Calibration of Parameter Fields Consisting of Multiple Statistical Populations

If a parameter field to be calibrated consists of more than one statistical population, usually not only the parameter values are uncertain, but the spatial distributions of the populations are uncertain as well. In this study, we demonstrate the potential of the multimodal calibration method we proposed recently for the calibration of such fields, as applied to real-world ground water models with several additional stochastic parameter fields. Our method enables the calibration of the spatial distribution of the statistical populations, as well as their spatially correlated parameterization, while honoring the complete prior geostatistical definition of the multimodal parameter field. We illustrate the implications of the method in terms of the reliability of the posterior model by comparing its performance to that of a "conventional" calibration approach in which the positions of the statistical populations are not allowed to change. Information from synthetic calibration runs is used to show how ignoring the uncertainty involved in the positions of the statistical populations not only denies the modeler the opportunity to use the measurement information to improve these positions but also unduly influences the posterior intrapopulation distributions, causes unjustified adjustments to the cocalibrated parameter fields, and results in poorer observation reproduction. The proposed multimodal calibration allows a more complete treatment of the relevant uncertainties, which prevents the abovementioned adverse effects and renders a more trustworthy posterior model.     

HYDRO_GEN: A spatially distributed random field generator for correlated properties

This paper describes a new method for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences. The method is based on two observations: (i) spatially distributed attributes usually display a stationary correlation structure, and (ii) the screening effect of measurements leads to the sufficiency of a small search neighborhood when it comes to projecting measurements and data in space. The algorithm which was developed based on these principles is called HYDRO_GEN, and its features and properties are discussed in depth. HYDRO_GEN is found to be accurate and extremely fast. It is also versatile: it can simulate fields of different nature, starting from weakly stationary fields with a prescribed covariance and ending with fractal fields. The simulated fields can display statistical isotropy or anisotropy.     

Structure function as a characteristic of geophysical fields

Summary Facts about the statistical properties of random fields may be obtained by analysing their increments (i.e. the differences of values at two points). The properties of structure functions are described and the possibility of testing the statistical homogeneity of geophysical fields and their possible homogeneization are discussed.     

Influence of spatial variations of microtopography and infiltration on surface runoff and field scale hydrological connectivity

Surface runoff on agricultural fields arises when rainfall exceeds infiltration. Excess water ponding in and flowing through local microtopography increases the hydrological connectivity of fields. In turn, an increased level of hydrological connectivity leads to a higher surface runoff flux at the field boundaries. We investigated the functional hydrological connectivity of synthetical elevation fields with varying statistical properties. For this purpose, we developed an object-oriented ponding and redistribution model to which Philip’s infiltration model was coupled. The connectivity behaviour is determined by the presence of depressions with a large area and spatial organization of microtopography in rills or channels. The presence of microdepressions suppresses the effect of the spatial variation of infiltration properties. Connectivity behaviour of a field with a varying spatial distribution of infiltration properties can be predicted by transforming the unique connectivity function that was defined for a designated microtopography.     

Distance-based kriging relying on proxy simulations for inverse conditioning

Let us consider a large set of candidate parameter fields, such as hydraulic conductivity maps, on which we can run an accurate forward flow and transport simulation. We address the issue of rapidly identifying a subset of candidates whose response best match a reference response curve. In order to keep the number of calls to the accurate flow simulator computationally tractable, a recent distance-based approach relying on fast proxy simulations is revisited, and turned into a non-stationary kriging method where the covariance kernel is obtained by combining a classical kernel with the proxy. Once the accurate simulator has been run for an initial subset of parameter fields and a kriging metamodel has been inferred, the predictive distributions of misfits for the remaining parameter fields can be used as a guide to select candidate parameter fields in a sequential way. The proposed algorithm, Proxy-based Kriging for Sequential Inversion (ProKSI), relies on a variant of the Expected Improvement, a popular criterion for kriging-based global optimization. A statistical benchmark of ProKSI’s performances illustrates the efficiency and the robustness of the approach when using different kinds of proxies.     

Modeling, synthetics and engineering applications of strong earthquake wave motion

State of the art in modeling, synthetics, statistical estimation, and engineering applications of strong ground motion is reported in this paper. In particular, models for earthquake wave motion are presented, in which uncertainties both in the earth medium and the seismic source are taken into consideration. These models can be used to synthesize realistic strong earthquake ground motion, specifically near-field ground motion which is quite often not well recorded in real earthquakes. Statistical estimation techniques are also presented so that the characteristics of spatially-correlated earthquake motion can be captured and consequently used in investigating the seismic response of such large scale structures as pipelines and long-span bridges. Finally, applications of synthesized strong ground motion in a variety of engineering fields are provided. Numerical examples are shown for illustration.     

Lateral stirring of large-scale tracer fields by altimetry

Ocean surface fronts and filaments have a strong impact on the global ocean circulation and biogeochemistry. Surface Lagrangian advection with time-evolving altimetric geostrophic velocities can be used to simulate the submesoscale front and filament structures in large-scale tracer fields. We study this technique in the Southern Ocean region south of Tasmania, a domain marked by strong meso- to submesoscale features such as the fronts of the Antarctic Circumpolar Current (ACC). Starting with large-scale surface tracer fields that we stir with altimetric velocities, we determine ‘advected’ fields which compare well with high-resolution in situ or satellite tracer data. We find that fine scales are best represented in a statistical sense after an optimal advection time of ～2 weeks, with enhanced signatures of the ACC fronts and better spectral energy. The technique works best in moderate to high EKE regions where lateral advection dominates. This technique may be used to infer the distribution of unresolved small scales in any physical or biogeochemical surface tracer that is dominated by lateral advection. Submesoscale dynamics also impact the subsurface of the ocean, and the Lagrangian advection at depth shows promising results. Finally, we show that climatological tracer fields computed from the advected large-scale fields display improved fine-scale mean features, such as the ACC fronts, which can be useful in the context of ocean modelling.     

On the relationship between indicators of geostatistical,flow and transport connectivity

Connectivity of high conductivity (K) paths is important because it can lead to channeling, i.e. flow along preferential paths, which can reduce travel times very significantly. Nevertheless, limited effort has been devoted to defining the concept quantitatively. We propose and evaluate nine indicators of connectivity. Three account for the presence of flow connectivity, that is, the flow rate increase caused by preferential flow paths. Two account for the presence of transport connectivity, that is, the existence of fast paths allowing early solute arrival. The remaining four are statistical indicators based on two- and multiple-point statistics. We test these indicators on heterogeneous conductivity fields with different visual connectivity. The indicators of flow connectivity and one of the transport connectivity indicators succeed in identifying the increased presence of connected high-K features. The two-point statistical indicators fail to do so. The directional multi-point statistical indicator performs better. None of the statistical indicators correlate with the flow and transport indicators. We find only weak dependence between the flow and transport indicators. Our results suggest that transport connectivity is much less sensitive to barriers, which control flow connectivity. Instead, transport connectivity appears to be controlled by the existence of narrow, possibly discontinuous high-K paths. Therefore, we conclude that connectivity is a process-dependent concept.     

Estimation of the magnetotelluric impedance functions

The successful interpretation of magnetotelluric data demands well presented, and accurate, estimates of the impedance and tipper functions.In this paper, a method based on the singular value decomposition of the local data matrix, using well known results from multivariate statistical analysis, is proposed as an alternative to current least-squares methods. The advantage obtained is that error on all data channels is recognised, so that impedance estimates are not biased by the choice of “independent noise-free” fields.An important result of the method is an extensive and structured capability for the analysis of the frequency-dependent noise which could be used to improve the resulting impedance estimates.     

Impedance-admittance regression analysis of magnetotelluric fields

The paper is devoted to the development of the theory of magnetotelluric field processing. A new method is proposed for complete consistent robust impedance-admittance regression estimation. This approach eliminates divergences between results obtained by independent solution of linear systems for the determination of impedance and admittance matrices and, moreover, is a good stabilizer of solution. Formulas for statistical estimates of results obtained by this method are derived. The theory developed in the paper is based on a linear algebraic approach. The regression problem is analyzed in a linear complex space with a nonrigidly specified metric. The metric of the solution space is formed concurrently with the solution of the problem on the basis of currently processed time series. All statistical estimations of results are performed in the metric obtained as a consequence of the solution and, in this sense, are optimal. The full regression model is effective for diagnosing the presence of electromagnetic fields that cannot be completely reduced to the plane wave approximation. the possibilities of the regression estimation are considered in detail on the basis of correlation analysis applied to sets of spectral components of electromagnetic fields.     

A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere

Many measurements have shown that the random temperature fields in the stably stratified atmosphere are not locally isotropic (LI). The local axial symmetry (LAS) hypothesis looks more appropriate under these conditions. The object of this paper consists in the development of a flexible tool for spectral studies of LAS scalar fields independently of their origin in stably stratified geophysical flows. A heuristic model of a 3D spatial spectrum is proposed in order to describe and study statistical properties of LAS temperature inhomogeneities from LI structures up to quasi-layered ones. To simplify the solution of this problem, a main assumption was accepted: the consideration is restricted to 3D spectra which may be given on a one-parametric family of surfaces of rotation. Such 3D spectra may be represented by a single function of one variable which is the parameter of the family. This approach allows one to introduce the generalized energy spectrum which describes an energy distribution according to inhomogeneity sizes. The family of surfaces determines the shape of inhomogeneities. The family of ellipsoids of rotation and power-law generalized energy spectrum is used as the simplest example of the model application in order to study the general properties of LAS-structure spectra. The behavior of vertical, horizontal, and oblique 1D spectra and coherency spectra is studied. The relationship between the suggested model and some existing models of temperature spectra is considered. The application of the model for the analysis of experimental data is shown for two sets of measurements. It is shown that the suggested model may quantitatively describe experimental 1D spectra and coherency spectra from a unique point of view. It is noted that the model may be used for both the planning of measurements and data processing. Possible generalizations of the model are considered for random fields with more degenerate symmetry and for space-temporal spectra.     

Erosion and terrace failure due to agricultural land abandonment in a semi‐arid environment

Agricultural land abandonment is currently widely spread in Mediterranean countries and a further increase is expected. Previous research has shown that abandoned fields in semi‐arid areas are more vulnerable to gully erosion. The absence of ploughing and slow vegetation recovery cause the formation of soil crusts with low infiltration rates, resulting in increased runoff and gully erosion risk. The objective of our study was to assess the extent and causes of erosion and terrace failure on abandoned fields and to discuss options for mitigation. The study was carried out in the Carcavo basin, a semi‐arid catchment in southeast Spain. At catchment scale all abandoned fields were surveyed and characteristics of each field were described. Additionally we surveyed abandoned and cultivated terraces and used statistical analyses to determine the factors that induce terrace failure. At field scale we constructed a detailed digital elevation model (DEM) for an abandoned terrace field in order to calculate sediment losses since time of abandonment. The results revealed that more than half the abandoned fields had moderate to severe erosion and the statistical analysis showed that these fields had significantly steeper slopes, were terraced and had cereals as previous land use. Factors that increase the risk of terrace failure were land abandonment, steeper terrace slope, loam texture, valley‐bottom position and shrubs on the terrace wall. The reconstructed erosion rate (87 ton ha^?1 year^?1) confirmed the importance of gully erosion on these abandoned terrace fields. Potential soil and water conservation practices to mitigate soil erosion after abandonment are: (1) maintenance of terrace walls, as a result more water is retained, which increases vegetation cover and consequently decreases erosion. (2) Revegetation with indigenous grass species on spots with concentrated flow, especially near terrace walls. Copyright © 2008 John Wiley & Sons, Ltd.     

The relationship between electric fields, conductances and currents in the high-latitude ionosphere: a statistical study using EISCAT data

The relationship between electric fields, height-integrated conductivities and electric currents in the high-latitude nightside electrojet region is known to be complex. The tristatic nature of the EISCAT UHF radar facility provides an excellent means of exploring this interrelationship as it enables simultaneous estimates to be made of the full electric field vector and the ionospheric Hall and Pedersen conductances, further allowing the determination of both field-perpendicular electric current components. Over 1300 h of common programme observations by the UHF radar system provide the basis of a statistical study of electric fields, conductances and currents in the high-latitude ionosphere, from which preliminary results are presented. Times at which there is significant solar contribution to the ionospheric conductances have been excluded by limiting the observations according to solar zenith angle. Initial results indicate that, in general, the times of peak conductance, identified from the entire set of EISCAT observations, do not correspond to the times of the largest electric field values; the relative contribution of ionospheric conductance and electric field to the electrojet currents therefore depends critically on local time, a conclusion which corroborates work by previous authors. Simultaneous measurements confirm a tendency for a decrease in both Hall and Pedersen conductances to be accompanied by an increase in the electric field, at least for moderate and large electric field value, a tendency which is also identified to some extent in the ratio of the conductances, which acts as an indicator of the energy of precipitating particles.     

The possibilities of paleomagnetic and geohistorical analyses of “tiny wiggles” short-period marine magnetic anomalies

Marine magnetic anomalies of the tiny wiggles (TW) type can be used to solve geohistorical and paleomagnetic problems. The model fields corresponding to Paleocene–Eocene anomalies in the northwestern Indian Ocean, which were formed during the fast-spreading stage, were studied. For these fields, widely used interpretation methods were compared with a method proposed previously by the authors. The testing was performed with first the classical block model and then more complex models reflecting actual processes of oceanic accretion and magnetic field variations in the past. It was shown that the proposed method has advantages for this problem; it gives an error close to the minimum possible error and can adequately be used in interpretations. Spectral and statistical methods are used to estimate the magnetic anomaly resolving power and to study some factors that can exert a distorting influence. In addition, model examples have been used to indicate how the TW determination accuracy is affected by diurnal variations in the main magnetic field (MMF) and by ancient magnetization vector determination errors.     

How does the U-shaped potential close above the acceleration region? A study using Polar data

We present a statistical study of Polar electric field observations using auroral oval passes over Scandinavia above the acceleration region. We are especially interested in seeing whether we can find large perpendicular electric fields associated with an upward extended classical U-shaped potential drop for these passes, during which Polar is in the northern hemisphere usually at about 4 R_E altitude. We also use Polar magnetic field data to infer the existence of a field-aligned current (FAC) and conjugate ground-based magnetometers (the IMAGE magnetometer network) to check whether the event is substorm-related or not. We find several events with a FAC but only weak perpendicular electric fields at Polar. In those rare cases where the Polar electric field was large, its direction was mostly found to be incompatible with the U-shaped potential model, or it was associated with disturbed conditions (substorms), where one cannot easily distinguish between inductive and static perpendicular electric fields. We found only two cases which are compatible with the upward extended U-shaped potential picture, and even in those cases the potential value is quite small (1–kV). To check the validity of the analysis method we also estimate the perpendicular electric field on the southern hemisphere, where Polar flies within or below the acceleration region, and we found a large number of inverted-V-type signatures as expected from previous studies. To explain the lack of perpendicular electric fields at high altitudes we suggest an O-shaped potential model instead of the U-shaped one.     

Worth of secondary data compared to piezometric data for the probabilistic assessment of radionuclide migration

A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions.     

Worth of secondary data compared to piezometric data for the probabilistic assessment of radionuclide migration

A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions.     

On the problem of the existence and uniqueness of a discrete,surface, optimum wiener filter,applied to the filtering of geophysical fields

Summary Proof is given of the existence and uniqueness of a discrete, surface, optimum (in the Wiener sense) filter for filtering geophysical fields considering a spectral approach to the construction of the said filter. It is also shown that the filtration coefficients and the filtration errors of the filter, constructed with the help of statistical estimates of the required spectral densities, converge towards their theoretical values. From the mathematical point of view, this paper concludes the building-up of the mathematical model of the discrete Wiener optimum surface filtration, suitable for geophysical fields.