Adaptive Kalman Filtering for Streamflow Models with Application to the Camastra Basin

Abstract

Accurate streamflow estimation requires a consistent representation of model and observation uncertainty. Such consistency is difficult to obtain when rainfall information is unavailable, or not temporally aligned with the discharge observations. We develop an adaptive Kalman filter for Generalized Shot Noise streamflow models, with recursive estimation of the measurement and process-noise covariances. The process-noise update includes a correction for the covariance propagated through the state dynamics, without which the recursion has no finite stationary point. With the correction, the expected increment vanishes when the mean normalized innovation squared reaches one. The filter is assessed using 37 years of daily inflow observations from the Camastra Basin in southern Italy, under two rainfall configurations. The first supplies a synthetic effective-rainfall realization as a deterministic input, whereas the second represents the unresolved forcing through the adaptive process noise. The second configuration yields the more accurate estimates, since the synthetic rainfall events, although statistically calibrated, do not coincide in time with those that generated the observed discharge. Over the full record, it attains a Nash--Sutcliffe efficiency of 0.95 and a median relative error of about 1%. Regime-conditional consistency diagnostics are reported and discussed for the second configuration.