Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
J. Hydrol. Eng., 19(2), 328–338. (2014).
Mohamoud, Y.
Ecosystems Research Division, U.S. Environmental Protection Agency, Athens, GA 30605.
ABSTRACT
High suspended sediment concentrations (SSCs) from natural and anthropogenic sources are responsible for biological impairments of many streams, rivers, lakes, and estuaries, but techniques to estimate sediment concentrations or loads accurately at the daily temporal resolution are not available. This paper presents a time series separation and reconstruction technique (TSSR) that separates time series data (e.g., streamflow or SSC series) into two components: magnitude or duration curve and time sequence or simply sequence as referred throughout this paper. This technique uses only magnitude to estimate sediment rating curves (SRCs) and sediment duration curves (SDCs) and uses both components to estimate daily SSC series for gauged and ungauged sites. Nash-Sutcliffe model efficiency between observed and TSSR estimated SDCs for study watersheds ranged from 0.89 to 0.99. For two selected gauged sites, model efficiencies between observed and TSSR estimated SSC series were 0.96 and 0.98, and for two ungauged sites model efficiencies were 0.65 and 0.88. TSSR’s improved performance is attributed to its ability to separate time series into two components, build individual SRCs, complete SDCs from the magnitude, and convert the estimated SDCs to SSC series using stored sequence to reshuffle the SDCs. For gauged sites, sequence embedded in the observed SSC series of the site itself is used, but for ungauged sites, sequence is obtained from nearby gauged sites.
Significance Statement:
Time series separation and reconstruction (TSSR) technique has important applications to environmental management, ecological studies, clinical research, and financial analysis and planning. It is a simple concept that is based on the realization that time series data consist of two components: magnitude (how large or small are the values observed at any given time interval) and time sequence (when each observed magnitude value occurred in relation to other values). Magnitude is represented by the exceedance probability curves also known as duration curves. As such, ranked magnitude curve, duration curve, and exceedance probability curve are treated as similar. It is noteworthy that sequence is embedded in the observed time series itself and can be represented by observation dates or user-specified row numbers that get rearranged when the observed time series data is ranked according to their magnitude.
If an analyst wants to build a regression model to predict sediment concentrations in the Mississippi River or the price of a stock, the analyst would use observed time series which inherently consist of combined magnitude and sequence components. Building a regression model from time series data (combined magnitude and sequence) often results in poor regression models. The reason is because time series data has time influences (sequence) that are difficult for independent variables to predict. Capturing both the magnitude and the sequence at the same time through regression methods is very difficult (e.g., due to presence of nonlinearity, time influences, and hysteresis in the observed data) and the solution of the problem lays the separation of the two components – eliminating the time influences temporarily and building regression models only from the magnitude component. It may be hypothesized that removing time influences temporarily and building regression models only from the magnitude component may minimize what statisticians termed as noise or random errors in regression models. Figure 1 shows a flow chart of the TSSR technique.
When a time series is converted to exceedance probability curves, information about the sequence is stored separately as dates or arbitrarily assigned as row numbers. The stored sequence is then used to reconstruct the predicted magnitude to predicted complete time series (combined magnitude and sequence). Without time influences in the data, it is easier to develop regression models only from the magnitude component using quantile regression – that is developing separate regression equations for different segments of the exceedance probability curve (e.g., normally 10 to 15 equations cover all segments of the curve). Performing segment-wise quantile regression achieves better results than fitting a single equation to the complete exceedance probability curve.
Figure: Steps required to building a regression model using TSSR.
