principles of networked weather radar operation at attenuating frequencies. Proc. ERAD 2004, Gotland, Sweden, ERAD, 109–114.

  • Delrieu, G., , Caoudal S. , , and Creutin J. D. , 1997: Feasibility of using mountain return for the correction of ground-based X-band weather radar. J. Atmos. Oceanic Technol., 14 , 368385.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delrieu, G., , Andrieu H. , , and Creutin J. D. , 2000: Quantification of path-integrated attenuation for X- and C-band weather radar systems operating in Mediterranean heavy rainfall. J. Appl. Meteor., 39 , 840850.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., , Scarchilli G. , , and Chandrasekar V. , 2000: Practical aspects of radar rainfall estimation using specific differential propagation phase. J. Appl. Meteor., 39 , 945955.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., , Chandrasekar V. , , Bringi V. N. , , and Scarchilli G. , 2002: Estimation of raindrop size distribution parameters from polarimetric radar measurements. J. Atmos. Sci., 59 , 23732384.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., , Kingsmill D. E. , , Martner B. E. , , and Ralph F. M. , 2005: The utility of X-band polarimetric radar for quantitative estimates of rainfall parameters. J. Hydrometeor., 6 , 248262.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, S. G., , Bringi V. N. , , Chandrasekar V. , , Maki M. , , and Iwanami K. , 2005a: Correction of radar reflectivity and differential reflectivity for rain attenuation at X-band. Part I: Theoretical and empirical basis. J. Atmos. Oceanic Technol., 22 , 16211632.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, S. G., , Maki M. , , Iwanami K. , , Bringi V. N. , , and Chandrasekar V. , 2005b: Correction of radar reflectivity and differential reflectivity for rain attenuation at X-band. Part II: Evaluation and application. J. Atmos. Oceanic Technol., 22 , 16331655.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli, G., , Gorgucci E. , , Chandrasekar V. , , and Dobaie A. , 1996: Self-consistency of polarization diversity measurement of rainfall. IEEE Trans. Geosci. Remote Sens., 34 , 2226.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sekhon, R. S., , and Srivastava R. C. , 1971: Doppler radar observations of drop size distributions in a thunderstorm. J. Atmos. Sci., 28 , 983994.

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  • Seliga, T. A., , and Bringi V. N. , 1976: Potential use of the radar reflectivity at orthogonal polarizations for measuring precipitation. J. Appl. Meteor., 15 , 6976.

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  • Testud, J., , Amayenc P. , , and Marzoug M. , 2000: The rain profiling algorithm applied to polarimetric weather radar. J. Atmos. Oceanic Technol., 17 , 322356.

    • Search Google Scholar
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  • Testud, J., , Oury S. , , Black R. A. , , Amayenc P. , , and Dou X. , 2001: The concept of “normalized” distributions to describe raindrop spectra: A tool for cloud physic and cloud remote sensing. J. Appl. Meteor., 40 , 11181140.

    • Crossref
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  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop-size distribution. J. Climate Appl. Meteor., 22 , 17641775.

    • Crossref
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  • Willis, P. T., 1984: Functional fits to some observed drop size distributions and parameterization of rain. J. Atmos. Sci., 41 , 16481661.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    Scatterplot of (a) reflectivity and (b) differential reflectivity at S and X band for widely varying drop size distributions.

  • View in gallery

    Scatterplot of (a) intrinsic reflectivity obtained by theoretical simulation using widely varying DSD vs simulated reflectivity by (11) and (b) intrinsic specific attenuation vs simulated specific attenuation by (12) for X band.

  • View in gallery

    (a) Reflectivity at S band, (b) differential reflectivity at S band, (c) simulated reflectivity at X band by (11), (d) simulated specific attenuation at X band by (12), and (e) attenuated reflectivity at X band by (13); “x” indicates the X-band radar location.

  • View in gallery

    The block diagram of the DSD sampling method.

  • View in gallery

    (a) Range profile of reflectivity and differential reflectivity from S-band polarimetric radar collected over central Florida; (b) simulated range profile of reflectivity at X band (solid line) and the corresponding attenuated profile (dashed line); (c) simulated range profile of differential reflectivity at X band (solid line) and the corresponding attenuated profile (dashed line); (d) differential phase profile at S band (solid line) and the corresponding profile at X band (dashed line).

  • View in gallery

    (a) Reflectivity, (b) differential reflectivity at S band, (c) retrieved median volume diameter, and (d) retrieved normalized intercept parameter.

  • View in gallery

    (a) Simulated reflectivity, (b) simulated differential reflectivity, (c) simulated specific attenuation, (d) simulated differential attenuation corresponding to Fig. 6, (e) attenuated reflectivity, (f) attenuated differential reflectivity obtained by (13), (g) simulated specific differential phase, and (h) differential propagation phase obtained by (7) at X band.

  • View in gallery

    (Continued)

  • View in gallery

    (a) Range profile of reflectivity at S band (solid line) and simulated reflectivity at X band using proposed methodologies; (b) corresponding attenuated reflectivity at X band using proposed methodologies; (c) range profile of differential reflectivity at S band (solid line) and simulated differential reflectivity at X band; (d) attenuated differential reflectivity at X band; and (e) differential phase profile at S band (solid line) and the corresponding differential phase profile at X band.

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Simulation of X-Band Rainfall Observations from S-Band Radar Data

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  • 1 Colorado State University, Fort Collins, Colorado
  • 2 Istituto di Scienze dell’Atmosfera e del Clima (CNR), Rome, Italy
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Abstract

To design X-band radar systems as well as evaluate algorithm development, it is useful to have simultaneous X-band observation with and without the impact of path attenuation. One way to develop that dataset is through theoretical models. This paper presents a methodology to generate realistic range profiles of radar variables at attenuating frequencies, such as X band, for rain medium. Fundamental microphysical properties of precipitation, namely, size and shape distribution information, are used to generate realistic profiles of X band starting with S-band observation. Conditioning the simulation from S band maintains the natural distribution of rainfall microphysical parameters. Data from the Colorado State University’s University of Chicago–Illinois State Water Survey (CHILL) radar and the National Center for Atmospheric Research S-band dual-polarization Doppler radar (S-POL) are used to simulate X-band radar variables. Three procedures to simulate the radar variables and sample applications are presented.

Corresponding author address: S. Lim, Colorado State University, 1373 Campus Delivery, Fort Collins, CO 80523. Email: sang-hun.lim@colostate.edu

Abstract

To design X-band radar systems as well as evaluate algorithm development, it is useful to have simultaneous X-band observation with and without the impact of path attenuation. One way to develop that dataset is through theoretical models. This paper presents a methodology to generate realistic range profiles of radar variables at attenuating frequencies, such as X band, for rain medium. Fundamental microphysical properties of precipitation, namely, size and shape distribution information, are used to generate realistic profiles of X band starting with S-band observation. Conditioning the simulation from S band maintains the natural distribution of rainfall microphysical parameters. Data from the Colorado State University’s University of Chicago–Illinois State Water Survey (CHILL) radar and the National Center for Atmospheric Research S-band dual-polarization Doppler radar (S-POL) are used to simulate X-band radar variables. Three procedures to simulate the radar variables and sample applications are presented.

Corresponding author address: S. Lim, Colorado State University, 1373 Campus Delivery, Fort Collins, CO 80523. Email: sang-hun.lim@colostate.edu

1. Introduction

Monitoring of precipitation using high-frequency radar systems such as X band is becoming increasingly popular because of their lower cost compared to their counterpart at S band (Chandrasekar et al. 2004b; Park et al. 2005a). For urban or mountain hydrological applications, the X-band radar systems have been implemented in Europe and Japan (Delrieu et al. 1997; Testud et al. 2000; Park et al. 2005b). Meteorological radar systems operating at S-band frequencies are mostly not affected by attenuation resulting from precipitation, except in some regions of wet hail. The S-band radar systems with narrow beams (say 1° beamwidth) are typically expensive, with large antennas and high-power transmitters to cover large areas. Recently, networks of meteorological radar systems at higher frequencies such as X band have been pursued, especially for low-cost and targeted applications, such as coverage over a city or a small basin. However, at higher frequencies, the impact of attenuation resulting from precipitation needs to be resolved for successful implementation. Chandrasekar et al. (2002, 2004a) studied the relationship between the intrinsic radar variables of S and X bands in rain medium. Note that “intrinsic” refers to the radar variables that are nonattenuated and obtained by theoretical simulation. Extensive dual-polarization observations of precipitation at S band are available today from research radar facilities such as the Colorado State University’s (CSU’s) University of Chicago–Illinois State Water Survey (CHILL) radar and the National Center for Atmospheric Research (NCAR) S-band dual-polarized Doppler radar (S-POL).

This paper presents three methodologies to simulate X-band radar variables in rain from S-band data. These methodologies can simulate the realistic dual-polarization radar variables maintaining the natural spatial structure of the rainfall event. The simulated dataset with and without attenuation effect can be used effectively in the design of the X-band radar system as well as in the evaluation of algorithm development such as attenuation correction. The paper is organized as follows. In section 2 the theoretical background of the rain model is described, whereas the methods that simulate X-band variables from S-band data are discussed in section 3. The important results of this paper are summarized in section 4.

2. Rain model and polarimetric radar observables

Microphysical properties of rain medium can be described by the drop size distribution (DSD). Natural variation of drop size distribution can be approximated by a gamma model as (Ulbrich 1983)
i1520-0426-23-9-1195-e1
where N(D) is the number of the raindrops per unit volume per unit size interval, D (mm) is the volume equivalent spherical diameter, and N0 (intercept parameter, mm−1−μ m−3), Λ (slope parameter, mm−1), and μ (shape parameter) are the parameters of the gamma distribution. One of disadvantage of this gamma model is that the unit of N0 depends on μ. To study the shape of DSD with widely varying rainfall rates, gamma distribution can be expressed in a normalized form as (Sekhon and Srivastava 1971; Willis 1984; Testud et al. 2001; Bringi and Chandrasekar 2001)
i1520-0426-23-9-1195-e2
i1520-0426-23-9-1195-e3
where D0 is the median volume diameter, μ is a measure of the shape of the DSD, and Nw (mm−1 m−3) is the normalized intercept parameter of an equivalent exponential distribution with the same water content and D0.
Radar variables in rain medium can be expressed in terms of DSD. Reflectivity factors Zh,υ at horizontal (h) and vertical (υ) polarizations can be described as
i1520-0426-23-9-1195-e4
where λ is the wavelength of the radar, σh,υ represents the radar cross sections at horizontal and vertical polarizations, and Kw is the dielectric factor of water defined as Kw = (ɛr − 1)/(ɛr + 2), where ɛr is the complex dielectric constant of water. Differential reflectivity can be expressed as the ratio of reflectivity factors at horizontal and vertical polarizations (Seliga and Bringi 1976),
i1520-0426-23-9-1195-e5
Specific differential phase is proportional to the real part of the difference in the complex forward-scatter amplitudes f at horizontal and vertical polarizations. It can be defined as
i1520-0426-23-9-1195-e6
The two-way differential propagation phase ϕdp is defined as
i1520-0426-23-9-1195-e7
The measured differential propagation phase can be defined as
i1520-0426-23-9-1195-e8
where Δ is the backscattering propagation phase. Specific attenuation at two polarization states and differential attenuation are related to DSD as
i1520-0426-23-9-1195-e9
Two-way cumulative attenuation Ah and differential attenuation Adp can be expressed as
i1520-0426-23-9-1195-e10
where s is range for integration.

3. Relationship between X- and S-band radar variables

Three different methodologies for simulating Xband radar variables from S-band data will be discussed in the following, namely, the empirical conversion method, DSD sampling method, and DSD inversion method.

a. Empirical conversion method

The intrinsic measurements of Zh, Zdr exhibit a nearly one-to-one relation between S and X bands. This principle was used by Chandrasekar et al. (2003) to characterize spaceborne radar observations at multiple frequencies. Figure 1 shows a scatterplot of Zh and Zdr at S and X bands for widely varying drop size distributions (0.5 ≤ D0 ≤ 3.5 mm, 3 ≤ log10Nw ≤ 5, and −1 < μ ≤ 4 for R < 300 mm h−1 and Zh < 55 dBZ). The data were obtained by scattering simulation using the shape model proposed by Bringi et al. (2003), which combines the Andsager et al. (1999) fit and the Beard and Chuang (1987) model at a temperature of 10°C (henceforth referred as the ABC model). Under Rayleigh scattering assumptions, reflectivity will not change with frequency. However, at X band Rayleigh scattering assumptions are not strictly valid as shown in Fig. 1a. The comparison of Zdr in Fig. 1b shows the non-Rayleigh scattering very well.

Under the assumption that S-band radar observations are nonattenuated, the empirical conversion method synthesizes the simulated X-band radar variables from high-resolution S-band dual-polarization measurements using the relationship between S- and X-band radar variables, which is derived from scattering simulation of drop size distribution. The relationship can be expressed as
i1520-0426-23-9-1195-e11
and
i1520-0426-23-9-1195-e12
where subscripts X and S indicate simulated radar variables at X band and measured (assumed to be nonattenuated) radar measurements at S band, respectively. The relationship between X- and S-band radar data can be obtained by curve fitting using the data that come from the theoretical simulation using DSD parameters. This method is simple and reliable for reflectivity and differential reflectivity simulation. Figure 2a shows the scatterplot of intrinsic reflectivity obtained by theoretical simulation using widely varying DSD parameters versus simulated reflectivity by (11), whereas the scatterplot of intrinsic specific attenuation versus simulated specific attenuation by (12) is shown in Fig. 2b.
The attenuated reflectivity Zh,X and attenuated differential reflectivity Zdr,X with attenuation effects resulting from precipitation can be generated with respect to radar variables simulated by (11)(12) as
i1520-0426-23-9-1195-e13
where r0 is the first range that has precipitation echo, and r is the range of echo (r0 < r). Note that the attenuation impact by clouds and gases are not considered in (13), because attenuation from clouds and gases are negligible compared to attenuation resulting from rain. An example for simulation of attenuated X-band reflectivity is shown in Fig. 3. Figures 3a and 3b show S-band radar observations, whereas Figs. 3c and 3d show the simulated X-band radar variables obtained by (11) and (12) using the S-band dataset in Figs. 3a and 3b. Figure 3e shows the attenuated X-band reflectivity obtained by (13) using simulated X-band variables in Figs. 3c and 3d.

b. DSD sampling method

It was shown by Scarchilli et al. (1996) that the triplet of measurements Zh, Zdr, and Kdp nearly lie on a three-dimensional surface. Therefore, once Zh and Zdr are specified, the choice of possible Kdp fall in a narrow range. As a result, if we choose a value of Kdp at S band corresponding to Zh and Zdr, then the Kdp value at X band can be obtained by direct frequency scaling, because Kdp is linearly proportional to frequency as (6). This procedure to choose Kdp at S band avoids the problem of direct Kdp estimation (Gorgucci et al. 2000), which can suppress peaks resulting from the slope estimation process, which is used to derive Kdp from ϕdp. The above principle is implemented in a detailed manner as explained in the following. A large dataset of Zh, Zdr, and Kdp values at S band are generated by the ABC model corresponding to a wide range of DSD parameters (0.5 ≤ D0 ≤ 3.5 mm, 3 ≤ log10Nw ≤ 5, −1 < μ ≤ 4) under the constraints of Zh < 55 dB and R < 300 mm h−1. For a given set of Zh and Zdr, a search of this database provides possible choices of DSDs that satisfy the radar variables Zh and Zdr. One of those DSDs is randomly chosen to compute the X-band radar variables. Because the process is structured on DSD, the observed reflectivity and differential reflectivity can be computed according to (13). The block diagram in Fig. 4 provides a description of the simulation procedure. Figure 5a shows the range profile of reflectivity and differential reflectivity from the NCAR SPOL radar observed over central Florida. The simulated X-band profiles of Zh,X(r), Zh,X(r) as well as Zdr,X(r), Zdr,X(r) are shown in Figs. 5b and 5c, whereas the profiles of ϕdp at S and X bands are shown in Fig. 5d. A cursory glance of Fig. 5 shows that the simulation procedure produces reasonable range profiles of X-band radar variables. Once again, the purpose of this simulation is to simulate realistic range profiles of X-band dual-polarization variables in order to maintain the spatial correlation structure of the naturally occurring rainfall. It should be noted that the procedure is not to simulate the “exact” observation, but simulate profiles that fall within the range of observations.

c. DSD inversion method

The third method to simulate the X-band radar variables is to explicitly invert the DSD for each resolution volume and then compute the X-band radar variables. Gorgucci et al. (2002) and Bringi et al. (2002, 2003) proposed the method to retrieve the parameters of Gamma drop size distribution for rain medium from S-band dual-polarization observations (Zh,S, Zdr,S, and Kdp,S). The method is based on the concept of an effective mean axis ratio versus diameter model, which is a linear relationship (r = 1 − βD). They developed an algorithm for estimating β (magnitude of the slope of the shape–size relationship) using radar measurements at S band. For 10log10(Zh,S) ≥ 35 dBZ, 10log10(Zdr,S) ≥ 0.2 dB, and Kdp,S ≥ 0.3 km−1, D0 and Nw are retrieved as
i1520-0426-23-9-1195-e14
For other cases in which Kdp is noisy and 10log10Zh is below 35 dBZ, the retrieval method of D0 and Nw proposed by Bringi et al. (2002) is applied. After retrieving DSD from convective event data observed by the CSU CHILL radar, X-band radar variables (Zh,X, Zdr,X, αh,X, αdp,X, Kdp,X, and Δco,X) with a realistic scenario of the precipitation event are simulated by theoretical simulation. Here Zh,X and Zdr,X are generated by (13), whereas ψdp,X is obtained from Kdp,X and Δ using (8). Figure 6 shows the S-band observations (Zh,S, Zdr,S) and parameters (D0 and Nw) of DSD retrieved from S-band observations. Simulated X-band radar variables and attenuated radar variables corresponding to S-band radar measurements in Fig. 6 are shown in Fig. 7. The results show that this method can produce reasonable X-band radar variables. Though one type of DSD retrieval is shown, this procedure can be applied with any DSD retrieval algorithm using dual-polarization radar data.

d. Comparison of three methodologies

For comparison of the proposed methodologies, radar variables at X band are simulated using a ray profile observed by CSU CHILL radar. Observed reflectivity, differential reflectivity, and differential phase at S band are shown in Figs. 8a, 8c and 8e as a solid line, whereas simulated reflectivity, differential reflectivity, and differential phase at X band are shown in Figs. 8a, 8c and 8e according to the three methodologies. Note that the ψdp observations are filtered to remove measurement error. The corresponding attenuated reflectivity and differential reflectivity are shown in Figs. 8b and 8d. From the results of Fig. 8, we can see that all of the proposed methods can simulate reasonable radar variable profiles at X band falling within the range of observed S-band radar measurements. The empirical conversion method is based on a nearly one-to-one relation of the intrinsic radar measurements between S and X band. The method is simple and reliable, particularly for reflectivity and differential reflectivity. If the simulated Kdp or ϕdp is needed, the DSD sampling method or DSD inversion method will be useful. The DSD inversion method connects X-band variables and DSD retrieved from S-band radar measurements. This method is more sophisticated because of the DSD inversion procedure. The DSD sampling method lies between the empirical conversion method and the full DSD inversion method.

4. Summary and conclusions

Owing to the success of the dual-polarization methodology for attenuation correction in rain (Bringi et al. 1990; Testud et al. 2000; Bringi and Chandrasekar 2001; Delrieu et al. 2000; Anagnostou et al. 2004; Matrosov et al. 2005; Park et al. 2005b), X-band radars are becoming more viable for targeted short-range applications. To validate the performance of the radar retrieval algorithm during the test phase of algorithm development, it is necessary to use the empirical data based on actual precipitation event. One way to obtain that dataset for higher frequencies is to simulate it from radar observations of nonattenuated or low attenuated frequencies, such as at S band. This paper presents three such methodologies to simulate “realistic” dual-polarization radar variables at X-band. The conversion methods start from S-band dual-polarization radar observations and use the fundamental microphysical properties of rainfall, namely, size and shape distribution, to transform S-band into X-band variables. As a result, these methods maintain the connection between the realistic scenarios of rain events with the natural distribution of rainfall microphysical properties. The simulated X-band radar variables can give a possible scenario with wide varying drop size distribution. These simulations have been used in evaluating the performance of X-band radar designs and algorithms in our research.

Acknowledgments

This research was supported by the ERC program (0313747) and NSF ATM (0313881).

REFERENCES

  • Anagnostou, E. N., , Anagnostou M. N. , , Krajewski W. F. , , Kruger A. , , and Miriovsky B. J. , 2004: High-resolution rainfall estimation from X-band polarimetric radar measurements. J. Hydrometeor., 5 , 110128.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andsager, K., , Beard K. V. , , and Laird N. F. , 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56 , 26732683.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beard, K. V., , and Chuang C. , 1987: A new model for the equilibrium shape of raindrops. J. Atmos. Sci., 44 , 15091524.

  • Bringi, V. N., , and Chandrasekar V. , 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Chandrasekar V. , , Balakrishnan N. , , and Zrnić D. S. , 1990: An examination of propagation effects in rainfall on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol., 7 , 829840.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Huang G. J. , , Chandrasekar V. , , and Gorgucci E. , 2002: A methodology for estimating the parameters of a gamma raindrop size distribution model from polarimetric radar data: Application to a squall-line event from the TRMM/Brazil campaign. J. Atmos. Oceanic Technol., 19 , 633645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , Chandrasekar V. , , Hubbert J. , , Gorgucci E. , , Randeu W. L. , , and Schoenhuber M. , 2003: Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci., 60 , 354365.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., , Gorgucci E. , , and Baldini L. , 2002: Evaluation of polarimetric radar rainfall algorithms at X-band. Proc. ERAD 2002, Delft, Netherlands, ERAD, 277–281.

  • Chandrasekar, V., , Fukatsu H. , , and Mubarak K. , 2003: Global mapping of attenuation at Ku- and Ka-band. IEEE Trans. Geosci. Remote Sens., 41 , 21662176.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., , Gorgucci E. , , Lim S. , , and Baldini L. , 2004a: Simulation of X-band radar observation of precipitation from S-band measurements. Proc. IGARSS 2004, Anchorage, AK, IEEE, 2752–2755.

  • Chandrasekar, V., , Lim S. , , Bharadwaj N. , , Li W. , , McLaughlin D. , , Bringi V. N. , , and Gorgucci E. , 2004b: Principles of networked weather radar operation at attenuating frequencies. Proc. ERAD 2004, Gotland, Sweden, ERAD, 109–114.

  • Delrieu, G., , Caoudal S. , , and Creutin J. D. , 1997: Feasibility of using mountain return for the correction of ground-based X-band weather radar. J. Atmos. Oceanic Technol., 14 , 368385.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delrieu, G., , Andrieu H. , , and Creutin J. D. , 2000: Quantification of path-integrated attenuation for X- and C-band weather radar systems operating in Mediterranean heavy rainfall. J. Appl. Meteor., 39 , 840850.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., , Scarchilli G. , , and Chandrasekar V. , 2000: Practical aspects of radar rainfall estimation using specific differential propagation phase. J. Appl. Meteor., 39 , 945955.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., , Chandrasekar V. , , Bringi V. N. , , and Scarchilli G. , 2002: Estimation of raindrop size distribution parameters from polarimetric radar measurements. J. Atmos. Sci., 59 , 23732384.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., , Kingsmill D. E. , , Martner B. E. , , and Ralph F. M. , 2005: The utility of X-band polarimetric radar for quantitative estimates of rainfall parameters. J. Hydrometeor., 6 , 248262.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, S. G., , Bringi V. N. , , Chandrasekar V. , , Maki M. , , and Iwanami K. , 2005a: Correction of radar reflectivity and differential reflectivity for rain attenuation at X-band. Part I: Theoretical and empirical basis. J. Atmos. Oceanic Technol., 22 , 16211632.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, S. G., , Maki M. , , Iwanami K. , , Bringi V. N. , , and Chandrasekar V. , 2005b: Correction of radar reflectivity and differential reflectivity for rain attenuation at X-band. Part II: Evaluation and application. J. Atmos. Oceanic Technol., 22 , 16331655.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Fig. 1.
Fig. 1.

Scatterplot of (a) reflectivity and (b) differential reflectivity at S and X band for widely varying drop size distributions.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 2.
Fig. 2.

Scatterplot of (a) intrinsic reflectivity obtained by theoretical simulation using widely varying DSD vs simulated reflectivity by (11) and (b) intrinsic specific attenuation vs simulated specific attenuation by (12) for X band.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 3.
Fig. 3.

(a) Reflectivity at S band, (b) differential reflectivity at S band, (c) simulated reflectivity at X band by (11), (d) simulated specific attenuation at X band by (12), and (e) attenuated reflectivity at X band by (13); “x” indicates the X-band radar location.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 4.
Fig. 4.

The block diagram of the DSD sampling method.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 5.
Fig. 5.

(a) Range profile of reflectivity and differential reflectivity from S-band polarimetric radar collected over central Florida; (b) simulated range profile of reflectivity at X band (solid line) and the corresponding attenuated profile (dashed line); (c) simulated range profile of differential reflectivity at X band (solid line) and the corresponding attenuated profile (dashed line); (d) differential phase profile at S band (solid line) and the corresponding profile at X band (dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 6.
Fig. 6.

(a) Reflectivity, (b) differential reflectivity at S band, (c) retrieved median volume diameter, and (d) retrieved normalized intercept parameter.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 7.
Fig. 7.

(a) Simulated reflectivity, (b) simulated differential reflectivity, (c) simulated specific attenuation, (d) simulated differential attenuation corresponding to Fig. 6, (e) attenuated reflectivity, (f) attenuated differential reflectivity obtained by (13), (g) simulated specific differential phase, and (h) differential propagation phase obtained by (7) at X band.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 7.
Fig. 7.

(Continued)

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

Fig. 8.
Fig. 8.

(a) Range profile of reflectivity at S band (solid line) and simulated reflectivity at X band using proposed methodologies; (b) corresponding attenuated reflectivity at X band using proposed methodologies; (c) range profile of differential reflectivity at S band (solid line) and simulated differential reflectivity at X band; (d) attenuated differential reflectivity at X band; and (e) differential phase profile at S band (solid line) and the corresponding differential phase profile at X band.

Citation: Journal of Atmospheric and Oceanic Technology 23, 9; 10.1175/JTECH1909.1

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