scholarly journals Over-whitening or Pre-whitening in Hydro-climatological Trend Analysis?

2022 ◽  
Author(s):  
Zekai Sen
Keyword(s):  
Time Series ◽  
White Noise ◽  
Trend Analysis ◽  
Serial Correlation ◽  
Original Time Series ◽  
Trend Component ◽  
The Difference ◽  
Temperature Records ◽  
Original Time ◽  
Trend Identification

Abstract To meet the basic assumption of classical Mann-Kendall (MK) trend analysis, which requires serially independent time series, a pre-whitening (PW) procedure is proposed to alleviate the serial correlation structure of a given hydro-meteorological time series records for application. The procedure is simply to take the lagged differences in a given time series in the hope that the new time series will have an independent serial correlation coefficient. The whole idea was originally based on the first-order autoregressive AR (1) process, but such a procedure has been documented to damage the trend component in the original time series. On the other hand, the over-whitening procedure (OW) proposes a white noise process superposition of the same length with zero mean and some standard deviation on the original time series to convert it into serially independent series without any damage to the trend component. The stationary white noise addition does not have any trend components. For trend identification, annual average temperature records in New Jersey and Istanbul are presented to show the difference between PW and OW procedures. It turned out that the OW procedure was superior to the PW procedure, which did not cause a loss in the original trend component.

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

scholarly journals Investigation of GPS draconitic year effect on GPS time series of eliminated eclipsing GPS satellite data

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
A. Allahverdi-zadeh ◽  
J. Asgari ◽  
A.R. Amiri-Simkooei
Keyword(s):  
Time Series ◽  
Original Position ◽  
Year Effect ◽  
The Earth ◽  
Gps Satellites ◽  
Position Time Series ◽  
The Difference ◽  
Original Time ◽  
Almost All ◽  
New Time

AbstractGPS draconitic signal (351.6 ± 0.2 days) and its higher harmonics are observed at almost all IGS products such as position time series of IGS permanent stations. Orbital error and multipath are known as two possible sources of these signals. The effect of Earth shadow crossing of GPS satellites is another suspect for this signal. Up to now there is no serious attempt to investigate this dependence. AMATLAB toolbox is developed and used to determine the satellites located at the earth shadow. RINEX observation files and precise ephemeris are imported to the toolbox and a cylindrical model is used to detect the shadow regions. Data of these satellites were removed from the RINEX observation files of three IGS permanent stations (GRAZ,ONSAandWSRT) and new RINEX observation fileswere created. The time span of these data is about 11 years. The new and original fileswere then processed using precise point positioning (PPP) method to determine position time series, for further analysis. Both the original and new time series were analyzed using the least squares harmonic estimation (LS-HE) in the following steps. The 1st step is the validation of the draconitic harmonics signature in the original position time series of the three stations. The 2nd step does the same for the new time series. It confirms that the power spectrum at the draconitic signals decreases to some extent for the new time series. The difference between the original and new time series (difference between all three position quantity (X, Y and Z)) is then analyzed in the 3rd step. Signature of the draconitic harmonics is also observed to the differences. The results represent that all eight harmonics of GPS draconitic period do exist at the residuals and mainly they decrease. All of the three stations were then processed together using the multivariate LS-HE method. At the 4th step, the difference of the spectral values between the original time series and new times serieswere analyzed. Decreasing of the spectral values at most harmonics (e.g. 1st, 2nd, 4th, 6th, 7th and 8th) represents the effect of removing satellite observations at shadow of the earth on draconitic harmonics. At least, five harmonics among seven shows the amelioration of results (draconitic error reduction) after removing the earth shadowed data from RINEX raw data. The results show that the draconitic year’s component of data is in part due to eclipsing satellites.

Precipitation Forecast Based on WA-SVM Theory

2012 ◽  
Vol 518-523 ◽  
pp. 4039-4042
Author(s):  
Zhen Min Zhou
Keyword(s):  
Time Series ◽  
Support Vector Machine ◽  
Wavelet Analysis ◽  
Precipitation Forecast ◽  
Support Vector ◽  
Estimation Model ◽  
Original Time Series ◽  
Set Up ◽  
Original Time

In order to improve the precision of medium-long term rainfall forecast, the rainfall estimation model was set up based on wavelet analysis and support vector machine (WA-SVM). It decomposed the original rainfall series to different layers through wavelet analysis, forecasted each layer by means of SVM, and finally obtained the forecast results of the original time series by composition. The model was used to estimate the monthly rainfall sequence in the watershed. Comparing with other method which only uses support vector machine(SVM), it indicates that the estimated accuracy was improved obviously.

scholarly journals An assessment of differences in lower stratospheric temperature records from (A)MSU, radiosondes, and GPS radio occultation

2011 ◽  
Vol 4 (9) ◽  
pp. 1965-1977 ◽  
Author(s):  
F. Ladstädter ◽  
A. K. Steiner ◽  
U. Foelsche ◽  
L. Haimberger ◽  
C. Tavolato ◽  
...  
Keyword(s):  
Time Series ◽  
Radio Occultation ◽  
Sampling Error ◽  
Vertical Resolution ◽  
Stratospheric Temperature ◽  
Microwave Sounding ◽  
The Difference ◽  
Temperature Records ◽  
Atmospheric Variations ◽  
The Tropics

Abstract. Uncertainties for upper-air trend patterns are still substantial. Observations from the radio occultation (RO) technique offer new opportunities to assess the existing observational records there. Long-term time series are available from radiosondes and from the (Advanced) Microwave Sounding Unit (A)MSU. None of them were originally intended to deliver data for climate applications. Demanding intercalibration and homogenization procedures are required to account for changes in instrumentation and observation techniques. In this comparative study three (A)MSU anomaly time series and two homogenized radiosonde records are compared to RO data from the CHAMP, SAC-C, GRACE-A and F3C missions for September 2001 to December 2010. Differences of monthly anomalies are examined to assess the differences in the datasets due to structural uncertainties. The difference of anomalies of the (A)MSU datasets relative to RO shows a statistically significant trend within about (−0.2±0.1) K/10 yr (95% confidence interval) at all latitudes. This signals a systematic deviation of the two datasets over time. The radiosonde network has known deficiencies in its global coverage, with sparse representation of most of the southern hemisphere, the tropics and the oceans. In this study the error that results from sparse sampling is estimated and accounted for by subtracting it from radiosonde and RO datasets. Surprisingly the sampling error correction is also important in the Northern Hemisphere (NH), where the radiosonde network is dense over the continents but does not capture large atmospheric variations in NH winter. Considering the sampling error, the consistency of radiosonde and RO anomalies is improving substantially; the trend in the anomaly differences is generally very small. Regarding (A)MSU, its poor vertical resolution poses another problem by missing important features of the vertical atmospheric structure. This points to the advantage of homogeneously distributed measurements with high vertical resolution.

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

scholarly journals Piecewise Trend Approximation: A Ratio-Based Time Series Representation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jingpei Dan ◽  
Weiren Shi ◽  
Fangyan Dong ◽  
Kaoru Hirota
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Series Representation ◽  
Feature Space ◽  
Original Data ◽  
Series Data ◽  
High Dimensional ◽  
Original Time Series ◽  
Data Space ◽  
Original Time

A time series representation, piecewise trend approximation (PTA), is proposed to improve efficiency of time series data mining in high dimensional large databases. PTA represents time series in concise form while retaining main trends in original time series; the dimensionality of original data is therefore reduced, and the key features are maintained. Different from the representations that based on original data space, PTA transforms original data space into the feature space of ratio between any two consecutive data points in original time series, of which sign and magnitude indicate changing direction and degree of local trend, respectively. Based on the ratio-based feature space, segmentation is performed such that each two conjoint segments have different trends, and then the piecewise segments are approximated by the ratios between the first and last points within the segments. To validate the proposed PTA, it is compared with classical time series representations PAA and APCA on two classical datasets by applying the commonly used K-NN classification algorithm. For ControlChart dataset, PTA outperforms them by 3.55% and 2.33% higher classification accuracy and 8.94% and 7.07% higher for Mixed-BagShapes dataset, respectively. It is indicated that the proposed PTA is effective for high dimensional time series data mining.

INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

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