A topological approach for quantitative comparisons of ocean model fields to satellite ocean color data

In an effort to more fully employ underutilized satellite observations in ocean modeling, this work demonstrates a method for quantifying the agreement between time-evolving spatial features evident in fields of differing, but functionally related, variables that are more commonly compared qualitatively via visual inspection. This is achieved through application of the Modified Hausdorff Distance metric to the evaluation of ocean model simulations of surface salinity near riverine sources using satellite ocean color data. The Modified Hausdorff Distance is a metric from the field of topology designed to compare shapes and the methodology provides quantitative assessment of similarity of spatial fields. The Modified Hausdorff Distance can be applied for comparison of many geophysical and ecological fields that vary spatially and temporally. Here, the utility of the metric is demonstrated by applying it to evaluate numerical simulations of the time-evolving spatial structure of the surface salinity fields from three ocean models in the vicinity of large riverine sources in the northeast Gulf of Mexico. Using the Modified Hausdorff Distance, quantitative comparison of modeled sea surface salinity contours to contours of a gridded satellite-derived ocean color product is made under the assumption that the modeled fields are related to optically significant quantities that indicate the spatial extent of riverine influenced water. Three different ocean models are evaluated and are compared individually to the satellite data. The sea surface salinity values and ocean color index values that most closely match (lowest Modified Hausdorff Distance score) are identified for each model. The Modified Hausdorff Distance scores for these best pairings are used to both determine the degree to which surface salinity fields from the models match the satellite observations and obtain an empirical relationship between the two variables for each model. Furthermore, the best pairings are compared between models allowing key differences in the simulated riverine water distributions to be distinguished. The Modified Hausdorff Distance proves a robust and useful diagnostic tool that has the potential to be utilized in many geophysical applications and facilitates the use of satellite ocean color data for quantitative evaluation of hydrodynamic ocean models.