Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate

Standard Deviation of Spatially-Averaged Surface Cross Section Data from the TRMM Precipitation Radar

We investigate the spatial variability of the normalized radar cross section of the surface (NRCS or Sigma(sup 0)) derived from measurements of the TRMM Precipitation Radar (PR) for the period from 1998 to 2009. The purpose of the study is to understand the way in which the sample standard deviation of the Sigma(sup 0) data changes as a function of spatial resolution, incidence angle, and surface type (land/ocean). The results have implications regarding the accuracy by which the path integrated attenuation from precipitation can be inferred by the use of surface scattering properties

Method to combine spaceborne radar and radiometric observations of precipitation, A

2010 Fall.Includes bibliographical references.This dissertation describes the development and application of a combined radar-radiometer rainfall retrieval algorithm for the Tropical Rainfall Measuring Mission (TRMM) satellite. A retrieval framework based upon optimal estimation theory is proposed wherein three parameters describing the raindrop size distribution (DSD), ice particle size distribution (PSD), and cloud water path (cLWP) are retrieved for each radar profile. The retrieved rainfall rate is found to be strongly sensitive to the a priori constraints in DSD and cLWP; thus, these parameters are tuned to match polarimetric radar estimates of rainfall near Kwajalein, Republic of Marshall Islands. An independent validation against gauge-tuned radar rainfall estimates at Melbourne, FL shows agreement within 2% which exceeds previous algorithms' ability to match rainfall at these two sites. The algorithm is then applied to two years of TRMM data over oceans to determine the sources of DSD variability. Three correlated sets of variables representing storm dynamics, background environment, and cloud microphysics are found to account for approximately 50% of the variability in the absolute and reflectivity-normalized median drop size. Structures of radar reflectivity are also identified and related to drop size, with these relationships being confirmed by ground-based polarimetric radar data from the North American Monsoon Experiment (NAME). Regional patterns of DSD and the sources of variability identified herein are also shown to be consistent with previous work documenting regional DSD properties. In particular, mid-latitude regions and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Intertropical Convergence Zone. Due to properties of the DSD and rain water/cloud water partitioning that change with column water vapor, it is shown that increases in water vapor in a global warming scenario could lead to slight (1%) underestimates of a rainfall trends by radar but larger overestimates (5%) by radiometer algorithms. Further analyses are performed to compare tropical oceanic mean rainfall rates between the combined algorithm and other sources. The combined algorithm is 15% higher than the version 6 of the 2A25 radar-only algorithm and 6.6% higher than the Global Precipitation Climatology Project (GPCP) estimate for the same time-space domain. Despite being higher than these two sources, the combined total is not inconsistent with estimates of the other components of the energy budget given their uncertainties

Spatial and temporal properties of precipitation uncertainty structures over tropical oceans, The

2015 Spring.Includes bibliographical references.The global distribution of precipitation has been measured from space using a series of passive microwave radiometers for over 40 years. However, our knowledge of precipitation uncertainty is still limited. While previous studies have shown that the uncertainty associated with the surface rain rate tends to vary with geographic location and season, most likely as a consequence of inappropriate and inaccurate microphysical assumptions in the forward model, the internal uncertainty structure remains largely unknown. Hence, a classification scheme is introduced, in which the overall precipitation uncertainty consists of random noise, constant biases, and region-dependent cyclic patterns. It is hypothesized that those cyclic patterns are the result of an imperfect forward model simulation of precipitation variation associated with regional atmospheric cycles. To investigate the hypothesis, differences from ten years of collocated surface rain rate measurements from TRMM Microwave Imager and Precipitation Radar are used as a proxy to characterize the precipitation uncertainty structure. The results show that the recurring uncertainty patterns over tropical ocean basins are clearly impacted by a hierarchy of regionally prominent atmospheric cycles with multiple time scales, from the diurnal cycle to multi-annual oscillation. Spectral analyses of the uncertainty time series have also confirmed the same argument. Moreover, the relative importance of major uncertainty sources varies drastically not only from one basin to another, but also with different choices of sampling resolutions. Following the classification scheme and hypothesis proposed in this study, the magnitudes of un-explained precipitation uncertainty can be reduced up to 68% and 63% over the equatorial central Pacific and eastern Atlantic, respectively

Simultaneous Wind and Rain Retrieval using Seawinds Data

The Sea Winds scatterometer is designed primarily to retrieve winds over the ocean. Since the deployment of Sea Winds on QuikSCAT in 1999, rain corruption in wind measurements has been recognized as one of the largest contributors to wind retrieval error. This paper presents a new estimation method that incorporates rain effects into Sea Winds wind retrieval. The new method simultaneously retrieves wind and rain, giving improved wind estimates in rain-corrupted areas and providing Sea Winds-derived estimates of the rain rate. The simultaneous wind/rain estimation method works especially well in the sweet spot of Sea Winds\u27 swath. On the outer-beam edges of the swath, rain estimation is not possible. This area, however, is only a small fraction of the total data. Wind speeds from simultaneous wind/rain retrieval are nearly unbiased, while the wind-only wind speeds become increasingly biased with rain rate. A synoptic example demonstrates that the new method has the capability of visually reducing the error due to rain while producing a consistent (yet somewhat noisy) estimate of the rain rate

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate

Development Of An Oceanic Rain Accumulation Product In Support Of Sea Surface Salinity Measurements From Aquarius/sac-d

Aquarius/SAC-D is a joint mission by National Aeronautics and Space Administration (NASA) and the Comision Nacional de Actividades Espaciales (CONAE), Argentine Space Agency. The satellite was launched in June 2011 and the prime remote sensing instrument is also named Aquarius (AQ). The main objective of this science program is to provide Sea Surface Salinity (SSS) maps of the global oceans every 7 days for understanding the Earth’s hydrologic cycle and for assessing long-term global climate change. The Aquarius instrument was built jointly by NASA’s Goddard Space Flight Center and the Jet Propulsion Laboratory. It is an active/passive L-band remote sensor that measures ocean brightness temperature (Tb) and radar backscatter, and these quantities are used to infer sea surface salinity. Other environmental parameters (e.g., sea surface temperature, wind speed and rain) also affect the microwave emitted radiance or brightness temperature. The SSS geophysical retrieval algorithm considers all these environmental parameters and makes the Tb corrections before retrieving SSS. Instantaneous rainfall can cause increase roughness that raises the ocean surface Tb. Further short term rain accumulation can produce a fresh water lens that floats on the ocean surface and dilutes the surface salinity. iv This thesis presents results of a study to develop an oceanic rain accumulation (RA) product that may be valuable to remote sensing engineers and algorithm developers and Aquarius scientists. The use of this RA product, along with in situ ocean salinity measurements from buoys, may be used to mitigate the effects of rain on the SSS retrieva

Assessment of the Performance of a Dual-Frequency Surface Reference Technique

The high correlation of the rain-free surface cross sections at two frequencies implies that the estimate of differential path integrated attenuation (PIA) caused by precipitation along the radar beam can be obtained to a higher degree of accuracy than the path-attenuation at either frequency. We explore this finding first analytically and then by examining data from the JPL dual-frequency airborne radar using measurements from the TC4 experiment obtained during July-August 2007. Despite this improvement in the accuracy of the differential path attenuation, solving the constrained dual-wavelength radar equations for parameters of the particle size distribution requires not only this quantity but the single-wavelength path attenuation as well. We investigate a simple method of estimating the single-frequency path attenuation from the differential attenuation and compare this with the estimate derived directly from the surface return

Exploring the limits of variational passive microwave retrievals

2017 Summer.Includes bibliographical references.Passive microwave observations from satellite platforms constitute one of the most important data records of the global observing system. Operational since the late 1970s, passive microwave data underpin climate records of precipitation, sea ice extent, water vapor, and more, and contribute significantly to numerical weather prediction via data assimilation. Detailed understanding of the observation errors in these data is key to maximizing their utility for research and operational applications alike. However, the treatment of observation errors in this data record has been lacking and somewhat divergent when considering the retrieval and data assimilation communities. In this study, some limits of passive microwave imager data are considered in light of more holistic treatment of observation errors. A variational retrieval, named the CSU 1DVAR, was developed for microwave imagers and applied to the GMI and AMSR2 sensors for ocean scenes. Via an innovative method to determine forward model error, this retrieval accounts for error covariances across all channels used in the iteration. This improves validation in more complex scenes such as high wind speed and persistently cloudy regimes. In addition, it validates on par with a benchmark dataset without any tuning to in-situ observations. The algorithm yields full posterior error diagnostics and its physical forward model is applicable to other sensors, pending intercalibration. This retrieval is used to explore the viability of retrieving parameters at the limits of the available information content from a typical microwave imager. Retrieval of warm rain, marginal sea ice, and falling snow are explored with the variational retrieval. Warm rain retrieval shows some promise, with greater sensitivity than operational GPM algorithms due to leveraging CloudSat data and accounting for drop size distribution variability. Marginal sea ice is also detected with greater sensitivity than a standard operational retrieval. These studies ultimately show that while a variational algorithm maximizes the effective signal to noise ratio of these observations, hard limitations exist due to the finite information content afforded by a typical microwave imager