Bandpass-resampling effects on the retrieval of radiance and surface reflectance

Radiative transfer models are often employed to derive the surface reflectance for Earth-looking multispectral scanners or imaging spectrometers. For this purpose the calculated radiances have to be resampled with the spectral channel response functions of the instrument. Three methods of bandpass resampling the product terms of the radiative transfer equation are compared: the exact method and two commonly used approximations. Error budgets for the two approximate methods are given for typical multispectral and hyperspectral sensors. The error depends on the wavelength, bandwidth, atmospheric parameters, and atmospheric path length.     

A local convergence analysis of bilevel decomposition algorithms

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.     

Interferometer for ground-based observations of emitted spectral radiance from the troposphere: evaluation and retrieval performance

We evaluate the spectral quality, radiometric noise, and retrieval performance of a Fourier transform infrared spectrometer, which has been developed for recording spectrally resolved observations in a region of the spectrum which is important both for the science of Earth's climate and applications, such as the remote sensing of temperature and atmospheric gas species. This spectral region extends from 100 to 1600 cm(-1) and encompasses the two fundamental, rotation and vibration, absorption bands of water vapor. The instrument is a customized version of a Bomem AERI (Atmospheric Emitted Radiance Interferometer) spectrometer, whose spectral coverage has been extended in the far infrared with the use of uncooled pyroelectric detectors. Retrieval examples for water vapor and temperature profiles are shown, which also allow us to intercompare the retrieval performance of both H(2)O vibration and rotation bands.     

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Numerous situations in continuum mechanics, structural stability, optimization and related fields generate problems requiring the solution of nonlinear algebraic equations. To solve such problems, a large assortment of schemes has evolved over the years. This paper will consider the formal numerical properties of the newly developed constrained type incremental Newton-Raphson operator schemes. Specifically the evaluation of the formal behavior of the elliptically constrained version is treated in detail. Note this procedure has the versatility to efficiently handle a wide range of nonlinearities including the possibilities of positive, negative, semi and indefinite tangent properties in an inherently stable manner. The formalism includes such items as determining from both a global as well as local point of view the existence, uniqueness and convergence characteristics. Also included in the developments will be the determination of the occurrence of global safety zones wherein convergence is assured. The approach taken is general enough to provide a framework to enable applications to a wide variety of constrained schemes involving continuous, piecewise continuous, closed or open constraint conditions.     

Stability and convergence of some finite element algorithms for nonlinear elastodynamics

A series of direct-integration and model-expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable appromixation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy method.     

A practical comparison of several algorithms for reliability calculations

This is a report on the time complexity of several algorithms for symbolic fault-tree analysis. The investigations are limited to the Boolean domain. Mostly, Boolean functions are transformed to short sums of disjoint terms, such that in the case of stochastically independent binary state indicator variables X_i ( = 1 for component i being in a faulty state) simply X has to be replaced by U (for unavailability) or R(t) (for unreliability) in order to obtain system unavailability or unreliability, respectively. The main overall result is that the Shannon decomposition is almost always the best approach.     

Tomographic retrieval of atmospheric parameters from infrared limb emission observations

Typical inversion of limb-sounding measurements assumes local horizontal homogeneity of the atmosphere. This simplification corresponds to spectral radiance errors that can exceed the noise level of a typical infrared instrument by a factor of 10 and causes errors in retrieved state parameters. To avoid these errors and to take the horizontal structure of the atmosphere into account, a two-dimensional (2D) tomographic sequential estimation approach is described. Application to temperature retrievals from simulated measurements yields typical retrieval errors of the order of 1 K, and a one-dimensional retrieval with the same synthetic measurements shows differences to the true values up to 10 K in regions with strong horizontal inhomogeneities. The horizontal resolution of the 2D retrieval is even better (up to 40 km) than the horizontal tangent point spacing.     

Satellite retrieval of inherent optical properties by inversion of an oceanic radiance model: a preliminary algorithm

A previously published radiance model inversion theory has been field tested by using airborne water-leaving radiances to retrieve the chromophoric dissolved organic matter (CDOM) and detritus absorption coefficient, the phytoplankton absorption coefficient, and the total backscattering coefficient. The radiance model inversion theory was tested for potential satellite use by comparing two of the retrieved inherent optical properties with concurrent airborne laser-derived truth data. It was found that (1) matrix inversion of water-leaving radiances is well conditioned even in the presence of instrument-induced noise, (2) retrieved CDOM and detritus and phytoplankton absorption coefficients are both in reasonable agreement with absorption coefficients derived from airborne laser-induced fluorescence spectral emissions, (3) the total backscattering retrieval magnitude and variability are consistent with expected values for the Middle Atlantic Bight, and (4) the algorithm performs reasonably well in Sargasso Sea, Gulf Stream, slope, and shelf waters but is less consistent in coastal waters.     

Accelerating the convergence of iterative error correction algorithms for measuring instruments

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 21–23, January, 1989.     

Order batching algorithms and travel-time estimation for automated storage/retrieval systems

In this paper we present heuristics and analytical models for the order batching problem. Orders are batched into tours such that the total travel time is minimized. Four heuristics are developed for the order batching problem, for which no exact solution exists. All heuristics are based on the time-saving criterion of combining two or more orders in a single tour rather than processing them one order at a time. Among the heuristics that are presented, the SL algorithm has the best performance. An analytical model is developed to estimate the travel time of the S/R machine as a function of the number of locations to be visited and the physical specifications of the structure. Expressions for upper and lower bounds for travel time are presented.     

Objective algorithms for the retrieval of optical depths from ground-based measurements

Optical depth retrieval by means of Langley regression is complicated by cloud transits and other time-varying interferences. An algorithm is described that objectively selects data points from a continuous time series and performs the required regression. The performance of this algorithm is compared by a double-blind test with an analysis done subjectively. The limits to accuracy imposed by time-averaged data are discussed, and an additional iterative postprocessing algorithm is described that improves the accuracy of optical depth inferences made from data with time-averaging periods longer than 5 min. Such routine algorithms are required to provide intercomparable retrievals of optical depths from widely varying historical data sets and to support large networks of instruments such as the multifilter rotating shadow-band radiometer.     

Acceleration of the convergence speed of evolutionary algorithms using multi-layer neural networks

Despite the global optimization capability and low sensitivity to initial parameter estimates, evolutionary algorithms suffer from heavy computational loads especially when the fitness evaluation is time-consuming. The proposed acceleration method implements an online multi-layer neural network approximating the fitness calculation, which greatly decreases the computation time because the time-consuming fitness calculation can be replaced by the simple network output. The acceleration is achieved as the number of individuals used for the network training gradually decreases according to an adaptive scheme. A convergence theorem guarantees convergence to the optimal solution as well as ensuring the network stability. The proposed method is verified by a numerical example.     

On the rates of convergence for moments convergence in regression models

In one-dimensional regression models, we establish a rate for the rth moment convergence \((r \geqslant 1)\) of the ordinary least-squares estimator involving explicitly the regressors, answering to an open question raised lately by Afendras and Markatou (Test 25:775–784, 2016). An extension of the classic Theorem 2.6.1 of Anderson (The statistical analysis of time series, Wiley, New York, 1971) is also presented.     

Using shaded filter instruments for measurements of sky radiance: retrieval of the apparent sky-view factor from ultraviolet radiation measurements

There is a growing need for sky radiometric measurements that encapsulate spatial as well as temporal variability. Since the advent of fast data acquisition systems in the 1980s, recent studies have utilized radiation filter instruments deployed in various sky-shading platforms. One cost effective method provides azimuthally averaged sky radiance distribution data at time scales down to fractions of a minute. Successful operation of this scheme requires knowledge of the apparent sky-view factor of the deployed sensor--an artifact of the instrument input optics, instrument filter design, and the instrument shading device employed. We provide a methodology for a determination of the sensor sky-view factor by using the employed shading device and the sun as a light source. The effect of an incorrect determination of instrument sky-view factor is also analyzed in context of the measurements.     

Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model

Inherent optical property (IOP) spectral models for the phytoplankton absorption coefficient, chromophoric dissolved organic matter (CDOM) absorption coefficient, and total constituent backscattering (TCB) coefficient are linear in the reference wavelength IOP and nonlinear in the spectral parameters. For example, the CDOM absorption coefficient IOP a(CDOM)(lambda(i)) = a(CDOM)(lambda(ref))exp[-S(lambda(i)- lambda(ref))] is linear in a(CDOM)(lambda(ref)) and nonlinear in S. Upon linearization by Taylor's series expansion, it is shown that spectral model parameters, such as S, can be concurrently accommodated within the same conventional linear matrix formalism used to retrieve the reference wavelength IOP's. Iteration is used to adjust for errors caused by truncation of the Taylor's series expansion. Employing an iterative linear matrix inversion of a water-leaving radiance model, computer simulations using synthetic data suggest that (a) no instabilities or singularities are introduced by the linearization and subsequent matrix inversion procedures, (b) convergence to the correct value can be expected only if starting values for a model parameter are within certain specific ranges, (c) accurate retrievals of the CDOM slope S (or the phytoplankton Gaussian width g) are generally reached in 3-20 iterations, (d) iterative retrieval of the exponent n of the TCB wavelength ratio spectral model is not recommended because the starting values must be within approximately +/-5% of the correct value to achieve accurate convergence, and (e) concurrent retrieval of S and g (simultaneously with the phytoplankton, CDOM, and TCB coefficient IOP's) can be accomplished in a 5 x 5 iterative matrix inversion if the starting values for S and g are carefully chosen to be slightly higher than the expected final retrieved values.     

Emissivity and reflection model for calculating unpolarized isotropic water surface-leaving radiance in the infrared. I: Theoretical development and calculations

Although published sea surface infrared (IR) emissivity models have gained widespread acceptance for remote sensing applications, discrepancies have been identified against field observations obtained from IR Fourier transform spectrometers at view angles approximately > 40 degrees. We therefore propose, in this two-part paper, an alternative approach for calculating surface-leaving IR radiance that treats both emissivity and atmospheric reflection in a systematic yet practical manner. This first part presents the theoretical basis, development, and computations of the proposed model.     

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that they provide a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.     

Asymptotic rates of convergence of iterative methods applied to finite difference calculations on non-uniform grids

In this paper the use of strongly stretched finite difference grids is examined in detail for a simple model equation. Numerical solutions of this equation demonstrate the overall second-order accuracy of the difference approximations. The behaviour of two simple iterative methods, S.O.R. and stationary A.D.I. is discussed for several cases with strong grid stretching and with variable diffusion coefficients. The results show that grid compression near to boundaries can greatly enhance the rates of convergence of these iterative methods, whereas with grid compression in the centre the rate of convergence can be extremely slow. The case of a diffusion coefficient which increases away from the boundaries of a region is analogous to grid compression in the centre and again the convergence rates can degrade considerably.     

A comparison of rubber stress relaxation models for conveyor belt indentation rolling resistance calculations

Rubber stress relaxation models are the main material input data for numerical and analytical conveyor belt indentation rolling resistance calculations. Stress relaxation data for rubbers, such as those used in the construction of conveyor belts, are difficult to measure directly due to their fast relaxation times and, as such, they are usually derived via a dynamic mechanical analysis; unfortunately, relaxation data for the strain levels reached in conveyor belting cannot be produced with typical dynamic mechanical analysis machines. This paper utilizes high strain level data produced on a high capacity dynamic mechanical analysis machine and compares the indentation rolling resistance predictions derived from the measured high strain relaxation moduli with other high strain relaxation moduli extrapolated from low strain level measurements that can be measured on dynamic mechanical analysers with smaller capacities. Jonker’s equation and a two dimensional finite element analysis model are used to compare the different sets of relaxation moduli and these are compared with results from large scale indentation rolling resistance experiments.

     

Lambertian radiance and transmission of an integrating sphere

The importance of Lambertian transmission, rather than total transmission, is argued and expressions for both are given. Exact expressions for output radiance are given in terms of both total sphere area and port area. A formula for choosing sphere size to give the maximum Lambertian transmission is developed. Port fractions in the range of 0.1-0.2 are recommended.