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Haddad, Ziad S.

Publications and source records attributed to Haddad, Ziad S..

27 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

The TRMM 'Day-1' Radar/Radiometer Combined Rain-Profiling Algorithm

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.

Rain-Profiling Algorithm Tropical Rainfall↗
NASA NTRS1996

Optimal Estimation of Rain-Rate Profiles from Single-Frequency Radar Echoes

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.

Haddad, Ziad S.↗
NASA NTRS1996

Stochastic Filtering of Rain Profiles Using Radar, Surface-Referenced Radar, or Combined Radar-Radiometer Measurements

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.

Haddad, Ziad S.↗
NASA NTRS1996

Parameterizing the Raindrop Size Distribution

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.

Haddad, Ziad S.↗
NASA NTRS1996

A New Parametrization of the Rain Drop Size Distribution

This paper revisits the problem of finding a parametric form for the rain drop size distribution (DSD) which 1) is an appropriate model for tropical rainfall, and 2) involves statistically independent parameters. Using TOGA/COARE data, we derive a parametrization which meets these criteria. This new parametrization is an improvement on the one that was derived in [3] using TRMM ground truth data from Darwin, Australia. The new COARE data allows us to verify that the spatial variability fo the two

rain↗
NASA NTRS1995

Filtering Image Records Using Wavelets and the Zakai Equation

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.

Haddad, Ziad S.↗
NASA NTRS1993

Simultaneous Retrieval of Surface and Rain Backscattering Parameters from Spaceborne Radar Measurements

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)...

Im, Eastwood↗
NASA NTRS1992

Optimal Estimation of Rain Rate Profiles from Single-Frequency Radar Echoes

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.

deep space flight computer real-time advanced spac↗