Predicting chlorophyll-a concentrations in two temperate reservoirs with different trophic states using Principal Component Regression (PCR)

The intensified human activities have accelerated the rate of cultural eutrophication of water bodies worldwide (Najar & Khan 2012), resulting in cyanobacterial blooms, reduced oxygen and eventually fish kills (Anita & Pooja 2013). The effects of these activities on water bodies can be estimated by the degree of eutrophication. The eutrophication level is often determined by the chlorophyll-a (chl-a) content in the water column of aquatic systems (Huszar et al. 2006).

Chl-a concentration, a proxy for the abundance of phytoplankton in aquatic systems, depends on the physical and chemical properties of the water column, including the availability of nutrients, light, temperature and grazing pressure as well as interactions between these variables (Jeppesen et al. 2004). Reduction in nutrient loading results in a reduction in phytoplankton biomass and this, in turn, results in better ecological status of water bodies (Phillips et al. 2008).

Statistical methods are widely used in eutrophication studies to explore the interactions between water quality parameters and primary production (Irvine et al. 2015). However, it is difficult to study eutrophication in surface waters when there are a large number of variables. In these cases, researchers face a major difficulty regarding the choice of analytical parameters due to the multicollinearity (Johnson et al. 1982).

One way to overcome this problem is to use principal component analysis (PCA) followed by multiple linear regression (MLR) (Çamdevirena et al. 2005). The process is called principal component regression, PCR, where the principal components (PCs) of PCA are used in MLR. This process reduces the complexity of the multidimensional system by maximizing the variance of component loadings and by eliminating the invalid components (Zhang et al. 2013).

The PCR method has recently been used in various studies to identify factors driving the eutrophication of aquatic systems (Praveena et al. 2011). PCR provides information on the most meaningful variables by reducing the number of latent factors contributing to eutrophication, MLR examines the relationships between a dependent variable and a set of independent variables.

The aim of this study is to apply PCR to data from two temperate freshwater reservoirs with different trophic states. Studies using PCR methodology from this region have so far used data sets either from a single lentic (Çamdevirena et al. 2005) or lotic system (Köklü et al. 2010). The presented work also aims at determining whether the results of PCR application to a eutrophic reservoir are different from those for a mesotrophic reservoir. For this purpose, 17 physicochemical and biological water quality parameters from eutrophic temperate Çaygören and mesotrophic Ikizcetepeler reservoirs were used in PCA, and then the PCs of PCA were used in MLR to predict chl-a concentrations in both reservoirs.

X² calculated as 702.7 for the Çaygören Reservoir and 1223 for the Ikizcetepeler Reservoir by Barttlett’s sphericity test (d.f. = 136, p < 0.01), showing that both data sets have an adequate number of samples for the application of PCA. The residual statistics are given in Table 1 and Table 2 for each reservoir.

Table 1

Residual statistics (n = 17) for Çaygören Reservoir

Table 2

Residual statistics (n = 17) for Ikizcetepeler Reservoir

In both reservoirs, six out of 17 PCs were selected for MLR, which was called the first approach (Tables 3 and 4). In the first approach, the selected PCs explained 71% of the total variation in the Çaygören Reservoir and 75% in the Ikizcetepeler Reservoir (Tables 5 and 6).

Table 3

Descriptive statistics of PCs for Çaygören Reservoir

Table 4

Descriptive statistics of PCs for Ikizcetepeler Reservoir

Table 5

Results of regression analysis (n = 17) with six PCs for Çaygören Reservoir

Table 6

Results of regression analysis (n = 17) with six PCs for Ikizcetepeler Reservoir

PCA component loadings of the first six PCs for the Çaygören Reservoir are presented in Table 7. The bold-marked loads indicate the highest existing correlation between the variables and the corresponding component. The high values of communalities indicate that the variance was efficiently reflected in the regression analysis.

Table 7

Results of principal component analysis for Çaygören Reservoir

All 17 variables were included in the six selected PCs. However, only certain variables had significant loads within each PC, such as NO₂–N had the most significant loads in PC1, NH₄–N in PC2, PO₄ and TSS in PC3, pH in PC4, chl-a and Secchi disk transparency in PC5 and TDS and TP in PC6.

The component loadings of the first six PCs for the Ikizcetepeler Reservoir are given in Table 8. In this reservoir, TSS and NO₂–N had the most significant loads in PC3, COD and SO₄ in PC4, TDS and pH in PC5 and chl-a and Secchi disk depth in PC6.

Table 8

Results of principal component analysis for Ikizcetepeler Reservoir

According to MLR, where all PCs were used as independent variables (called the second approach), only PC scores 7, 10 and 12 were found to have significant linear relationships with chl-a in the Çaygören Reservoir (Table 9). In the Ikizcetepeler Reservoir, when all PCs were included in the regression analysis, only PC scores 1 and 12 had significant linear relationships with chl-a (Table 10).

Table 9

Results of regression analysis (n = 16) with all PCs for Çaygören Reservoir

Table 10

Results of regression analysis (n = 16) with all PCs for Ikizcetepeler Reservoir

As can be seen in Table 5, 71% of the variation in chl-a was explained by PC3 in the Çaygören Reservoir. If the five unselected PCs were included in the model, the coefficient of determination would rise to 75%. However, this difference is not statistically significant. Chl-a levels were strongly correlated with PC score 3. In other words, the chl-alevel would be expected to increase as the scores of PC3 increase. Consequently, a total increase in significant variables in PC3, namely, TSS and PO₄ would lead to an increase in the chl-a level.

In the Ikizcetepeler Reservoir, 75% of the variation in chl-a was explained by PC1. If the five unselected PCs were included in the model, the coefficient of determination would rise to 80.3%. However, this difference is not statistically significant. Chl-a levels were strongly correlated with PC score 1. In other words, the chl-a level would be expected to increase as the scores of PC1 increase. Consequently, a total increase in significant variables in PC1, namely, water temperature, TN and BOD would lead to an increase in the chl-a level.

In the Çaygören Reservoir, six variables that had significant impacts on PC scores 1, 2, 4, 5 and 6, i.e. pH, chl-a, TDS, TP, NH₄–N and NO₂–N, were excluded from the regression model of the first approach. However, linear effects of these variables on chl-a were partially incorporated in the model, since these variables were also included in PC3. In the Çaygören Reservoir, chl-a values of the first approach were calculated by the following formula:

Chl-a=1.2+1.325(score 3) $$\begin{array}{} \text{Chl-}a=1.2+1.325 \ (\text{score }3) \end{array} $$

In the Ikizcetepeler Reservoir, eleven variables that had significant impacts on PC scores 2, 3, 4, 5 and 6, i.e. pH, chl-a, TDS, TSS, TP, PO₄, Secchi disk transparency, NH₄–N, NO₃–N, NO₂–N and SO₄, were excluded from the regression model of the first approach. However, linear effects of these variables were partially incorporated in the model since they were also included in PC1. In this reservoir, the chl-a level of the first approach was calculated by the following formula:

Chl-a=1.09+1.9(score 1) $$\begin{array}{} \text{Chl-}a=1.09+1.9\ (\text{score }1) \end{array} $$

Results of the residual analysis were used to verify the applicability of the assembled regression models in both reservoirs. The existences of influential and outlier observations were checked in the models (Tables 1 and 2). Values of chl-a predicted (modeled) using regression models and the observed values are given in Table 11 and 12 for each reservoir.

Table 11

Observed and predicted Chlorophyll-a values for Çaygören Reservoir

Table 12

Observed and predicted Chlorophyll-a values for Ikizcetepeler Reservoir

In the Çaygören Reservoir, 71% of the variation in the water quality parameters was explained by the PC3 scores, while 75% of the variation in the Ikizcetepeler Reservoir was explained by the PC1 scores, implying that chl-a could be reliably estimated by using the scores of PCs in the MLR modeling approach.

Chl-a was further predicted by the second approach where scores of all PCs were included in the stepwise MLR. In the Çaygören Reservoir, PC scores 7, 10 and 12 were found to be significantly correlated with chl-a (Table 9). In the first approach, none of these scores were found to be significantly correlated with chl-a (p > 0.05), while in this approach they were found to be significantly correlated with chl-a (p = 0.004).

In the Ikizcetepeler Reservoir, when scores of all PCs were included in MLR (second approach), PC scores 1 and 12 were found to be significantly correlated with chl-a (Table 10). In the first approach, PC scores of 12 were not found to be significantly correlated with chl-a (p > 0.05), while in the second approach they were found to be significantly correlated with chl-a (p = 0.004).

The main difference between the PCR and the classic MLR is that zero correlations exist between the scores and thus the problem of multi-collinearity is eliminated in PCR. The regression coefficient of PC scores obtained through this approach is presented in Table 9 for the Çaygören Reservoir. The determination coefficient of this model was found to be 76.8% and the following model was used to predict chl-a:

Chl-a=1.14+0.77(PC score 7)+3.42(PC score 10)+0.8(PC score 12) $$\begin{array}{} \text{Chl-}a=1.14+0.77\ (\text{PC score }7)+3.42\ (\text{PC }\\ \qquad\,\text{ score 10})+0.8\ (\text{PC score 12}) \end{array} $$

In the Ikizcetepeler Reservoir, the regression coefficients of PC scores obtained through the PCR approach are presented in Table 10. The determination coefficient of this model was found to be 80.3% and the following model was used to predict chl-a:

Chl-a=1.06+0.57(PC score 1)+0.8(PC score 12) $$\begin{array}{} \text{Chl-}a=1.06+0.57\ (\text{PC score }1)+0.8\ (\text{PC score 12}) \end{array} $$

In the eutrophic Çaygören Reservoir, six PCs explained 71% of the total variation in the relationships of water quality variables, while in the mesotrophic Ikizcetepeler Reservoir, the same number of components explained 75% of the total variation. These results show that PCR is a suitable tool for showing the relationships between the water quality variables in lakes with different trophic states (Chang et al. 2012).

In the Çaygören Reservoir, all variables were included in the six selected PCs. However, only nine variables (NO₃–N, NO₂–N, NH₄–N, PO₄, TSS, pH, Secchi disk depth, TDS and TP) had significant loads within these PCs. The results showed that phosphorus and nitrogen ions were more effective on primary production than the other factors in the eutrophic Çaygören Reservoir. The research has shown that in eutrophic lakes nitrogen limitation occurs in a short time, usually in early summer, followed by the appearance of nitrogen-fixing Cyanobacteria, after which the algal community returns to phosphorus limitation (Schindler 2012).

In the mesotrophic Ikizcetepeler Reservoir, all variables were included in the six selected PCs. However, only seven variables (TSS, NO₂–N, COD, SO₄, TDS, pH and Secchi disk depth) had significant loads within these PCs. These results showed that in the mesotrophic Ikizcetepeler Reservoir, mostly water transparency (light availability) was effective on primary production rather than phosphorus and nitrogen. High loadings of TSS and Secchi disk depth into the selected PCs suggest that chl-a was mostly controlled by the variation in light intensity in this mesotrophic reservoir. Light intensity is an important factor contributing to seasonal differences in primary production (chl-a concentration) in aquatic ecosystems (Karlsson et al. 2009).

In the eutrophic Çaygören Reservoir, when all 16 PC scores were included in the stepwise MLR to predict chl-a (the second approach), PC scores 7, 10 and 12 were selected as significant factors. None of these scores were selected in the first approach. In the mesotrophic Ikizcetepeler Reservoir, when all 16 PC scores were included in the regression analysis (the second approach), PC scores 1 and 12 were selected for the prediction of chl-a. In the first approach, PC score 12 was not selected. This is due to lower degrees of freedom in the models. Researchers argue that the degree of freedom for stepwise procedures is close to the number of candidate predictors (Hakanson et al. 2003). Since only six PCs were used in the regression analysis in the first approach, the low degree of freedom restricted the selection of parameters, even though they had high loads within the excluded PCs.

In the eutrophic Çaygören Reservoir, the determination coefficient (R²) was 71% for the first approach’s model and 76.8% for the second approach’s model. In the mesotrophic Ikizcetepeler Reservoir, the determination coefficient was 75% for the first approach’s model and 80.3% for the second approach’s model. There is a 5% rise in R² in both reservoirs, but this rise was not significant. R² values are used as criteria for the predictive success of the regression models (Steyerberg et al. 2001). Generally, univariate simple regression models can yield high R² values, but they may obscure the complexity of the natural ecosystems. The predictive power of the present models show that the multidimensional approach for predicting chl-a levels is reliable in temperate reservoirs.

The results of this study show that PCR is an appropriate tool for predicting chl-a levels in mesotrophic and eutrophic temperate reservoirs. Furthermore, the results showed that by using the PCR approach, it was possible to reduce the number of analytical parameters from 16 to 3 in the eutrophic Çaygören Reservoir and from 16 to 2 in the mesotrophic Ikizcetepeler Reservoir to accurately estimate chl-a levels. Finally, the results show that PCR is a more robust tool than direct MLR for predicting chl-a concentrations and concurrently showing the difference between trophic states in temperate reservoirs.