Previous solutions of the idealized saltwater intrusion problem known as the Henry problem are discussed, and possible reasons for the observed discrepancies between them are given. High‐accuracy finite difference techniques are used to solve the nondimensionalized equations governing the problem, and a fine grid is used so that the solutions obtained contain only very small truncation errors. Such errors are investigated by means of grid refinement. Comparison of past results with the present solutions indicate, first, the presence of significant inaccuracy in certain earlier results and, second, the effects of numerical dispersion in other previous solutions calculated using relatively few grid points.

The utility of marine protected areas (MPAs) as a means of protecting exploited species and conserving biodiversity within MPA boundaries is supported by strong empirical evidence. However, the potential contribution of MPAs to fished populations beyond their boundaries is still highly controversial; empirical measures are scarce and modelling studies have produced a range of predictions, including both positive and negative effects. Using a combination of genetic parentage and relatedness analysis, we measured larval subsidies to local fisheries replenishment for Australasian snapper (: Sparidae) from a small (5.2 km), well-established, temperate, coastal MPA in northern New Zealand. Adult snapper within the MPA contributed an estimated 10.6% (95% CI: 5.5-18.1%) of newly settled juveniles to surrounding areas (approx. 400 km), with no decreasing trend in contributions up to 40 km away. Biophysical modelling of larval dispersal matched experimental data, showing larvae produced inside the MPA dispersed over a comparable distance. These results demonstrate that temperate MPAs have the potential to provide recruitment subsidies at magnitudes and spatial scales relevant to fisheries management. The validated biophysical model provides a cost-efficient opportunity to generalize these findings to other locations and climate conditions, and potentially informs the design of MPA networks for enhancing fisheries management.

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A high-resolution 3D biophysical model was used to investigate the patterns of larval transport for an important commercial and recreational temperate fish, snapper Pagrus auratus, from a well-established marine reserve (Cape Rodney to Okakari Point marine reserve, CROP), and spawning ground. Our focus was to study the effects of local hydrodynamics, contrasting larval vertical behaviours and changing El Niño-Southern Oscillation (ENSO) cycles (via their effect on wind forcing) on the potential larval supply to adjacent non-protected areas. The model suggests the CROP marine reserve provides significant larval subsidies within a relatively small scale (≤40 km), the details of which depend on larval behaviour and ENSO patterns. Changing ENSO patterns mostly affected the dispersal direction of larvae, while larval behaviour was a strong driver only under La Niña conditions. Modelling suggests that under El Niño conditions, snapper larvae are more likely to settle successfully and hence make a strong contribution to surrounding fished stocks. Understanding the contribution of MPAs to fisheries management will require multiple approaches. Modelling will help identify the strength of contributing physical and biological factors, and in due course enable site-and time-specific examples of larval subsidy to be generalised.