Regression Analysis.

Regression analysis was performed according to a previous report (47). First, time-series data of average GSI values sampled approximately every 2 wk were interpolated and converted to daily data. Time-series data for the four types of inputs, specifically solar radiation (SR, i = 1), water temperature (WT, i = 2), day length (DL, i = 3), and GSI (i = 4), were normalized to have a mean of 0 and variance of 1. The regression weights w_{i, j} (i = 1, …, 4; j = −T, …, 0) in Eq. 1 were estimated via ridge regression by minimizing the following cost function E:

where λ is a positive constant that controls the strength of the regularization term. In our regression analysis, λ was tuned to minimize the regression error in the test dataset.