Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

A continuum of sudden stratospheric warmings

The k-means cluster technique is used to examine 43 yr of daily winter Northern Hemisphere (NH) polar stratospheric data from the 40-yr ECMWF Re-Analysis (ERA-40). The results show that the NH winter stratosphere exists in two natural well-separated states. In total, 10% of the analyzed days exhibit a warm disturbed state that is typical of sudden stratospheric warming events. The remaining 90% of the days are in a state typical of a colder undisturbed vortex. These states are determined objectively, with no preconceived notion of the groups. The two stratospheric states are described and compared with alternative indicators of the polar winter flow, such as the northern annular mode. It is shown that the zonally averaged zonal winds in the polar upper stratosphere at 7 hPa can best distinguish between the two states, using a threshold value of 4 m s−1, which is remarkably close to the standard WMO criterion for major warming events. The analysis also determines that there are no further divisions within the warm state, indicating that there is no well-designated threshold between major and minor warmings, nor between split and displaced vortex events. These different manifestations are simply members of a continuum of warming events.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Assimilation of stratospheric ozone from MIPAS into a global general-circulation model: The September 2002 vortex split

Ozone and temperature profiles from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) have been assimilated, using three-dimensional variational assimilation, into a stratosphere troposphere version of the Met Office numerical weather-prediction system. Analyses are made for the month of September 2002, when there was an unprecedented split in the southern hemisphere polar vortex. The analyses are validated against independent ozone observations from sondes, limb-occultation and total column ozone satellite instruments. Through most of the stratosphere, precision varies from 5 to 15%, and biases are 15% or less of the analysed field. Problems remain in the vortex and below the 60 hPa. level, especially at the tropopause where the analyses have too much ozone and poor agreement with independent data. Analysis problems are largely a result of the model rather than the data, giving confidence in the MIPAS ozone retrievals, though there may be a small high bias in MIPAS ozone in the lower stratosphere. Model issues include an excessive Brewer-Dobson circulation, which results both from known problems with the tracer transport scheme and from the data assimilation of dynamical variables. The extreme conditions of the vortex split reveal large differences between existing linear ozone photochemistry schemes. Despite these issues, the ozone analyses are able to successfully describe the ozone hole split and compare well to other studies of this event. Recommendations are made for the further development of the ozone assimilation system.

The propagation mechanism of a vortex on the β plane

The propagation velocity and propagation mechanism for vortices on a β plane are determined for a reduced-gravity model by integrating the momentum equations over the β plane. Isolated vortices, vortices in a background current, and initial vortex propagation from rest are studied. The propagation mechanism for isolated anticyclones as well as cyclones, which has been lacking up to now, is presented. It is shown that, to first order, the vortex moves to generate a Coriolis force on the mass anomaly of the vortex to compensate for the force on the vortex due to the variation of the Coriolis parameter. Only the mass anomaly of the vortex is of importance, because the Coriolis force due to the motion of the bulk of the layer moving with the vortex is almost fully compensated by the Coriolis force on the motion of the exterior flow. Because the mass anomaly of a cyclone is negative the force and acceleration have opposite sign. The role of dipolar structures in steadily moving vortices is discussed, and it is shown that their overall structure is fixed by the steady westward motion of the mass anomaly. Furthermore, it is shown that reduced-gravity vortices are not advected with a background flow. The reason for this behavior is that the background flow changes the ambient vorticity gradient such that the vortex obtains an extra self-propagation term that exactly cancels the advection by the background flow. Last, it is shown that a vortex initially at rest will accelerate equatorward first, after which a westward motion is generated. This result is independent of the sign of the vortex.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere

The Northern Hemisphere stratospheric polar vortex is linked to surface weather. After Stratospheric Sudden Warmings in winter, the tropospheric circulation is often nudged towards the negative phase of the Northern Annular Mode (NAM) and the North Atlantic Oscillation (NAO). A strong stratospheric vortex is often associated with subsequent positive NAM/NAO conditions. For stratosphere–troposphere associations to be useful for forecasting purposes it is crucial that changes to the stratospheric vortex can be understood and predicted. Recent studies have proposed that there exist tropospheric precursors to anomalous vortex events in the stratosphere and that these precursors may be understood by considering the relationship between stationary wave patterns and regional variability. Another important factor is the extent to which the inherent variability of the stratosphere in an atmospheric model influences its ability to simulate stratosphere–troposphere links. Here we examine the lower stratosphere variability in 300-year pre-industrial control integrations from 13 coupled climate models. We show that robust precursors to stratospheric polar vortex anomalies are evident across the multi-model ensemble. The most significant tropospheric component of these precursors consists of a height anomaly dipole across northern Eurasia and large anomalies in upward stationary wave fluxes in the lower stratosphere over the continent. The strength of the stratospheric variability in the models was found to depend on the variability of the upward stationary wave fluxes and the amplitude of the stationary waves.

Thermo-responsive microphase separated supramolecular polyurethanes

The ability to generate very stable assemblies via non-covalent interactions has enabled materials to be constructed that were not feasible via traditional covalent bond formation processes. A series of low molecular mass bisurethane and bisurea polymers have been developed that form stable self-assembled networks through hydrogen bonding interactions. Thermo-responsive polymers were generated by end-capping poly(ethylene-co-butylene) or polybutadiene chains with the bisurethane or bisurea motif. Microphase separation is observed via TEM and small-angle X-ray scattering (SAXS) for the modified pseudo polymers and significant differences in the temperature dependence of microphase separation are analysed via SAXS. The importance of the polarity of the end groups is manifested in distinct temperature-dependent microphase separation behaviour. Information on the local hydrogen bonding structure is provided by wide-angle X-ray scattering and variable temperature FTI

Apolipoprotein E enrichment of immuno-separated chylomicron and chylomicron remnants following saturated fatty acids

Aim: We examined the effect of meat fatty acids on lipid and apolipoprotein concentrations of very low density lipoprotein (VLDL) and chylomicron/chylomicron remnants in lipid fractions with a Svedberg flotation rate (S-f) 60-400 and S-f 20-60. Methods and results: Six healthy middle-aged men received in random order mixed meals enriched with saturated (SFA), polyunsaturated (PUFA) or monounsaturated (MUFA) fatty acids on 3 occasions. VLDL and chylomicron/chylomicron remnants in the lipid fractions were separated by immunoaffinity chromatography against apo B-100. In the S-f 60-400 chylomicron/chylomicron remnants, triacylglycerol and cholesterol concentrations were significantly tower following PUFA compared with SFA and MUFA (P <= 0.05). Apolipoprotein (apo) E responses were significantly higher after SFA in chylomicron/chylomicron remnants and VLDL compared with PUFA and MUFA (P < 0.007). However, apo B responses (particle number) were higher following MUFA than SFA (P = 0.039 for chylomicron/chylomicron remnants). Composition of the chylomicron/chylomicron remnants (expressed per particle) revealed differences in their triacylglycerol and apo E contents; in the Sf 60-400 fraction, SFA-rich chylomicron/chylomicron remnants contained significantly more triacylglycerol than MUFA (P = 0.028), more apo E than PUFA- and MUFA-rich particles (P < 0.05) and in the S-f 20-60 fraction, more apo E than MUFA (P = 0.009). Conclusion: There are specific differences in the composition of chylomicron/ chylomicron remnants formed after saturated compared with unsaturated fatty acid-rich meals which could determine their metabolic fate in the circulation and subsequent atherogenicity. (C) 2005 Elsevier B.V. All rights reserved.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient shock capturing scheme for the pseudo-unsteady equations representing steady inviscid flow

An efficient algorithm is presented for the solution of the steady Euler equations of gas dynamics. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme is applied to a standard test problem of flow down a channel containing a circular arc bump for three different mesh sizes.