Identifying linear and non-linear behaviour in reduced complexity modelling output using surrogate data methods

Validation of model output is an important issue in the environmental sciences. This is particularly the case for reduced complexity modelling approaches where verification of the underlying equations is often problematic. Hence, methods that go beyond validation based on average values or the histogram of model output, are clearly advantageous. In this paper we show that a validation method based on the serial properties of time–space data, and developed in geomorphology, is a useful alternative but is nevertheless still insensitive to certain asymmetric characteristics of the signal. Hence, use of this method for validation may be enhanced by the adoption of an accompanying test for asymmetry in the model output.     

Reduced complexity strategies for modelling urban floodplain inundation

Significant advances in flood inundation modelling have been made in the last decade through the use of a new generation of 2D hydraulic numerical models. These offer the potential to predict the local pattern and timing of flood depth and velocity, enabling informed flood risk zoning and improved emergency planning. With the availability of high resolution DEMs derived from airborne lidar, these models can theoretically now be routinely parameterized to represent considerable topographic complexity, even in urban areas where the potential exists to represent flows at the scale of individual buildings. Currently, however, computational constraints on conventional finite element and volume codes typically require model discretization at scales well below those achievable with lidar and are thus unable to make optimal use of this emerging data stream.In this paper we review two strategies that attempt to address this mismatch between model and data resolution in an effort to improve urban flood forecasts. The first of these strives for a solution by simplifying the mathematical formulation of the numerical model by using a computationally efficient 2D raster storage cell approach coupled to a 1D channel model. This parsimonious model structure enables simulations over large model domains offering the opportunity to employ a topographic discretization strategy which explicitly represents the built environment. The second approach seeks to further reduce the computational overhead of this raster method by employing a subgrid parameterization to represent the effect of buildings and micro-relief on flow pathways and floodplain storage. This multi-scale methodology enables highly efficient model applications at coarse spatial resolutions while retaining information about the complex geometry of the built environment.These two strategies are evaluated through numerical experiments designed to reconstruct a flood in the small town of Linton in southern England, which occurred in response to a 1 in 250 year rainfall event in October 2001. Results from both approaches are encouraging, with the spatial pattern of inundation and flood wave propagation matching observations well. Both show significant advantages over a coarse resolution model without subgrid parameterisation, particularly in terms of their ability to reproduce both hydrograph and inundation depth measurements simultaneously, without need for recalibration. The subgrid parameterization is shown to achieve this without contributing significant computational complexity and reduces model run-times by an order of magnitude.     

Installation of a vertical slurry wall around an Italian quarry lake: complications arising and simulation of the effects on groundwater flow

Slurry walls are non-structural barriers that are constructed underground to impede groundwater flow or manage groundwater control problems. The study area is in the Piemonte plain (Italy), close to the River Po. Quarrying works carried out below the piezometric surface created two big quarry lakes. The local groundwater system is characterized by a lower semi-confined aquifer, which is overlain by a semi-permeable bed of clayey peat (aquitard) and an upper unconfined aquifer. Locally, the peat fades away and the granulometry of this horizon becomes silty sandy. A planned enlargement of the quarry will increase the size and depth of the quarry lakes. So the aquitard bed between the two aquifers will be damaged, creating a mixing rate of groundwater. Such a procedure would not be compatible with the presence of two municipal wells upstream from the quarries. Consequently, the installation of a vertical diaphragm (slurry wall) is recommended to separate the aquifers and to act as a filter for the groundwater flowing from the unconfined to the semi-confined aquifer. To predict the consequences caused by the installation of the vertical diaphragm separating the unconfined aquifer and the semi-confined one, a specifically adjusted finite-difference model was used. The model showed a maximum rising of the water table equal to 12 cm, just upstream of the diaphragm and for a distance of about 100 m, and a maximum lowering of 2 cm just downstream of the diaphragm. However, the slurry wall would not cause any change in the piezometric head in the area where there are municipal wells and, hence, will not have any negative effect on the functionality of the municipal wells. Moreover, the migration of water from the unconfined aquifer through the vertical diaphragm will stimulate a series of attenuation and auto-depuration processes of eventual contaminants. These processes are due to the higher crossing time that the groundwater flow takes to go through the vertical barrier (t _a = 96.5 days, whereas for the horizontal semi-permeable layer t _a = 9.6 days). So, the vertical diaphragm can be a resolutive element, representing a mediation and separation factor between the unconfined and the semi-confined aquifers along the border of the quarrying areas, and a protective barrier for the water quality of the quarry lake and the semi-confined aquifer.     

Inverse groundwater modelling in the Willunga Basin,South Australia

A new inverse technique for modelling groundwater flow, based on a functional minimization technique, has been used to calibrate a groundwater flow model of a subregion of the Port Willunga aquifer within the Willunga Basin in South Australia. The Willunga Basin is the location of extensive viticulture, irrigated primarily by groundwater, the levels and quality of which have declined significantly over the last 40 years. The new method is able to generate estimates of transmissivity, storativity and groundwater recharge over the whole subregion as a time-varying continuous surface; previous methods estimate local discrete parameter values at specific times. The new method has also been shown to produce accurate head values for the subregion and very good estimates of groundwater recharge. Its ultimate goal will be to provide a new and invaluable tool for significantly improved groundwater resource management. Supported in part by US National Science Foundation grants, DMS-0107492 and DMS-0079478.     

Core–mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J ₂) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10¹⁸ Pa s, the postseismic J ₂ variation in the next years is expected to leave a detectable signal in geodetic observations.     

A structural model for the seismicity of the Arudy (1980) epicentral area (Western Pyrenees, France)

The Western Pyrenees presents a diffuse and moderate ( M ≤ 5.7) instrumental seismicity. It nevertheless historically suffered from strong earthquakes (I = IX MSK). The seismic sources of these events are not yet clearly identified. We focus on the Arudy (1980) epicentral area ( M = 5.1) and propose here the reactivation of early Cretaceous normal faults of the Iberian margin as a potential source. The late Cretaceous inversion of this basin, first in a left-lateral strike-slip mode and then in a more frontal convergence, resulted in a pop-up geometry. This flower structure attests of the presence of a deep crustal discontinuity.
The present-day geodynamic arrangement suggests that this accident is reactivated in a right lateral mode. This reactivation leads to a strain partitioning between the deep discontinuity that accommodates the lateral component of the motion and shallow thrusts, rooted on this discontinuity. These thrusts accommodate the shortening component of the strain. The distribution of the instrumental seismicity fits well the structural model of the Arudy basin. Whatever the compressive regional context, the structural behaviour of the system explains too the extensive stress tensor determined for the Arudy crisis if we interpret it in terms of strain ellipsoid. Indeed numerical modelling has shown that this concomitant activity of strike-slip and thrust faulting results in an extensive component that can rise 50 per cent of the finite strain.
We identify too a 25–30 km long potential seismic source for the Arudy area. The size of the structure and its potential reactivation in a strike-slip mode suggest that a maximum earthquake magnitude of ∼6.5 could be expected. The extrapolation of this model at the scale of the Western Pyrenees allows to propose other potential sources for major regional historical earthquakes.     

Fault induced permanent ground deformations: Experimental verification of wet and dry soil, numerical findings’ relation to field observations of tunnel damage and implications for design

Few building codes contains provisions fault surface ruptures and accompanying soil deformations which constitutes a great risk to human lives, buildings and infrastructure. A numerical and experimental comparison show a fair agreement of result. Analysis of “real” scale show the how water increases the incompressibility of wet soil causing shear deformations to become larger and conjugate ruptures to appear for reverse faults. Field observations and numerical analysis indicates that horizontal compression of soil surrounding underground structures should be taken into account in design.     

Influence of the Kunlun Mountain Ms8.1 Earthquake on Horizontal Crustal Deformation in the Sichuan and Yunnan Area

In order to track the space-time variation of regional strain field holistically(in a large scale) and to describe the regional movement field more objectively,the paper uses a nonlinear continuous strain model focused on extracting medium-low frequency strain information on the basis of a region with no rotation.According to the repeated measurements(1999～2001～2004) from GPS monitoring stations in the Sichuan and Yunnan area obtained by the Project of "China Crust Movement Measuring Network",and with the movement of 1999～2001(stage deformation background) as the basic reference,we separated the main influencing factors of the Kunlun Mountain M-S8.1 earthquake in 2001 from the data of 2001 and 2004,and the results indicate:(1) the Kunlun Mountain M-S8.1 earthquake has a discriminating effect on the Sichuan and Yunnan area,moreover,the deformation mode and background had not only certain similitude but also some diversity;(2) The movement field before the earthquake was very ordinal,while after the earthquake,order and disorder existed simultaneously in the displacement field;The displacement quantities of GPS monitoring stations were generally several millimeters;(3) The principal strain field before earthquake was basically tensile in an approximate EW direction and compressive in the SN direction,and tension was predominant.After the earthquake,the principal strain field in the Sichuan area was compressive in the EW direction and tensile in the SN direction,and the compression was predominant.In the Yunnan area,it was tensional in the NE direction and compressive in the NW direction,and tension was predominant;(4) The surficial strain before the earthquake was dominated by superficial expansion,the contractive area being located basically in the east boundary of Sichuan and Yunnan block and its neighborhood.After the earthquake,the Sichuan area was surface contractive(the further north,the greater it was),and south of it was an area of superficial expansion.Generally speaking,the Kunlun Mountain M-S8.1 earthquake played an active role in the accumulation of energy in the Sichuan and Yunnan area.Special attention shall be focused on the segment of Xichang-Dongchuan and its neighborhood.