NUMERICAL SIMULATIONS OF THE ELBE FLOOD CASE: SENSITIVITY TO INITIAL AND BOUNDARY DATA

Numerical experiments with the model chain of the German Weather Service are conducted to find the reasons for the bad performance of the operational precipitation forecast in the case of the Elbe flood in August 2002. The sensitivity to initial and to boundary data as well as to a new precipitation scheme and the horizontal model resolution is inspected. The greatest improvement concerning the amount and location of the predicted precipitation field is achieved by using ECMWF analysis data as initial fields. Also, the implementation of a precipitation scheme that allows the rain to be advected with the wind exhibits a positive effect. Last, the better resolution of the global model improves the rainfall forecast, whereas the better resolution of the regional model produces worse results

Time-lagged ensemble simulations of the dispersion of the Eyjafjallajökull plume over Europe with COSMO-ART

An extended version of the German operational weather forecast model was used to simulate the ash dispersion during the eruption of the Eyjafjallajökull. As an operational forecast was launched every 6 hours, a time-lagged ensemble was obtained. Sensitivity runs show the ability of the model to simulate thin ash layers when an increased vertical resolution is used. Calibration of the model results with measured data allows for a quantitative forecast of the ash concentration. After this calibration an independent comparison of the simulated number concentration of 3 μm particles and observations at Hohenpeißenberg gives a correlation coefficient of 0.79. However, this agreement could only be reached after additional modifications of the emissions. Based on the time lagged ensemble the conditional probability of violation of a certain threshold is calculated. Improving the ensemble technique used in our study such probabilities could become valuable information for the forecasters advising the organizations responsible for the closing of the airspace

Time-lagged ensemble simulations of the dispersion of the Eyjafjallajökull plume over Europe with COSMO-ART

An extended version of the German operational weather forecast model was used to simulate the ash dispersion during the eruption of the Eyjafjallajökull. As an operational forecast was launched every 6 hours, a time-lagged ensemble was obtained. Sensitivity runs show the ability of the model to simulate thin ash layers when an increased vertical resolution is used. Calibration of the model results with measured data allows for a quantitative forecast of the ash concentration. After this calibration an independent comparison of the simulated number concentration of 3 μm particles and observations at Hohenpeißenberg gives a correlation coefficient of 0.79. However, this agreement could only be reached after additional modifications of the emissions. Based on the time lagged ensemble the conditional probability of violation of a certain threshold is calculated. Improving the ensemble technique used in our study such probabilities could become valuable information for the forecasters advising the organizations responsible for the closing of the airspace

Modelling of a strong dust event in the complex terrain of the Dead Sea valley during the passage of a gust front

The area of the Dead Sea valley and the adjacent regions are often affected by mineral dust. This study focuses on an extreme dust episode occurring on 22 March 2013, where near-surface dust concentrations of up to 7000 µg m−3 were encountered in the Dead Sea region. This episode is of great interest as it was accompanied by high wind speeds and a gust front that rapidly passed the Judean Mountains. Wind was even accelerated on the lee side of the Judean Mountains leading to a severe downslope wind. We simulated this situation with the comprehensive online-coupled weather forecast model COSMO-ART. Fair agreement was found between the simulated meteorological variables and the observations. The model was capable of producing a reasonable spatiotemporal distribution of near-surface dust concentration, consistent with available measurements in this area. With respect to the time of the maximum near-surface dust concentration in the Dead Sea valley, the model captured it almost perfectly compared to the observed total suspended particle (TSP) concentrations. COSMO-ART showed that the high near-surface dust concentration in the Dead Sea valley was mainly determined by local emissions. These emissions were caused by strong winds on the lee side of the Judean Mts. The model showed that an ascending airflow in the Dead Sea valley lifted dust particles, originating mainly from the upwind side of the Judean Mts., up to approximately 7 km. These dust particles contributed to the pronounced maximum in modelled dust aerosol optical depth (AOD) over the valley. Here we highlight the important point that the simulated maximum dust AOD was reached in the eastern part of the Dead Sea valley, while the maximum near-surface dust concentration was reached in the western part of the valley

A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy

We review mathematical results about the qualitative structure of chemotherapy protocols that were obtained with the methods of optimal control. As increasingly more complex features are incorporated into the mathematical model—progressing from models for homogeneous, chemotherapeutically sensitive tumor cell populations to models for heterogeneous agglomerations of subpopulations of various sensitivities to models that include tumor immune-system interactions—the structures of optimal controls change from bang-bang solutions (which correspond to maximum dose rate chemotherapy with restperiods) to solutions that favor singular controls (representing reduced dose rates). Medically, this corresponds to a transition from standard MTD (maximum tolerated dose) type protocols to chemo-switch strategies towards metronomic dosing

Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy

We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples

The scheduling of angiogenic inhibitors minimizing tumor volume

The efficiency of piecewise constant protocols with a small number of switchings is investigated for a mathematical model of tumor anti-angiogenesis formulated originally by Hahnfeldt et al. in [8]. By comparing with the theoretically optimal solution derived earlier [12] it will be seen that for the problem of minimizing the primary cancer volume with a given amount of angiogenic inhibitors to be administered constant protocols already provide very good suboptimal strategies