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It is not practical to run each individual model every year. To meet the research objectives outlined in Section 1 and to determine the most accurate ordinary kriging model for changing the current Gulf of Mexico hypoxia monitoring and management practices (Section 4), it is only necessary to assess model performance for moderate and large hypoxic years (2002, 2007, and 2008).

3.8.1 Ordinary Kriging Model Assessment Statistics

The individual model assessment statistics are included in Appendix E and will not be discussed here. Summary points regarding the assessment statistics from the Appendix E tables are:

a. All values are near zero with no deviations greater than 0.05 in the mean and standardized means.

b. The RMSE and standardized RMSE are close to 1 for all models in all hypoxic years.

c. The largest deviations in the accuracy of the estimates occurred in 2007 (models G TX A and G TX A Adj), because of underestimating the variability (negative SRMSE) of the bottom dissolved oxygen and thus overestimating the hypoxic area. However, in 2002 and 2008, these two models more accurately estimate the variability and area on the Texas shelf.

3.8.2 Ordinary Kriging Model Assessment Methods

Rather than focusing on individual models, I attempted to determine model success by testing the SRMSE for all years versus hypoxic years and conducted a nonparametric rank comparison to evaluate all Gaussian models (recall there was no significance between Gaussian and Spherical models, Section 3.2) based on the six criteria outlined in Section 3.4.

To support the overall observations from all criteria, I conducted 1-way ANOVA and 2-sample independent t-tests for the parameters versus the SRMSE, which validated

whether the model was correctly estimating the variability in bottom dissolved oxygen on the Texas shelf.

3.8.3 Ordinary Kriging Model Assessment Results

Table 3.7 shows the results for both ANOVA comparisons for all years (2002 to 2011, excluding 2010) and hypoxic years (2002, 2004, 2007, and 2008). The 1-way ANOVA results showed all three parameters to be significantly different in SRMSE values for all years and only Data and Spatial to be important in hypoxic years. If each variable were not important in predicting area, there would be no significant differences in the SRMSE values. A N-way ANOVA with the three variables against Year also proved all possible combinations to be significantly different (p-value < 0.001).

ANOVA tests of the parameters in only hypoxic years resulted in only Data and

Spatial being significantly different (p-value < 0.05) and Lag not significantly different

in the SRMSE comparisons (Table 3.7). Results based on SRMSE assessment show that the interpolated shelf area, as well as the anisotropic trends, was critical to estimate the hypoxic area on the Texas shelf. Manually adjusting the lag distance in the model was important for examining changes in bottom dissolved oxygen across the shelf, but was not crucial to estimating area in hypoxic years.

I used non-parametric ranked assessments for the model criteria (recall Section 3.4) to reduce the number of suitable models down to 1 per year that best predicted bottom dissolved oxygen and estimate hypoxic area on the Texas shelf. Table 3.8 shows the non-parametric mean rank score results from ranking all Gaussian models to

the criteria outline in Section 3.4. The first column of the Table lists the models considered for the three years (2002, 2007, and 2008), which were selected to represent one year in each size category (small-2002, moderate-2007, and large-2008). One hypoxic year, 2004, was excluded because four of six Gaussian models did not estimate a hypoxic area on the Texas shelf. The second column orders the mean rank score for each of the models based on the average calculated from assessment criteria and the third column includes the hypoxic area estimated by each of the models.

Based on the mean rank ordering, one model has the lowest, or best score, of the six models considered – Gaussian SEAMAP TX Anisotropic (G TX A). In each year, the average rank was 2.6 and below with the lowest rank in 2002. This meant G TX A yearly models estimate most accurately the true bottom dissolved oxygen on the Texas shelf. The lowest performing model was the Gaussian SEAMAP ALL Isotropic (G All I) model in 2002 and the Gaussian SEAMAP TX Isotropic (G TX I) model in 2007 and 2008. Both models resulted in mean rank scores above 4.4 indicating that model poorly performed in the lower rankings for the assessment criteria.

Examining how the Data parameter performed was also important, since earlier results showed more accuracy in in area estimates on the Texas shelf for SEAMAP TX models. In 2007 and 2008, SEAMAP ALL models performed better than SEAMAP TX models ranking in the 2nd to 4th positions. The Data models alternated positions in 2002 with 2 of 3 SEAMAP ALL models ranking in the lower 50 % of the assessment ranking. No one model received a ranking below 5, indicating that no one particular model received consistent lowest rankings of 6. On the other hand, no particular model ranked

lower than a 2, likewise indicating that no particular model performed in the top scores for assessment criteria ranking.

3.8.4 Summary of Model Parameters & Assessment

The analysis of assessment criteria, both with the ANOVA and non-parametric ranking, further supported that two parameters were more important in ordinary kriging model design – Spatial and Data. In the first assessment comparing SRMSE, Data and

Spatial were most important for all years, not just hypoxic years as seen with the Lag

parameter. In the rank comparisons, the model with the best performance in categorical hypoxic years was Gaussian SEAMAP TX Anisotropic. The consistency of this model in estimating bottom dissolved oxygen in the three years considered further supported the importance of only considering data on the Texas shelf to prevent masking of hypoxic area by the Louisiana shelf. Furthermore, this model showed the importance of considering the along- and across-shelf spatial autocorrelation in bottom dissolved oxygen across the Texas shelf and the importance of including anisotropy in model design to accurately estimate and categorize hypoxic area on the Texas shelf.