scholarly journals Comparison of Harmonic Analysis of Time Series (HANTS) and Multi-Singular Spectrum Analysis (M-SSA) in Reconstruction of Long-Gap Missing Data in NDVI Time Series

2020 ◽  
Vol 12 (17) ◽  
pp. 2747
Author(s):  
Hamid Reza Ghafarian Malamiri ◽  
Hadi Zare ◽  
Iman Rousta ◽  
Haraldur Olafsson ◽  
Emma Izquierdo Verdiguier ◽  
...  
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Harmonic Analysis ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Vegetation Changes ◽  
Singular Spectrum ◽  
Ndvi Time Series ◽  
Reconstructed Data ◽  
Analysis Of Time Series

Monitoring vegetation changes over time is very important in dry areas such as Iran, given its pronounced drought-prone agricultural system. Vegetation indices derived from remotely sensed satellite imageries are successfully used to monitor vegetation changes at various scales. Atmospheric dust as well as airborne particles, particularly gases and clouds, significantly affect the reflection of energy from the surface, especially in visible, short and infrared wavelengths. This results in imageries with missing data (gaps) and outliers while vegetation change analysis requires integrated and complete time series data. This study investigated the performance of HANTS (Harmonic ANalysis of Time Series) algorithm and (M)-SSA ((Multi-channel) Singular Spectrum Analysis) algorithm in reconstruction of wide-gap of missing data. The time series of Normalized Difference Vegetation Index (NDVI) retrieved from Landsat TM in combination with 250m MODIS NDVI time image products are used to simulate and find periodic components of the NDVI time series from 1986 to 2000 and from 2000 to 2015, respectively. This paper presents the evaluation of the performance of gap filling capability of HANTS and M-SSA by filling artificially created gaps in data using Landsat and MODIS data. The results showed that the RMSEs (Root Mean Square Errors) between the original and reconstructed data in HANTS and M-SSA algorithms were 0.027 and 0.023 NDVI value, respectively. Further, RMSEs among 15 NDVI images extracted from the time series artificially and reconstructed by HANTS and M-SSA algorithms were 0.030 and 0.025 NDVI value, respectively. RMSEs of the original and reconstructed data in HANTS and M-SSA algorithms were 0.10 and 0.04 for time series 6, respectively. The findings of this study present a favorable option for solving the missing data challenge in NDVI time series.

scholarly journals Evidence of structured Brownian dynamics from temperature time series analysis

1997 ◽  
Vol 4 (4) ◽  
pp. 251-254
Author(s):  
A. Pasini ◽  
V. Pelino ◽  
S. Potestà
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Spectrum Analysis ◽  
Brownian Dynamics ◽  
Singular Spectrum Analysis ◽  
Temperature Time Series ◽  
Singular Spectrum ◽  
The Usa ◽  
Temperature Time ◽  
Analysis Of Time Series

Abstract. An analysis of time series of monthly mean temperatures ranging from 1895 to 1989 is performed through application of Singular Spectrum Analysis (SSA) to data of several places in the USA. A common dynamics in the reconstructed spaces is obtained, with the evidence of a non-trivial and structured coupling of two Brownian motions, resembling the so-called Lévy flights. The idea that these two correlated functions are related to the zonal and eddy components of the atmospheric motions is suggested.

scholarly journals Improved singular spectrum analysis for time series with missing data

2014 ◽  
Vol 1 (2) ◽  
pp. 1947-1966
Author(s):  
Y. Shen ◽  
F. Peng ◽  
B. Li
Keyword(s):  
Time Series ◽  
Missing Data ◽  
San Francisco ◽  
Principal Components ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Singular Spectrum ◽  
Relative Errors

Abstract. Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution will develop an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach was evaluated with the synthetic and real incomplete time series data of suspended-sediment concentration from San Francisco Bay. The result from the synthetic time series with missing data shows that the relative errors of the principal components reconstructed by ISSA are much smaller than those reconstructed by SSAM. Moreover, when the percentage of the missing data over the whole time series reaches 60%, the improvements of relative errors are up to 19.64, 41.34, 23.27 and 50.30% for the first four principal components, respectively. Besides, both the mean absolute errors and mean root mean squared errors of the reconstructed time series by ISSA are also much smaller than those by SSAM. The respective improvements are 34.45 and 33.91% when the missing data accounts for 60%. The results from real incomplete time series also show that the SD derived by ISSA is 12.27 mg L−1, smaller than 13.48 mg L−1 derived by SSAM.

scholarly journals Reconstruction of the Cloud-Free Time Series Satellite Observations of Land Surface Temperature (LST) Using Singular Spectrum Analysis (SSA)

2018 ◽  
Author(s):  
Hamid Reza Ghafarian Malamiri ◽  
Iman Rousta ◽  
Haraldur Olafsson ◽  
Hadi Zare ◽  
Hao Zhang
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Surface Temperature ◽  
Land Surface Temperature ◽  
Spectrum Analysis ◽  
Land Surface ◽  
Cloud Cover ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Singular Spectrum

Land Surface Temperature (LST) is a basic parameter in energy exchange between the land and atmosphere and is frequently used in many sciences such as climatology, hydrology, agriculture, ecology, etc. LST time series data have usually deficient, missing and unacceptable data caused by the presence of clouds in images, presence of dust in atmosphere and sensor failure. In this study, Singular Spectrum Analysis (SSA) algorithm was used to resolve the problem of missing and outlier data caused by cloud cover. The region studied in the present research included an image frame of MODIS with horizontal number 22 and vertical number 05 (h22v05). This image involved a large part of Iran and Turkmenistan and Caspian Sea. In this study, MODIS LST sensor (MOD11A1) was used during 2015 with 1×1 Km spatial resolution and day/night LST data (daily temporal resolution). The results of the data quality showed that cloud cover caused 36.37% of missing data in the studied time series with 730 day/night LST images. Further, the results of SSA algorithm in reconstruction of LST images indicated the Root Mean Square Error (RMSE) of 2.95 K between the original and reconstructed data in LST time series in the study region. In general, the findings showed that SSA algorithm using spatio-temporal interpolation in LST time series can be effectively used to resolve the problem of missing data caused by cloud cover.

scholarly journals Improved singular spectrum analysis for time series with missing data

2015 ◽  
Vol 22 (4) ◽  
pp. 371-376 ◽  
Author(s):  
Y. Shen ◽  
F. Peng ◽  
B. Li
Keyword(s):  
Time Series ◽  
Missing Data ◽  
San Francisco ◽  
Principal Components ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Singular Spectrum ◽  
Relative Errors

Abstract. Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution develops an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach is evaluated with the synthetic and real incomplete time series data of suspended-sediment concentration from San Francisco Bay. The result from the synthetic time series with missing data shows that the relative errors of the principal components reconstructed by ISSA are much smaller than those reconstructed by SSAM. Moreover, when the percentage of the missing data over the whole time series reaches 60 %, the improvements of relative errors are up to 19.64, 41.34, 23.27 and 50.30 % for the first four principal components, respectively. Both the mean absolute error and mean root mean squared error of the reconstructed time series by ISSA are also smaller than those by SSAM. The respective improvements are 34.45 and 33.91 % when the missing data accounts for 60 %. The results from real incomplete time series also show that the standard deviation (SD) derived by ISSA is 12.27 mg L−1, smaller than the 13.48 mg L−1 derived by SSAM.

scholarly journals ANÁLISE DE SÉRIES TEMPORAIS DA TEMPERATURA DO AR E UMIDADE RELATIVA EM CUIABÁ ATRAVÉS DO MÉTODO DE ANÁLISE DE ESPECTRO SINGULAR (ANALYSIS OF TIME SERIES OF AIR TEMPERATURE AND RELATIVE HUMIDITY IN CUIABÁ THROUGH THE METHOD OF ANALYSIS OF SINGULAR SPECTRUM)

2016 ◽  
Vol 19 ◽  
Author(s):  
Hozana Silva Ferreira ◽  
Sérgio Roberto de Paulo ◽  
Iramaia Jorge Cabral de Paulo ◽  
Anna Carolinna Albino Santos ◽  
Raphael De Souza Rosa Gomes
Keyword(s):  
Time Series ◽  
Relative Humidity ◽  
Air Temperature ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Spectrum ◽  
Singular Analysis ◽  
Analysis Of Time Series

Nos últimos anos o método de Análise de Espectro Singular (SSA- Singular Spectrum Analysis) tem sido utilizado como uma técnica na análise de séries temporais de dados meteorológicos e climáticos, possibilitando extrair informações úteis a partir de séries temporais estudadas. Nessa pesquisa, essa técnica foi utilizada no estudo das variáveis de temperatura do ar e umidade relativa em Cuiabá dos anos de 2000 a 2013, utilizando dados fornecidos pelo Instituto Nacional de Meteorologia (INMET).  O foco principal do estudo foi extrair informações sobre as tendências e efeitos sazonais das séries temporais. A ação conjunta desses dois fatores é particularmente evidente no caso da temperatura, que apresenta, comumente, dois máximos anuais.  

Application of singular spectrum analysis in reconstruction of the annual signal from GRACE

2020 ◽  
Vol 14 (3) ◽  
pp. 295-302
Author(s):  
Chuandong Zhu ◽  
Wei Zhan ◽  
Jinzhao Liu ◽  
Ming Chen
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Mixture Effect ◽  
Singular Spectrum ◽  
Grace Data ◽  
Terrestrial Water ◽  
Annual Signal ◽  
Long Term Variations

AbstractThe mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.

scholarly journals Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

2018 ◽  
Vol 17 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Mahdi Kalantari ◽  
Masoud Yarmohammadi ◽  
Hossein Hassani ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Missing Values ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
L1 Norm ◽  
Nonparametric Approach ◽  
Singular Spectrum ◽  
Simulated Time

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the [Formula: see text] norm-based version of Singular Spectrum Analysis (SSA), namely [Formula: see text]-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially [Formula: see text]-SSA can provide better imputation in comparison to other methods.

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