A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

The basic ingredients of the North Atlantic Storm Track. Part II: Sea surface temperatures

The impact of North Atlantic SST patterns on the storm track is investigated using a hierarchy of GCM simulations using idealized (aquaplanet) and “semirealistic” boundary conditions in the atmospheric component (HadAM3) of the third climate configuration of the Met Office Unified Model (HadCM3). This framework enables the mechanisms determining the tropospheric response to North Atlantic SST patterns to be examined, both in isolation and in combination with continental-scale landmasses and orography. In isolation, a “Gulf Stream” SST pattern acts to strengthen the downstream storm track while a “North Atlantic Drift” SST pattern weakens it. These changes are consistent with changes in the extratropical SST gradient and near-surface baroclinicity, and each storm-track response is associated with a consistent change in the tropospheric jet structure. Locally enhanced near-surface horizontal wind convergence is found over the warm side of strengthened SST gradients associated with ascending air and increased precipitation, consistent with previous studies. When the combined SST pattern is introduced into the semirealistic framework (including the “North American” continent and the “Rocky Mountains”), the results suggest that the topographically generated southwest–northeast tilt in the North Atlantic storm track is enhanced. In particular, the Gulf Stream shifts the storm track south in the western Atlantic whereas the strong high-latitude SST gradient in the northeastern Atlantic enhances the storm track there.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Further investigation of the impact of idealised continents and SST distributions on the Northern Hemisphere storm tracks

Building on studies by Brayshaw et al. (2009, 2011) of the basic ingredients of the North Atlantic storm track (land-sea contrast, orography and SST), this article investigates the impact of Eurasian topography and Pacific SST anomalies on the North Pacific and Atlantic storm tracks through a hierarchy of atmospheric GCM simulations using idealised boundary conditions in the HadGAM1 model. The Himalaya-Tibet mountain complex is found to play a crucial role in shaping the North Pacific storm track. The northward deflection of the westerly flow around northern Tibet generates an extensive pool of very cold air in the north-eastern tip of the Asian continent, which strengthens the meridional temperature gradient and favours baroclinic growth in the western Pacific. The Kuroshio SST front is also instrumental in strengthening the Pacific storm track through its impact on near-surface baroclinicity, while the warm waters around Indonesia tend to weaken it through the impact on baroclinicity of stationary Rossby waves propagating poleward from the convective heating regions. Three mechanisms by which the Atlantic storm track may be affected by changes in the boundary conditions upstream of the Rockies are discussed. In the model configuration used here, stationary Rossby waves emanating from Tibet appear to weaken the North Atlantic storm track substantially, whereas those generated over the cold waters off Peru appear to strengthen it. Changes in eddy-driven surface winds over the Pacific generally appear to modify the flow over the Rocky Mountains, leading to consistent modifications in the Atlantic storm track. The evidence for each of these mechanisms is, however, ultimately equivocal in these simulations.

High resolution Northern Hemisphere wintertime mid-latitude dynamics during the Last Glacial Maximum

Hourly winter weather of the Last Glacial Maximum (LGM) is simulated using the Community Climate Model version 3 (CCM3) on a globally resolved T170 (75 km) grid. Results are compared to a longer LGM climatological run with the same boundary conditions and monthly saves. Hourly-scale animations are used to enhance interpretations. The purpose of the study is to explore whether additional insights into ice age conditions can be gleaned by going beyond the standard employment of monthly average model statistics to infer ice age weather and climate. Results for both LGM runs indicate a decrease in North Atlantic and increase in North Pacific cyclogenesis. Storm trajectories react to the mechanical forcing of the Laurentide Ice Sheet, with Pacific storms tracking over middle Alaska and northern Canada, terminating in the Labrador Sea. This result is coincident with other model results in also showing a significant reduction in Greenland wintertime precipitation – a response supported by ice core evidence. Higher-temporal resolution puts in sharper focus the close tracking of Pacific storms along the west coast of North America. This response is consistent with increased poleward heat transport in the LGM climatological run and could help explain “early” glacial warming inferred in this region from proxy climate records. Additional analyses shows a large increase in central Asian surface gustiness that support observational inferences that upper-level winds associated with Asian- Pacific storms transported Asian dust to Greenland during the LGM.

Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Case-to-case variability of predictability of deep convection in a mesoscale model

Successful quantitative precipitation forecasts under convectively unstable conditions depend on the ability of the model to capture the location, timing and intensity of convection. Ensemble forecasts of two mesoscale convective outbreaks over the UK are examined with a view to understanding the nature and extent of their predictability. In addition to a control forecast, twelve ensemble members are run for each case with the same boundary conditions but with perturbations added to the boundary layer. The intention is to introduce perturbations of appropriate magnitude and scale so that the large-scale behaviour of the simulations is not changed. In one case, convection is in statistical equilibrium with the large-scale flow. This places a constraint on the total precipitation, but the location and intensity of individual storms varied. In contrast, the other case was characterised by a large-scale capping inversion. As a result, the location of individual storms was fixed, but their intensities and the total precipitation varied strongly. The ensemble shows case-to-case variability in the nature of predictability of convection in a mesoscale model, and provides additional useful information for quantitative precipitation forecasting.

Future change of precipitation extremes in Europe: intercomparison of scenarios from regional climate mode

An analysis of the climate of precipitation extremes as simulated by six European regional climate models (RCMs) is undertaken in order to describe/quantify future changes and to examine/interpret differences between models. Each model has adopted boundary conditions from the same ensemble of global climate model integrations for present (1961–1990) and future (2071–2100) climate under the Intergovernmental Panel on Climate Change A2 emission scenario. The main diagnostics are multiyear return values of daily precipitation totals estimated from extreme value analysis. An evaluation of the RCMs against observations in the Alpine region shows that model biases for extremes are comparable to or even smaller than those for wet day intensity and mean precipitation. In winter, precipitation extremes tend to increase north of about 45°N, while there is an insignificant change or a decrease to the south. In northern Europe the 20-year return value of future climate corresponds to the 40- to 100-year return value of present climate. There is a good agreement between the RCMs, and the simulated change is similar to a scaling of present-day extremes by the change in average events. In contrast, there are large model differences in summer when RCM formulation contributes significantly to scenario uncertainty. The model differences are well explained by differences in the precipitation frequency and intensity process, but in all models, extremes increase more or decrease less than would be expected from the scaling of present-day extremes. There is evidence for a component of the change that affects extremes specifically and is consistent between models despite the large variation in the total response.

Evaluation of water and energy budgets in regional climate models applied over Europe

This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation

A cloud-resolving model is modified to implement the weak temperature gradient approximation in order to simulate the interactions between tropical convection and the large-scale tropical circulation. The instantaneous domain-mean potential temperature is relaxed toward a reference profile obtained from a radiative–convective equilibrium simulation of the cloud-resolving model. For homogeneous surface conditions, the model state at equilibrium is a large-scale circulation with its descending branch in the simulated column. This is similar to the equilibrium state found in some other studies, but not all. For this model, the development of such a circulation is insensitive to the relaxation profile and the initial conditions. Two columns of the cloud-resolving model are fully coupled by relaxing the instantaneous domain-mean potential temperature in both columns toward each other. This configuration is energetically closed in contrast to the reference-column configuration. No mean large-scale circulation develops over homogeneous surface conditions, regardless of the relative area of the two columns. The sensitivity to nonuniform surface conditions is similar to that obtained in the reference-column configuration if the two simulated columns have very different areas, but it is markedly weaker for columns of comparable area. The weaker sensitivity can be understood as being a consequence of a formulation for which the energy budget is closed. The reference-column configuration has been used to study the convection in a local region under the influence of a large-scale circulation. The extension to a two-column configuration is proposed as a methodology for studying the influence on local convection of changes in remote convection.

Evaluation of water and energy budgets in regional climate models applied over Europe

Abstract This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

Predictability and uncertainty in a regional climate model

The evaluation of the quality and usefulness of climate modeling systems is dependent upon an assessment of both the limited predictability of the climate system and the uncertainties stemming from model formulation. In this study a methodology is presented that is suited to assess the performance of a regional climate model (RCM), based on its ability to represent the natural interannual variability on monthly and seasonal timescales. The methodology involves carrying out multiyear ensemble simulations (to assess the predictability bounds within which the model can be evaluated against observations) and multiyear sensitivity experiments using different model formulations (to assess the model uncertainty). As an example application, experiments driven by assimilated lateral boundary conditions and sea surface temperatures from the ECMWF Reanalysis Project (ERA-15, 1979–1993) were conducted. While the ensemble experiment demonstrates that the predictability of the regional climate varies strongly between different seasons and regions, being weakest during the summer and over continental regions, important sensitivities of the modeling system to parameterization choices are uncovered. In particular, compensating mechanisms related to the long-term representation of the water cycle are revealed, in which summer dry and hot conditions at the surface, resulting from insufficient evaporation, can persist despite insufficient net solar radiation (a result of unrealistic cloud-radiative feedbacks).

The influence of anthropogenic landscape changes on weather in south Florida

Using identical observed meteorology for lateral boundary conditions, the Regional Atmospheric Modeling System was integrated for July-August 1973 for south Florida. Three experiments were performed-one using the observed 1973 landscape, another the 1993 landscape, and the third the 1900 landscape, when the region was close to its natural state. Over the 2-month period, there was a 9% decrease in rainfall averaged over south Florida with the 1973 landscape and an 11% decrease with the 1993 landscape, as compared with the model results when the 1900 landscape is used. The limited available observations of trends in summer rainfall over this region are consistent with these trends.

A Possible Change in Mass Balance of Greenland and Antarctic Ice Sheets in the Coming Century

A high-resolution GCM is found to simulate precipitation and surface energy balance of high latitudes with high accuracy. This opens new possibilities to investigate the future mass balance of polar glaciers and its effect on sea level. The surface mass balance of the Greenland and the Antarctic ice sheets is simulated using the ECHAM3 GCM with TI06 horizontal resolution. With this model, two 5-year integrations for the present and doubled carbon dioxide conditions based on the boundary conditions provided by the ECHAM1/T21 transient experiment have been conducted. A comparison of the two experiments over Greenland and Antarctica shows to what extent the effect of climate change on the mass balance on the two largest glaciers of the world can differ. On Greenland one sees a slight decrease in accumulation and a substantial increase in melt, while on Antarctica a large increase in accumulation without melt is projected. Translating the mass balances into terms of sea-level equivalent. the Greenland discharge causes a sea level rise of 1.1 mm yr−1, while the accumulation on Antarctica tends to lower it by 0.9 mm yr−1. The change in the combined mass balance of the two continents is almost zero. The sea level change of the next century can be affected more effectively by the thermal expansion of seawater and the mass balance of smaller glaciers outside of Greenland and Antarctica.