Improving Bowen-ratio estimates of evaporation using a rejection criterion and multiple-point statistics

The application of the Bowen ratio method to estimate evaporation is heavily affected by uncertainties on the measured quantities. Time series collected with a hydro-meteorological monitoring station often contain measurements for which a reliable estimate of evaporation cannot be computed. Such measurements can be identified with standard error propagation methods. However, simply discarding some values might introduce a bias in the cumulative evaporation for long time intervals, also depending on the threshold of acceptance. In this paper, we propose the use of multiple-point statistics simulation to integrate the time series of reliable evaporation estimates. A test conducted on a two-year-long time series of data collected with a hydro-meteorological station in the Po plain (Italy) shows that the usage of a rejection criteria in conjunction with multiple-point statistics simulation is a promising and useful tool for the reconstruction of reliable evaporation time series. In particular, it is shown that if the rejected values are not replaced by simulation, then the cumulative evaporation curves are estimated with a bias comparable with estimates of cumulative annual evaporation. Moreover, the test gives some insights for the selection of the best rejection threshold

A new perspective to model subsurface stratigraphy in alluvial hydrogeological basins, introducing geological hierarchy and relative chronology

This paper presents a novel perspective for modelling alluvial stratigraphy. It integrates the spatial geological information, geological maps and well-log descriptions, with the rules describing the hierarchy and relative chronology of the geological entities. As geological modelling tools are moving fast forward, the urgent need for expert geological input, codified as modelling rules, persists. Concerning subsurface alluvial architectures, the concepts of \u201cstratigraphic hierarchy\u201d and \u201crelative chronology\u201d provide the most relevant rules which permit to link the modelling procedure to the geo-history of a region. The paper shows how to formalize this knowledge into modelling rules. This is illustrated and implemented in a Python\u2122 module named HIEGEO which is applied on a 2-D cross-section from the Po Basin (N-Italy). The stratigraphic correlation yields 2-D pictures of the hierarchic stratigraphy and relative chronology of the units. The input are: an attribute table of stratigraphic boundaries expressing their hierarchy and chronology; contact points where these boundaries cross the control logs. Since the aim of HIEGEO is to illustrate the principle of the method but not to replace existing 3-D geological modelling tools, it implements a linear interpolation algorithm which creates joins between contact points. It plots linear joins framing polygons based on their hierarchy, at any user\u2019s desired detail. HIEGEO highlights potential inconsistencies of the input dataset, helping to re-evaluate the geological interpretation. The proposed workflow allows to: i) translate geological knowledge into modelling rules; ii) compute stratigraphic models constrained by the hierarchy of stratigraphic entities and the relative chronology of geological events; iii) represent internal geometries of the stratigraphic units, accounting for their composite nature; iv) reduce uncertainty in modelling alluvial architectures. It represents a starting point for multi-scale applications and could be easily integrated into 3-D modelling packages, to couple the hierarchical concept proposed here with existing advanced interpolation methods

Frequency map analysis of a three-dimensional particle in the core model of a high intensity linac

We consider the dynamical properties of a particle-core model for a uniformly filled triaxial ellipsoid in a periodic lattice of a high intensity linac. The mismatched oscillation modes are analytically computed in the smooth approximation and are compared with the numerical results of a tracking program. The study of the phase space in the mismatched case is performed by the frequency map analysis. In particular, we can analyze the effect of the nonlinear resonances between the envelope modes and the single particle sincrobetatron frequencies. A chaoticity criterion based on the frequency map analysis allows one to compute the stability region around the beam core. An estimate of the transport and its enhancement due to mismatch is provided by tracking orbits at the border of the stability region

Land Settlement Act Amendment Act, 1957, No. 26

In recent years, there has been a widespread interest in the economic development role played by 'Bohemian' occupations and the 'creative class'. It is believed that creative people and occupations generate external effects which foster economic growth. However, the degree to which these externalities affect production and consumption is as yet not clear. As part of this debate, we investigate the ability of creative individuals to internalize the rents accruing from creative occupations in comparison with other types of activities. In order to do this, the paper analyzes the employment opportunities and wages earned by graduates in artistic occupations (Bohemians) and compares them with those of non-Bohemians. Using a uniquely longitudinal dataset of UK university graduates, we examine these issues using a Mincer-type framework, both in the short and in medium term after graduation. Our findings suggest that there is a persistent gap between Bohemian and non-Bohemians in terms of both the wages earned and employment status. This observation sharpens the need to better understanding the nature and extent of the externalities associated with the creative class which remains an unresolved issue

3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells

We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances

Hybrid Inversion Method to Estimate Hydraulic Transmissivity by Combining Multiple-Point Statistics and a Direct Inversion Method

Inversion methods that rely on measurements of the hydraulic head h cannot capture the fine-scale variability of the hydraulic properties of an aquifer. This is particularly true for direct inversion methods, which have the further limitation of providing only deterministic results. On the other hand, stochastic simulation methods can reproduce the fine-scale heterogeneity but cannot directly incorporate information about the hydraulic gradient. In this work, a hybrid approach is proposed to join a direct inversion method (the comparison model method, CMM) and multiple-point statistics (MPS), for determination of a hydraulic transmissivity field T from a map of a reference hydraulic head and a prior model of the heterogeneity (a training image). The hybrid approach was tested and compared with pure MPS and pure CMM approaches in a synthetic case study. Also, sensitivity analysis was performed to test the importance of the acceptance threshold , a simulation parameter that allows one to tune the influence of on the final results. The transmissivity fields T obtained using the hybrid approach take into account information coming from the hydraulic gradient while simultaneously reproducing some of the fine-scale features provided by the training image. Furthermore, many realizations of T can be obtained thanks to the stochasticity of MPS. Nevertheless, it is not straightforward to exploit the correlation between the T maps provided by the CMM and the prior model introduced by the training image, because the former depends on the boundary conditions and flow settings. Another drawback is the growing number of simulation parameters introduced when combining two diverse methods. At the same time, this growing complexity opens new possibilities that deserve further investigation

Reproducing the small-scale variability of a transmissivity field by embedding direct-inversion methods in multiple-point geostatistics

Parameter estimation represents one of the critical steps in every modeling workflow. Among the techniques proposed to tackle this problem, direct inversion methods are appealing because they are faster than indirect methods by some order of magnitude. Nevertheless, they cannot reproduce the small-scale variability of the parameters fields because they rely upon information, like for example hydraulic head measurements h, that represents only the long-wavelength components of the parameter field. In this work we apply a direct inversion method, the Comparison Model Method (CMM) [1], which is used to estimate the long-wavelength components of a transmissivity field T . The CMM is used in conjunction with a geostatistical simulation method, multiple-point geostatistics (MPG) [2], which is based on the concept of training image (TI) [3]. The TI is a conceptual model containing the heterogeneity patterns that could be found in a given geological environment (akin to the site under investigation) and that contains all the components of the expected heterogeneity. The long-wavelength T field, estimated with the CMM using the reference h fields estimated on measurements and other information from the conceptual model, is used as an auxiliary variable in the MPG simulation. This allows injecting into the MPG simulation additional site-specific information. The procedure can be iterated to improve the agreement with the measurements. The T field resulting from this hybrid-inversion procedure contains the short-wavelength components that cannot be reproduced by direct inversion methods alone. In addition, multiple realizations of the estimated T field can be obtained using different random seeds. Both the advantages and the disadvantages of the proposed procedure lie in the usage of a TI image. The TI allows including useful soft information in the inversion procedure, but at the same time represents a strong a priori assumption

A hybrid inversion method to estimate hydraulic transmissivity using multiple-point statistics and the comparison model method

An accurate parameterization of the subsurface is required to properly model fluid flow and transport in porous media. For example, when modelling a 2D confined aquifer, one of the parameters required is the hydraulic transmissivity T, which is rarely accessible for all the nodes of the simulation grid. Inverse modelling provides a number of tools and methods to tackle this problem. Among the others, the Comparison Model Method (CMM) is a direct method of inversion and allows to estimate a T field for a confined aquifer given one reference hydraulic head field (interpolated on the same simulation grid), the corresponding source/sink terms and a tentative initial model for T (comparison model, CM). One of the advantages of the CMM is its computational efficiency as it is based on the solution of a forward problem or the CM. Nevertheless, the CMM suffers from some drawbacks. For example, as the information used in the inversion process mainly come from the hydraulic heads, the fine-scale details of the T field are lost because the hydraulic heads only represent the long-wavelength components of the parameter field. To cope with this drawback, we propose an hybrid inversion method that allows to inject additional information coming from a prior model of heterogeneity making use of multiple-point statistics (MPS). MPS is a geostatistical simulation technique based on the concept of training image (TI), which is a conceptual model that contains the expected patterns of heterogeneity. In the proposed hybrid inversion method the CMM and MPS are applied iteratively. For the first iteration, the tentative initial T field is extracted from a TI. Then, the T field resulting from each CMM inversion step is used as auxiliary variable to perform an MPS simulation. These auxiliary variables, which contain the information related to the available measurements of hydraulic head, are used in the following iteration steps to improve the MPS simulation of a new tentative initial T field for the CMM. The proposed method is tested on two synthetic datasets. The prior information provided by the TI allows to reduce the loss of short-wavelength components of the T fields which cannot be reproduced by the application of the CMM alone. At the same time, the proposed hybrid inversion method allows to inject information coming from hydraulic head measurements and to improve MPS simulation

Identifying the hydraulic transmissivity of an aquifer with noisy hydraulic head data: a comparison study using three direct inversion methods

The parameters required to set up an hydrological model are often obtained by solving an inverse problem, using indirect or direct solution methods. Indirect methods are widely used, in particular when the state variable (here the hydraulic head h) is known at sparse locations only. Despite their flexibility, when the number of parameters rises, their computational requirements can become a challenging issue, together with problems related to non-uniqueness and instability. On the other side, direct methods have other limitations, including a more exhaustive knowledge of the state variables, but are less demanding in terms of computational resources. In this work three direct inversion methods are compared: the Comparison Model Method (CMM), the Double Constraint Method (DCM) and the Differential System Method (DSM). The three methods are compared on a two-dimensional synthetic aquifer, whose geometry, boundary conditions and h measurements are realistic and extracted from a data set collected for the aquifer of Weiach, north of Switzerland. Sequential-Gaussian simulation (SGS) was used to generate a transmissivity field (T ) for the aquifer, which was then used to obtain the h data required by the three methods. A noise of increasing magnitude was added to h to verify the stability of the methods with respect to noisy input data. For a small noise on the input h, the results obtained with the three methods are comparable. However, for more noisy data, the DCM is more robust, whereas the DSM is very sensitive to the position of the starting point for integration and to the T value assigned there