How many facets are needed to represent the surface energy balance of an urban area?

We investigate the question of how many facets are needed to represent the energy balance of an urban area by developing simplified 3-, 2- and 1-facet versions of a 4-facet energy balance model of two-dimensional streets and buildings. The 3-facet model simplifies the 4-facet model by averaging over the canyon orientation, which results in similar net shortwave and longwave balances for both wall facets, but maintains the asymmetry in the heat fluxes within the street canyon. For the 2-facet model, on the assumption that the wall and road temperatures are equal, the road and wall facets can be combined mathematically into a single street-canyon facet with effective values of the heat transfer coefficient, albedo, emissivity and thermodynamic properties, without further approximation. The 1-facet model requires the additional assumption that the roof temperature is also equal to the road and wall temperatures. Idealised simulations show that the geometry and material properties of the walls and road lead to a large heat capacity of the combined street canyon, whereas the roof behaves like a flat surface with low heat capacity. This means that the magnitude of the diurnal temperature variation of the street-canyon facets are broadly similar and much smaller than the diurnal temperature variation of the roof facets. Consequently, the approximation that the street-canyon facets have similar temperatures is sound, and the road and walls can be combined into a single facet. The roof behaves very differently and a separate roof facet is required. Consequently, the 2-facet model performs similarly to the 4-facet model, while the 1-facet model does not. The models are compared with previously published observations collected in Mexico City. Although the 3- and 2-facet models perform better than the 1-facet model, the present models are unable to represent the phase of the sensible heat flux. This result is consistent with previous model comparisons, and we argue that this feature of the data cannot be produced by a single column model. We conclude that a 2-facet model is necessary, and for numerical weather prediction sufficient, to model an urban surface, and that this conclusion is robust and therefore applicable to more general geometries.

Exploitation of Geostationary Earth Radiation Budget data using simulations from a numerical weather prediction model: Methodology and data validation

We describe a new methodology for comparing satellite radiation budget data with a numerical weather prediction (NWP) model. This is applied to data from the Geostationary Earth Radiation Budget (GERB) instrument on Meteosat-8. The methodology brings together, in near-real time, GERB broadband shortwave and longwave fluxes with simulations based on analyses produced by the Met Office global NWP model. Results for the period May 2003 to February 2005 illustrate the progressive improvements in the data products as various initial problems were resolved. In most areas the comparisons reveal systematic errors in the model's representation of surface properties and clouds, which are discussed elsewhere. However, for clear-sky regions over the oceans the model simulations are believed to be sufficiently accurate to allow the quality of the GERB fluxes themselves to be assessed and any changes in time of the performance of the instrument to be identified. Using model and radiosonde profiles of temperature and humidity as input to a single-column version of the model's radiation code, we conduct sensitivity experiments which provide estimates of the expected model errors over the ocean of about ±5–10 W m−2 in clear-sky outgoing longwave radiation (OLR) and ±0.01 in clear-sky albedo. For the more recent data the differences between the observed and modeled OLR and albedo are well within these error estimates. The close agreement between the observed and modeled values, particularly for the most recent period, illustrates the value of the methodology. It also contributes to the validation of the GERB products and increases confidence in the quality of the data, prior to their release.

The role of mean ocean salinity in climate

We describe numerical simulations designed to elucidate the role of mean ocean salinity in climate. Using a coupled atmosphere-ocean general circulation model, we study a 100-year sensitivity experiment in which the global-mean salinity is approximately doubled from its present observed value, by adding 35 psu everywhere in the ocean. The salinity increase produces a rapid global-mean sea-surface warming of C within a few years, caused by reduced vertical mixing associated with changes in cabbeling. The warming is followed by a gradual global-mean sea-surface cooling of C within a few decades, caused by an increase in the vertical (downward) component of the isopycnal diffusive heat flux. We find no evidence of impacts on the variability of the thermohaline circulation (THC) or El Niño/Southern Oscillation (ENSO). The mean strength of the Atlantic meridional overturning is reduced by 20% and the North Atlantic Deep Water penetrates less deeply. Nevertheless, our results dispute claims that higher salinities for the world ocean have profound consequences for the thermohaline circulation. In additional experiments with doubled atmospheric carbon dioxide, we find that the amplitude and spatial pattern of the global warming signal are modified in the hypersaline ocean. In particular, the equilibrated global-mean sea-surface temperature increase caused by doubling carbon dioxide is reduced by 10%. We infer the existence of a non-linear interaction between the climate responses to modified carbon dioxide and modified salinity.

A Proposed Modification to the Robert–Asselin Time Filter

The Robert–Asselin time filter is widely used in numerical models of weather and climate. It successfully suppresses the spurious computational mode associated with the leapfrog time-stepping scheme. Unfortunately, it also weakly suppresses the physical mode and severely degrades the numerical accuracy. These two concomitant problems are shown to occur because the filter does not conserve the mean state, averaged over the three time slices on which it operates. The author proposes a simple modification to the Robert–Asselin filter, which does conserve the three-time-level mean state. When used in conjunction with the leapfrog scheme, the modification vastly reduces the impacts on the physical mode and increases the numerical accuracy for amplitude errors by two orders, yielding third-order accuracy. The modified filter could easily be incorporated into existing general circulation models of the atmosphere and ocean. In principle, it should deliver more faithful simulations at almost no additional computational expense. Alternatively, it may permit the use of longer time steps with no loss of accuracy, reducing the computational expense of a given simulation.

A groove-ploughing theory for the production of mega-scale glacial lineations, and implications for ice-stream mechanics

Mega-scale glacial lineations (MSGLs) are longitudinally aligned corrugations (ridge-groove structures 6-100 km long) in sediment produced subglacially. They are indicators of fast flow and a common signature of ice-stream beds. We develop a qualitative theory that accounts for their formation, and use numerical modelling, and observations of ice-stream beds to provide supporting evidence. Ice in contact with a rough (scale of 10-10(3) m) bedrock surface will mimic the form of the bed. Because of flow acceleration and convergence in ice-stream onset zones, the ice-base roughness elements experience transverse strain, transforming them from irregular bumps into longitudinally aligned keels of ice protruding downwards. Where such keels slide across a soft sedimentary bed, they plough through the sediments, carving elongate grooves, and deforming material up into intervening ridges. This explains MSGLs and has important implications for ice-stream mechanics. Groove ploughing provides the means to acquire new lubricating sediment and to transport large volumes of it downstream. Keels may provide basal drag in the force budget of ice streams, thereby playing a role in flow regulation and stability We speculate that groove ploughing permits significant ice-stream widening, thus facilitating high-magnitude ice discharge.

Modelling monsoons: understanding and predicting current and future behaviour

The global monsoon system is so varied and complex that understanding and predicting its diverse behaviour remains a challenge that will occupy modellers for many years to come. Despite the difficult task ahead, an improved monsoon modelling capability has been realized through the inclusion of more detailed physics of the climate system and higher resolution in our numerical models. Perhaps the most crucial improvement to date has been the development of coupled ocean-atmosphere models. From subseasonal to interdecadal time scales, only through the inclusion of air-sea interaction can the proper phasing and teleconnections of convection be attained with respect to sea surface temperature variations. Even then, the response to slow variations in remote forcings (e.g., El Niño—Southern Oscillation) does not result in a robust solution, as there are a host of competing modes of variability that must be represented, including those that appear to be chaotic. Understanding the links between monsoons and land surface processes is not as mature as that explored regarding air-sea interactions. A land surface forcing signal appears to dominate the onset of wet season rainfall over the North American monsoon region, though the relative role of ocean versus land forcing remains a topic of investigation in all the monsoon systems. Also, improved forecasts have been made during periods in which additional sounding observations are available for data assimilation. Thus, there is untapped predictability that can only be attained through the development of a more comprehensive observing system for all monsoon regions. Additionally, improved parameterizations - for example, of convection, cloud, radiation, and boundary layer schemes as well as land surface processes - are essential to realize the full potential of monsoon predictability. A more comprehensive assessment is needed of the impact of black carbon aerosols, which may modulate that of other anthropogenic greenhouse gases. Dynamical considerations require ever increased horizontal resolution (probably to 0.5 degree or higher) in order to resolve many monsoon features including, but not limited to, the Mei-Yu/Baiu sudden onset and withdrawal, low-level jet orientation and variability, and orographic forced rainfall. Under anthropogenic climate change many competing factors complicate making robust projections of monsoon changes. Absent aerosol effects, increased land-sea temperature contrast suggests strengthened monsoon circulation due to climate change. However, increased aerosol emissions will reflect more solar radiation back to space, which may temper or even reduce the strength of monsoon circulations compared to the present day. Precipitation may behave independently from the circulation under warming conditions in which an increased atmospheric moisture loading, based purely on thermodynamic considerations, could result in increased monsoon rainfall under climate change. The challenge to improve model parameterizations and include more complex processes and feedbacks pushes computing resources to their limit, thus requiring continuous upgrades of computational infrastructure to ensure progress in understanding and predicting current and future behaviour of monsoons.

A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

The triggering of orographic rainbands by small-scale topography

The triggering of convective orographic rainbands by small-scale topographic features is investigated through observations of a banded precipitation event over the Oregon Coastal Range and simulations using a cloud-resolving numerical model. A quasi-idealized simulation of the observed event reproduces the bands in the radar observations, indicating the model’s ability to capture the physics of the band-formation process. Additional idealized simulations reinforce that the bands are triggered by lee waves past small-scale topographic obstacles just upstream of the nominal leading edge of the orographic cloud. Whether a topographic obstacle in this region is able to trigger a strong rainband depends on the phase of its lee wave at cloud entry. Convective growth only occurs downstream of obstacles that give rise to lee-wave-induced displacements that create positive vertical velocity anomalies w_c and nearly zero buoyancy anomalies b_c as air parcels undergo saturation. This relationship is quantified through a simple analytic condition involving w_c, b_c, and the static stability N_m^2 of the cloud mass. Once convection is triggered, horizontal buoyancy gradients in the cross-flow direction generate circulations that align the bands parallel to the flow direction.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.