Slope-aware and self-adaptive forecasting of water levels: a transparent model for the Great Lakes under climate variability

Abstract

Real-time forecasting of water levels and surface-area dynamics is vital for climate-responsive management in the Great Lakes Basin. A slope-aware, Multi-Scale Weighted-Slope Regression (MS-WSR) model was developed, combining daily calendar lags for seasonal memory and multi-scale linear-trend slopes (1, 7, and 14-day) for evolving trend momentum. Coefficients are updated online via Recursive Least Squares (RLS) with an adaptive forgetting factor, allowing regime shifts to be tracked while damping isolated shocks. When applied to 65 years (1958–2023) of 6-min interval water-stage records from 42 National Oceanic and Atmospheric Administration (NOAA) gauges (six lakes, three rivers; 80 % training/20 % testing), the MS-WSR model achieved the lowest errors (Root Mean Square Error-RMSE = 0.07 m; MAE = 0.04 m; MAPE < 5 %; R² = 0.94; Pearson’s r = 0.97) and sustained r > 0.85 up to five years ahead (±10-day phase bias). Annual surface-area changes (1985–2023) were quantified via the Normalized Difference Water Index (NDWI) on Landsat imagery in Google Earth Engine (GEE), revealing strong spatiotemporal coherence with stage trends. The transparency, low latency, and scalability of MS-WSR recommend it as an alternative to black-box models for early warning, reservoir management, and resilient infrastructure design.