Lagrangian particle dispersion models require interpolation of all meteorological input variables to the position in space and time of computational particles. The widely used model FLEXPART uses linear interpolation for this purpose, implying that the discrete input fields contain point values. As this is not the case for precipitation (and other fluxes) which represent cell averages or integrals, a preprocessing scheme is applied which ensures the conservation of the integral quantity with the linear interpolation in FLEXPART, at least for the temporal dimension. However, this mass conservation is not ensured per grid cell, and the scheme thus has undesirable properties such as temporal smoothing of the precipitation rates. Therefore, a new reconstruction algorithm was developed, in two variants. It introduces additional supporting grid points in each time interval and is to be used with a piecewise linear interpolation to reconstruct the precipitation time series in FLEXPART. It fulfils the desired requirements by preserving the integral precipitation in each time interval, guaranteeing continuity at interval boundaries, and maintaining non-negativity. The function values of the reconstruction algorithm at the sub-grid and boundary grid points constitute the degrees of freedom, which can be prescribed in various ways. With the requirements mentioned it was possible to derive a suitable piecewise linear reconstruction. To improve the monotonicity behaviour, two versions of a filter were also developed that form a part of the final algorithm. Currently, the algorithm is meant primarily for the temporal dimension. It was shown to significantly improve the reconstruction of hourly precipitation time series from 3-hourly input data. Preliminary considerations for the extension to additional dimensions are also included as well as suggestions for a range of possible applications beyond the case of precipitation in a Lagrangian particle model.
Hittmeir, S., Philipp, A., & Seibert, P. (2018). A conservative reconstruction scheme for the interpolation of extensive quantities in the Lagrangian particle dispersion model FLEXPART. Geoscientific Model Development, 11(6), 2503–2523. https://doi.org/10.5194/gmd-11-2503-2018