The proper weighting function for retrieving temperatures from satellite measured radiances

One class of methods for converting satellite measured radiances into atmospheric temperature profiles, involves a linearization of the radiative transfer equation: delta r = the sum of (W sub i) (delta T sub i) where (i=1...s) and where delta T sub i is the deviation of the temperature in layer i from that of a reference atmosphere, delta R is the difference in the radiance at satellite altitude from the corresponding radiance for the reference atmosphere, and W sub i is the discrete (or vector) form of the T-weighting (i.e., temperature weighting) function W(P), where P is pressure. The top layer of the atmosphere corresponds to i = 1, the bottom layer to i = s - 1, and i = s refers to the surface. Linearization in temperature (or some function of temperature) is at the heart of all linear or matrix methods. The weighting function that should be used is developed

Progressive Transient Photon Beams

In this work we introduce a novel algorithm for transient rendering in participating media. Our method is consistent, robust, and is able to generate animations of time-resolved light transport featuring complex caustic light paths in media. We base our method on the observation that the spatial continuity provides an increased coverage of the temporal domain, and generalize photon beams to transient-state. We extend the beam steady-state radiance estimates to include the temporal domain. Then, we develop a progressive version of spatio-temporal density estimations, that converges to the correct solution with finite memory requirements by iteratively averaging several realizations of independent renders with a progressively reduced kernel bandwidth. We derive the optimal convergence rates accounting for space and time kernels, and demonstrate our method against previous consistent transient rendering methods for participating media

Sensor performance analysis

The theory is described and the equations required to design are developed and the performance of electro-optical sensor systems that operate from the visible through the thermal infrared spectral regions are analyzed. Methods to compute essential optical and detector parameters, signal-to-noise ratio, MTF, and figures of merit such as NE delta rho and NE delta T are developed. A set of atmospheric tables are provided to determine scene radiance in the visible spectral region. The Planck function is used to determine radiance in the infrared. The equations developed were incorporated in a spreadsheet so that a wide variety of sensor studies can be rapidly and efficiently conducted

High resolution observations of low contrast phenomena from an Advanced Geosynchronous Platform (AGP)

Present technology allows radiometric monitoring of the Earth, ocean and atmosphere from a geosynchronous platform with good spatial, spectral and temporal resolution. The proposed system could provide a capability for multispectral remote sensing with a 50 m nadir spatial resolution in the visible bands, 250 m in the 4 micron band and 1 km in the 11 micron thermal infrared band. The diffraction limited telescope has a 1 m aperture, a 10 m focal length (with a shorter focal length in the infrared) and linear and area arrays of detectors. The diffraction limited resolution applies to scenes of any brightness but for a dark low contrast scenes, the good signal to noise ratio of the system contribute to the observation capability. The capabilities of the AGP system are assessed for quantitative observations of ocean scenes. Instrument and ground system configuration are presented and projected sensor capabilities are analyzed

Calculation of the radiance distribution at the boundary of an isotropically scattering slab

The radiance arising from an anisotropically scattering illuminated stack of n slabs is calculated using the equation of radiative transfer. It appears to be unnecessary to calculate the radiance inside the material; including only the radiance at the boundary surfaces is sufficient to obtain the desired result. The novel method used for the solution of this problem leads immediately in a straightforward and systematic way to the known appropriate basic equations valid for the problem at hand, otherwise derived by ad hoc methods. A new simple set of linear equations for the radiance at the boundary surfaces is derived. This method applies equally well to similar problems with other geometries. Apart from this analytical derivation, this paper presents the results of the numerical solution of the set of equations that we obtained from the equation of radiative transfer, for n = 1. The results of the numerical calculations are compared with what is found in the literature and are found to give very good agreement.

WCRP surface radiation budget shortwave data product description, version 1.1

Shortwave radiative fluxes which reach the Earth's surface are key elements that influence both atmospheric and oceanic circulation. The World Climate Research Program has established the Surface Radiation Budget climatology project with the ultimate goal of determining the various components of the surface radiation budget from satellite data on a global scale. This report describes the first global product that is being produced and archived as part of that effort. The interested user can obtain the monthly global data sets free of charge using e-mail procedures

Calibration of a general optical equation for remote sensing of suspended sediments in a moderately turbid estuary

Abstract A general algorithm for determining suspended sediment concentrations in the surface waters of estuaries has been developed for use with satellite data. The algorithm uses a three-parameter general optical equation to relate suspended sediment concentrations to water reflectances that have been corrected for sun angle effects, atmospheric path radiance, and tidal excursion. Using data collected by the advanced very high resolution radiometer on five different dates, reflectances were determined using two different methods, one providing maximum correction for haze and the other providing minimum sensitivity to pigments. For both methods, in situ and remotely sensed samples from Delaware Bay acquired within 3.5 hours of each other agreed to within 60% at the 95% confidence level. Pixel and subpixel scale spatial variations and variability associated with in situ measurements produced about 50% of the differences. Chlorophyll concentrations of \u3e50 μg/L produced a discrepancy in the reflectance method that provided the best haze correction. The parameter values may be adjusted to allow for variations in sediment size and pigment variations, allowing application of the calibration to estuaries having optically different suspended sediments

An Approach to Retrieve BRDF from Satellite and Airborne Measurements of Surface-Reflected Radiance Based on Decoupling of Atmospheric Radiative Transfer and Surface Reflection

Bi-directional Reflection Distribution Function (BRDF) defines anisotropy of the surface reflection. It is required to specify the boundary condition for radiative transfer (RT) modeling. Measurements of reflected radiance by satellite- and air-borne sensors provide information about anisotropy of surface reflection. Atmospheric correction needs to be performed to derive BRDF from the reflected radiance. Common approach for BRDF retrievals consists of the use of kernel-based BRDF and RT modeling that needs to be done anew at every step of the iterative process. The kernels weights are obtained by minimization of the difference between measured and modeled radiance. This study develops a new method of retrieving kernel-based BRDF that requires RT calculations to be done only once. The method employs the exact analytical expression of radiance at any atmospheric level through the solutions of two auxiliary atmosphere-only RT problems and the surface-reflected radiance at the surface level. The latter is related to BRDF and solutions of the auxiliary RT problems by a Fredholm integral equation of the second kind. The approach requires to perform RT calculations one time before the iterations. It can use observations taken at different atmospheric conditions assuming that surface conditions remain unchanged during the time span of observations. The algorithm accurately catches zero weights of the kernels that may be a concern if the number of kernels is greater than 3 in current mainstream approaches. The study presents numerical tests of the BRDF retrieval algorithm for various surface and atmospheric conditions