Equilibrium shoreline change model with non-stationary free parameters at Hasaki Beach, Japan

Abstract

The ability to accurately predict shoreline response to changing wave conditions is crucial for coastal management, with equilibrium-based shoreline models demonstrating success in forecasting shoreline evolution across various temporal scales. However, the conventional use of time-invariant parameters in these models may limit their capability to capture the full range of beach responses, particularly during extreme events. This study investigates the non-stationary characteristics of free parameters in the equilibrium shoreline model ShoreFor and evaluates alternative wave-forcing variants to enhance model performance. Using a unique, high-frequency dataset of shoreline positions collected at daily to weekly intervals with low measurement uncertainty from 1991 to 2015 at Hasaki Beach, Japan, we implement both stationary and non-stationary parameter approaches. We develop a novel segmentation method where the 20-year calibration period (1991-2010) is divided into monthly segments to capture wave seasonal patterns, with model performance evaluated over a 10-year interval within calibration and a 5-year validation period. Comparative analysis of three wave-forcing variants—significant wave height ($H_s$), dimensionless settling velocity ($\Omega$), and wave energy ($P$)—reveals that $H_s$ provides more stable and superior performance at Hasaki Beach compared to the alternatives. Analysis of segment-derived relationships shows highly variable accretion efficiency coefficients ($C^a$) with a weak positive correlation between significant wave height and accretion efficiency, potentially indicating more efficient shoreline restoration during higher wave periods. Notably, these segment-derived parameter relationships maintain their validity when applied to longer continuous simulations, despite being calibrated within discrete temporal windows. The non-stationary model with $H_s$ as forcing variant substantially improves model performance during calibration, increasing the correlation coefficient from 0.36 to 0.61, and better captures extreme erosion and accretion events throughout both calibration and validation periods. These findings demonstrate the importance of incorporating time-varying parameters in equilibrium-based models and guide the selection of appropriate wave-forcing variants for improving future shoreline change predictions under changing wave climate.