Time series modeling of rainfall and lake elevation in relation to breaching events at the Lake Earl and Tolowa lagoon system, coastal northern California

Abstract

I evaluated trends in spatial and temporal variability in historical levels of rainfall, water elevation, and breach events for lakes Earl, Tolowa, and their combined lagoon system along the coast of northern California. I examined the efficacy of time series analyses to model and forecast rainfall and lake elevation at a regional scale from 2008 to 2021. I employed semi-parametric Generalized Additive Model regression to investigate the historical relationship between anthropogenic breaching of the lagoon and simultaneous occurrences of environmental parameters to better understand conditions surrounding each breach event. Evaluation of the central tendency of rainfall and surface lake elevation showed high fluctuations in their mean, positive skewed, and leptokurtic curves. Augmented Dickey-Fuller tests found that seasonal rainfall was stationary, but surface lake elevation attained stationarity only after the first seasonal difference. Decomposition of each time series and MannKendall and Sen’s slope estimators, found a significant decreasing trend in seasonal surface lake elevation but no trend was found in rainfall. Seasonal Autoregressive Integrated Moving Average (SARIMA) time series analysis and diagnostic tests of stability and reliability found best fit models for rainfall (SARIMA[1,0,0] [2,1,1]12) and surface lake elevation (SARIMA [1,1,2] [1,0,0]12) used to forecast future values for each parameter. Multiple regression of variables obtained at each breach event showed that the proportion of variance (55.0%) and null deviance (72.1%) explained by the combination of rainfall, hightide, and wave height was the “best” model with the lowest Generalized Cross-Validation statistic of all other models evaluated. All models agreed that rainfall was the most significant factor within each set of predictor attributes used to model surface lake elevation. A declining trend in surface elevation in combination with variation in the historical area and extent of wetland plant communities may be attributable to systematic breaching of the lagoon annually.