Characterizing the spatial correlation of daily streamflows

Betterle, Andrea; Schirmer, Mario; Botter, Gianluca

doi:10.1002/2016wr019195

Cited by 18 publications

(35 citation statements)

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“…While Klemeš () suggests that the proxy‐basin test is adequate to demonstrate spatial transferability in the context of stable (stationary) conditions, we argue that such a test could select for overly complex models. Recognizing that an event (or year, or similar temporal unit) in two nearby basins could be similarly structured (e.g., in terms of timing and magnitude), we suggest that each event's model error could be similar in the two basins, even if the basins are different (Betterle et al, ). This parallels our situation where each site's model error was similar across two time blocks (Figure ).…”

Section: Discussionmentioning

confidence: 90%

Are Model Transferability And Complexity Antithetical? Insights From Validation of a Variable‐Complexity Empirical Snow Model in Space and Time

Lute

Luce

2017

Water Resources Research

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The related challenges of predictions in ungauged basins and predictions in ungauged climates point to the need to develop environmental models that are transferable across both space and time. Hydrologic modeling has historically focused on modelling one or only a few basins using highly parameterized conceptual or physically based models. However, model parameters and structures have been shown to change significantly when calibrated to new basins or time periods, suggesting that model complexity and model transferability may be antithetical. Empirical space‐for‐time models provide a framework within which to assess model transferability and any tradeoff with model complexity. Using 497 SNOTEL sites in the western U.S., we develop space‐for‐time models of April 1 SWE and Snow Residence Time based on mean winter temperature and cumulative winter precipitation. The transferability of the models to new conditions (in both space and time) is assessed using non‐random cross‐validation tests with consideration of the influence of model complexity on transferability. As others have noted, the algorithmic empirical models transfer best when minimal extrapolation in input variables is required. Temporal split‐sample validations use pseudoreplicated samples, resulting in the selection of overly complex models, which has implications for the design of hydrologic model validation tests. Finally, we show that low to moderate complexity models transfer most successfully to new conditions in space and time, providing empirical confirmation of the parsimony principal.

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Section: Discussionmentioning

confidence: 90%

Are Model Transferability And Complexity Antithetical? Insights From Validation of a Variable‐Complexity Empirical Snow Model in Space and Time

Lute

Luce

2017

Water Resources Research

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“…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.…”

Section: Methodsmentioning

confidence: 99%

“…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.…”

Section: Methodsmentioning

confidence: 99%

“…The joint streamflow process at the two sites is described in probabilistic terms by the Master Equation for the joint probability density function of q 1 and q 2 . From the steady‐state solution of the Master Equation the following analytical expressions for the streamflow correlation are obtained (Betterle, Schirmer, et al, ):

ρ_{model}^{false(1 false)} = \frac{λ_{12}}{\sqrt{λ_{1 t} λ_{2 t}}} \frac{1}{2} ((), 1 + r_{α}) \frac{2 \sqrt{k_{1} k_{2}}}{k_{1} + k_{2}},

\begin{matrix} right ρ_{model}^{(2)} & left = \frac{λ_{12} α_{1}^{_{12}} α_{2}^{_{12}}}{\sqrt{[λ_{1} {(α_{1})}^{2} + λ_{12} {(α_{1}^{_{12}})}^{2}] [λ_{2} {(α_{2})}^{2} + λ_{12} {(α_{2}^{_{12}})}^{2}]}} & right \\ right & left \frac{1}{2} (1 + r_{α}) \frac{2 \sqrt{k_{1} k_{2}}}{k_{1} + k_{2}} . \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Betterle

Schirmer

Botter

2019

Hydrological Processes

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Streamflow variability in space and time critically affects anthropic water uses and ecosystem services. Unfortunately, spatiotemporal patterns of flow regimes are often unknown, as discharge measurements are usually recorded at a limited number of hydrometric stations unevenly distributed along river networks. Advances in understanding the physical processes that control the spatial patterns of river flows are therefore necessary to predict water availability at ungauged locations or to extrapolate pointwise streamflow observations. This work explores the use of the spatial correlation of river flows as a metric to quantify the similarity between hydrological responses of two catchments. Following a stochastic framework, 340,000 cross-correlations between pairs of daily streamflows time series are predicted at a seasonal timescale across the contiguous United States using 413 catchments of the MOPEX dataset.Model predictions of streamflow correlation obtained in absence of run-off information are successfully used to identify catchment outlets sharing similar discharge dynamics and flow regimes across a broad range of geomorphoclimatic conditions, without relying on calibration. The selection of reference streamgauges based on predicted streamflow correlation generally outperforms the selection based on spatial proximity, especially as the density of available gauged sections decreases. Interestingly, correlated outlets share a broad spectrum of hydrological signatures (mean discharge, flow variability, and recession properties), suggesting that catchments forced by analogous frequency and intensity of effective rainfall events might exhibit common geomorphoecological traits leading to similar hydrological responses. The proposed framework provides a physical basis to assist the regionalization of flow dynamics and to interpret the spatial variability of flow regimes along stream networks.

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

Betterle

Radny

Schirmer

et al. 2017

Water Resources Research

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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.

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Characterizing the spatial correlation of daily streamflows

Cited by 18 publications

References 60 publications

Are Model Transferability And Complexity Antithetical? Insights From Validation of a Variable‐Complexity Empirical Snow Model in Space and Time

Are Model Transferability And Complexity Antithetical? Insights From Validation of a Variable‐Complexity Empirical Snow Model in Space and Time

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

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

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