Full length articleA topological approach for quantitative comparisons of ocean model fields to satellite ocean color data
Introduction
For decades satellite sensors have been used to detect the color of the ocean surface by measuring light reflectance in different spectral bands (McClain, 2009). These ocean color data products have been utilized to identify and analyze ocean features that affect pigment and particulate content of the water and hence the ocean color, including oil spills, algal blooms and river plumes (e.g. Hu et al., 2004; Androulidakis and Kourafalou, 2013; Liu et al., 2013; Hu et al., 2015). They have also been integrated into observation and detection systems for harmful algal blooms and oil spills (e.g. Stumpf et al., 2003; Brekke and Solberg, 2005; Hu et al., 2016). With both broad spatial and frequent temporal coverage, satellite ocean color observations also have the potential to be valuable resources for numerical ocean modeling, however the ocean circulation modeling community has not fully capitalized on the utility of this data.
Satellite ocean color data have been used for ocean model assessment qualitatively, as patterns evident in the ocean color are often similar to, and may generally be visually compared to, features in dynamical fields (e.g. Binding and Bowers, 2003; Gregg et al., 2003; Chassignet et al., 2006; Liu et al., 2011; Schiller et al., 2011). Quantitative comparisons generally rely on point-wise differences that demand the same field be used and/or an empirical relationship between different but related fields is determined (e.g. Binding and Bowers, 2003; Gregg et al., 2003; Gregg, 2008; Mariano et al., 2011; Chaichitehrani et al., 2014; Zhang et al., 2014). While the types of statistical measures derived from point-wise comparisons (e.g. biases or correlations) are useful, they do not necessarily provide comparison of spatial distributions and/or shape that are related to circulation patterns or dynamical processes, and neither are they expressly designed for such a purpose. In an effort to more fully utilize the vast amount of remotely sensed data for ocean model assessment and analysis, the objective of this work is to apply and demonstrate the potential of a metric called the Modified Hausdorff Distance (MHD) to quantitatively compare spatial and temporal patterns derived from satellite ocean color observations to ocean circulation models. It is anticipated that the methodology introduced here will have extensions in future to new satellite observations (such as surface salinity) and the development of cost functions for adjoint data assimilation techniques.
Section snippets
Background
The MHD originates from the field of topology and is designed specifically to compare shapes (Dubuisson and Jain, 1994). The MHD and Hausdorff distance, from which the former is derived, are frequently used in imaging software for object location and pattern recognition (Huttenlocher et al., 1993; Huttenlocher and Rucklidge, 1993; Rucklidge, 1997; Daoudi et al., 1999; Zhang and Lu, 2004). There has been some application to analysis of geospatial data, an example being precipitation patterns
Data and methods
This study demonstrates application of the MHD for comparing satellite-derived and ocean model fields of different, but related quantities. In particular, an ocean color product derived from satellite optical data is compared to salinity fields from three different models to evaluate the models’ representations of the distribution of riverine water. In this section, the MHD and Hausdorff distance (from which the MHD is derived) are introduced, the ocean color product and the model simulations
Qualitative representation of the plume
The seasonality of surface salinity in the region, characterized by summer spreading and winter retraction (Walker et al., 1996, Morey et al., 2003a, Androulidakis and Kourafalou, 2013) is evident in the satellite OCI and model SSS contours (Fig. 3, Fig. 4). During the fall and winter OCI and SSS contours are often compacted near the coast as northwestward prevailing winds drive a coastally trapped current. During the spring and summer, generally northward winds allow spreading to the east
Discussion and summary
Borrowing from the field of topology, the MHD has been introduced and demonstrated as a tool for quantitative comparison of ocean model fields to satellite remotely sensed data. This approach provides a method to quantify the agreement in shape and spatial structure between fields of either similar or different but related variables as well as producing an empirical relationship between the variables. Typically in ocean modeling, satellite optical data have been used to qualitatively compare
Acknowledgments
This research was made possible by grants from the Bureau of Ocean Energy Management (BOEM) (M12PC00003) and the Gulf of Mexico Research Initiative, and the US NASA (NNX14AM63G and NNX14AL98G). V. Kourafalou acknowledges additional support from NOAA (NA15OAR4320064 and NA15NOS4510226). DSC-ROMS and NGoM-HYCOM model data are publicly available through the Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC) at https://data.gulfresearchinitiative.org (UDI:
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