Multifractal analysis of spatial heterogeneity in Spanish arid rangelands

2021 ◽  
Author(s):  
Ernesto Sanz Sancho ◽  
Antonio Saa-Requejo ◽  
Carlos G. Diaz-Ambrona ◽  
Margarita Ruiz-Ramos ◽  
Ana M. Tarquis
Keyword(s):  
Time Series ◽  
Spatial Heterogeneity ◽  
Agricultural Landscapes ◽  
Absolute Difference ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Vegetation Types ◽  
Tree Crops ◽  
Arid Rangelands ◽  
Arid Rangeland

<p>Rangeland and agricultural landscapes are complex and multifractal based on the interaction of biotic and abiotic factors such as soil, meteorology, and vegetation. The effects of land-uses on these areas modify their characteristics and dynamics.  The use of Normalized Difference Vegetation Index (NDVI) and NDVI anomalies (NDVIa) from satellite time series can effectively aid on understanding the differences among rangeland uses and types.</p><p>Multifractal detrended fluctuation analysis (MDFA) focuses on measuring variations of the moments of the absolute difference of their values at different scales. This allows us to use different multifractal exponent such as generalized Hurst exponent (H(q)), and the scaling exponent (ζ(q)) to characterize each area.</p><p>We collected the time series using satellite data of MODIS (MOD09Q1.006) from 2002 to 2019. Two areas from southeastern Spain (Murcia province) of 6.25 Km<sup>2</sup> were selected. Each area has 132 pixels with a spatial resolution of 250 x 250 m<sup>2</sup> and a temporal resolution of 8 days. The areas were selected to compare two types of arid rangeland. Area 1 (A1) is mainly covered by a mixed herbaceous cropland and grassland, Area 2 (A2) presents tree crops as well as a small patch of Mediterranean scrubland.</p><p>MDFA was used on every pixel of each area and H(q), and ζ(q) were plotted and compared. Our results report different exponent behaviours for diverse rangeland type or use. Within each area when different vegetation types are present MFDFA can allow us to distinguish among them such as in A2 where the pixels composing the river that crosses the area show less antipersistent character than the surrounding tree crops.<br>Comparing the scaling exponent of NDVI and NDVIa also suggest a difference of influence on the multifractal character of long-range correlations. This influence is much stronger in A4 than the three others, having their multifractal character due more heavily to probability density function.</p><p>We conclude that MDFA is a good tool to characterize arid rangelands spatial heterogeneity, particularly for rangeland with different vegetation types. It can be used to monitor and manage arid rangeland. It can be useful for policy-makers for short- and long-term solutions.</p><p><strong>Acknowledgements: </strong>The authors acknowledge the support of Project No. PGC2018-093854-B-I00 of the Ministerio de Ciencia Innovación y Universidades of Spain, “Garantía Juvenil” scholarship from Comunidad de Madrid, and the financial support from Boosting Agricultural Insurance based on Earth Observation data - BEACON project under agreement Nº 821964, funded under H2020EU, DT-SPACE-01-EO-2018-2020.</p>

scholarly journals Detecting Cover Crop End-Of-Season Using VENµS and Sentinel-2 Satellite Imagery

2020 ◽  
Vol 12 (21) ◽  
pp. 3524
Author(s):  
Feng Gao ◽  
Martha C. Anderson ◽  
W. Dean Hively
Keyword(s):  
Remote Sensing ◽  
Time Series ◽  
Cover Crops ◽  
Cover Crop ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Agricultural Research ◽  
Agricultural Landscapes ◽  
Absolute Difference ◽  
Sentinel 2

Cover crops are planted during the off-season to protect the soil and improve watershed management. The ability to map cover crop termination dates over agricultural landscapes is essential for quantifying conservation practice implementation, and enabling estimation of biomass accumulation during the active cover period. Remote sensing detection of end-of-season (termination) for cover crops has been limited by the lack of high spatial and temporal resolution observations and methods. In this paper, a new within-season termination (WIST) algorithm was developed to map cover crop termination dates using the Vegetation and Environment monitoring New Micro Satellite (VENµS) imagery (5 m, 2 days revisit). The WIST algorithm first detects the downward trend (senescent period) in the Normalized Difference Vegetation Index (NDVI) time-series and then refines the estimate to the two dates with the most rapid rate of decrease in NDVI during the senescent period. The WIST algorithm was assessed using farm operation records for experimental fields at the Beltsville Agricultural Research Center (BARC). The crop termination dates extracted from VENµS and Sentinel-2 time-series in 2019 and 2020 were compared to the recorded termination operation dates. The results show that the termination dates detected from the VENµS time-series (aggregated to 10 m) agree with the recorded harvest dates with a mean absolute difference of 2 days and uncertainty of 4 days. The operational Sentinel-2 time-series (10 m, 4–5 days revisit) also detected termination dates at BARC but had 7% missing and 10% false detections due to less frequent temporal observations. Near-real-time simulation using the VENµS time-series shows that the average lag times of termination detection are about 4 days for VENµS and 8 days for Sentinel-2, not including satellite data latency. The study demonstrates the potential for operational mapping of cover crop termination using high temporal and spatial resolution remote sensing data.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

scholarly journals Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States

Atmosphere ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 1116
Author(s):  
Adarsh Sankaran ◽  
Jaromir Krzyszczak ◽  
Piotr Baranowski ◽  
Archana Devarajan Sindhu ◽  
Nandhineekrishna Kumar ◽  
...  
Keyword(s):  
Time Series ◽  
Cross Correlation ◽  
Reference Evapotranspiration ◽  
Multifractal Spectrum ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
The Individual

The multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA were examined. The investigation of multifractality of datasets from stations with differing terrain conditions using the Multifractal Detrended Fluctuation Analysis (MFDFA) showed the existence of a long-term persistence and multifractality irrespective of the location. The scaling exponents of SR and T time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. The MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from weekly to inter-annual time scales. The multifractal exponents of P and U are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the MFCCA studies for agro-meteorological time series. The temporal evolution of cross-correlation determined by the MFCCA successfully captured the dynamics in the nature of associations in the P-ET0 link.

scholarly journals Significance of trends in gait dynamics

2020 ◽  
Vol 16 (10) ◽  
pp. e1007180
Author(s):  
Klaudia Kozlowska ◽  
Miroslaw Latka ◽  
Bruce J. West
Keyword(s):  
Time Series ◽  
Large Scale ◽  
Fundamental Problem ◽  
Multivariate Adaptive Regression Splines ◽  
Human Gait ◽  
Small Scale ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Treadmill Speed

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

Detrended Fluctuation Analysis of Arrhythmia: Scaling Exponent as an Index of Heart Wellness

2011 ◽  
Author(s):  
Toru Yazawa ◽  
Albert M. Hutapea ◽  
Tomoo Katsuyama ◽  
Yukio Shimoda
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
A Value ◽  
Healthy State ◽  
Interval Time Series ◽  
Detrended Fluctuation ◽  
Analytical Technology ◽  
Heart Condition

Well-established technologies to analyze biological signals including rhythmic heartbeat are available and accessible to scholars. However, stronger empirical evidence is required to justify the use of these technologies as practical tools in the field of biomedicine. Here we conducted analyses of heartbeat interval time series using an analytical technology developed across three decades—detrended fluctuation analysis (DFA)—to verify the power-law/scaling characteristics of signals that fluctuate in a regular, irregular, or erratic manner. We believe that DFA is a useful tool because it can quantify the heart condition by a scaling exponent, with a value of one (1) set as the default for a healthy state. This baseline value can be compared to a clinical thermometer, where the baseline is 37 °C for a physiologically healthy condition. Our study aimed to ascertain and confirm the utility of DFA in evaluating heart wellness, specifically in the context of studying arrhythmic heartbeat. We present case studies to confirm that DFA is a beneficial tool that quantifies the scaling exponent of a heart’s condition as “nonstationarily” beating and dynamically controlled. From an engineering perspective, we show that the heart condition can be classified into two typical categories: a healthy rhythm with a scaling exponent of one (1.0), and arrhythmia with a lower scaling exponent (0.7 or less).

Self-affinity in the dengue fever time series

2016 ◽  
Vol 27 (12) ◽  
pp. 1650143 ◽  
Author(s):  
S. M. Azevedo ◽  
H. Saba ◽  
J. G. V. Miranda ◽  
A. S. Nascimento Filho ◽  
M. A. Moret
Keyword(s):  
Time Series ◽  
Long Range ◽  
Control Strategies ◽  
Public Health Problem ◽  
Physical Symptoms ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Short Time ◽  
Scale Behavior

Dengue is a complex public health problem that is common in tropical and subtropical regions. This disease has risen substantially in the last three decades, and the physical symptoms depict the self-affine behavior of the occurrences of reported dengue cases in Bahia, Brazil. This study uses detrended fluctuation analysis (DFA) to verify the scale behavior in a time series of dengue cases and to evaluate the long-range correlations that are characterized by the power law [Formula: see text] exponent for different cities in Bahia, Brazil. The scaling exponent ([Formula: see text]) presents different long-range correlations, i.e. uncorrelated, anti-persistent, persistent and diffusive behaviors. The long-range correlations highlight the complex behavior of the time series of this disease. The findings show that there are two distinct types of scale behavior. In the first behavior, the time series presents a persistent [Formula: see text] exponent for a one-month period. For large periods, the time series signal approaches subdiffusive behavior. The hypothesis of the long-range correlations in the time series of the occurrences of reported dengue cases was validated. The observed self-affinity is useful as a forecasting tool for future periods through extrapolation of the [Formula: see text] exponent behavior. This complex system has a higher predictability in a relatively short time (approximately one month), and it suggests a new tool in epidemiological control strategies. However, predictions for large periods using DFA are hidden by the subdiffusive behavior.

Everyday Life Quantification Using mDFA: Heart Health Monitoring and Structural Health Monitoring

2015 ◽  
Author(s):  
Toru Yazawa
Keyword(s):  
Time Series ◽  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Natural World ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Heart Health ◽  
Structural Health ◽  
Wheel Vibration

The aim of this study was to make a method usable in an early detection of malfunction, e.g., abnormal vibration/fluctuation in recorded signals. We conducted experimentations of heart health and structural health monitoring. We collected natural world signals, e.g., heartbeat fluctuation and mechanical vibration. For the analysis, we used modified detrended fluctuation analysis (mDFA) method that we have made recently. mDFA calculated the scaling exponent (SI, the acronym SI is derived from the scaling indices) from the time series data, e.g., R-R interval time series obtained from electrocardiograms. In the present study, peaks were identified by our own method. In every single mDFA computation, we identified ∼2000 consecutive peaks from a data: “2000” was necessary number to conduct mDFA. mDFA was able to distinguish between normal and abnormal behaviors: Normal healthy hearts exhibited an SI around 1.0, which is a phenomena comparable to 1/f fluctuation. Job-related stressful hearts and extrasystolic hearts both exhibited a low SI such as 0.7. Normally running car’s vibration — recorded steering wheel vibration — exhibited an SI around 0.5, which is white noise like fluctuation. Normally spinning ball-bearings (BB) exhibited an SI around 0.1, which belongs to the anti-correlation phenomena. A malfunctioning BB showed an increased SI. At an SI value over 0.2, an inspector must check BB’s correct functioning. Here we propose that healthiness in various cyclic vibration behaviors can be quantitatively analyzed by mDFA.

scholarly journals Multifractal Cross Correlation Analysis of Agro-meteorological Datasets (Including Reference Evapotranspiration) of California, United States

2020 ◽  
Author(s):  
Adarsh Sankaran ◽  
Jaromir Krzyszczak ◽  
Piotr Baranowski ◽  
Archana Devarajan Sindhu ◽  
Nandhinee Krishna Pradeep ◽  
...  
Keyword(s):  
Time Series ◽  
Los Angeles ◽  
Cross Correlation ◽  
Reference Evapotranspiration ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Air Humidity ◽  
Scaling Exponents ◽  
Relative Air Humidity ◽  
Cross Correlation Analysis

This paper examined the multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA. The investigation of multifractality of datasets from stations with differing terrain conditions: Dagget, Bakersfield, Santa Maria, Los Angeles and San Diego using the Multifractal Detrended Fluctuation Analysis showed the existence of a long term persistence and multifractality irrespective of the location. The scaling exponents of SR and ET0 time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from seasonal to multi-annual time scale. The multifractal exponents of pressure and relative air humidity are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the mutifractal cross correlation studies for agro-meteorological time series. The temporal evolution of cross-correlation showed similar pattern for all pair-wise associations involving ET0, except for the RH-ET0 link.

SCALING ANALYSIS OF THE A-PHASE DYNAMICS DURING SLEEP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050050
Author(s):  
V. E. ARCE-GUEVARA ◽  
M. O. MENDEZ ◽  
J. S. MURGUÍA ◽  
A. ALBA ◽  
H. GONZÁLEZ-AGUILAR ◽  
...  
Keyword(s):  
Binary Sequence ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Sleep State ◽  
Phase Dynamics ◽  
A Value ◽  
Sleep Condition ◽  
Detrended Fluctuation

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

scholarly journals AUTOMATICALLY DETECTING "SIGNIFICANT EVENTS" ON SenseCam

2013 ◽  
Vol 11 (06) ◽  
pp. 1350050 ◽  
Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Time Windows ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Dominant Eigenvalue ◽  
Multiple Time ◽  
Correlation Relationship ◽  
Significant Events ◽  
Detrended Fluctuation

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

Sign in / Sign up

Export Citation Format

Share Document