Data Assimilation (4D-VAR) for Shallow-Water Flow: The Case of the Chicoutimi River

This is a web presentation of the work presented at the 10th Annual Conference of the CFD Society of Canada, “CFD 2002”, at the University of Windsor on June 9-11, 2002. This discussion paper presents the four-dimensional variational data assimilation (4D-VAR) technique as a tool to forecast floods. This discussion will be limited to hydrological forecast. We assume that the weather, here a large rainstorm, had already been forecasted by the meteorological services. In the 4D-VAR technique, we need to minimize, in the sense of Lagrange, a cost function which measures the difference between the forecast and the observations. The physical equations acts as a set of constraints. Here, the model is the shallow-water equations modified to include sediment transport. The minimum was found by using the steepest descent algorithm. This is made possible because the gradient of the cost function can be calculated analytically by using the adjoint equations of the model. To illustrate the 4D-VAR technique, the bypass of a simple theoretical dam as well as the more complex overflowing of the Chicoutimi River at the Chute-Garneau dam (during the 1996 flood) are investigated.     

A record of accelerated erosion in the recent sediments of Blelham Tarn in the English Lake district

Two frozen cores from Blelham Tarn were subsampled and measured using mineral magnetic, loss-on-ignition (LOI), radiometric, granulometric and diatom analyses. A detailed chronology was established using varves, radioisotopes and diatoms. This has enabled an accurately dated reconstruction of sedimentation over the past forty years. Despite a large increase in lake productivity, evidence suggests that the observed exponential increase in sedimentation rates can be attributed to erosion within the catchment. The predominant sediment source has been identified as surface soil. A comparison between the trend of accelerated sedimentation and the record of increased sheep stocking density for the area within which the most of the catchment lies, as well as observations of contemporary surface processes within the catchment, both suggest that much of the recent erosion is a direct response to increased pressure from sheep grazing.     

任意圆弧形凸起地形中隧洞对入射平面SH波的影响

借助辅助函数的思想， 采用波函数展开法给出了圆弧形凸起地形中隧洞对入射平面SH波影响问题的一个解析解．数值结果表明，凸起地形中隧洞的存在以及隧洞大小，对凸起地形表面运动，以及凸起地形中的隧洞的动应力集中均具有显著影响．      

Long term variations in the mesospheric mean flow observed at Grahamstown (South Africa) and Adelaide (Australia)

The seasonal and interannual behaviour of monthly mean winds at a height of 90 km recorded at Grahamstown (33.3°S, 26.5°E) and Adelaide (34.5°S, 138.5°E) between 1987 and 1994 are compared. The zonal wind is found to be consistently stronger at Grahamstown and is always eastward, whereas at Adelaide it sometimes reverses. Maxima tend to occur near the solstices, the primary maximum during summer at Grahamstown, in agreement with satellite results, and during winter at Adelaide. The meridional wind also tends to be stronger at Grahamstown, but at both stations is predominantly northward with a maximum in summer and generally not as strong as the zonal component. This seasonal behaviour is reasonably well understood in terms of the interaction of the mean flow with gravity waves propagating up from below, with coriolis forces also playing an important role in the case of the meridional wind. Satellite observations do not generally support the idea that longitudinal differences between the stations could be attributed to the presence of a tropospheric/stratospheric stationary wave. It is suggested that these differences are more probably associated with local effects. Interannual zonal wind patterns at the two sites are similar over the summer months but are less well correlated during the rest of the year. The underlying causes of this variability are not well understood but are most probably global in nature, at least during the summer.     

The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid

This paper discusses surface displacements, surface strain, rocking, and energy partitioning during reflection-of-plane waves in a fluid-saturated poroelastic half-space. The medium is modeled by Biot's theory, and is assumed to be saturated with inviscid fluid. A linear porosity-modulus relation based on experimental data on sandstones is used to determine the material parameters for Biot's model. Numerical results in terms of angle of incident waves and Poisson's ratio are illustrated for various porosities and degrees of solid frame stiffness. The results show that the amount of solid frame stiffness controls the response of a fluid-saturated porous system. A poroelastic medium with essentially dry-frame stiffness behaves like an elastic medium, and the influence of pore fluid increases as dry-frame stiffness is reduced. The effects of a second P-wave become noticeable in poroelastic media with low dry-frame stiffness.     

Data assimilation (4D-VAR) to forecast flood in shallow-waters with sediment erosion

In this paper, the four-dimensional variational data assimilation technique (4D-VAR) is presented as a tool to forecast floods. Our study is limited to purely hydrological flows and supposes that the weather, here a big rain, has been already forecasted by meteorological services. The technique consists in minimizing, in the sense of Lagrange, the cost function: a measure of the difference between calculated data and available observations, here the water level. This is done under constraints that are the equations of the physical model. In our case, we modified the shallow-water equations to include a simplified sediment transport model. The steepest descent algorithm is then used to find the minimum. This is made possible because we can compute analytically the gradient of the cost function by using the adjoint equations of the model. As an application of the 4D-VAR technique, the overflowing of the Chicoutimi River at the Chute-Garneau dam, during the 1996 flood, is investigated. It is found that the 4D-VAR method reduces the error in the water height forecast even when the erosion model is not activated. In terms of Lyapunov exponents, we estimate the predictability horizon of such an event to be about half-an-hour after a big rain. However, this limit of predictability can be increased by using more observations or by using a finer computational grid.