On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

The effects of rotation and ice shelf topography on frazil-laden ice shelf water plumes

A model of the dynamics and thermodynamics of a plume of meltwater at the base of an ice shelf is presented. Such ice shelf water plumes may become supercooled and deposit marine ice if they rise (because of the pressure decrease in the in situ freezing temperature), so the model incorporates both melting and freezing at the ice shelf base and a multiple-size-class model of frazil ice dynamics and deposition. The plume is considered in two horizontal dimensions, so the influence of Coriolis forces is incorporated for the first time. It is found that rotation is extremely influential, with simulated plumes flowing in near-geostrophy because of the low friction at a smooth ice shelf base. As a result, an ice shelf water plume will only rise and become supercooled (and thus deposit marine ice) if it is constrained to flow upslope by topography. This result agrees with the observed distribution of marine ice under Filchner–Ronne Ice Shelf, Antarctica. In addition, it is found that the model only produces reasonable marine ice formation rates when an accurate ice shelf draft is used, implying that the characteristics of real ice shelf water plumes can only be captured using models with both rotation and a realistic topography.

How well can we measure the ocean’s mean dynamic topography from space?

Recent gravity missions have produced a dramatic improvement in our ability to measure the ocean’s mean dynamic topography (MDT) from space. To fully exploit this oceanic observation, however, we must quantify its error. To establish a baseline, we first assess the error budget for an MDT calculated using a 3rd generation GOCE geoid and the CLS01 mean sea surface (MSS). With these products, we can resolve MDT spatial scales down to 250 km with an accuracy of 1.7 cm, with the MSS and geoid making similar contributions to the total error. For spatial scales within the range 133–250 km the error is 3.0 cm, with the geoid making the greatest contribution. For the smallest resolvable spatial scales (80–133 km) the total error is 16.4 cm, with geoid error accounting for almost all of this. Relative to this baseline, the most recent versions of the geoid and MSS fields reduce the long and short-wavelength errors by 0.9 and 3.2 cm, respectively, but they have little impact in the medium-wavelength band. The newer MSS is responsible for most of the long-wavelength improvement, while for the short-wavelength component it is the geoid. We find that while the formal geoid errors have reasonable global mean values they fail capture the regional variations in error magnitude, which depend on the steepness of the sea floor topography.

Integrated analysis of climate, soil, topography and vegetative growth in Iberian viticultural regions

The Iberian viticultural regions are convened according to the Denomination of Origin (DO) and present different climates, soils, topography and management practices. All these elements influence the vegetative growth of different varieties throughout the peninsula, and are tied to grape quality and wine type. In the current study, an integrated analysis of climate, soil, topography and vegetative growth was performed for the Iberian DO regions, using state-of-the-art datasets. For climatic assessment, a categorized index, accounting for phenological/thermal development, water availability and grape ripening conditions was computed. Soil textural classes were established to distinguish soil types. Elevation and aspect (orientation) were also taken into account, as the leading topographic elements. A spectral vegetation index was used to assess grapevine vegetative growth and an integrated analysis of all variables was performed. The results showed that the integrated climate-soil-topography influence on vine performance is evident. Most Iberian vineyards are grown in temperate dry climates with loamy soils, presenting low vegetative growth. Vineyards in temperate humid conditions tend to show higher vegetative growth. Conversely, in cooler/warmer climates, lower vigour vineyards prevail and other factors, such as soil type and precipitation acquire more important roles in driving vigour. Vines in prevailing loamy soils are grown over a wide climatic diversity, suggesting that precipitation is the primary factor influencing vigour. The present assessment of terroir characteristics allows direct comparison among wine regions and may have great value to viticulturists, particularly under a changing climate.

Use of fused airborne scanning laser altimetry and digital map data for urban flood modelling

Flood modelling of urban areas is still at an early stage, partly because until recently topographic data of sufficiently high resolution and accuracy have been lacking in urban areas. However, Digital Surface Models (DSMs) generated from airborne scanning laser altimetry (LiDAR) having sub-metre spatial resolution have now become available, and these are able to represent the complexities of urban topography. The paper describes the development of a LiDAR post-processor for urban flood modelling based on the fusion of LiDAR and digital map data. The map data are used in conjunction with LiDAR data to identify different object types in urban areas, though pattern recognition techniques are also employed. Post-processing produces a Digital Terrain Model (DTM) for use as model bathymetry, and also a friction parameter map for use in estimating spatially-distributed friction coefficients. In vegetated areas, friction is estimated from LiDAR-derived vegetation height, and (unlike most vegetation removal software) the method copes with short vegetation less than ~1m high, which may occupy a substantial fraction of even an urban floodplain. The DTM and friction parameter map may also be used to help to generate an unstructured mesh of a vegetated urban floodplain for use by a 2D finite element model. The mesh is decomposed to reflect floodplain features having different frictional properties to their surroundings, including urban features such as buildings and roads as well as taller vegetation features such as trees and hedges. This allows a more accurate estimation of local friction. The method produces a substantial node density due to the small dimensions of many urban features.

Benchmarking 2D hydraulic models for urban flooding

This paper describes benchmark testing of six two-dimensional (2D) hydraulic models (DIVAST, DIVASTTVD, TUFLOW, JFLOW, TRENT and LISFLOOD-FP) in terms of their ability to simulate surface flows in a densely urbanised area. The models are applied to a 1·0 km × 0·4 km urban catchment within the city of Glasgow, Scotland, UK, and are used to simulate a flood event that occurred at this site on 30 July 2002. An identical numerical grid describing the underlying topography is constructed for each model, using a combination of airborne laser altimetry (LiDAR) fused with digital map data, and used to run a benchmark simulation. Two numerical experiments were then conducted to test the response of each model to topographic error and uncertainty over friction parameterisation. While all the models tested produce plausible results, subtle differences between particular groups of codes give considerable insight into both the practice and science of urban hydraulic modelling. In particular, the results show that the terrain data available from modern LiDAR systems are sufficiently accurate and resolved for simulating urban flows, but such data need to be fused with digital map data of building topology and land use to gain maximum benefit from the information contained therein. When such terrain data are available, uncertainty in friction parameters becomes a more dominant factor than topographic error for typical problems. The simulations also show that flows in urban environments are characterised by numerous transitions to supercritical flow and numerical shocks. However, the effects of these are localised and they do not appear to affect overall wave propagation. In contrast, inertia terms are shown to be important in this particular case, but the specific characteristics of the test site may mean that this does not hold more generally.

A new look at stratospheric sudden warmings. Part III. Polar vortex evolution and vertical structure

The evolution of the Arctic polar vortex during observed major mid-winter stratospheric sudden warmings (SSWs) is investigated for the period 1957-2002, using European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 Ertel’s potential vorticity (PV) and temperature fields. Time-lag composites of vertically weighted PV, calculated relative to the SSW onset time, are derived for both vortex displacement SSWs and vortex splitting SSWs, by averaging over the 15 recorded displacement and 13 splitting events. The evolving vertical structure of the polar vortex during a typical SSW of each type is clearly illustrated by plotting an isosurface of the composite PV field, and is shown to be very close to that observed during representative individual events. Results are verified by comparison with an elliptical diagnostic vortex moment technique. For both types of SSW, little variation is found between individual events in the orientation of the developing vortex relative to the underlying topography, i.e. the location of the vortex during SSWs of each type is largely fixed in relation to the Earth’s surface. During each type of SSW, the vortex is found to have a distinctive vertical structure. Vortex splitting events are typically barotropic, with the vortex split occurring near-simultaneously over a large altitude range (20-40 km). In the majority of cases, of the two daughter vortices formed, it is the ‘Siberian’ vortex that dominates over its ‘Canadian’ counterpart. In contrast, displacement events are characterized by a very clear baroclinic structure; the vortex tilts significantly westward with height, so that the top and bottom of the vortex are separated by nearly 180◦ longitude before the upper vortex is sheared away and destroyed.

Improving flood inundation models using remotely sensed data

The paper discusses the wide variety of ways in which remotely sensed data are being utilized in river flood inundation modeling. Model parameterization is being aided using airborne LiDAR data to provide topography of the floodplain for use as model bathymetry, and vegetation heights in the floodplain for use in estimating floodplain friction factors. Model calibration and validation are being aided by comparing the flood extent observed in SAR images with the extent predicted by the model. The recent extension of this to the observation of urban flooding using high resolution TerraSAR-X data is described. Possible future research directions are considered.

Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow

Inertia-gravity waves exist ubiquitously throughout the stratified parts of the atmosphere and ocean. They are generated by local velocity shears, interactions with topography, and as geostrophic (or spontaneous) adjustment radiation. Relatively little is known about the details of their interaction with the large-scale flow, however. We report on a joint model/laboratory study of a flow in which inertia-gravity waves are generated as spontaneous adjustment radiation by an evolving large-scale mode. We show that their subsequent impact upon the large-scale dynamics is generally small. However, near a potential transition from one large-scale mode to another, in a flow which is simultaneously baroclinically-unstable to more than one mode, the inertia-gravity waves may strongly influence the selection of the mode which actually occurs.

Why we need new spectacles: Mapping the experiential dimension in prehistoric Cretan landscapes

The Bronze to Iron Age transition in Crete, a period of state collapse and insecurity, saw the island's rugged, high-contrast topography used in striking new ways. The visual drama of many of the new site locations has stimulated significant research over the last hundred years, with explanation of the change as the main focus. The new sites are not monumental in character: the vast majority are settlements, and much of the information about them comes from survey. Perhaps as a result, the new site map has not been much studied from phenomenological perspectives. A focus on the visual and experiential aspects of the new landscape can offer valuable insights into social structures at this period, and illuminate social developments prefiguring the emergence of polis states in Crete by c. 700 BC. To develop, share and evaluate this type of integrated study, digital reconstructive techniques are still under-used in this region. I highlight their potential value in addressing a regularly-identified shortcoming of phenomenological approaches-their necessarily subjective emphasis.

The use of earth observation techniques to improve catchment-scale pollution predictions

Remote sensing can potentially provide information useful in improving pollution transport modelling in agricultural catchments. Realisation of this potential will depend on the availability of the raw data, development of information extraction techniques, and the impact of the assimilation of the derived information into models. High spatial resolution hyperspectral imagery of a farm near Hereford, UK is analysed. A technique is described to automatically identify the soil and vegetation endmembers within a field, enabling vegetation fractional cover estimation. The aerially-acquired laser altimetry is used to produce digital elevation models of the site. At the subfield scale the hypothesis that higher resolution topography will make a substantial difference to contaminant transport is tested using the AGricultural Non-Point Source (AGNPS) model. Slope aspect and direction information are extracted from the topography at different resolutions to study the effects on soil erosion, deposition, runoff and nutrient losses. Field-scale models are often used to model drainage water, nitrate and runoff/sediment loss, but the demanding input data requirements make scaling up to catchment level difficult. By determining the input range of spatial variables gathered from EO data, and comparing the response of models to the range of variation measured, the critical model inputs can be identified. Response surfaces to variation in these inputs constrain uncertainty in model predictions and are presented. Although optical earth observation analysis can provide fractional vegetation cover, cloud cover and semi-random weather patterns can hinder data acquisition in Northern Europe. A Spring and Autumn cloud cover analysis is carried out over seven UK sites close to agricultural districts, using historic satellite image metadata, climate modelling and historic ground weather observations. Results are assessed in terms of probability of acquisition probability and implications for future earth observation missions. (C) 2003 Elsevier Ltd. All rights reserved.

Palaeohydrology of the Fazzan Basin and surrounding regions: The last 7 million years

We have integrated information on topography, geology and geomorphology with the results of targeted fieldwork in order to develop a chronology for the development of Lake Megafazzan, a giant lake that has periodically existed in the Fazzan Basin since the late Miocene. The development of the basin can be best understood by considering the main geological and geomorphological events that occurred thought Libya during this period and thus an overview of the palaeohydrology of all Libya is also presented. The origin of the Fazzan Basin appears to lie in the Late Miocene. At this time Libya was dominated by two large rivers systems that flowed into the Mediterranean Sea, the Sahabi River draining central and eastern Libya and the Wadi Nashu River draining much of western Libya. As the Miocene progressed the region become increasingly affected by volcanic activity on its northern and eastern margin that appears to have blocked the River Nashu in Late Miocene or early Messinian times forming a sizeable closed basin in the Fazzan within which proto-Lake Megafazzan would have developed during humid periods. The fall in base level associated with the Messinian desiccation of the Mediterranean Sea promoted down-cutting and extension of river systems throughout much of Libya. To the south of the proto Fazzan Basin the Sahabi River tributary know as Wadi Barjuj appears to have expanded its headwaters westwards. The channel now terminates at Al Haruj al Aswad. We interpret this as a suggestion that Wadi Barjuj was blocked by the progressive development of Al Haruj al Aswad. K/Ar dating of lava flows suggests that this occurred between 4 and 2 Ma. This event would have increased the size of the closed basin in the Fazzan by about half, producing a catchment close to its current size (-350,000 km(2)). The Fazzan Basin contains a wealth of Pleistocene to recent palaeolake sediment outcrops and shorelines. Dating of these features demonstrates evidence of lacustrine conditions during numerous interglacials spanning a period greater than 420 ka. The middle to late Pleistocene interglacials were humid enough to produce a giant lake of about 135,000 km(2) that we have called Lake Megafazzan. Later lake phases were smaller, the interglacials less humid, developing lakes of a few thousand square kilometres. In parallel with these palaeohydrological developments in the Fazzan Basin, change was occurring in other parts of Libya. The Lower Pliocene sea level rise caused sediments to infill much of the Messinian channel system. As this was occurring, subsidence in the Al Kufrah Basin caused expansion of the Al Kufrah River system at the expense of the River Sahabi. By the Pleistocene, the Al Kufrah River dominated the palaeohydrology of eastern Libya and had developed a very large inland delta in its northern reaches that exhibited a complex distributary channel network which at times fed substantial lakes in the Sirt Basin. At this time Libya was a veritable lake district during humid periods with about 10% of the country underwater. (C) 2008 Elsevier B.V. All rights reserved.

The Phosphorus Indicators Tool: a simple model of diffuse P loss from agricultural land to water

The Phosphorus Indicators Tool provides a catchment-scale estimation of diffuse phosphorus (P) loss from agricultural land to surface waters using the most appropriate indicators of P loss. The Tool provides a framework that may be applied across the UK to estimate P loss, which is sensitive not only to land use and management but also to environmental factors such as climate, soil type and topography. The model complexity incorporated in the P Indicators Tool has been adapted to the level of detail in the available data and the need to reflect the impact of changes in agriculture. Currently, the Tool runs on an annual timestep and at a 1 km(2) grid scale. We demonstrate that the P Indicators Tool works in principle and that its modular structure provides a means of accounting for P loss from one layer to the next, and ultimately to receiving waters. Trial runs of the Tool suggest that modelled P delivery to water approximates measured water quality records. The transparency of the structure of the P Indicators Tool means that identification of poorly performing coefficients is possible, and further refinements of the Tool can be made to ensure it is better calibrated and subsequently validated against empirical data, as it becomes available.