scholarly journals Adaptation of Classical Tidal Harmonic Analysis to Nonstationary Tides, with Application to River Tides

2013 ◽  
Vol 30 (3) ◽  
pp. 569-589 ◽  
Author(s):  
Pascal Matte ◽  
David A. Jay ◽  
Edward D. Zaron
Keyword(s):  
Time Series ◽  
Harmonic Analysis ◽  
River Flow ◽  
Water Levels ◽  
Spectral Lines ◽  
Noise Model ◽  
Analysis Tool ◽  
Tidal Analysis ◽  
Nonstationary Signals ◽  
Analysis Methods

Abstract One of the most challenging areas in tidal analysis is the study of nonstationary signals with a tidal component, as they confront both current analysis methods and dynamical understanding. A new analysis tool has been developed, NS_TIDE, adapted to the study of nonstationary signals, in this case, river tides. It builds the nonstationary forcing directly into the tidal basis functions. It is implemented by modification of T_TIDE; however, certain concepts, particularly the meaning of a constituent and the Rayleigh criterion, are redefined to account for the smearing effects on the tidal spectral lines by nontidal energy. An error estimation procedure is included that constructs a covariance matrix of the regression coefficients, based on either an uncorrelated or a correlated noise model. The output of NS_TIDE consists of time series of subtidal water levels [mean water level (MWL)] and tidal properties (amplitudes and phases), expressed in terms of external forcing functions. The method was tested using records from a station on the Columbia River, 172 km from the ocean entrance, where the tides are strongly altered by river flow. NS_TIDE hindcast explains 96.4% of the signal variance with a root-mean-square error of 0.165 m obtained from 288 parameters, far better than traditional harmonic analysis (38.5%, 0.604 m, and 127 parameters). While keeping the benefits of harmonic analysis, its advantages compared to existing tidal analysis methods include its capacity to distinguish frequencies within tidal bands without losing resolution in the time domain or data at the endpoints of the time series.

scholarly journals Analysis Methods for Characterizing Salinity Variability from Multivariate Time Series Applied to the Apalachicola Bay Estuary

2012 ◽  
Vol 29 (4) ◽  
pp. 613-628 ◽  
Author(s):  
Steven L. Morey ◽  
Dmitry S. Dukhovskoy
Keyword(s):  
Time Series ◽  
Time Scales ◽  
River Discharge ◽  
River Flow ◽  
High Salinity ◽  
Multivariate Time Series ◽  
Salinity Range ◽  
Apalachicola Bay ◽  
Analysis Methods ◽  
Salinity Variability

Abstract Statistical analysis methods are developed to quantify the impacts of multiple forcing variables on the hydrographic variability within an estuary instrumented with an enduring observational system. The methods are applied to characterize the salinity variability within Apalachicola Bay, a shallow multiple-inlet estuary along the northeastern Gulf of Mexico coast. The 13-yr multivariate time series collected by the National Estuary Research Reserve at three locations within the bay are analyzed to determine how the estuary responds to variations in external forcing mechanisms, such as freshwater discharge, precipitation, tides, and local winds at multiple time scales. The analysis methods are used to characterize the estuarine variability under differing flow regimes of the Apalachicola River, a managed waterway, with particular focus on extreme events and scales of variability that are critical to local ecosystems. Multivariate statistical models are applied that describe the salinity response to winds from multiple directions, river flow, and precipitation at daily, weekly, and monthly time scales to understand the response of the estuary under different climate regimes. Results show that the salinity is particularly sensitive to river discharge and wind magnitude and direction, with local precipitation being largely unimportant. Applying statistical analyses with conditional sampling quantifies how the likelihoods of high-salinity and long-duration high-salinity events, conditions of critical importance to estuarine organisms, change given the state of the river flow. Intraday salinity range is shown to be negatively correlated with the salinity, and correlated with river discharge rate.

scholarly journals Assimilation of Piezometric Data to Calibrate Parsimonious Daily Hydrological Models

Water ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2342
Author(s):  
Axel Flinck ◽  
Nathalie Folton ◽  
Patrick Arnaud
Keyword(s):  
Time Series ◽  
River Flow ◽  
Hydrological Model ◽  
Water Levels ◽  
Model Parameters ◽  
Rainfall Time Series ◽  
Time Step ◽  
Processing Methods ◽  
Analysis System ◽  
Set Up

Low water levels are a seasonal phenomenon, which can be long, short, and more or less intense, affecting entire watercourses. This phenomenon has become a concern for many countries who seek better understanding of the processes that affect it and learn how to optimally manage water resources (pumping, irrigation). Consequently, a lumped rainfall model at daily time step (GR) has been defined, calibrated, and regionalised over French territories. The input data come from SAFRAN, the distributed mesoscale atmospheric analysis system, which provides daily solid and liquid precipitation and temperature data throughout the French territory. This model could be improved, in particular to more accurately simulate the hydrological response of watersheds interacting with groundwater. The idea is to use piezometric data from the ADES bank, available in France, and to use it for the calibration phase of the hydrological model. The analysis was carried out across ten French catchments that are representative of various hydrometeorological behaviours and are located in a diverse hydrogeological context. Each catchment must be represented by a piezometer that closely represents the main aquifer that interacts with the basin. This piezometer is located on part of the watershed that is most covered in terms of its drainage network, and closest to its outlet. Different signal processing methods are used to characterise the relationship between the fluctuation of river flow, piezometric levels and rainfall time series. Potential processing methods will be carried out in the temporal domain. To quantify groundwater table inertia and that of the catchment area, correlograms were calculated from daily chronicles of flows and piezometric levels. A cross-correlatory analysis was set up to see, in more detail, the correlations between the flow rates (especially base flows) and piezometric level time series. This type of analysis makes it possible to study relationships between various observations, and tests were carried out to take this information into account during the phase of the calibration of hydrological model parameters. These different analyses will hopefully help us to use piezometric data to consolidate the quality and robustness of the modelling.

Comparative evaluation of simulation ways of the economic time series with periodic oscillations

2017 ◽  
Vol 31 (2) ◽  
pp. 181-187
Author(s):  
Y. М. Protasov ◽  
V. М. Yurov
Keyword(s):  
Time Series ◽  
Computer Simulation ◽  
Harmonic Analysis ◽  
Comparative Evaluation ◽  
Economic Time Series ◽  
Periodic Oscillations ◽  
Analysis Methods ◽  
Economic Time

Three ways of computer simulation of economic time series with periodic oscillations are compared in accordance with the criteria of accuracy and informativeness. The ways implement the harmonic analysis methods, however, the often used restriction on the length of the series is not used in this case. For example, the time series of quarterly sales volumes of the company for the last 7 years are given.

scholarly journals Application of the EMD Method to River Tides

2018 ◽  
Vol 35 (4) ◽  
pp. 809-819 ◽  
Author(s):  
Haidong Pan ◽  
Zheng Guo ◽  
Yingying Wang ◽  
Xianqing Lv
Keyword(s):  
Water Level ◽  
River Flow ◽  
Internal Tides ◽  
Analysis Tool ◽  
Tidal Analysis ◽  
Mode Decomposition ◽  
Mean Water Level ◽  
Nonstationary Tides ◽  
Tidal Processes ◽  
Emd Method

AbstractA lot of tidal phenomena, including river tides, tides in ice-covered bays, and internal tides in fjords, are nonstationary. These tidal processes present a severe challenge for the conventional tidal analysis method. The empirical mode decomposition (EMD) method is useful for nonstationary and nonlinear time series and has been used for different geophysical data. However, application of EMD to nonstationary tides is rare. This paper is meant to demonstrate a new tidal analysis tool that can help study nonstationary tides, in this case river tides. EMD is applied to a set of hourly water level records on the lower Columbia River, where the tides are greatly influenced by the fluctuating river flow. The results show that the averaged period of any EMD mode almost exactly doubles that of the previous one, suggesting that EMD is a dyadic filter. The highest and second highest frequency modes of EMD represent the semidiurnal (D2) and diurnal (D1) tides, respectively. The sum of the EMD modes except for the first two is the mean water level (MWL). The study finds that the EMD method successfully captured the nonstationary characteristics of the D1 tides, the D2 tides, and the MWL induced by river flow.

scholarly journals A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

2018 ◽  
Vol 25 (1) ◽  
pp. 175-200 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighbouring times in order to reduce its variance. The Shannon–Nyquist exclusion zone is however defined as the area corrupted by local aliasing issues. The local amplitude in the time–frequency plane is then estimated with least-squares methods. We also derive an approximate formula linking the squared amplitude and the scalogram. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

Multivariate Transfer Function-Noise Model of River Flow for Hydropower Operation

1986 ◽  
Vol 17 (3) ◽  
pp. 185-202 ◽  
Author(s):  
Tryggvi Olason ◽  
W. Edgar Watt
Keyword(s):  
Time Series ◽  
Transfer Function ◽  
River Flow ◽  
Moving Average ◽  
Noise Model ◽  
Lead Times ◽  
Autoregressive Moving Average ◽  
Northern Ontario ◽  
Daily Data ◽  
Univariate Time Series

The formulation of multivariate autoregressive moving average (ARMA) time series models and their transfer function noise (TFN) form is described. Development of a multivariate TFN model is difficult if the multiple inputs are correlated. Various methods for developing a multivariate TFN models with correlated multiple inputs are critically reviewed. A simple approach to developing multiple input TFN models with correlated inputs is described. This approach is successfully applied to developing a forecasting model for average daily flow of the Mattagami River at Little Long Generation Station in Northern Ontario, Canada. System inputs are upstream and tributary flows. Only three years of daily data for the period April 1st to October 31st were required to calibrate the model. Two further years were used to verify the model. Forecasts at lead times of one and two days were good for both calibration and verification periods. The average standard errors were 8% of average inflows (1-day lead) and 18% (2-day lead). The system produces significantly better forecasts than a univariate time series model.

scholarly journals A general theory on frequency and time-frequency analysis of irregularly sampled time series based on projection methods. II. Extension to time-frequency analysis

2017 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform-equivalent of the extended Lomb-Scargle periodogram defined in part I of this study (Lenoir and Crucifix, 2017). The signal being analyzed is modeled as the sum of a locally periodic component in the time-frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighboring times in order to reduce its variance. The Shannon-Nyquist exclusion zone is on the other hand defined as the area corrupted by local aliasing issues. The local amplitude in the time-frequency plane is then estimated with least-squares methods. We show that the squared amplitude and the scalogram are approximately proportional. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov Chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

scholarly journals Assessment of Automatically Monitored Water Levels and Water Quality Indicators in Rivers with Different Hydromorphological Conditions and Pollution Levels in Greece

Hydrology ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 86
Author(s):  
Angeliki Mentzafou ◽  
George Varlas ◽  
Anastasios Papadopoulos ◽  
Georgios Poulis ◽  
Elias Dimitriou
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Quality Indicators ◽  
High Frequency ◽  
Automatic Monitoring ◽  
Water Levels ◽  
High Temporal Resolution ◽  
Water Quality Indicators ◽  
Pollution Levels ◽  
Riverine Ecosystems

Water resources, especially riverine ecosystems, are globally under qualitative and quantitative degradation due to human-imposed pressures. High-temporal-resolution data obtained from automatic stations can provide insights into the processes that link catchment hydrology and streamwater chemistry. The scope of this paper was to investigate the statistical behavior of high-frequency measurements at sites with known hydromorphological and pollution pressures. For this purpose, hourly time series of water levels and key water quality indicators (temperature, electric conductivity, and dissolved oxygen concentrations) collected from four automatic monitoring stations under different hydromorphological conditions and pollution pressures were statistically elaborated. Based on the results, the hydromorphological conditions and pollution pressures of each station were confirmed to be reflected in the results of the statistical analysis performed. It was proven that the comparative use of the statistics and patterns of the water level and quality high-frequency time series could be used in the interpretation of the current site status as well as allowing the detection of possible changes. This approach can be used as a tool for the definition of thresholds, and will contribute to the design of management and restoration measures for the most impacted areas.

scholarly journals Analysis of Noise and Velocity in GNSS EPN-Repro 2 Time Series

2021 ◽  
Vol 13 (14) ◽  
pp. 2783
Author(s):  
Sorin Nistor ◽  
Norbert-Szabolcs Suba ◽  
Kamil Maciuk ◽  
Jacek Kudrys ◽  
Eduard Ilie Nastase ◽  
...  
Keyword(s):  
Time Series ◽  
Visual Inspection ◽  
Flicker Noise ◽  
Vertical Component ◽  
Likelihood Estimation ◽  
Noise Model ◽  
Noise Amplitude ◽  
Allan Deviation ◽  
Power Spectral ◽  
Position Time Series

This study evaluates the EUREF Permanent Network (EPN) station position time series of approximately 200 GNSS stations subject to the Repro 2 reprocessing campaign in order to characterize the dominant types of noise and amplitude and their impact on estimated velocity values and associated uncertainties. The visual inspection on how different noise model represents the analysed data was done using the power spectral density of the residuals and the estimated noise model and it is coherent with the calculated Allan deviation (ADEV)-white and flicker noise. The velocities resulted from the dominant noise model are compared to the velocity obtained by using the Median Interannual Difference Adjusted for Skewness (MIDAS). The results show that only 3 stations present a dominant random walk noise model compared to flicker and powerlaw noise model for the horizontal and vertical components. We concluded that the velocities for the horizontal and vertical component show similar values in the case of MIDAS and maximum likelihood estimation (MLE), but we also found that the associated uncertainties from MIDAS are higher compared to the uncertainties from MLE. Additionally, we concluded that there is a spatial correlation in noise amplitude, and also regarding the differences in velocity uncertainties for the Up component.

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