The dependence of southern ocean meridional overturning on wind stress

An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.

Interhemispheric coupling, the West Antarctic Ice Sheet and warm Antarctic interglacials

Ice core evidence indicates that even though atmospheric CO2 concentrations did not exceed ~300 ppm at any point during the last 800 000 years, East Antarctica was at least ~3–4 °C warmer than preindustrial (CO2~280 ppm) in each of the last four interglacials. During the previous three interglacials, this anomalous warming was short lived (~3000 years) and apparently occurred before the completion of Northern Hemisphere deglaciation. Hereafter, we refer to these periods as "Warmer than Present Transients" (WPTs). We present a series of experiments to investigate the impact of deglacial meltwater on the Atlantic Meridional Overturning Circulation (AMOC) and Antarctic temperature. It is well known that a slowed AMOC would increase southern sea surface temperature (SST) through the bipolar seesaw and observational data suggests that the AMOC remained weak throughout the terminations preceding WPTs, strengthening rapidly at a time which coincides closely with peak Antarctic temperature. We present two 800 kyr transient simulations using the Intermediate Complexity model GENIE-1 which demonstrate that meltwater forcing generates transient southern warming that is consistent with the timing of WPTs, but is not sufficient (in this single parameterisation) to reproduce the magnitude of observed warmth. In order to investigate model and boundary condition uncertainty, we present three ensembles of transient GENIE-1 simulations across Termination II (135 000 to 124 000 BP) and three snapshot HadCM3 simulations at 130 000 BP. Only with consideration of the possible feedback of West Antarctic Ice Sheet (WAIS) retreat does it become possible to simulate the magnitude of observed warming.

Quantifying the importance of galactic cosmic rays in cloud microphysical processes

Galactic Cosmic Rays are one of the major sources of ion production in the troposphere and stratosphere. Recent studies have shown that ions form electrically charged clusters which may grow to become cloud droplets. Aerosol particles charge by the attachment of ions and electrons. The collision efficiency between a particle and a water droplet increases, if the particle is electrically charged, and thus aerosol-cloud interactions can be enhanced. Because these microphysical processes may change radiative properties of cloud and impact Earth's climate it is important to evaluate these processes' quantitative effects. Five different models developed independently have been coupled to investigate this. The first model estimates cloud height from dew point temperature and the temperature profile. The second model simulates the cloud droplet growth from aerosol particles using the cloud parcel concept. In the third model, the scavenging rate of the aerosol particles is calculated using the collision efficiency between charged particles and droplets. The fourth model calculates electric field and charge distribution on water droplets and aerosols within cloud. The fifth model simulates the global electric circuit (GEC), which computes the conductivity and ionic concentration in the atmosphere in altitude range 0–45 km. The first four models are initially coupled to calculate the height of cloud, boundary condition of cloud, followed by growth of droplets, charge distribution calculation on aerosols and cloud droplets and finally scavenging. These models are incorporated with the GEC model. The simulations are verified with experimental data of charged aerosol for various altitudes. Our calculations showed an effect of aerosol charging on the CCN concentration within the cloud, due to charging of aerosols increase the scavenging of particles in the size range 0.1 µm to 1 µm.

Mid-Holocene land-surface conditions in northern Africa and the Arabian peninsula: a data set for the analysis of biogeophysical feedbacks in the climate system

Large changes in the extent of northern subtropical arid regions during the Holocene are attributed to orbitally forced variations in monsoon strength and have been implicated in the regulation of atmospheric trace gas concentrations on millenial timescales. Models that omit biogeophysical feedback, however, are unable to account for the full magnitude of African monsoon amplification and extension during the early to middle Holocene (˜9500–5000 years B.P.). A data set describing land-surface conditions 6000 years B.P. on a 1° × 1° grid across northern Africa and the Arabian Peninsula has been prepared from published maps and other sources of palaeoenvironmental data, with the primary aim of providing a realistic lower boundary condition for atmospheric general circulation model experiments similar to those performed in the Palaeoclimate Modelling Intercomparison Project. The data set includes information on the percentage of each grid cell occupied by specific vegetation types (steppe, savanna, xerophytic woods/scrub, tropical deciduous forest, and tropical montane evergreen forest), open water (lakes), and wetlands, plus information on the flow direction of major drainage channels for use in large-scale palaeohydrological modeling.

Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels

A lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries. The mass conservation for the boundary condition is tested in detail. The viscous flow in elastic vessels is simulated with a pressure-radius relationship similar to that of the Pulmonary blood vessels. The numerical results for steady flow agree with the analytical prediction to very high accuracy, and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally. The model is expected to find many applications for studying blood flows in large distensible arteries, especially in those suffering from atherosclerosis. stenosis. aneurysm, etc.

Assessing the reliability of probabilistic flood inundation model predictions

An ability to quantify the reliability of probabilistic flood inundation predictions is a requirement not only for guiding model development but also for their successful application. Probabilistic flood inundation predictions are usually produced by choosing a method of weighting the model parameter space, but previous study suggests that this choice leads to clear differences in inundation probabilities. This study aims to address the evaluation of the reliability of these probabilistic predictions. However, a lack of an adequate number of observations of flood inundation for a catchment limits the application of conventional methods of evaluating predictive reliability. Consequently, attempts have been made to assess the reliability of probabilistic predictions using multiple observations from a single flood event. Here, a LISFLOOD-FP hydraulic model of an extreme (>1 in 1000 years) flood event in Cockermouth, UK, is constructed and calibrated using multiple performance measures from both peak flood wrack mark data and aerial photography captured post-peak. These measures are used in weighting the parameter space to produce multiple probabilistic predictions for the event. Two methods of assessing the reliability of these probabilistic predictions using limited observations are utilized; an existing method assessing the binary pattern of flooding, and a method developed in this paper to assess predictions of water surface elevation. This study finds that the water surface elevation method has both a better diagnostic and discriminatory ability, but this result is likely to be sensitive to the unknown uncertainties in the upstream boundary condition

Processes controlling surface, bottom and lateral melt of Arctic sea ice in a state of the art sea ice model

We present a modelling study of processes controlling the summer melt of the Arctic sea ice cover. We perform a sensitivity study and focus our interest on the thermodynamics at the ice–atmosphere and ice–ocean interfaces. We use the Los Alamos community sea ice model CICE, and additionally implement and test three new parametrization schemes: (i) a prognostic mixed layer; (ii) a three equation boundary condition for the salt and heat flux at the ice–ocean interface; and (iii) a new lateral melt parametrization. Recent additions to the CICE model are also tested, including explicit melt ponds, a form drag parametrization and a halodynamic brine drainage scheme. The various sea ice parametrizations tested in this sensitivity study introduce a wide spread in the simulated sea ice characteristics. For each simulation, the total melt is decomposed into its surface, bottom and lateral melt components to assess the processes driving melt and how this varies regionally and temporally. Because this study quantifies the relative importance of several processes in driving the summer melt of sea ice, this work can serve as a guide for future research priorities.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Boundary layer structure and decoupling from synoptic scale flow during NAMBLEX

This paper presents an overview of the meteorology and planetary boundary layer structure observed during the NAMBLEX field campaign to aid interpretation of the chemical and aerosol measurements. The campaign has been separated into five periods corresponding to the prevailing synoptic condition. Comparisons between meteorological measurements ( UHF wind profiler, Doppler sodar, sonic aneometers mounted on a tower at varying heights and a standard anemometer) and the ECMWF analysis at 10 m and 1100 m identified days when the internal boundary layer was decoupled from the synoptic flow aloft. Generally the agreement was remarkably good apart from during period one and on a few days during period four when the diurnal swing in wind direction implies a sea/land breeze circulation near the surface. During these periods the origin of air sampled at Mace Head would not be accurately represented by back trajectories following the winds resolved in ECMWF analyses. The wind profiler observations give a detailed record of boundary layer structure including an indication of its depth, average wind speed and direction. Turbulence statistics have been used to assess the height to which the developing internal boundary layer, caused by the increased surface drag at the coast, reaches the sampling location under a wide range of marine conditions. Sampling conducted below 10 m will be impacted by emission sources at the shoreline in all wind directions and tidal conditions, whereas sampling above 15 m is unlikely to be affected in any of the wind directions and tidal heights sampled during the experiment.

Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.