Author details

Fortunately, the parameterization of a geometric anisotropic covariance function is such that if anisotropy were unnecessary, the parameters would take values that effectively result in an isotropic covariance function. The cost of this added flexibility is the need to estimate two additional covariance parameters per time period, for a total of 80 additional parameters. Computation time might be less here than for

We created a statistical model combining a process mean function with an exponential spatial covariance function with a nugget to predict salinity in a lagoonal estuary. This model can generate predictions of bottom salinity for Pamlico Sound, NC that are more spatially-resolute than any previous bottom salinity predictions encountered in the literature for this system. The salinity maps produced using the model are useful for researchers to build an intuitive understanding of salinity dynamics under PS conditions covered by these 40 time periods. Salinity predictions can also be used to inform future analyses including, but not limited to, the examination of historical distribution patterns of estuarine species relative to salinity variability and the prediction of salinity changes under various global

We thank the North Carolina Division of Marine Fisheries and the United States Geological Survey for providing datasets used in this study. We also thank editor A. Manning for helpful comments that improved the manuscript. Funding for this project was provided by the Environmental Defense Fund (Program Manager Pam Baker), North Carolina Coastal Recreational Fishing License Program (Grant No. 2010-H-004), North Carolina Sea Grant (R12-HCE-2) and the National Science Foundation (OCE-1155609) to D. Eggleston. A. Nail was supported as a VIGRE

With nugget effect Without nugget effect

Ι dij ≤ ρ<sup>t</sup> σ<sup>2</sup>

<sup>t</sup> >0, and θ<sup>t</sup> ≥0, �∞ < ρ< ∞, and dij is the distance separating sites i and j.

σ2 <sup>t</sup> exp �dij θt 

σ2 <sup>t</sup> exp �d<sup>2</sup> ij θ2 t 

> <sup>t</sup> <sup>1</sup> � <sup>3</sup>dij 2ρt <sup>þ</sup> <sup>d</sup><sup>3</sup> ij 2ρ<sup>3</sup> t

Ι dij ≤ρ<sup>t</sup> 

Matern, since anisotropic covariance functional forms are less complex.

Lagoon Environments Around the World - A Scientific Perspective

4. Conclusions

climate change scenarios.

Acknowledgements

Appendix

Name of covariance function

See Table A1.

Exponential σ<sup>2</sup>

Gaussian <sup>σ</sup><sup>2</sup>

Spherical <sup>σ</sup><sup>2</sup>

Note: For all models, σ<sup>2</sup>

Table A1.

180

Postdoctoral Fellow by NSF grant DMS 0354189.

Cov εti, εtj <sup>¼</sup>

I dij <sup>¼</sup> <sup>0</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup>

I dij <sup>¼</sup> <sup>0</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup>

I dij <sup>¼</sup> <sup>0</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup>

Formulas for the three spatial covariance functions used in this analysis.

<sup>t</sup> exp �dij θt 

<sup>t</sup> exp �d<sup>2</sup> ij θ2 t 

<sup>t</sup> <sup>1</sup> � <sup>3</sup>dij 2ρt <sup>þ</sup> <sup>d</sup><sup>3</sup> ij 2ρ<sup>3</sup> t

nt

nt

nt

Note: I(statement) = 1 if statement is true and 0 otherwise.

nt , σ<sup>2</sup> Christina L. Durham<sup>1</sup> , David B. Eggleston<sup>1</sup> \* and Amy J. Nail<sup>2</sup>

1 Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC, United States

2 Department of Statistics, North Carolina State University, Raleigh, NC, United States

\*Address all correspondence to: eggleston@ncsu.edu

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
