Quinpi: Integrating Conservation Laws with CWENO Implicit Methods

Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration is quite straightforward for first-order schemes. High order schemes instead also need to control spurious oscillations, which requires limiting in space and time also in the linear case. We propose a framework to simplify considerably the application of high order non-oscillatory schemes through the introduction of a low order implicit predictor, which is used both to set up the nonlinear weights of a standard high order space reconstruction, and to achieve limiting in time. In this preliminary work, we concentrate on the case of a third-order scheme, based on diagonally implicit Runge Kutta (DIRK) integration in time and central weighted essentially non-oscillatory (CWENO) reconstruction in space. The numerical tests involve linear and nonlinear scalar conservation laws

Validation and analysis of regional present-day climate and climate change simulations over Europe

In the European Commission (EC) project "Regionalization of Anthropogenic Climate Change Simulations, RACCS, recently terminated, 11 European institutions have carried out tests of dynamical and statistical regionalization techniques. The outcome of the "dynamical part" of the project, utilizing a series of high resolution LAMs and a variable resolution global model (all of which we shall refer to as RCMs, Regional Climate Models), is presented here. The per- formance of the dqterent LAMs had first, in a preceding EC project, been tested with "perfect" boundary forcing fields (ECMWF analyses) and also multi-year present-day climate simula- tions with AMIP "perfect ocean " or mixed layer ocean GCM boundary conditions had been validated against available climatological data. The present report involves results of vali- dation and analysis of RCM present-day climate simulations and anthropogenic climate change experiments. Multi-year (5 - 30 years) present-day climate simulations have been per- formed with resolutions between 19 and 70 km (grid lengths) and with boundary conditions from the newest CGCM simulations. The climate change experiments involve various 2xCO2 - ]xCO2 transient greenhouse gas experiments and in one case also changing sulphur aerosols. A common validation and inter-comparison was made at the coordinating institution, MPIfor Meteorology. The validation of the present-day climate simulations shows the importance of systematic errors in the low level general circulation. Such errors seem to induce large errors in precipitation and surface air temperature in the RCMs as well as in the CGCMs providing boundary conditions. Over Europe the field of systematic errors in the mean sea level pressure (MSLP) usually involve an area of too low pressure, often in the form of an east-west trough across Europe with too high pressure to the north and south. New storm-track analyses confirm that the areas of too low pressure are caused by enhanced cyclonic activity and similarly that the areas of too high pressure are caused by reduced such activity. The precise location and strength of the extremes in the MSLP error field seems to be dependent on the physical param- eterization package used. In model pairs sharing the same package the area of too low pressure is deepened further in the RCM compared to the corresponding CGCM, indicating an increase of the excessive cyclonic activity with increasing resolution. From the experiments performed it seems not possible to decide to what extent the systematic errors in the general circulation are the result of local errors in the physical parameterization schemes or remote errors trans- mitted to the European region via the boundary conditions. Additional errors in precipitation and temperature seems to be due to direct local effects of errors in certain parameterization schemes and errors in the SSTs taken from the CGCMs. For all seasons many biases are fOund to be statistically significant compared to estimates of the internal model variability of the time- slice mean values. In the climate change experiments statistically significant European mean temperature changes which are large compared to the corresponding biases are found. How- ever, the changes in the deviations from the European mean temperature as well as the changes in precipitation are only partly sign wcan ce and are of the same order of magnitude or smaller than the corresponding biases found in the present-day climate simulations. Cases of an inter- action between the systematic model errors and the radiative forcing show that generally the errors are not canceling out when the changes are computed. Therefore, reliable regional cli- mate changes can only be achieved after model improvements which reduce their systematic errors sufficiently. Also in future RCM experiments sujiciently long time-slices must be used in order to obtain statistically sign ijicant climate changes on the sub-continental scale aimed at with the present regionalization technique

Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models. In this paper, resting on the methods of kinetic theory, we introduce a new traffic model which takes into account the heterogeneous nature of the flow of vehicles along a road. In more detail, the model considers traffic as a mixture of two or more populations of vehicles (e.g., cars and trucks) with different microscopic characteristics, in particular different lengths and/or maximum speeds. With this approach we gain some insights into the scattering of the data in the regime of congested traffic clearly shown by actual measurements

Coupling a distributed grid based hydrological model and MM5 meteorological model for flooding alert mapping

International audienceThe increased number of extreme rainfall events seems to be one of the common feature of climate change signal all over the world (Easterlin et al., 2000; Meehl et al., 2000). In the last few years a large number of floods caused by extreme meteorological events has been observed over the river basins of Mediterranean area and they mainly affected small basins (few hundreds until few thousands of square kilometres of drainage area) . A strategic goal of applied meteorology is now to try to predict with high spatial resolution the segments of drainage network where floods may occur. A possible way to reach this aim is the coupling of meteorological mesoscale model with high resolution hydrological model. In this work few case studies of observed floods in the Italian Mediterranean area will be presented. It is shown how a distributed hydrological model, using the precipitation fields predicted by MM5 meteorological model, is able to highlight the area where the major floods may occur

Continuous limits of residual neural networks in case of large input data

Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean-field limit and show well-posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings

A combined Rayleigh-Raman lidar for measurements of tropospheric water vapour and aerosol profiles

The receiver of the Differential Absorption Lidar system of the University of L’Aquila (Italy) has been upgraded for the detection of Raman scattering from nitrogen and water vapour induced by XeCl and XeF excimer laser lines. In this configuration, only the XeF source is activated, so we can measure the tropospheric water vapour mixing ratio profiles with a height resolution of 300 m and 10 min in time. The lower limit sensitivity for the mixing ratio of water vapour is about 2 Q1024 and the precision ranges between 5% at 2 km and 50% at 9 km. The aerosol back-scattering ratio profiles can be measured with the same altitude and time resolution up to the lower stratosphere, the relative error is below 5% in the troposphere and about 30% at the highest altitudes. Comparisons with coincident PTU balloon-sondes show that the performances of the system in measuring the tropospheric water vapour are well calibrated for studying the water vapour evolution and cloud formation in the troposphere