A parallel algorithm is described for variational assimilation of observations into oceanic and atmospheric models. The algorithm may be coded first for execution on a serial computer and then trivially modified for execution on a parallel computer such as the Intel iPSC/860. The speedup factor for parallel execution is roughly P(2M+3) (2M+3P)−1, where P is the number of processors and M is the number of observations (M≥P). The speedup factor approaches P from below as M→∞.
The algorithm has been applied in serial form to ocean tides (Bennett and McIntosh 1982; McIntosh and Bennett 1984; Bennett 1985) and oceanic equatorial interannual variability (Bennett 1990). It has been applied in parallel form to oceanic synoptic-scale circulation (Bennett and Thorburn 1992); a parallel application to operational forecasting of tropical cyclones is in progress (Bennett et al. 1992).
For the sake of simplicity, the parallel algorithm is described here for a model consisting of a linear, first-order wave equation with initial and boundary conditions plus a dataset consisting of observations at isolated points in space and time. However, measurements of parallel performance are given for a nonlinear quasigeostrophic model.