Combining statistical learning and geostatistical approaches in a spatiotemporal framework for low flow estimation

<p><span>This paper aims to develop a spatiotemporal model to estimate monthly low flow quantiles Q95 [P(Q<Q95=0.05)] standardized by catchment area in Austria. Our dataset consists of 325 gauging stations that where consistently monitored between 1976 to 2015, and it covers about 60% of the national territory of Austria. </span></p><p><span>In a first step we are adapting a spatiotemporal model initially designed for modeling air pollution data. This approach is based on empirical orthogonal functions (EOF), that should capture the temporal structure of the spatiotemporal model. The EOFs are weighted by regression coefficients estimated by universal kriging. We extend the model by using GLM-boosting, LASSO, Principal Component Regression (PCR) and Random Forest (RF) for selecting the regression coefficients of the EOFs. Furthermore, we do not limit the kriging structure of the residual field to geographical coordinates but use a broader approach of physiographic kriging. In a second step we implement separate models for the mean parts of the model and the residual parts of the model. The mean field is defined by statistical learning methods as RF, GAM-boosting, LASSO and Support Vector Machines (SVM). For the residual field we define two different approaches, either the </span><span>method developed in the first step</span><span> or spatiotemporal kriging.</span></p><p><span>Model performance is evaluated by cross validation and the best model is selected by the mean squared error (MSE). </span></p><p> </p>

Structure of unital 3-fields

We investigate fields in which addition requires three summands. These ternary fields are shown to be isomorphic to the set of invertible elements in a local ring $$\mathcal{R}$$ R having $$\mathbb{Z}\diagup 2\mathbb{Z}$$ Z / 2 Z as a residual field. One of the important technical ingredients is to intrinsically characterize the maximal ideal of $$\mathcal{R}$$ R . We include a number of illustrative examples and prove that the structure of a finite 3‑field is not connected to any binary field.

Investigation of the Influence of Distant Parameters on Horizontal Component of Ground Magnetic Field.

The influence of distant parameters on the horizontal component of magnetic field was investigated for two years within two locations in Africa. The measure of storm occurrence (Dst-index) was used to select successful storm days. The effect of distant parameters on residual field was investigated using filter analysis. This study was considered on both time domain and frequency domain. The results showed very close correspondence of rapid changes in amplitudes between residual H–component and the selected IMF parameters especially the solar wind velocity, proton density and Bz. The correlation analysis between the distant parameters and residual H–component completely revealed effective dependence of the depression of residual field on the selected parameters. The value of the correlation coefficient (r) with solar wind velocity, proton density and Bz showed significant values of the range of 0.5 and above. This is direct evidence that Solar wind velocity, proton density and Bz are more effective in causing geomagnetic fluctuations at equatorial low latitude stations.

Low-rank matrix decomposition method for potential field data separation

Separation of potential field data forms the basis of inversion and interpretation. The low-rank matrix theory is used for the separation of potential field data. A theoretical analysis led to the approximate equation that demonstrates the relation between the amplitudes of the wavenumber components of potential field data and the singular values of the trajectory matrix embedded from the potential field data matrix. Therefore, the low-rank feature of the trajectory matrix of regional field data and the sparse feature of the trajectory matrix of residual field data can be obtained based on the features of the power spectrum of the potential field data. Based on this, we have developed a low-rank matrix decomposition model for the separation of the trajectory matrix of the potential field data. Minimizing the rank of the trajectory matrix of the regional field data and the [Formula: see text]-norm of the trajectory matrix of the residual field data is a double-objective optimization task, and this optimization task can be solved by the inexact augmented Lagrange multiplier algorithm. The weighting parameter is robust and easy to set. Numerical experiment results indicate that our method is robust, and the separation errors of the method are smaller compared to the matched filtering and wavelet analysis methods. In addition, our method can be easily implemented and has clear geophysical significance. Finally, our method is applied on real data sets in the Daye area, Hubei Province, China. The separated gravity and magnetic fields coincide well with target geologic sources.

On the HN-integration of spatial (integral) derivatives of multivector fields with singularities in RN

A method of spatial (integral) differentiation of multivector fields in an N -dimensional manifold M, into which a hyper-rectangle [a,b] is mapped by a bijective smooth map r : [a,b] ? M, has been introduced. For a class of discontinuous multivector fields a new concept of a residual field as well as the concept of total HN integrability have been defined. Finally, this led naturally to an extension of Cauchy?s residue theorem in M.

THE METHOD TO SOLVE DRIFT IN MAIN GEOMAGNETIC FIELD

The method to solve the velocity of drift in MGF is written in this paper. This method is based on the dynamo theory for geomagnetic field. The velocity of drift in the main geomagnetic field is also solved from the condition that the power variation of residual field equals zero in few years.