10 Salinity ~ elevation deviation time series
To better characterize changes in the surface salinity~lake elevation relationship over time, I used the UGS dataset to model the historical (1966-1984) salinity~lake elevation relationship and predict salinities that would be expected under historical conditions through the entire dataset. The differences between observed and expected salinities represent the degree of change in the surface salinity~lake elevation relationship between observed and historical conditions, with negative values indicating fresher than historical conditions and higher values indicating more saline than historical conditions. I fit a second degree polynomial regression to historical (1966-1985) surface salinities (model summary below & figure 10.1). As expected, observed and expected salinities are consistent through the historical time period used for model calibration (Figures 10.2 & 10.3). Obeserved salinities begin to deviate from historical expected in the late 1980s. The strongest deviations begin in the mid 2000s (Figure 10.2). Observed minus historical expected salinities show a strong pattern of freshening of surface waters in Gilbert Bay since approximately 1990. The total freshening since 1990 is a change in salinity of about 12%, substantially larger than the change observed following the causeway breach in 2016 (Figure 10.3). Under historical inflow, culvert, & breach conditions, Gilbert Bay salinities under current lake elevations would likely approach 20% salinity as opposed to the currently observed salinities of about 12%.
10.1 Model pre-1985 salinity ~ elevation relationship
mod_train_data=subset(surf, pre_post=='pre 1985')
poly2_lm=lm(salinity_pct ~ poly(elev_ft, 2, raw = TRUE), data = mod_train_data)
summary(poly2_lm)##
## Call:
## lm(formula = salinity_pct ~ poly(elev_ft, 2, raw = TRUE), data = mod_train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1844 -0.2304 0.0024 0.4130 4.6785
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.896e+05 4.538e+04 17.40 <2e-16 ***
## poly(elev_ft, 2, raw = TRUE)1 -3.749e+02 2.160e+01 -17.35 <2e-16 ***
## poly(elev_ft, 2, raw = TRUE)2 4.449e-02 2.571e-03 17.31 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.933 on 292 degrees of freedom
## Multiple R-squared: 0.9643, Adjusted R-squared: 0.9641
## F-statistic: 3944 on 2 and 292 DF, p-value: < 2.2e-16Figure 10.1: Gilbert Bay pre-1985 salinity on elevation relationship and model.
10.2 Observed and pre-1985 predicted salinity
Figure 10.2: Observed (blue circles) and predicted (purple triangles) salinity through time. Predicted salinity is derived from the pre-1985 salinity on elevation relationship.
Figure 10.3: Gilbert Bay surface salinity deviance (observed - expected) through time.