Methods for source determination in the context of the CTBT radionuclide monitoring system

A variety of methods applicable to the problem of source determination or inverse modelling of atmospheric trace constituents has been suggested and used so far. They include trajectory statistics (Stohl, 1998), inverse methods based on the source-receptor matrix, and iterative methods based on adjoint Eulerian dispersion models. Source-receptor matrices (SRMs) can be computed by different kinds of models, in forward as well as in backward mode. The different methods are characterised and their advantages and drawbacks will be discussed, with special emphasis on CTBT verification. 2. The nature of the source determination problem The source determination problem is sometimes associated with terms such as ‘backward modelling’ or ‘backtracking’. Though dispersion models may be run in a backward mode, this is neither necessary nor sufficient for source determination. There is no direct way of calculating sources from observed concentrations, comparable to the forward simulations of concentrations fields from given sources. The source determination is an optimisation problem. We want to find the sources leading to calculated concentrations that fit best the observed concentrations when being plugged in a transport & dispersion model. In mathematical terms, we want to minimise a cost function that measures the misfit of the model output , using the source strength (in general, a function of time and space) as the control variable. Eventually, we want to include further terms in the cost function to represent additional ap rioriknowledge or assumptions. The methods that can be used to find this minimum depend on whether the gradient of the cost function and the model operator are linear with respect to or not. In the nonlinear case, iterations are necessary, whereas in the linear case an analytical solution can be set up. The transport, dispersion, deposition and radioactive decay of chemically inert species (or species whose chemical transformations follow predescribed rates) is a linear problem, and thus so is the CTBT verification problem. The typical assumption for the cost function, namely to be equal to the sum of the squared deviations between model output and observations, also fulfils the linearity requirement. Replacing with the SRM , and considering a regularisation term expressed as a matrix applied to the source vector , with regularisation parameter (weight) , this can be written as a formula: