7 Salinity and lake elevation

There is a significant difference in the relationship between salinity and WSE in Gilbert Bay between pre- and post-breach samples (Figure 7.1). Linear regressions show that the slopes of the relationships are equal among groups, but that the pre-breach data have a higher intercept (higher salinity) than the post-breach data. Ancova analysis confirms this interpretation with both elevation and pre/post breach grouping having significant coefficients, but no significant interaction between the two variables (Section 7.2). This pattern is also consistent with related measures of salinity, density and specific conductance (Figures 7.2 and 7.3).

7.1 Regressions

Figure 7.1: Gilbert Bay surface (<=1 m depth) salinity on water surface elevation for all USGS monitoring locations in Gilbert Bay. Data from USGS NWIS. Samples are binned by pre-breach (2010-2016) and post-breach (2017-present).

Figure 7.2: Gilbert Bay surface (<=1 m depth) density on water surface elevation for all USGS monitoring locations in Gilbert Bay. Data from USGS NWIS. Samples are binned by pre-breach (2010-2016) and post-breach (2017-present).

Figure 7.3: Gilbert Bay surface (<=1 m depth) specific conductance on water surface elevation for all USGS monitoring locations in Gilbert Bay. Data from USGS NWIS. Samples are binned by pre-breach (2010-2016) and post-breach (2017-present).

7.2 Ancova

summary(lm(value ~ elev_ft, data = subset(sal_elev_data, pre_post=='pre')))

## 
## Call:
## lm(formula = value ~ elev_ft, data = subset(sal_elev_data, pre_post == 
##     "pre"))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.806  -1.497   0.951   2.458  65.765 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 38630.6188   742.2195   52.05   <2e-16 ***
## elev_ft        -9.1774     0.1769  -51.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.951 on 296 degrees of freedom
## Multiple R-squared:  0.9009, Adjusted R-squared:  0.9006 
## F-statistic:  2691 on 1 and 296 DF,  p-value: < 2.2e-16

summary(lm(value ~ elev_ft, data = subset(sal_elev_data, pre_post=='post')))

## 
## Call:
## lm(formula = value ~ elev_ft, data = subset(sal_elev_data, pre_post == 
##     "post"))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -46.954  -1.103   1.352   2.449  10.995 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39179.4227  2203.5423   17.78   <2e-16 ***
## elev_ft        -9.3138     0.5254  -17.73   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.63 on 172 degrees of freedom
## Multiple R-squared:  0.6462, Adjusted R-squared:  0.6442 
## F-statistic: 314.2 on 1 and 172 DF,  p-value: < 2.2e-16

sal_aov <- aov(value ~ elev_ft*pre_post, data = sal_elev_data)
summary(sal_aov)

##                   Df Sum Sq Mean Sq  F value Pr(>F)    
## elev_ft            1  71971   71971 1866.945 <2e-16 ***
## pre_post           1  54548   54548 1415.005 <2e-16 ***
## elev_ft:pre_post   1      3       3    0.067  0.795    
## Residuals        468  18041      39                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1