What Do They Have in Common? Drivers of Streamflow Spatial Correlation and Prediction of Flow Regimes in Ungauged Locations

Abstract

The spatial correlation of daily streamflows represents a statistical index encapsulating the similarity between hydrographs at two arbitrary catchment outlets. In this work, a process‐based analytical framework is utilized to investigate the hydrological drivers of streamflow spatial correlation through an extensive application to 78 pairs of stream gauges belonging to 13 unregulated catchments in the eastern United States. The analysis provides insight on how the observed heterogeneity of the physical processes that control flow dynamics ultimately affect streamflow correlation and spatial patterns of flow regimes. Despite the variability of recession properties across the study catchments, the impact of heterogeneous drainage rates on the streamflow spatial correlation is overwhelmed by the spatial variability of frequency and intensity of effective rainfall events. Overall, model performances are satisfactory, with root mean square errors between modeled and observed streamflow spatial correlation below 10% in most cases. We also propose a method for estimating streamflow correlation in the absence of discharge data, which proves useful to predict streamflow regimes in ungauged areas. The method consists in setting a minimum threshold on the modeled flow correlation to individuate hydrologically similar sites. Catchment outlets that are most correlated ( ρ>0.9) are found to be characterized by analogous streamflow distributions across a broad range of flow regimes.

Flow dynamics at the continental scale: Streamflow correlation and hydrological similarity

“…The method, which is designed to statistically characterize the spatial variability of river flows, relies on a stochastic representation of specific (i.e., mm/day) streamflow dynamics (Botter, Porporato, Rodriguez‐Iturbe, & Rinaldo, ; Doulatyari et al, ). The Pearson correlation between synchronous daily streamflow time series at two river sites is expressed as a function of a limited number of hydroclimatic parameters (Betterle, Radny, et al, , Betterle, Schirmer, et al, ). The method is suited to describe the hydrological response of catchments whose streamflow dynamics are directly driven by intermittent precipitation and where the effects of water storages (snow and lakes), anthropogenic activities or inter‐seasonal carryover effects can be neglected.…”

“…The analytical characterization of streamflow spatial correlation requires the joint streamflow dynamics at two catchment outlets to be specified. When a generic pair of outlets is concerned, effective rainfall events can be divided into two independent classes: joint and disjoint (Betterle, Radny, et al, ; Betterle, Schirmer, et al, ). Joint events produce a simultaneous streamflow increment in the hydrographs of the two sites.…”

“…In Equations and , r α is the correlation between the intensities of joint effective rainfall events and k 1 and k 2 are the recession rates in the two catchments (for a comprehensive summary of the model parameters, the reader is referred to table 1 in Betterle, Radny, et al, ). Equations and differ in the probability distributions assigned to the intensities of effective rainfall events.…”

“…The frequency of rainfall is generally higher than the frequency of effective rainfall because a fraction of the incoming rainfall is normally buffered by the soil moisture dynamics in the root zones and does not appear as streamflow. However, the assumption behind the rainfall‐based estimation of the model parameters is rooted in the idea that the relative frequency and intensity of simultaneous run‐off events is mainly controlled by the joint rainfall dynamics in the two catchments (Betterle, Radny, et al, ; Betterle, Schirmer, et al, ). Additionally, as reliable estimates of catchment drainage rates in absence of direct streamflow measurements are problematic (Biswal & Marani, ; Doulatyari et al, ), and considering that moderate inter‐catchment heterogeneity in recession properties bear a limited impact on the spatial correlation of streamflows (Betterle, Radny, et al, ; Betterle, Schirmer, et al, ), as a first approximation it is assumed that in Equations and .…”

“…This study explores on a large scale the use of cross‐correlation between pairs of streamflow time series as a metric of hydrological similarity. A recently developed physically‐based model that accounts for the probabilistic nature of joint streamflow dynamics at two river sections (Betterle, Radny, Schirmer, & Botter, ; Betterle, Schirmer, & Botter, ) is used to estimate 340,000 inter‐catchment seasonal streamflow correlations at 413 catchments of the MOPEX dataset. The model relies on a limited number of parameters and on a set of simple mechanistic hypothesis concerning catchment responses to link the spatial variability of streamflow dynamics to the underlying heterogeneity of catchment‐scale hydrological and climatic drivers.…”