G. J. M. Copeland

Water quality in Sepetiba Bay, Brazil.

Sepetiba Bay is located at 23 degrees S, 44 degrees W in Rio de Janeiro State, Brazil. Water samples were taken at eight locations adjacent to the north shore of the Bay, near to villages and towns without sewage treatment provision. The samples were analysed and total and faecal coliform concentrations determined. A hydrodynamic model of the Bay was used together with a species dispersion model based on an adaptive quadtree mesh to predict faecal concentrations in the Bay. Effluent sources used in the model were defined using population data from census returns with flow and concentration values estimated using standard values recommended by the World Bank (WB) and the World Health Organisation (WHO). Sufficient agreement was obtained between the measured and predicted concentrations to support the use of WB and WHO summary statistics to estimate sources of sewage.

Open Boundary Control Problem for Navier-Stokes Equations Including a Free Surface: Adjoint Sensitivity Analysis

This paper develops the adjoint sensitivities to the free-surface barotropic Navier- Stokes equations in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution by open-boundary control. To calculate a variation in a surface variable, a mapping is used in the vertical to shift the problem into a fixed domain. A variation is evaluated in the transformed space from the Jacobian matrix of the mapping. This variation is then mapped back into the original space where it completes a tangent linear model. The adjoint equations are derived using the scalar product formulas redefined for a domain with variable bounds. The method is demonstrated by application to an unsteady fluid flow in a one-dimensional open channel in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface (a 2D vertical section model). This requires the proper treatment of open boundaries in both the forward and adjoint models. A particular application is to the construction of a fully three-dimensional coastal ocean model that allows assimilation of tidal elevation and current data. However, the results are general and can be applied in a wider context.

Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics

Abstract The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term.

Open Boundary Control Problem for Navier-Stokes Equations Including a Free Surface: Data Assimilation

This paper develops the data-assimilation procedure in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution governed by the free-surface barotropic Navier-Stokes equations. The flow is considered in a 2D vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface. Since a possible application is to the construction of a coastal (limited area) circulation model, the open boundary control problem is the main scope of the paper. The assimilation algorithm is built on the limited memory quasi-Newton LBFGS method guided by the adjoint sensitivities. The analytical step search, which is based on the solution of the tangent linear model, is used. We process the gradients to regularize the solution. In numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements, which could be sufficient for boundary-control identification. As a result of these experiments we formulate some important practical conclusions.

Adjoint Data Assimilation into a 3D Unstructured Mesh Coastal Finite Element Model

An adaptive mesh adjoint model has been developed to invert for uncertain parameters in the simulation of coastal flows. These may include, for example, open boundary conditions and initial conditions. The objective in this paper is to obtain a better representation of water flows around and over coastal topography. In this paper a first attempt has been made at using mesh adaptivity in both transient forward and adjoint models. Although the resulting method has inconsistent discrete schemes for the forward and adjoint models, the inversion results shown here are nevertheless good. The derivation of the continuous adjoint model is presented. A description of the adaptive mesh joint technique is also given. As a study case, the method is applied to the inversion of boundary conditions for flow past a headland.

Cover: Observing estuarine currents and fronts in the Tay Estuary, Scotland, using an airborne SAR with along track interferonmetry (ATI)

Estuaries are extremely dynamic environments where large and frequent changes in bathymetry and channel locations can occur. Because estuaries are major centres of population and industry, there is an ongoing requirement to monitor and predict changes in the current fields. The tidal range, surface wind speed, atmospheric pressure, fresh water inflow and most importantly the stage of the tidal cycle affect the flow vectors. Existing boat‐based methods are unable to provide measurements of current fields with sufficient spatial and depth coverage for accurate modelling of hydrodynamic processes in estuaries. Remotely sensed data offer more extensive, synoptic, spatial coverage. However, previous studies to map the full details of the current field based on conventional optical and thermal imaging have been limited by insufficient temporal coverage and the lack of identifiable features that can be tracked. Synthetic aperture radar (SAR) imaging with along‐track interferometry (ATI) has the potential to overcome both of these limitations because it can retrieve quantitative measurements of sea surface state parameters and instantaneous surface flow from a single pass over a whole estuary. The preliminary results of ATI observations over the Tay Estuary, Scotland, validated with coincident in situ boat based observations, are presented here.

A Progress Report on the Control of the Free Surface in a 3D Navier Stokes Solver for Coastal Applications

This paper reports work in progress on the development of a data assimilation capacity for an existing 3D Navier Stokes solver with application as an ocean model. The project is a collaboration between University of Strathclyde and Imperial College, London with the assistance of Dr. Neill from the University of Wales, Bangor. This paper reports work carried out at Strathclyde University. The 3D NS solver developed by the Imperial team uses finite element methods and adaptive meshing, is non-hydrostatic and includes the free surface. However, proper treatment of the free surface in the adjoint problem is not straightforward. This paper describes a method of controlling the forward solution using either surface elevation or current data by solving an appropriate adjoint problem. This is formulated in a new way using a co-ordinate transformation such that the control problem appears in a fixed domain even though the forward problem has a variable domain due to the presence of the free surface.