A Nonlinear Dynamical Systems‐Based Modeling Approach for Stochastic Simulation of Streamflow and Understanding Predictability

Rajagopalan, Balaji; Erkyihun, Solomon Tassew; Lall, Upmanu; Zagona, Edith; Nowak, K.

doi:10.1029/2018wr023650

Cited by 14 publications

(9 citation statements)

References 73 publications

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“…Here we approximate the information content of daily streamflow series, an extremely complex problem well beyond the scope of this study. Credible efforts to characterize daily streamflows involve characterization of marginal distributions, spatiotemporal correlation structures, and intermittency (Papalexiou & Serinaldi, 2020), as well as climatic indices and epochal variations in predictability (Rajagopalan et al, 2019). Archfield et al (2013) argue that at least seven fundamental streamflow statistics are needed to fully characterize daily streamflow.…”

Section: Resultsmentioning

confidence: 99%

Improved Estimators of Model Performance Efficiency for Skewed Hydrologic Data

Lamontagne

Barber

Vogel

2020

Water Resources Research

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The Nash-Sutcliffe efficiency (NSE) and the Kling-Gupta efficiency (KGE) are now the most widely used indices in hydrology for evaluation of the goodness of fit between model simulations S and observations O. We introduce two theoretical (probabilistic) definitions of efficiency, E and E′, based on the estimators NSE and KGE, respectively, which enable controlled Monte Carlo experiments at 447 watersheds to evaluate their performance. Although NSE is generally unbiased, it exhibits enormous variability from one sample to another, due to the remarkable skewness and periodicity of daily streamflow data. However, use of NSE with logarithms of daily streamflow leads to estimates of E with almost no variability from one sample to the next, though with high upward bias. We introduce improved estimators of E and E′ based on a bivariate lognormal monthly mixture model that are shown to yield considerable improvements over NSE and slight improvements over KGE in controlled Monte Carlo experiments. Our new estimators of E should avoid most previous criticisms of NSE implied by the literature. Improved estimators of E that account for skewness and periodicity are needed for daily and subdaily streamflow series because NSE is not suited to such applications. Plain Language Summary Reliable metrics are needed, which summarize the degree to which simulation model output reproduces the observations. Two of the most widely used metrics are Nash-Sutcliffe efficiency (NSE) and the Kling-Gupta efficiency (KGE). Remarkably, this is the first study to provide a theoretical definition and treatment of these indices enabling controlled Monte Carlo experiments to evaluate their performance. Controlled experiments at 447 U.S. watersheds enable us to report the degree of bias and variability associated with these indices when applied to daily data. As expected, NSE is on average, equal to its theoretical value; thus, it provides an unbiased estimate of its theoretical value. However, NSE exhibits enormous variability from one sample to another due to the enormous skewness and periodicity of daily streamflows. Improved estimators are introduced, which account for skewness and periodicity of daily streamflow observations. Our improved estimators yield considerable improvements over NSE and slight improvements over KGE and are shown to avoid most previous criticisms of NSE implied by the literature. Simulation models are increasingly being used to mimic high frequency observations, which exhibit highly skewed and periodic behavior. In such instances, improved estimators of efficiency are needed because NSE is no longer suited to such applications. 1.1. Model Simulation and Calibration Consider the problem of evaluating the goodness of fit of watershed simulation model output S, to observations O. Let S t and O t represent the simulated and observed daily streamflow on day t, t ¼ 1, …, n, at the outlet of a watershed. A conceptual simulation model H[X, Ω] is envisioned, which converts a suite of model parameters Ω and inputs X t , such as rai...

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Section: Resultsmentioning

confidence: 99%

Improved Estimators of Model Performance Efficiency for Skewed Hydrologic Data

Lamontagne

Barber

Vogel

2020

Water Resources Research

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“…(2016), Rajagopalan et al. (2019), and Sangoyomi et al. (1996) utilized it for hydroclimatic forecasting and simulation.…”

Section: Introductionmentioning

confidence: 99%

“…Jayawardena and Lai (1994) applied it to predict rainfall and SF and Delforge et al (2020) to analyze and forecast SF recessions. Erkyihun et al (2016), Rajagopalan et al (2019), and Sangoyomi et al (1996) utilized it for hydroclimatic forecasting and simulation. Also, studies that identified low-dimensional dynamics across different hydrological processes showed that complexity can emerge from a small set of governing equations, which underpins the idea that simple deterministic hydrological models can adequately describe complex hydrological processes (Procaccia, 1988).…”

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confidence: 99%

Identifying Causal Interactions Between Groundwater and Streamflow Using Convergent Cross‐Mapping

Bonotto

Peterson

Fowler

et al. 2022

Water Resources Research

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Due to multiple interacting factors, global water scarcity is projected to increase in the coming decades. As projected by the United Nations, the world's population will reach 9.8 billion by 2050 (U.N., 2017), which combined with income growth of Asian (led by China and India) and African countries, will lead to a 50% increase in demand for agricultural output mostly in water-stressed regions and developing countries (FAO, 2017). Moreover, as climate change is expected to increase variability in rainfall and temperatures (IPCC, 2014;Sheffield et al., 2012;Wasko & Nathan, 2019), reliable water sources such as groundwater (GW) are likely to represent an increasing share of global water consumption. Therefore, understanding the role of GW usage on the availability of both subsurface and surface water is of paramount importance for global food, water, and environmental security.Although it is common to conceptualize GW as causally linked to streamflow (SF), it remains challenging to identify where and how this interaction occurs (e.g., strength and direction). Interactions between GW and

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“…The different characteristics of the original real series and their DLs may be due to the noises from many sources and therefore, noise cancellation may be important for obtaining original property of the time series. On the other hand, Rajagopalan et al (2019) extracted the dominant quasi-periodic components through the wavelet analysis of the flow rate at the Lees Ferry station in the Colorado River and quantified the trajectory branching in the phase space over time using local Lyapunov exponents [20]. As a result, the flow rate of the Colorado River was revealed to be highly predictable.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Features of Decomposed Time Series from Tidal River Water Level

et al. 2021

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This study assessed the characteristics of water-level time series of a tidal river by decomposing it into tide, wave, rainfall-runoff, and noise components. Especially, the analysis for chaotic behavior of each component was done by estimating the correlation dimension with phase-space reconstruction of time series and by using a close returns plot (CRP). Among the time series, the tide component showed chaotic characteristics to have a correlation dimension of 1.3. It was found out that the water level has stochastic characteristics showing the increasing trend of the correlation exponent in the embedding dimension. Other components also showed the stochastic characteristics. Then, the CRP was used to examine the characteristics of each component. The tide component showed the chaotic characteristics in its CRP. The CRP of water level showed an aperiodic characteristic which slightly strayed away from its periodicity, and this might be related to the tide component. This study showed that a low water level is mainly affected by a chaotic tide component through entropy information. Even though the water level did not show chaotic characteristics in the correlation dimension, it showed stochastic chaos characteristics in the CRP. Other components showed stochastic characteristics in the CRP. It was confirmed that the water level showed chaotic characteristics when it was not affected by rainfall and stochastic characteristics deviating from the bounded trajectory when water level rises due to rainfall. Therefore, we have shown that the water level related to the chaotic tide component can also have chaotic properties because water level is influenced by chaotic tide and rainfall shock, thus it showed stochastic chaos characteristics.

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A Nonlinear Dynamical Systems‐Based Modeling Approach for Stochastic Simulation of Streamflow and Understanding Predictability

Cited by 14 publications

References 73 publications

Improved Estimators of Model Performance Efficiency for Skewed Hydrologic Data

Improved Estimators of Model Performance Efficiency for Skewed Hydrologic Data

Identifying Causal Interactions Between Groundwater and Streamflow Using Convergent Cross‐Mapping

Chaotic Features of Decomposed Time Series from Tidal River Water Level

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