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  • 1
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    Optimal Estimation of Rain-Rate Profiles from Single-Frequency Radar Echoes (1996)
    In:  Other Sources
    Details
    Publication Date: 2011-08-23
    Description: The significant ambiguities inherent in the determination of a particular vertical rain intensity profile from a given time profile of radar echo powers measured by a downward-looking (spaceborne or airborne) radar at a single attenuating frequency are well documented. Indeed, one already knows that by appropriately varying the parameters of the reflectivity-rain rate (Z-R) and/or attenuation-rain rate (k- R) relationships one can produce several substantially different rain-rate profiles that would produce the same radar power profile. Imposing the additional constraint that the path-averaged rain rate be a given fixed number does reduce the ambiguities but falls far short of eliminating them. While formulas to generate all mutually ambiguous rain-rate profiles from a given profile of received radar reflectivities have already been derived, there remains to be produced a quantitative measure to assess how likely each of these profiles is, what the appropriate "average" profile should be, and what the "variance" of these multiple solutions is. To do this, one needs to spell out the stochastic constraints that can allow us to make sense of the words "average" and "variance" in a mathematically rigorous way. Such a quantitative approach would be particularly well suited for such systems as the planned precipitation radar of the Tropical Rainfall Measuring Mission (TRMM). Indeed, one would then be able to use the radar reflectivities measured by the TRMM radar to estimate the rain-rate profile that would most likely have produced the measurements, as well as the uncertainty in the estimated rain rates as a function of range. Such an optimal approach is described in this paper.
    Keywords: Meteorology and Climatology
    Type: Journal of Applied Meteorology; Volume 35; No. 2; 213-228
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  • 2
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    Parameterizing the Raindrop Size Distribution (1996)
    In:  Other Sources
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    Publication Date: 2011-08-23
    Description: This paper addresses the problem of finding a parametric form for the raindrop size distribution (DSD) that(1) is an appropriate model for tropical rainfall, and (2) involves statistically independent parameters. Such a parameterization is derived in this paper. One of the resulting three "canonical" parameters turns out to vary relatively little, thus making the parameterization particularly useful for remote sensing applications. In fact, a new set of r drop-size-distribution-based Z-R and k-R relations is obtained. Only slightly more complex than power laws, they are very good approximations to the exact radar relations one would obtain using Mie scattering. The coefficients of the new relations are directly related to the shape parameters of the particular DSD that one starts with. Perhaps most important, since the coefficients are independent of the rain rate itself, the relations are ideally suited for rain retrieval algorithms.
    Keywords: Meteorology and Climatology
    Type: Journal of Applied Meteorology; Volume 35; No. 1; 3-13
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  • 3
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    Stochastic Filtering of Rain Profiles Using Radar, Surface-Referenced Radar, or Combined Radar-Radiometer Measurements (1996)
    In:  Other Sources
    Details
    Publication Date: 2011-08-23
    Description: This paper describes a computationally efficient nearly optimal Bayesian algorithm to estimate rain (and drop size distribution) profiles, given a radar reflectivity profile at a single attenuating wavelength. In addition to estimating the averages of all the mutually ambiguous combinations of rain parameters that can produce the data observed, the approach also calculates the n-ns uncertainty in its estimates (this uncertainty thus quantifies "the amount of ambiguity" in the "solution"). The paper also describes a more general approach that can make estimates based on a radar reflectivity profile together with an approximate measurement of the path-integrated attenuation, or a radar reflectivity profile and a set of passive microwave brightness temperatures. This more general "combined" algorithm is currently being adapted for the Tropical Rainfall Measuring Mission.
    Keywords: Meteorology and Climatology
    Type: Journal of Applied Meteorology; Volume 35; No. 2; 229-242
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  • 4
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    Optimal Estimation of Rain Rate Profiles from Single-Frequency Radar Echoes (1992)
    In:  Other Sources
    Details
    Publication Date: 2018-06-11
    Description: The significant ambiguities inherent in the determination of a particular vertical rain intensity profile from a given time profile of radar echo powers measured by a downward-looking (spaceborne or airborne) radar at a single attenuating frequency are well-documented. Indeed, one already knows that by appropriately varying the parameters of the reflectivity-rain-rate (Z - R) and/or attenuation-rain-rate (k - R) relationships, one can produce several substantially different hypothetical rain rate profiles which would have the same radar power profile. Imposing the additional constraint that the path-averaged rain-rate be a given fixed number does reduce the ambiguities but falls far short of eliminating them. While we now know how to generate as many mutually ambiguous rain-rate profiles from a given profile of received radar reflectivities as we like, there remains to produce a quantitative measure to assess how likely each of these profiles is, what the appropriate 'average' profile should be, and what the 'variance' of these multiple solutions is. Of course, in order to do this, one needs to spell out the stochastic constraints that can allow us to make sense of the words 'average' and 'variance' in a mathematically rigorous way. Such a quantitative approach would be particularly well-suited for such systems as the proposed Precipitation Radar of the Tropical Rainfall Measuring Mission (TRMM). Indeed, one would then be able to use the radar reflectivities measured by the TRMM radar from one particular look in order to estimate the most likely rain-rate profile that would have produced the measurements, as well as the uncertainty in the estimated rain-rates as a function of range. Such an optimal approach is described in this paper.
    Keywords: Meteorology and Climatology
    Format: text
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  • 5
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    To What Extent Can Raindrop Size Be Determined by a Multiple-Frequency Radar? (2006)
    In:  Other Sources
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    Publication Date: 2018-06-11
    Description: In this paper, an analytical treatment of the atmospheric remote sensing problem of determining the raindrop size distribution (DSD) with a spaceborne multifrequency microwave nadir-looking radar system is presented. It is typically assumed that with two radar measurements at different frequencies one ought to be able to calculate two state variables of the DSD: a bulk quantity, such as the rain rate, and a distribution shape parameter. To determine if this nonlinear problem can indeed be solved, the DSD is modeled as a Gamma distribution and quadratic approximations to the corresponding radar-rain relations are used to examine the invertibility of the resulting system of equations in the case of two as well as three radar frequencies. From the investigation, it is found that for regions of DSD state space multiple solutions exist for two or even three different frequency radar measurements. This should not be surprising given the nonlinear coupled nature of the problem.
    Keywords: Meteorology and Climatology
    Type: Journal of Applied Meteorology and Climatology; Volume 45; No. 4; 529-536
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  • 6
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    Simultaneous Retrieval of Surface and Rain Backscattering Parameters from Spaceborne Radar Measurements (1993)
    In:  Other Sources
    Details
    Publication Date: 2018-06-08
    Description: The precipitation radar planned for the Tropical Rainfall Measuring Mission (TRMM) will be the first of its kind to measure vertical rainfall distributions from space. The TRMM radar will scan +/- 20 degrees across the nadir track. The range-gated backscattering powers over the entire scan swath will be measured, classified (rain versus no-rain), averaged, and processed to derive the rainfall rates. With this observation scheme, there are two major reasons why it is important to know the rain-perturbed backscattering coefficient of the surface background (tilde over sigma_0)...
    Keywords: Meteorology and Climatology
    Type: American Meteorological Society, 26th Intl. Conf. on Radar Meteorology; Norman, OK; United States
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  • 7
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    The TRMM 'Day-1' Radar/Radiometer Combined Rain-Profiling Algorithm (1997)
    In:  Other Sources
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    Publication Date: 2018-06-08
    Description: The Tropical Rainfall Measuring Mission (TRMM)'s 'day-1' combined rada/radiometer algorithm uses a rain-profiling approach which gives as much importance to the measurement of the TRMM satellite's precipitation radar (PR) and the TRMM microwave imager (TMI) as their respective intrinsic ambiguities warrant, which avoids any ad hoc shortcuts that might introduce large biases in the rain estimates, yet which is simple enough to be operatrional with TRMM is launched in late 1997.
    Keywords: Communications and Radar
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  • 8
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    Global variability of precipitation according to the Tropical Rainfall Measuring Mission (2004)
    In:  Other Sources
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    Publication Date: 2018-06-11
    Description: Numerous studies have documented the effect of El Nino-Southern Oscillation (ENSO) on rainfall in many regions of the globe. The question of whether ENSO is the single most important factor in interannual rainfall variability has received less attention, mostly because the kind of data that would be required to make such an assessment were simply not available. Until 1979 the evidence linking El Nino with changes in rainfall around the world came from rain gauges measuring precipitation over land masses and a handful of islands. From 1980 until the launch of the Tropical Rainfall Measuring Mission (TRMM) in November 1997 the remote sensing evidence was confined to ocean rainfall because of the very poor sensitivity of the instruments over land. In this paper we summarize the results of a principal component analysis of TRMM's 60-month (January 1998 to December 2002) global land and ocean remote-sensing record of monthly rainfall accumulations. Contrary to the first principal component of the rainfall itself, the first three indices of the anomaly are most sensitive to precipitation over the ocean rather than over the land. With the help of archived surface station data the first TRMM rain anomaly index is extended back several decades. Comparison of the extended index with the Southern Oscillation Index confirms that the first principal component of the rainfall anomaly is strongly correlated with the ENSO indices.
    Keywords: Geophysics
    Type: Journal of Geophysical Research; Volume 109; D17103
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  • 9
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    Passive and Active Microwave Remote Sensing of Precipitation and Latent Heating Distributions in the Tropics from TRMM (2002)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Passive and active microwave remote sensing data are analyzed to identify signatures of precipitation and vertical motion in tropical convection. A database of cloud/radiative model simulations is used to quantify surface rain rates and latent heating profiles that are consistent with these signatures. At satellite footprint-scale (approximately 10 km), rain rate and latent heating estimates are subject to significant random errors, but by averaging the estimates in space and time, random errors are substantially reduced, Bias errors have been minimized by improving the microphysics in the supporting cloud/radiative model simulations, and by imposing a consistent definition of remotely-sensed and model-simulated convective/stratiform rain coverage. Remotely-sensed precipitation and latent heating distributions in the tropics are derived from Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/ Imager (SSM/ I) sensor data. The prototype Version 6 TRMM passive microwave algorithm typically yields average heating profiles with maxima between 6 and 7 km altitude for organized mesoscale convective systems. Retrieved heating profiles for individual convective systems are compared to coincident estimates based upon a combination of dual-Doppler radar and rawinsonde data. Also, large-scale latent heating distributions are compared to estimates derived from a simpler technique that utilizes observations of surface rain rate and stratiform rain proportion to infer vertical heating structure. Results of these tests will be presented at the conference.
    Keywords: Earth Resources and Remote Sensing
    Type: International TRMM Science Conference; Jul 22, 2002 - Jul 26, 2002; Honolulu, HI; United States
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  • 10
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    Filtering Image Records Using Wavelets and the Zakai Equation (1995)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: Consider the problem of detecting and localizing a faint object moving In an "essentially stationary" background, using a sequence of two-dimensional low-SNR images of the scene. A natural approach consists of "digitizing" each snapshot into a discrete set of observations, sufficiently (perhaps not exactly) matched to the object In question, then tracking the object using an appropriate stochastic filter. The tracking would be expected to make up for the low signal-to-noise ratio, this allowing one to "coherently" process successive images in order to beat down the noise and localize the object. Thus, "tracking" here does not refer to the usual notion of detecting then tracking: rather, we track in order to detect The problem then becomes one of choosing the appropriate image representation as well as the optimal (and necessarily nonlinear filter. We propose exact and approximate solutions using wavelets and the Zakai equation. The smoothness of the wavelets used is required in the derivation of the evolution equation for the conditional density giving the filter, and their orthogonality makes it possible to carry out actual computations of the Ito- and change-of-gauge-terms in the algorithm effectively.
    Keywords: Cybernetics
    Type: IEECS-P95096 , IEEE Transactions on Pattern Analysis and Machine Intelligence; 17; 11; 1069-1078
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