Template for Electronic Submission to ACS Journals
Supporting Information
for “Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico”
by Daniel R. Obenour*, Anna M. Michalak, Yuntao Zhou, and Donald Scavia
consisting of 5 sections and 4 figures within 4 pages.
*corresponding author, [email protected]
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S1. Example of stratification metrics (described in Section 2.1 of primary text)
Figure S1: Example salinity profile with stratification metrics
S2. Covariance parameters for geostatistical regression The covariance parameters for the GR model were estimated using REML, as described in Section 2.3 of primary text. The parameters σε2 and ση2 (often referred to as the nugget and the partial sill in geostatistics literature) were determined to be 0.53 and 1.29 mg2L-2, respectively. The range parameter, r, was determined to be 30.5 km along the east-west direction, which means that the effective range of spatial correlation is 91.5 km in that direction. The anisotropy ratio was determined to be 1.56, which means that the effective range of spatial correlation in the north-south direction is 58.7 km. These effective ranges are considerably longer than the typical spacing between sampling locations (see Figure 1 in primary text). Overall, these results verify that there is substantial spatial correlation in the stochastic portion of the model.
S1
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S3. Test of linearity for geostatistical regression The geostatistical regression (GR) model assumes that BWDO concentrations can be modeled using linear relationships with the examined predictor variables (or transformations of the predictor variables, e.g. ln[ΔS]). Figure S2 provides a visual test of this assumption by plotting the BWDO residuals versus each of the selected predictor variables. These residuals are referred to as ‘e*’ because while a normal residual is calculated by subtracting the observed value from � - y), these residuals are calculated by also the deterministic portion of the model (e = X𝛃
� - xj𝛽̂ j - y). In this way, the relationship removing the effect of the variable of interest (e = X𝛃 between the variable of interest, xj, and BWDO is clearly illustrated, with the slope of the trend
line approximately equal to the regression coefficient, 𝛽̂ j. In general, these plots suggest that the assumption of linearity between the predictor variables and BWDO is reasonable.
� - xj𝛽̂ j - y Figure S2: BWDO residuals (e*) versus normalized predictor variables (Note: e* = X𝛃
where xj is the variable represented on the horizontal axis of each graph.)
S2
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S4. Site-specific GR model results
Figure S3: Observed and predicted BWDO concentrations for ten-year study period. Predicted values are from deterministic component of GR model (eq 2).
S3
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S5. Illustration of Elastic-net model (eq 11 of primary text)
Figure S4: Annual intercept reductions attributed to different predictor variables from elastic-net model. Each factor presented relative to its year of minimum impact.
S4
for “Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico”
by Daniel R. Obenour*, Anna M. Michalak, Yuntao Zhou, and Donald Scavia
consisting of 5 sections and 4 figures within 4 pages.
*corresponding author, [email protected]
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S1. Example of stratification metrics (described in Section 2.1 of primary text)
Figure S1: Example salinity profile with stratification metrics
S2. Covariance parameters for geostatistical regression The covariance parameters for the GR model were estimated using REML, as described in Section 2.3 of primary text. The parameters σε2 and ση2 (often referred to as the nugget and the partial sill in geostatistics literature) were determined to be 0.53 and 1.29 mg2L-2, respectively. The range parameter, r, was determined to be 30.5 km along the east-west direction, which means that the effective range of spatial correlation is 91.5 km in that direction. The anisotropy ratio was determined to be 1.56, which means that the effective range of spatial correlation in the north-south direction is 58.7 km. These effective ranges are considerably longer than the typical spacing between sampling locations (see Figure 1 in primary text). Overall, these results verify that there is substantial spatial correlation in the stochastic portion of the model.
S1
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S3. Test of linearity for geostatistical regression The geostatistical regression (GR) model assumes that BWDO concentrations can be modeled using linear relationships with the examined predictor variables (or transformations of the predictor variables, e.g. ln[ΔS]). Figure S2 provides a visual test of this assumption by plotting the BWDO residuals versus each of the selected predictor variables. These residuals are referred to as ‘e*’ because while a normal residual is calculated by subtracting the observed value from � - y), these residuals are calculated by also the deterministic portion of the model (e = X𝛃
� - xj𝛽̂ j - y). In this way, the relationship removing the effect of the variable of interest (e = X𝛃 between the variable of interest, xj, and BWDO is clearly illustrated, with the slope of the trend
line approximately equal to the regression coefficient, 𝛽̂ j. In general, these plots suggest that the assumption of linearity between the predictor variables and BWDO is reasonable.
� - xj𝛽̂ j - y Figure S2: BWDO residuals (e*) versus normalized predictor variables (Note: e* = X𝛃
where xj is the variable represented on the horizontal axis of each graph.)
S2
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S4. Site-specific GR model results
Figure S3: Observed and predicted BWDO concentrations for ten-year study period. Predicted values are from deterministic component of GR model (eq 2).
S3
Supporting Information for Quantifying the impacts of stratification and nutrient loading on hypoxia in the northern Gulf of Mexico S5. Illustration of Elastic-net model (eq 11 of primary text)
Figure S4: Annual intercept reductions attributed to different predictor variables from elastic-net model. Each factor presented relative to its year of minimum impact.
S4
