Trends, Shifting, or Oscillations? Stochastic Modeling of Nonstationary Time Series for Future Water‐Related Risk Management

Abstract

Hydrological time series often present nonstationarities such as trends, shifts, or oscillations due to anthropogenic effects and hydroclimatological variations, including global climate change. For water managers, it is crucial to recognize and define the nonstationarities in hydrological records. The nonstationarities must be appropriately modeled and stochastically simulated according to the characteristics of observed records to evaluate the adequacy of flood risk mitigation measures and future water resources management strategies. Therefore, in the current study, three approaches were suggested to address stochastically nonstationary behaviors, especially in the long‐term variability of hydrological variables: as an overall trend, shifting mean, or as a long‐term oscillation. To represent these options for hydrological variables, the autoregressive model with an overall trend, shifting mean level (SML), and empirical mode decomposition with nonstationary oscillation resampling (EMD‐NSOR) were employed in the hydrological series of the net basin supply in the Lake Champlain‐River Richelieu basin, where the International Joint Committee recently managed and significant flood damage from long consistent high flows occurred. The detailed results indicate that the EMD‐NSOR model can be an appropriate option by reproducing long‐term dependence statistics and generating manageable scenarios, while the SML model does not properly reproduce the observed long‐term dependence, that are critical to simulate sustainable flood events. The trend model produces too many risks for floods in the future but no risk for droughts. The overall results conclude that the nonstationarities in hydrological series should be carefully handled in stochastic simulation models to appropriately manage future water‐related risks.

Quantifying and Classifying Streamflow Ensembles Using a Broad Range of Metrics for an Evidence-Based Analysis: Colorado River Case Study

“…In addition to these common statistics, a range of other metrics are available to capture various aspects of streamflow ensembles. The Hurst coefficient is used to quantify long-term memory or persistence beyond what is captured by correlation (Chaves & Lorena, 2019;Hurst, 1951;Klemeš, 1974;Lee & Ouarda, 2023;Lee et al, 2020). Detecting trends is another useful approach to quantify non-stationarity in time series (Helsel et al, 2020;Kendall, 1955;Lee & Ouarda, 2023;Mann, 1945).…”

“…The Hurst coefficient is used to quantify long-term memory or persistence beyond what is captured by correlation (Chaves & Lorena, 2019;Hurst, 1951;Klemeš, 1974;Lee & Ouarda, 2023;Lee et al, 2020). Detecting trends is another useful approach to quantify non-stationarity in time series (Helsel et al, 2020;Kendall, 1955;Lee & Ouarda, 2023;Mann, 1945). Mutual information is a measure of dependence that, unlike correlation, accounts for both linear and nonlinear dependence present in the time series, offering a more comprehensive understanding of the relationships within the data (Gong et al, 2014;Harrold et al, 2001;Loritz et al, 2018;Pechlivanidis et al, 2016;.…”

“…Understanding the occurrence, duration, and severity of hydrological droughts, as well as the frequency and magnitude of surpluses, is essential for making informed decisions regarding water allocation, reservoir management, and drought preparedness. Previous studies have commonly explored these statistics using the run-sum approach (Lee & Ouarda, 2023;Lee et al, 2020;Prairie et al, 2006;Salas et al, 2005;Srinivas & Srinivasan, 2006). However, a limitation of this method is that it defines a drought or surplus event as events when all consecutive years are above a below a threshold, without any breaking year during that period.…”

Quantifying and Classifying Streamflow Ensembles Using a Broad Range of Metrics for an Evidence‐Based Analysis: Colorado River Case Study

“…In addition to these common statistics, a range of other metrics are available to capture various aspects of streamflow ensembles. The Hurst coefficient is used to quantify long-term memory or persistence beyond what is captured by correlation (Chaves & Lorena, 2019;Hurst, 1951;Klemeš, 1974;Lee & Ouarda, 2023;Lee et al, 2020). Detecting trends is another useful approach for quantifying non-stationarity in time series (Helsel et al, 2020;Kendall, 1955;Lee & Ouarda, 2023;Mann, 1945).…”

“…In addition to the above metrics, storage-related metrics quantify characteristics associated with the practical evaluation of the storage capacity needed in reservoirs to meet specific yields or to manage reservoirs to sustain desired demands (see for example Lee & Ouarda, 2023;Srinivas & Srinivasan, 2006). Storage metrics are thus directly meaningful to water resource management.…”