The Treatment of Uncertainty in Hydrometric Observations: A Probabilistic Description of Streamflow Records

Abstract

River discharge serves many different purposes and is recorded automatically in many watersheds worldwide to support water supply, use and management decisions, hydroelectric generation and water quality assessment. In hydrology, streamflow records may be used to improve our understanding of hydrologic processes (Tetzlaff

Confidence intervals of the Kling-Gupta efficiency

“…catchment summary metrics) of the measured discharge record. The modelfree duplication method of Oliveira and Vrugt (2022) satisfies these requirements and, thus, serves our purpose. A brief description of this method is given below, interested readers are referred to Oliveira and Vrugt (2022) for further details.…”

“…The 99% confidence intervals of the simulated hydrograph (gray region) are smallest, on average, at the end of a long recession period and reach a maximum width at peak discharge. This dependence of the width of the hmodel discharge confidence intervals on simulated flow level is a result of the heteroscedastic nature of the discharge measurement errors as evidenced by the measured streamflow record using nonparametric differencing (Vrugt et al, 2005;Oliveira and Vrugt, 2022). The 99% confidence intervals of the hmodel simulated streamflows exceed the discharge measurement uncertainty (red region) but appear rather small compared to the residuals of the optimal hmodel parameters, θ * .…”

“…where m ỹ = 1 n ∑ n t=1 ỹt (mm/d) denotes the mean of the n-record of streamflow observations. The entries of the n × 1 vector of measurement error variances, σ 2 ε , are computed from hourly discharge observations using the procedure described in Oliveira and Vrugt (2022). Specifically, the t th -entry, s 2 εt , of s 2 ε , is computed as follows (Oliveira and Vrugt, 2022)…”

“…The use of the discharge sample ACF in the measurement error covariance matrix, Σ ε , introduces serial correlation among the ε t 's. This is a necessary means to preserving the smoothness, statistical and hydrologic properties of the measured discharge record (Oliveira and Vrugt, 2022). The autocorrelation avoids overly bumpy replicate records that result from the use of the measured discharge time series rather than the underlying data generating process in Eq.…”

On Constructing Limits-of-Acceptability in Watershed Hydrology using Decision Trees

“…Priors over measurement uncertainty are typically constructed by making aleatoric assumptions about the nature of these errors. For example, one can obtain information about random measurement uncertainty in streamflow by using rating curve analysis (Kiang et al, 2018;Overleir et al, 2009;Reitan and Overleir, 2009;Le Coz et al, 2014) or other probabilistic methods (de Oliveira and Vrugt, 2022). But epistemic uncertainties in streamflow, such as those introduced by extrapolation of rating curve to gauge heights well above the observations, may not be knowable.…”