Trend or persistence: what are we really detecting in annual low-flow time series?

Trends in annual low-flow time series are central to water resources and drought management, yet estimates are strongly affected by serial persistence, and dependence can make persistence appear as trend. We compare nonparametric and parametric methods under short-term autocorrelation and long-term persistence (LTP) and evaluate their reliability with European streamflow data and simulation-based experiments.

For short-term autocorrelation, modified Mann–Kendall approaches with block-bootstrap-based significance correction (BBSMK) and simultaneous bias-corrected prewhitening yield robust results; alternative variants inflate significance and produce implausible findings. Parametric ARIMAX models indicate that, when analyses are based on the water year, only a small share of series require higher autoregressive orders, whereas calendar-year aggregation induces more complex correlation structures and, in turn, unreliable (too low) significance rates.

Under long-term dependence, the nonparametric Mann–Kendall–LTP approach markedly lowers the fraction of significant trends, while FARIMAX models (external trend + LTP) produce similar rates to BBSMK. Yet AIC-based selection typically replaces LTP with short-term autocorrelation, indicating that what appears as persistence is often explainable by short-range dependence.

We finally assess misclassification in parametric and nonparametric trend models under LTP using nature-based simulations across record lengths. Calibrated to stream-gauge records, the simulations test whether series with deterministic trends and short-term autocorrelation—but without true LTP—are misclassified as LTP, and how such misclassification biases trend estimates. Across four scenarios (high/low LTP × significant/non-significant trend), LTP misclassification and trend-detection errors are elevated: with a trend present, short-term autocorrelation is often mistaken for LTP, biasing estimates and reducing power. At hydrologically typical record lengths, errors remain substantial, declining only for extremely long series (1,000–10,000 years); misclassification of short-term correlation as LTP persists even then.

Overall, under common record lengths and dependence structures, deterministic trends are often misinterpreted as long-term persistence—and, conversely, genuine persistence can be mistaken for trend. Therefore, LTP-based trend analyses should be interpreted with caution; typical hydrological records are too short for reliable LTP inference.