Nonlinear dynamics of surfing participation, flow, and enjoyment.

Introduction: Understanding how participation in leisure sports shapes psychological experiences is an important issue in sport and recreation research. While previous studies have typically assumed a linear relationship between participation intensity and psychological outcomes, emerging perspectives suggest that such relationships may follow nonlinear patterns. The present study examines the nonlinear relationships between surfing participation behaviors, flow experience, and enjoyment among recreational surfers. Methods: A total of 404 participants were surveyed at major surfing locations along the Korean coast. Five behavioral participation variables were assessed, including participation duration, in-season frequency, off-season frequency, session duration, and financial expenditure. Flow was measured using the Short Flow Scale, and enjoyment was assessed using the Minor Sport Enjoyment Inventory. To explore potential nonlinear relationships, linear regression models were compared with spline-based nonparametric regression models. Results: The results indicated that spline models substantially outperformed linear models across all examined relationships, revealing distinct nonlinear patterns and identifiable inflection points. Participation duration showed a saturation pattern after approximately ten years of experience, while session frequency and session duration exhibited optimal thresholds beyond which additional participation yielded diminishing psychological benefits. Similarly, the relationship between flow and enjoyment demonstrated a saturation curve rather than a continuous linear increase. Discussion: These findings challenge the common assumption of linear participation-experience relationships and highlight the importance of identifying optimal participation levels in leisure sports. The study contributes to sport psychology and leisure research by demonstrating the value of nonlinear modeling approaches in understanding participation dynamics and psychological outcomes in nature-based recreational activities. These findings should be interpreted with appropriate caution given the cross-sectional design, bivariate analytic structure, and culturally specific sampling context of the study. Future research employing penalized spline or GAM approaches with formal cross-validation, longitudinal designs, and cross-cultural samples is warranted to confirm the stability and generalizability of the identified thresholds.