Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

Abstract. The purpose of this work is to evaluate the performance of a dual Kalman filter procedure in retrieving states and parameters of a one-dimensional soil water budget model based on the Richards equation, by assimilating near-surface soil water content values during evaporation experiments carried out under laboratory conditions. The experimental data set consists of simultaneously measured evaporation rates, soil water content and matric potential profiles. The parameters identified by assimilating the data measured at 1 and 2 cm soil depths are in very good agreement with those obtained by exploiting the observations carried out in the entire soil profiles. A reasonably good correspondence has been found between the parameter values obtained from the proposed assimilation technique and those identified by applying a non-sequential parameter estimation method. The dual Kalman filter also performs well in retrieving the water state in the porous system. Bias and accuracy of the predicted state profiles are affected by observation depth changes, particularly for the experiments involving low state vertical gradients. The assimilation procedure proved flexible and very stable in both experimental cases, independently from the selected initial conditions and the involved uncertainty

Kalman filters for assimilating near-surface observations into the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

Abstract. This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study

Mesoscopic rings with Spin-Orbit interactions

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground state properties. Spin currents are derived following an intuitive definition and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin 1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate Condensed Matter Physics course

Copper content and resistance mechanisms in the terrestrial moss ptychostomum capillare: A case study in an abandoned Copper Mine in Central Spain

We present a case study on the tissue absorption of copper of a widely distributed moss species, Ptychostomum capillare in the polluted soil of an abandoned copper mine in central Spain. We studied the soil properties in a copper soil pollution gradient and sampled the moss tufts growing on them in four plots with contrasted soil copper levels. We determined the copper content in the soil and in the moss tissues. On these moss samples, we also performed histochemical tests and X-ray dispersive spectrometry coupled with scanning electron microscopy (SEM-EDX), both in untreated shoots and in samples where surface waxes were removed. We checked the behavior of this species using a metallophillous moss, Scopelophila cataractae, for comparative purposes. Copper contents in P. capillare seem to depend more on available, rather than total soil copper contents. Our results indicate that this moss is able to concentrate 12-fold the available soil copper in soil with low available copper content, whereas in the most polluted soil the concentration of Cu in the moss was only half those levels. Both histochemical and SEM-EDX tests show no surface copper in the mosses from the least polluted plot, whereas in samples from the soil with highest copper content, the removal of surface waxes also reduces or removes copper from the moss shoots. Our observations point at a mixed strategy in P. capillare in this copper mine, with metal accumulation behavior in the lowest Cu plot, and an exclusion mechanism involving wax-like substances acting as a barrier in the most polluted plots. These distortions impede the estimation of environmental levels and thus compromise the value of this moss in biomonitoring. We highlight the need of extending these studies to other moss species, especially those used in biomonitoring program

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

Survey for ‘Candidatus Liberibacter’ and ‘Candidatus Phytoplasma’ in Citrus in Chile

The considerable economic losses in citrus associated with ‘Candidatus Liberibacter’ and ‘Candidatus Phytoplasma’ presence have alerted all producing regions of the world. In Chile, none of these bacteria have been reported in citrus species. During the years 2017 and 2019, 258 samples presenting symptoms similar to those associated with the presence of these bacteria were examined. No detection of ‘Ca. Liberibacter’ associated with “huanglongbing” disease was obtained in the tested samples; therefore, this quarantine pest is maintained as absent in Chile. However, 14 plants resulted positive for phytoplasmas enclosed in subgroups 16SrV-A (12 plants) and 16SrXIII-F (2 plants). Although they have been found in other plant species, this is the first report of these phy-toplasmas in citrus worldwide

Directed paths on hierarchical lattices with random sign weights

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition'' using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($n\to 0$) to obtain for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic'' structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure