Mathematics and statistical analysis are very useful tools to  probabilistic forecasting of natural hazard phenomena. Uncertainty quantification methods are very suitable for prediction and characterization of natural hazards and hence can be studied for risk assessment for the possible occurrence of natural hazards like hurricane, earthquake, release of toxic material, etc.

Dynamic data driven application system paradigm (DDDAS) are systems where data are dynamically integrated into simulation (or simulation driven workflows) to enhance the model outcomes, and where conversely the executing simulation steers the observation process. An example of DDDAS is simulation of a volcano eruption, where a numerical model is used to simulate the eruption phenomenon. Simultaneously, satellite imagery is integrated into the model to improve model outcome for future time steps. Following figure illustrates simulation of Eyjafjallajökull eruption which happened in 2010.

Like any other mathematical model, performance of applied numerical model for simulation of eruption is greatly influenced with the parameters and inputs like wind velocity, temperature, etc. Hence, it is of great interest to characterize possible outcomes of the process, given a range of uncertainty for the parameters whose values are not accurately known. Uncertainty Quantification can be used to predict the presence of ash over the region in probabilistic framework. An example of this is shown in the following figure.

Probability of presence of ash over the Europe in occurrence of Eyjafjallajökull eruption.

Integration of model prediction with satellite imagery can be used to improve accuracy of model output in future time steps. This has been shown in the following figure. We have used model prediction and satellite image (illustrated above) to improve the model output for the next time step.

Satellite Image

Model Prediction