Bayesian algorithm for microwave-based precipitation retrieval: description and application to TMI measurements over ocean

A physically oriented inversion algorithm to retrieve precipitation from satellite-based passive microwave measurements named the Bayesian algorithm for microwave-based precipitation retrieval (BAMPR) is proposed. First, we illustrate the procedure that BAMPR follows to produce precipitation estimates from observed multichannel brightness temperatures. Retrieval products are the surface rain rates, columnar equivalent water contents, and hydrometeor content profiles, together with the associated estimation uncertainties. Numerical tests performed on simulated measurements show that retrieval errors are reduced when a rain type and pattern classification procedure is employed, and that estimates are quite sensitive to the adopted error model. Finally, for different tropical storms that were observed by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), we compare the rain retrieved from BAMPR relative to those retrieved from the Goddard Profiling (Gprof) algorithm and the Precipitation Radar-adjusted TMI estimation of rainfall (PATER) algorithm. Despite a similar inversion approach, the algorithms exhibit different performances that can be mainly related to different training databases and retrieval constraints such as cloud classification.     

Global Simulation of Brightness Temperatures at 6.6 and 10.7 GHz Over Land Based on SMMR Data Set Analysis

In the framework of the Soil Moisture and Ocean Salinity mission, a two-year (1987–1988) global simulation of brightness temperatures (TB) at L-band was performed using a simple model [L-band microwave emission of the biosphere, (L-MEB)] based on radiative transfer equations. However, the lack of alternative L-band spaceborne measurements corresponding to real-world data prevented from assessing the realism of the simulated global-scale TB fields. In this study, using a similar modeling approach, TB simulations were performed at C-band and X-band. These simulations required the development of C-MEB and X-MEB models, corresponding to the equivalent of L-MEB at C-band and X-band, respectively. These simulations were compared with Scanning Multichannel Microwave Radiometer (SMMR) measurements during the period January to August 1987 (corresponding to the end of life of the SMMR mission). A sensitivity study was also carried out to assess, at a global scale, the relative contributions of the main MEB parameters (particularly the roughness and vegetation model parameters). Regional differences between simulated and measured TBs were analyzed, discriminating possible issues either linked to the radiative transfer model (C-MEB and X-MEB) or due to land surface simulations. A global agreement between observations and simulations was discussed and allowed to evaluate regions where soil moisture retrievals would give best results. This comparison step made at C-band and X-band allowed to better assess how realistic and/or accurate the L-band simulations could be.     

The beamfilling algorithm for retrieval of hydrometeor profileparameters from passive microwave measurements

The horizontal inhomogeneity of the atmosphere within a satellite microwave radiometer's field of view (FOV) has always been considered as a source of rainfall retrieval errors. The hydrometeor profile retrieval algorithm presented exploits it to obtain an approximation of a radiative transfer model, which allows relatively simple inversion. The atmosphere within the FOV is treated as a combination of horizontally homogeneous domains. Assuming that one of known “basic” hydrometeor profiles occurs in each domain, the inverse problem is reduced to a determination of “beamfilling coefficients.” The online procedure includes determination of beamfilling coefficients and a footprint-averaged hydrometeor profile as a linear combination of “basic” ones. Off-line procedures involve the selection of a minimum number of necessary “basic” brightness temperature vectors and correction of “basic” hydrometeor profiles to provide the best retrieval accuracy for a given cloud/radiative simulation. The performance of the algorithm is tested for both numerical simulations and TRMM/TMI data. Numerical simulation has allowed a comparison of the information content of radiometer measurements from SSM/I, TMI, and the future AMSR. The effectiveness of the algorithm is being tested for rain water integral and rain rate retrievals from TRMM TMI measurements     

Intercomparison of microwave radiative transfer models forprecipitating clouds

An intercomparison of microwave multiple scattering radiative transfer codes used in generating databases for satellite rainfall retrieval algorithms has been carried out to ensure that differences obtained from retrieval techniques do not originate from the underlying radiative transfer code employed for the forward modeling. A set of profiles containing liquid water and ice contents of cloud and rain water as well as snow, graupel and pristine ice were distributed to the participants together with a black box routine providing Mie single scattering, atmospheric background absorption and surface emissivity. Simulations were to be carried out for nadir and off-nadir (53.1°) observation angles at frequencies between 10 and 85 GHz. Among the radiative transfer models were two-stream, multiple stream and Monte Carlo models. The results showed that there were two major sources of differences between the codes. 1) If surface reflection/emission was considered isotropic, simulated brightness temperatures were significantly higher than for specular reflection and this effect was most pronounced at nadir observation and over ocean-type surfaces. 2) Flux-type models including delta-scaling could partially compensate for the errors introduced by the two-stream approximation. Largest discrepancies occurred at high frequencies where atmospheric scattering is most pronounced and at nadir observation. If the same surface boundary conditions, the same multiple-stream resolution and the same scaling procedures are used, the models were very close to each other with discrepancies below 1 K     

Precipitation retrieval from spaceborne microwave radiometers basedon maximum a a posteriori probability estimation

A retrieval technique for estimating rainfall rate and precipitating cloud parameters from spaceborne multifrequency microwave radiometers is described. The algorithm is based on the maximum a posteriori probability criterion (MAP) applied to a simulated data base of cloud structures and related upward brightness temperatures. The cloud data base is randomly generated by imposing the mean values, the variances, and the correlations among the hydrometeor contents at each layer of the cloud vertical structure, derived from the outputs of a time-dependent microphysical cloud model. The simulated upward brightness temperatures are computed by applying a plane-parallel radiative transfer scheme. Given a multifrequency brightness temperature measurement, the MAP criterion is used to select the most probable cloud structure within the cloud-radiation data base. The algorithm is computationally efficient and has been numerically tested and compared against other methods. Its potential to retrieve rainfall over land has been explored by means of Special Sensor Microwave/Imager measurements for a rainfall event over Central Italy. The comparison of estimated rain rates with available raingauge measurements is also shown     

An iterative inversion algorithm with application to thepolarimetric radar response of vegetation canopies

The retrieval of scene parameters from polarimetric radar data using an iterative inversion approach is considered. The theoretical development of a general, model-based iterative algorithm for inversion of polarimetric radar data is presented. Factors relevant to its implementation, such as sensor configuration, algorithm optimization and computational structure are discussed. The algorithm is applied to the specific problem of inverting the vector radiative transfer model for a simplified, representative vegetation canopy consisting of vertical trunks, leaves, and a rough ground surface. The results of this inversion are in excellent agreement with simulated data generated using the radiative transfer model. The convergence properties of the algorithm are evaluated, and it is found that successful convergence is achieved in about 90% to 95% of the cases tested for the implementation used in this work. An error analysis is presented which considers the effect of both systematic and measurement derived errors. Typical error bounds for the current application are approximately ±3%, allowing for ±0.5 dB accuracy in the measured radar data     

Statistical temperature profile retrievals in clear-air usingpassive 118-GHz O2 observations

Linear statistical temperature profile retrievals from nadiral passive 118-GHz O₂ spectra are demonstrated using time- and space-coincident microwave observations and radiosonde profiles. Separate retrievals are demonstrated for winter and summer midlatitude conditions in clear air over land; observations during both day and night are included. The retrieval operator is a linear-statistical minimum mean-squared-error estimator. A purely statistical retrieval operator circumvents the effects of radiative transfer model uncertainties and biases in either the radiosonde or Millimeter-wave Temperature Sounder data. The retrieved profile rms errors are ~0.7-1.2 K for either the winter or summer tropospheres     

Assessing the effect of uncertainty in intracavitary electrodeposition on endocardial potential estimates

The aim of this simulation study is to determine the effect of uncertainty in intracavitary probe electrode position on the accuracy of estimated endocardial potentials. Intracavitary probe position uncertainty is simulated by randomly moving an idealized probe surface about the center of an idealized left ventricular endocardial surface. These random deviations represent possible probe locations that are incorporated as correlated noise. An optimum inverse transfer coefficient matrix, relating intracavitary potentials to endocardial potentials, is computed and subsequently used to calculate the best linear estimate of the true endocardial potentials. For uncorrelated endocardial potentials and probe position uncertainty within 1.5 mm of the coordinates of the exact probe electrode locations, a root-mean-square (rms) error of 34.0% is obtained. Increasing probe position uncertainties to 3.0 and 6.0 mm results in rms errors of 60.8 and 88.3%, respectively. For endocardial potentials that are 90% dipolar, the rms errors for probe position uncertainties of 1.5, 3.0, and 6.0 mm are 11.3, 19.6, and 28.5%, respectively. These simulation results imply that position uncertainty of a multielectrode, intracavitary probe can be a major source of error in estimating endocardial potentials from intracavitary potentials.     

Retrieval of precipitable water vapor by the millimeter-waveimaging radiometer in the arctic region during FIRE-ACE

Millimeter-wave radiometric measurements obtained from the NASA ER-2 aircraft over the arctic region on May 20, 1998, were used to estimate precipitable water (PW) in the range⩽0.60 g/cm². The approach is a modified version of the recent work by J. Miao (1998), which utilized the radiometric measurements at 150, 183.3±3, and 183.3±7 GHz of the SSM/T-2 sensor to retrieve PW over the antarctic region. However, Miao has implicitly assumed a surface emissivity that is frequency independent over the 150-183 GHz range. This assumption turns out not to be a good one based on the airborne measurements described below and the errors introduced in the PW estimation were substantial in many cases. It is shown below that four-frequency radiometric measurements in the frequency range of 150-220 GHz provided a robust retrieval of PW, while allowing for a surface emissivity that varied linearly with frequency. The retrieved PW compared favorably with that calculated from rawinsonde data at two widely separated locations. The differences between the retrieved and calculated values are not more than ±0.02 g/cm², which is smaller than errors associated with measurement uncertainty. It is found necessary to account for the double side-band nature of the 183.3 GHz measurements in the radiative transfer calculations for development of the retrieval algorithm. The PW values estimated from the algorithm developed from single side band, 183.3 GHz radiative transfer calculations could be in error by as much as ±0.10 g/cm² . Finally, the effect of surface temperature variations is shown to introduce only a small error in the estimation of PW     

TES atmospheric profile retrieval characterization: an orbit of simulated observations

We test the accuracy of our error analysis and retrieval performance by examining retrievals over an orbits' worth of simulated data covering a variety of atmospheric conditions. The use of simulated data allows validation of the error analysis and retrieval algorithm by comparisons to the true values. To demonstrate typical results, two example retrievals are shown, along with associated diagnostic information. Curtain plots display comparisons between the retrieved results, the true values, and the initial guesses. The results show that the Tropospheric Emission Spectrometer (TES) retrieval algorithm is robust under a variety of atmospheric conditions, that TES can improve on the a priori for nadir species Tatim H/sub 2/O, O/sub 3/, and CO, and that the predicted errors match well with the actual retrieved errors. The target scenes (nadir, ocean, cloud-free) simulate conditions that are most easily validated with real data, and comparisons of on orbit results can be made with this baseline.     

Sensitivity analyses of satellite rainfall retrieval and sampling error on flood prediction uncertainty

The Global Precipitation Measurement mission planned jointly by the United States, Japanese, and European space agencies envisions providing global rainfall products from a constellation of passive microwave (PM) satellite sensors at time scales ranging from 3-6 h. In this paper, a sensitivity analysis was carried out to understand the implication of satellite PM rainfall retrieval and sampling errors on flood prediction uncertainty for medium-sized (/spl sim/100 km/sup 2/) watersheds. The 3-h rainfall sampling gave comparable flood prediction uncertainties with respect to the hourly sampling, typically used in runoff modeling, for a major flood event in Northern Italy. The runoff prediction error, though, was magnified up to a factor of 3 when rainfall estimates were derived from 6-h PM sampling intervals. The systematic and random error components in PM retrieval are shown to interact with PM sampling introducing added uncertainty in runoff simulation. The temporal correlation in the PM retrieval error was found to have a negligible effect in runoff prediction. It is shown that merging rain retrievals from hourly infrared (IR) and PM observations generally reduces flood prediction uncertainty. The error reduction varied between 50% (0%) and 80% (50%) for the 6-h (3-h) PM sampling scenarios, depending on the relative magnitudes of PM and IR retrieval errors. Findings from this paper are potentially useful for the design, planning, and application assessment of satellite remote sensing in flood and flash flood forecasting.     

大气气溶胶对用红外窗区通道遥感陆面温度的影响

分析了大气气溶胶对红外窗区通道辐射传输的影响,考察了在用红外窗区通道反演陆面温度中,大气温度和湿度廓线没有误差时,大气气溶胶的不确定性对反演精度的影响,以及大气温度、湿度和气溶胶同时有偏差对地面温度反演精度的影响。     

Post-launch calibration of the TRMM microwave imager

Three post-launch calibration methods are used to examine the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) on-orbit performance. The first method is a statistical analysis of TMI ocean observations that reveals a systematic along-scan error. The second method is an intercomparison of TMI and SSM/I observations that shows a warm bias in TMI. The last method is an analysis of TMI observations taken during TRMMs deep-space maneuver. These deep-space observations confirm both the along-scan error found from method 1 and the warm bias found from method 2. The along-scan error exhibits distinctive features having amplitudes near 1 K. The warm bias, which is related to the scene temperature, can be as large are 5 K for ocean measurements. The physical explanation of a slightly emissive main reflector is proposed to explain the calibration errors     

Polarimetric signatures of a layer of random nonspherical discretescatterers overlying a homogeneous half-space based on first- andsecond-order vector radiative transfer theory [geophysical radar remotesensing]

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. The vector radiative transfer equation contains a general nondiagonal extinction matrix and a phase matrix that are averaged over particle orientations. The nondiagonal extinction matrix accounts for the difference in propagation constants and the difference in attenuation rates between the two characteristic polarisations. The Mueller matrix based on the first-order and second-order multiple scattering solutions of the vector radiative transfer equation is calculated. The copolarized and depolarized returns are also calculated     

Analysis and improvement of tipping calibration for ground-basedmicrowave radiometers

The tipping-curve calibration method has been an important calibration technique for ground-based microwave radiometers that measure atmospheric emission at low optical depth. The method calibrates a radiometer system using data taken by the radiometer at two or more viewing angles in the atmosphere. In this method, the relationship between atmospheric opacity and viewing angle is used as a constraint for deriving the system calibration response. Because this method couples the system with radiative transfer theory and atmospheric conditions, evaluations of its performance have been difficult. In this paper, first a data-simulation approach is taken to isolate and analyze those influential factors in the calibration process and effective techniques are developed to reduce calibration uncertainties. Then, these techniques are applied to experimental data. The influential factors include radiometer antenna beam width, radiometer pointing error, mean radiating temperature error, and horizontal inhomogeneity in the atmosphere, as well as some other factors of minor importance. It is demonstrated that calibration uncertainties from these error sources can be large and unacceptable. Fortunately, it was found that by using the techniques reported, the calibration uncertainties can be largely reduced or avoided. With the suggested corrections, the tipping calibration method can provide absolute accuracy of about or better than 0.5 K     

Measuring trace gases in plumes from hyperspectral remotely sensed data

A method [joint reflectance and gas estimator (JRGE)] is developed to estimate a set of atmospheric gas concentrations in an unknown surface reflectance context from hyperspectral images. It is applicable for clear atmospheres without any aerosol in a spectral range between approximately 800 and 2500 nm. Standard gas by gas methods yield a 6% rms error in H/sub 2/O retrieval from Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data, reaching several tens percent for a set of widespread ground materials and resulting from an simplifying assumption of linear variations of the reflectance model within gas absorption bands and partial accounting of the gas induced signal. JRGE offers a theoretical framework consisting in a two steps algorithm that accounts for sensor characteristics, assumptions on gas concentrations and reflectance variations. It estimates variations in gas concentrations relatively to a standard atmosphere model. An adaptive cubic smoothing spline like estimation of the reflectance is first performed. Concentrations of several gaseous species are then simultaneously retrieved using a nonlinear procedure based on radiative transfer calculations. Applied to AVIRIS spectra simulated from reflectance databases and sensor characteristics, JRGE reduces the errors in H/sub 2/O retrieval to 2.87%. For an AVIRIS image acquired over the Quinault prescribed fire, far field CO/sub 2/ estimate (348 ppm, about 6% to 7% rms) is in agreement with in situ measurement (345-350 ppm) and aerosols yield an underestimation of total atmospheric CO/sub 2/ content equal to 5.35% about 2 km downwind the fire. JRGE smoothes and interpolates the reflectance for gas estimation but also provides nonsmoothed reflectance spectra. JRGE is shown to preserve various mineral absorption features included in the AVIRIS image of Cuprite Mining District test site.     

超高斯加载的稳健自适应波束形成及性能分析

该文提出了一种超高斯加载的稳健自适应波束形成方法,解决由于导向矢量和样本方差矩阵失配误差所导致的波束形成器性能下降的问题,利用p-范数来对两种误差不确定性进行总体修正,克服了2-范数不能同时兼顾两者实现最优修正的缺点。采用遗传算法求得最优范数p,验证了在不同实验设置下,当使用最优范数时,都比2-范数约束具有更好的性能。超高斯加载方法把复杂的不确定性建模问题转化为范数p的寻优问题,从而获得比对角加载方法更优异的性能。     

Markov model for dynamic behavior of ranging errors in indoor geolocation systems

Recently, considerable attention has been devoted to modeling and analysis of the behavior of the ranging error in indoor environment. The ranging error modeling is essential in design of precise time of arrival (TOA) based indoor geolocation systems. In this paper we present a new framework for simulation of the dynamic spatial variations of ranging error observed by a mobile user based on an application of Markov model. The model relegates the behavior of ranging error into four main categories associated with four states of the Markov process. The parameters of the model are extracted from empirical data collected from a measurement calibrated ray tracing (RT) algorithm in a typical office environment. Results of simulated errors from Markov model and actual errors from empirical data show close agreement.     

Inverse techniques in hyperthermia: a sensitivity study

Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures “measured” from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error <1.0°C), and 2) when the actual perfusion distribution contains a small random variation (±15%) which is neglected by the model, the reconstructed temperature distribution mill be in good agreement with the actual temperature distribution (maximum error ⩽0.3°     

A generalized split-window algorithm for retrieving land-surfacetemperature from space

Proposes a generalized split-window method for retrieving land-surface temperature (LST) from AVHRR and MODIS data. Accurate radiative transfer simulations show that the coefficients in the split-window algorithm for LST must vary with the viewing angle, if the authors are to achieve a LST accuracy of about 1 K for the whole scan swath range (±55° from nadir) and for the ranges of surface temperature and atmospheric conditions over land, which are much wider than those over oceans. The authors obtain these coefficients from regression analysis of radiative transfer simulations, and they analyze sensitivity and error over wide ranges of surface temperature and emissivity and atmospheric water vapor abundance and temperature. Simulations show that when atmospheric water vapor increases and viewing angle is larger than 45°, it is necessary to optimize the split-window method by separating the ranges of the atmospheric water vapor, lower boundary temperature, and the surface temperature into tractable subranges. The atmospheric lower boundary temperature and (vertical) column water vapor values retrieved from HIRS/2 or MODIS atmospheric sounding channels can be used to determine the range for the optimum coefficients of the split-window method. This new algorithm not only retrieves land-surface temperature more accurately, but is also less sensitive to uncertainty in emissivity and to instrument quantization error