A regression technique for evaluation and quantification for water quality parameters from remote sensing data

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined

Stem-root flow effect on soil–atmosphere interactions and uncertainty assessments

Abstract. Soil water can rapidly enter deeper layers via vertical redistribution of soil water through the stem–root flow mechanism. This study develops the stem–root flow parameterization scheme and coupled this scheme with the Simplified Simple Biosphere model (SSiB) to analyze its effects on land–atmospheric interactions. The SSiB model was tested in a single column mode using the Lien Hua Chih (LHC) measurements conducted in Taiwan and HAPEX-Mobilhy (HAPEX) measurements in France. The results show that stem–root flow generally caused a decrease in the moisture content at the top soil layer and moistened the deeper soil layers. Such soil moisture redistribution results in significant changes in heat flux exchange between land and atmosphere. In the humid environment at LHC, the stem–root flow effect on transpiration was minimal, and the main influence on energy flux was through reduced soil evaporation that led to higher soil temperature and greater sensible heat flux. In the Mediterranean environment of HAPEX, the stem–root flow significantly affected plant transpiration and soil evaporation, as well as associated changes in canopy and soil temperatures. However, the effect on transpiration could either be positive or negative depending on the relative changes in the moisture content of the top soil vs. deeper soil layers due to stem–root flow and soil moisture diffusion processes

On the expected uniform error of geometric Brownian motion approximated by the L\'evy-Ciesielski construction

It is known that the Brownian bridge or L\'evy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show for geometric Brownian motion that at level $N$, at which there are $d=2^N$ points evaluated on the Brownian path, the expected uniform error has an upper bound of order $\mathcal{O}(\sqrt{N/2^N})$, or equivalently, $\mathcal{O}(\sqrt{\ln d/d})$. This upper bound matches the known order for the expected uniform error of the standard Brownian motion. We apply the result to an option pricing example

Criteria for the use of regression analysis for remote sensing of sediment and pollutants

Data analysis procedures for quantification of water quality parameters that are already identified and are known to exist within the water body are considered. The liner multiple-regression technique was examined as a procedure for defining and calibrating data analysis algorithms for such instruments as spectrometers and multispectral scanners

Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the required variance reduction for the multilevel scheme to achieve an $\varepsilon$-error with a cost of $\mathcal{O}(\varepsilon^{-\theta})$ with $\theta < 2$, and in practice even $\theta \approx 1$, for sufficiently fast decaying covariance kernels of the underlying Gaussian random field inputs. This confirms that the computational gains due to the application of multilevel sampling methods and the gains due to the application of QMC methods, both demonstrated in earlier works for the same model problem, are complementary. A series of numerical experiments confirms these gains. The results show that in practice the multilevel QMC method consistently outperforms both the multilevel MC method and the single-level variants even for non-smooth problems.Comment: 32 page