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Variational retrieval of sea surface wind vectors using a polarimetric approach
Abstract
This study presents one-dimension variational retrieval of sea surface wind vectors using simulated microwave polarimetric measurements at 10.7, 18.7, and 37 GHz. The algorithm only requires four Stokes components at a single frequency; and therefore runs very efficiently. Under non-precipitation conditions, the errors of wind direction and speed are about 10° and 0.6 m/s, respectively, if the random noises of 0.1 K for vertical and horizontal polarization states and 0.15 K for the third and fourth Stokes components are taken into account. In hurricane conditions, polarimetric measurements at 10 GHz, especially for the 3rd and 4th Stokes components, vary within a few degree of Kelvin and provide unique information on surface wind direction.
... Three-dimensional radiative effects from ice and raining clouds may result in a small residual error for the third Stokes parameter. 6 Even for clouds having spherical particles, the contribution to the third Stokes parameter could result in a few degrees (in K) at 10.7 GHz. 6 Tables 1-3 show the monthly mean and standard deviation of the third and fourth Stokes parameters of Windsat measurements from September 2003 to February 2004. ...
... 6 Even for clouds having spherical particles, the contribution to the third Stokes parameter could result in a few degrees (in K) at 10.7 GHz. 6 Tables 1-3 show the monthly mean and standard deviation of the third and fourth Stokes parameters of Windsat measurements from September 2003 to February 2004. It is shown that the measurements from the Amazon and African rain forests display similar features, and the results there support our above assumption on the fourth Stokes parameter over rain forests. ...
Microwave observations made at the third and fourth Stokes parameters can be used to determine the surface wind direction over oceans. However, due to their smaller amplitudes (less than 3 K at the third Stokes parameter and 1 K at the fourth Stokes parameter), the absolute calibration to these measurements becomes crucial. A new methodology is developed in this study to calibrate the Windsat third and fourth Stokes parameters through tropical rain forest measurements over the Amazon and central Africa. It is found that the Windsat fourth Stokes parameter at 18 GHz has biases of the order of 0.5 K, which could severely affect the wind vector retrievals.
Due to the lack of meteorological observations over the tropical oceans, almost all the current hurricane models require bogusing of a vortex into the large-scale analysis of the model initial state. In this study, an algorithm to construct hurricane vortices is developed using the Advanced Microwave Sounding Unit (AMSU- A) data. Under rain-free atmospheric conditions, the temperature profile could be retrieved with a root-mean- square error of 1.58C. Under heavy rainfall conditions, measurements from channels 3-5 are removed in retrieving temperatures. An application of this algorithm to Hurricane Bonnie (1998) shows well the warm-core eye and strong thermal gradients across the eyewall. The rotational and divergent winds are obtained by solving the nonlinear balance and omega equations using the large-scale analysis as the lateral boundary conditions. In doing so, the sea level pressure distribution is empirically specified, and the geopotential heights are calculated from the retrieved temperatures using the hydrostatic equation. The so-derived temperature and wind fields associated with Bonnie compare favorably to the dropsonde observations taken in the vicinity of the storm. The initial moisture field is specified based on the AMSU-derived total precipitable water. The effectiveness of using the retrieved hurricane vortex as the model initial conditions is tested using three 48-h simulations of Bonnie with the finest grid size of the 4-km, triply nested version of the fifth- generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). It is found that the control run captures reasonably well the track and rapid deepening stage of the storm. The simulated radar reflectivity exhibits highly asymmetric structures of the eyewall and cloud bands, similar to the observed. A sensitivity simulation is conducted, in which an axisymmetric vortex is used in the model initial conditions. The simulated features are less favorable compared to the observations. Without the incorporation of the AMSU data, the simulated intensity and cloud structures differ markedly from the observed. The results suggest that this algorithm could provide an objective, observation-based way to in- corporate a dynamically consistent vortex with reasonable asymmetries into the initial conditions of hurricane models. This algorithm could also be utilized to estimate three-dimensional hurricane flows after the hurricane warm core and eyewall are developed.
A Global Land Data Assimilation System (GLDAS) has been developed. Its purpose is to ingest satellite- and ground-based observational data products, using advanced land surface modeling and data assimilation techniques, in order to generate optimal fields of land surface states and fluxes. GLDAS is unique in that it is an uncoupled land surface modeling system that drives multiple models, integrates a huge quantity of observation-based data, runs globally at high resolution (0.25degrees), and produces results in near-real time (typically within 48 h of the present). GLDAS is also a test bed for innovative modeling and assimilation capabilities. A vegetation-based "tiling" approach is used to simulate subgrid-scale variability, with a 1-km global vegetation dataset as its basis. Soil and elevation parameters are based on high-resolution global datasets. Observation-based precipitation and downward radiation and output fields from the best available global coupled atmospheric data assimilation systems are employed as forcing data. The high-quality, global land surface fields provided by GLDAS will be used to initialize weather and climate prediction models and will promote various hydrometeorological studies and applications. The ongoing GLDAS archive (started in 2001) of modeled and observed, global, surface meteorological data, parameter maps, and output is publicly available.
A nonhydrostatic extension to the Pennsylvania State University-NCAR Mesoscale Model is presented, which employs reference pressure as the basis for a terrain-following vertical coordinate, and the fully compressible system of equations. It is shown that this model, combined with the existing initialization techniques and the physics of the current hydrostatic model, is capable of real-data simulations on any scale, limited only by data quality and resolution and by computer resources. An example of an explosive cyclone simulation is presented, demonstrating the capability of the nonhydrostatic model to reproduce the hydrostatic model results at large scales.
We analyze the wind direction signal for vertically (v) and horizontally (h) polarized microwave radiation at 37 GHz, 19 GHz, and 11 GHz; and an Earth incidence angle of 53°. We use brightness temperatures from SSM/I and TMI and wind vectors from buoys and the QUIKSCAT scatterometer. The wind vectors are space and time collocated with the radiometer measurements. Water vapor, cloud water and sea surface temperature are obtained from independent measurements and are uncorrelated with the wind direction. We find a wind direction signal that is noticeably smaller at low and moderate wind speeds than a previous analysis had indicated. We attribute the discrepancy to errors in the atmospheric parameters that were present in the data set of the earlier study. We show that the polarization combination 2v-h is almost insensitive to atmospheric changes and agrees with the earlier results. The strength of our new signals agrees well with JPL aircraft radiometer measurements. It is significantly smaller than the prediction of the two-scale sea surface emission model for low and intermediate wind speeds.
A brief outline of the basic concepts of cloud filtering and atmospheric attenuation corrections used in the Multi-channel Sea Surface Temperature (MCSST) method is given. The operational MCSST procedures and products are described in detail. The comparative performance of AVHRR-based MCSST'S is discussed via the use of the results of the JPL Satellite-Derived Sea Surface Temperature workshops. For the four data periods there is surprisingly good correspondence in the sign and location of the major monthly mean SST anomaly features derived from MCSST's and those from a screened set of ship-based SST's. With the partial exception of the one data period severely affected in some areas by volcanic aerosol from El Chichon eruptions, global statistical measures of the MCSST anomalies relative to the the ship data are as follows: biases, 0.3–0.4°C (MCSST lower than ship); standard deviations, 0.5–0.6°C; and cross-correlations, +0.3 to +0.7. A refined technique in use with NOAA 9 data in 1985 has yielded consistent biases and rms differences near −0.1°C and 0.5°C, respectively.
The assimilation of satellite microwave measurements and the retrieval of geophysical parameters require a fast and accurate radiative transfer model. In this study, a scheme is developed to solve the vector radiative transfer equation using a polarimetric two-stream approximation. In the scheme, the integration of the phase matrix over azimuth angle is derived as an analytic form that can also be directly utilized for the general radiative transfer scheme. Each Stokes radiance component is expressed as an analytical function of atmospheric and surface optical parameters. The model is applicable for spherical and randomly oriented nonspherical scatters. The differences of brightness temperatures between the polarimetric two-stream model and the matrix operator method are less than 2 K for various frequencies.
A radiative-transport model has been developed to study the emitted radiation from variable cloud and rain systems at the frequencies of the special sensor microwave imagery (SSM/I). The theoretical standard errors of the retrievals lie in the range of 0.1-0.2 g/cm 2 for vapor paths of 0-7 g/cm 2, 0.02-0.03 g/cm 2 for total water paths of 0-1.2 g/cm 22, 0.015 g/cm 2 for ice paths of 0-0.25 g/cm 2, and 1.3 mm/h for rain rates of 0-30 mm/h. The algorithms are applied to global sets of SSM/I data for August 1987. The resulting fields of monthly rain amounts are compared to those of satellite infrared measurements, a surface climatology, and a general circulation model (GCM) experiment. The results are found to be mainly consistent with the climatology, whereas the IR data and the GCM experiment produce questionable inconsistencies. -from Authors
An algorithm is developed to retrieve sea surface wind vectors from satellite microwave polarimetry. The radiative transfer model produces simulated measurements under global atmospheric and surface conditions. The simulations for wind speeds less than 5 m s-1 are not utilized in the retrievals because of the unreliable performance of the current surface emissivity model. In the algorithm, the upwelling and downwelling radiative components are treated as one variable since the two components are highly correlated. As a result, under rain-free conditions, the full polarimtric measurements obtained at a single frequency can form a closure of a set of radiative transfer equations so that both surface and atmospheric column parameters can be simultaneously derived. The first guess to the solutions is normally required because the retrieval is nonlinear. In doing so, the third and fourth Stokes components and their ratio are utilized to estimate the wind direction. It is found that this ratio alone can determine the wind direction with an accuracy of 30 degrees. Without the sensor noises being added to the simulations, the algorithm can produce the wind direction with an RMS error of 6.5 degrees and the wind speed with an error of 0.3 m s-1, respectively. If the realistic random noises are taken into account with 0.1 K for vertical and horizontal polarizations and 0.15 K for the third and fourth Stokes components, the errors increase to about 10 degrees and 0.6 m s-1 for the wind direction and speed, respectively. This wind speed error is much smaller than that from the statistical algorithms (1.4 m s-1) applied for the same data set. Thus the physical retrieval significantly improves the uses of the microwave polarimetric data for remote sensing of ocean wind.
A remote measurement of the atmosphere with high spectral resolution form the ground or from space, such as might be made form one of the new generation of instruments such as the Fourier transform or grating spectrometers AIRS, MIPAS, TES, or IASI, would appear to contain a large amount of information about the atmosphere, but it is not immediately obvious how to quantify it or to use it efficiently or effectively. The usefulness of a particular remote measurement can be described by a wide range of parameters including the spatial resolution, precision and accuracy of the retrieved product. For optimization of a measurement method, however, a single scalar figure of merit is required, whereas all of the above are vectors because they are functions of altitude and/or quantity retrieved. Spatial averages of resolution, precision and accuracy could be used, but there are two quantities of general applicability which can be defined without reference to the specific retrieval method, and are therefore more straightforward in use. These are the information content, and the number of degrees of freedom for signal, the latter being a measure of the number of statistically independent quantities in any one measurement. It can be shown that both of these quantities are functions of the eigenvalues of a certain matrix, and are closely related. The information content and the degrees of freedom provide single parameters which can be used in the automated optimization of for example, instrument design parameters, the selection of microwindows or subsets of channels for retrieval, the optimization of retrieval strategy, and the understanding of the information content of a spectrum. Some such applications are illustrated by means of simulated spectra for the AIRS instrument.
A three-dimensional Monte Carlo transfer model for polarized radiation is developed and used to study three-dimensional (3-D) effects of raining clouds on the microwave brightness temperature. The backward method is combined with the forward method to treat polarization correctly within the cloud. In comparison with horizontally homogeneous clouds, two effects are observed: First, brightness temperatures from clouds are reduced in the 3-D case due to net leakage of radiation from the sidewalls of the cloud. Second, radiation which is emitted by the warm cloud and then reflected from the water surface increases the brightness temperatures of the cloud-free areas in the vicinity of the cloud. Both effects compete with each other, leading to either lower or higher overall brightness temperatures, depending on the geometry of the cloud, the satellite viewing angle, the coverage, and the position of the cloud within the field of view (FOV) of the satellite. At 37 GHz, for example, up to 10 K differences can occur for a cloud of 50% coverage. Finite homogeneous raining clouds matching the size of the FOV of the satellite show a similar relationship between rain rates and brightness temperatures (TB) as horizontally infinite clouds. Namely, an increase of TB with increasing rain rates at low rain rates, due to emission effects, is followed by a decrease due to temperature and scattering effects. For small horizontal cloud diameter, however, the 3-D brightness temperatures may show a second maximum due to the decrease of the leakage effect with increasing rain rates. At nadir, 3-D brightness temperatures are always lower than the 1-D values with differences up to 20 K for a cloud of 5-km vertical extent and a base of 1×1 km. To quantify the 3-D effects for more realistic cloud structures, we used results of a three-dimensional dynamic cloud model as input for the radiative transfer codes. The same 3-D effects are obtained, but the differences between 1-D and 3-D modeling are smaller. In general, most of the differences between the 1-D and 3-D results for off-nadir view angles are pure geometry effects, which can be accounted for in part by a modified 1-D model.
Remote measurements of the atmosphere with high spectral resolution from the ground or from space, are being or will be made from a new generation of instruments such as the Fourier transform or grating spectrometers AIRS, MIPAS, TES or IASI. Such measurements would appear to contain a large amount of information about the atmosphere, but it is not immediately obvious how to quantify it or to use it efficiently or effectively. The somewhat neglected concepts of ‘information content’ and ‘degrees of freedom for signal’ provide single parameters which can be used in the automated optimisation of, for example, instrument design parameters, the selection of microwindows or subsets of channels for retrieval, the optimisation of retrieval strategy, and the understanding of the information content of a spectrum. Some such applications are illustrated by means of simulated spectra for the AIRS instrument.
Active and passive microwave remote sensing of earth terrains is studied. Electromagnetic wave scattering and emission from stratified media and rough surfaces are considered with particular application to the remote sensing of soil moisture. Radiative transfer theory for both the random and discrete scatterer models is examined. Vector radiative transfer equations for nonspherical particles are developed for both active and passive remote sensing. Single and multiple scattering solutions are illustrated with applications to remote sensing problems. Analytical wave theory using the Dyson and Bethe-Salpeter equations is employed to treat scattering by random media. The backscattering enhancement effects, strong permittivity fluctuation theory, and modified radiative transfer equations are addressed. The electromagnetic wave scattering from a dense distribution of discrete scatterers is studied. The effective propagation constants and backscattering coefficients are calculated and illustrated for dense media.
There has been an increasing interest in the applications of
polarimetric microwave radiometers for ocean wind remote sensing.
Aircraft and spaceborne radiometers have found a few Kelvins wind
direction signals in sea surface brightness temperatures, in addition to
their sensitivities to wind speeds. However, it was not clear what
physical scattering mechanisms produced the observed brightness
dependence on wind direction. To this end, polarimetric microwave
emissions from wind-generated sea surfaces are investigated with a
polarimetric two-scale scattering model, which relates the directional
wind-wave spectrum to passive microwave signatures of sea surfaces.
Theoretical azimuthal modulations are found to agree well with
experimental observations for all Stokes parameters from near nadir to
65° incidence angles. The upwind and downwind asymmetries of
brightness temperatures were interpreted using the hydrodynamic
modulation. The contributions of Bragg scattering by short waves,
geometric optics scattering by long waves and sea foam are examined. The
geometric optics scattering mechanism underestimates the directional
signals in the first three Stokes parameters, and predicts no signals in
the fourth Stokes parameter (V). In contrast, the Bragg scattering was
found to dominate the wind direction signals from the two-scale model
and correctly predicted the phase changes of the upwind and crosswind
asymmetries in T<sub>υ</sub> and U from middle to high incidence
angles. The phase changes predicted by the Bragg scattering theory for
radiometric emission from water ripples is corroborated by the numerical
Monte Carlo simulation of rough surface scattering. This theoretical
interpretation indicates the potential use of polarimetric brightness
temperatures for retrieving the directional wave spectrum of short
gravity and capillary waves
Comparative performance of AVHRR-based multi-channel sea surface temperature An updated analysis of the ocean surface wind direction signal in passive microwave brightness tempera-tures Information content and optimization of high spectral resolution remote measurements
- E P Mcclain
- W Pichel
- C Walton
- T Meissner
- F J Wentz
McClain, E.P., Pichel, W., Walton, C. Comparative performance of AVHRR-based multi-channel sea surface temperature. J. Geophys. Res. 89, 11587–11601, 1985. Meissner, T., Wentz, F.J. An updated analysis of the ocean surface wind direction signal in passive microwave brightness tempera-tures. IEEE TGARS 40, 1230–1240, 2002. Rodgers, C.D. Information content and optimization of high spectral resolution remote measurements. Adv. Space Res. 21, 361–367, 1998.
On the use of different ocean surface models in radiative transfer calculation, in: Solimini Microwave Radiometry and Remote Sensing of the Environment Polarimetric emission model of the sea at microwave frequencies
- M Schrader
- Q Liu
- St
- K Germain
- G Poe
Schrader, M., Liu, Q. On the use of different ocean surface models in radiative transfer calculation, in: Solimini, (Ed.), Microwave Radiometry and Remote Sensing of the Environment. VPS, Utrecht, Netherlands, pp. 209–217, 1995. St. Germain, K., Poe, G., Polarimetric emission model of the sea at microwave frequencies, Part II: Comparison with measurements.
On the use of different ocean surface models in radiative transfer calculation
- Schrader
Schrader, M., Liu, Q. On the use of different ocean surface models in
radiative transfer calculation, in: Solimini, (Ed.), Microwave
Radiometry and Remote Sensing of the Environment. VPS,
Utrecht, Netherlands, pp. 209-217, 1995.
Polarimetric emission model of the sea at microwave frequencies, Part II: Comparison with measurements
- St
- K Germain
- G Poe
St. Germain, K., Poe, G., Polarimetric emission model of the sea at
microwave frequencies, Part II: Comparison with measurements.
Washington, DC, Naval Research Laboratory Report, 1998.