Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

"Ever-growing Amman", Jordan: Urban expansion, social polarisation and contemporary urban planning issues

Amman the primate capital city of the Hashemite Kingdom of Jordan currently has a population in excess of 2 million, but in 1924 it consisted of little more than a collection of dwellings and some 2000-3000 inhabitants. The present paper sets out to document and explain the phenomenal expansion of "ever-growing Amman". The physical geography of the urban region and the early growth of the city are considered at the outset and this leads directly to consideration of the highly polarised social structuring that characterises contemporary Amman. In doing this, original data derived from the recent Greater Amman Municipality's Geographical Information System are presented. In this respect, the essential modernity of the city is exemplified. The employment and industrial bases of the city and a range of pressing contemporary issues are then considered, including transport and congestion, the provision of urban water under conditions of water stress and privatisation, and urban and regional development planning for the city. The paper concludes by emphasizing the growing regional and international geopolitical salience of the city of Amman at the start of the 21st century. (C) 2008 Elsevier Ltd. All rights reserved.

Krakatoa lives: The effect of volcanic eruptions on ocean heat content and thermal expansion

A suite of climate model experiments indicates that 20th Century increases in ocean heat content and sea-level ( via thermal expansion) were substantially reduced by the 1883 eruption of Krakatoa. The volcanically-induced cooling of the ocean surface is subducted into deeper ocean layers, where it persists for decades. Temporary reductions in ocean heat content associated with the comparable eruptions of El Chichon ( 1982) and Pinatubo ( 1991) were much shorter lived because they occurred relative to a non-stationary background of large, anthropogenically-forced ocean warming. Our results suggest that inclusion of the effects of Krakatoa ( and perhaps even earlier eruptions) is important for reliable simulation of 20th century ocean heat uptake and thermal expansion. Inter-model differences in the oceanic thermal response to Krakatoa are large and arise from differences in external forcing, model physics, and experimental design. Systematic experimentation is required to quantify the relative importance of these factors. The next generation of historical forcing experiments may require more careful treatment of pre-industrial volcanic aerosol loadings.

Parameter estimation using a particle method: inferring mixing coefficients from sea level observations

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.