scholarly journals On the Enhanced Temporal Coherency of Radar Observations in Precipitation

2010 ◽  
Vol 49 (8) ◽  
pp. 1794-1804 ◽  
Author(s):  
A. R. Jameson ◽  
A. B. Kostinski
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Doppler Velocity ◽  
Autocorrelation Functions ◽  
Coherent Scatter ◽  
Incoherent Scatter ◽  
The Family ◽  
The Times ◽  
Temporal Coherency ◽  
Coherent Backscatter

Abstract In this work, the authors present observations of enhanced temporal coherency beyond that expected using the observations of the standard deviation of the Doppler velocities and the assumption of a family of exponentially decaying autocorrelation functions. The purpose of this paper is to interpret these observations by developing the complex amplitude autocorrelation function when both incoherent and coherent backscatter are present. Using this expression, it is then shown that when coherent scatter is present, the temporal coherency increases as observed. Data are analyzed in snow and in rain. The results agree with the theoretical expectations, and the authors interpret this agreement as an indication that coherent scatter is the likely explanation for the observed enhanced temporal coherency. This finding does not affect decorrelation times measured using time series. However, when the time series is not available (as in theoretical studies), the times to decorrelation are often computed based upon the assumptions that the autocorrelation function is a member of the family of exponentially decaying autocorrelation functions and that the signal decorrelation is due solely to the Doppler velocity fluctuations associated with incoherent scatter. Such an approach, at times, may significantly underestimate the true required times to decorrelation thus leading to overestimates of statistical reliability of parameters.

scholarly journals On the Temporal Characteristics of Radar Coherent Structures in Snow and Rain

2010 ◽  
Vol 49 (9) ◽  
pp. 1891-1893 ◽  
Author(s):  
A. R. Jameson
Keyword(s):  
Transverse Velocity ◽  
Temporal Structure ◽  
Ice Crystals ◽  
Doppler Velocity ◽  
Coherent Scatter ◽  
Velocity Fluctuations ◽  
Incoherent Scatter ◽  
To Come ◽  
Coherent Backscatter ◽  
Periodic Components

Abstract Previous work showed that the magnitudes of the radar-backscattered amplitudes have statistically significant periodic components of frequencies ( f ) in excess of those arising from the Doppler velocity fluctuations of incoherent scatter. Analyses in both rain and snow in the earlier work revealed what is interpreted as pervasive coherent scatter. This coherency is thought to come from precipitation structures acting like gratings in resonance with the radar wavelength that, when they move with a velocity component transverse to the beam, induce the observed f. The purpose of this article is to characterize briefly the temporal structure of f and, thereby indirectly, the temporal character of the structures producing the radar coherent backscatter. It is found that these structures last considerably longer than the decorrelation times of a few to 10 milliseconds, characteristic of Doppler velocity fluctuations associated with incoherent scatter. For the data analyzed, though, most last no more than a significant fraction of 1 s. Hence, for the observed transverse velocity of 2 ms−1, the dimensions of the gratings producing the radar coherent backscatter are only on the order of tens of centimeters to a few meters. Therefore, the typically large sampling volumes of most radars will contain many of these grids at any given time. Consequently, during 1 s of observations, one can envision the coherent scatter as coming from many individual grids twinkling on and off, much like the transient spectral reflections off ice crystals falling in sunlight.

scholarly journals Partially Coherent Backscatter in Radar Observations of Precipitation

2010 ◽  
Vol 67 (6) ◽  
pp. 1928-1946 ◽  
Author(s):  
A. R. Jameson ◽  
A. B. Kostinski
Keyword(s):  
Power Spectrum ◽  
Total Power ◽  
Coherent Scatter ◽  
Incoherent Scatter ◽  
Spectral Peaks ◽  
The Fourier Transform ◽  
Temporal Coherency ◽  
Coherent Backscatter ◽  
Periodic Components ◽  
Lower Frequencies

Abstract Classical radar theory only considers incoherent backscatter from precipitation. Can precipitation generate coherent scatter as well? Until now, the accepted answer has been no, because hydrometeors are distributed sparsely in space (relative to radar wavelength) so that the continuum assumption used to explain coherent scatter in clear air and clouds does not hold. In this work, a theory for a different mechanism is presented. The apparent existence of the proposed mechanism is then illustrated in both rain and snow. A new power spectrum Z( f ), the Fourier transform of the time series of the radar backscattered reflectivities, reveals statistically significant frequencies f of periodic components that cannot be ascribed to incoherent scatter. It is shown that removing those significant fs from Z( f ) at lower frequencies greatly reduces the temporal coherency. These lower frequencies, then, are associated with the increased temporal coherency. It is also shown that these fs are also directly linked to the Doppler spectral peaks through integer multiples of one-half the radar wavelength, characteristic of Bragg scatter. Thus, the enhanced temporal coherency is directly related to the presence of coherent scatter in agreement with theory. Moreover, the normalized backscattered power spectrum Z( f ) permits the estimation of the fractional coherent power contribution to the total power, even for an incoherent radar. Analyses of approximately 26 000 one-second Z( f ) in both rain and snow reveal that the coherent scatter is pervasive in these data. These findings present a challenge to the usual assumption that the scatter of radar waves from precipitation is always incoherent and to interpretations of backscattered power based on this assumption.

Autocorrelation

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Random Noise ◽  
Market Performance ◽  
Autocorrelation Functions ◽  
Maximum Information ◽  
Stock Market Performance ◽  
Serial Correlations ◽  
Scalar Time Series

This chapter discusses theoretical autocovariance, autocorrelation functions of autoregressive models of orders 1 and 2, and autocorrelation function-derived timescale. The autocorrelation function of a scalar time series is a prime tool for estimating the characteristic timescale separating successive independent realizations in the time series. Any process other than completely random noise has some serial correlations. Even variables as volatile and nondeterministic as measures of stock market performance, when valuated close enough, are unlikely to vary appreciably. Thus, a time series of the index at 1-second intervals likely contains significant redundancy; it can be almost as representative and contain almost as much information if degraded to valuation intervals of T > 1 second. Identifying an acceptable characteristic timescale T separating successive independent realization in the time series that balances the need to retain maximum information while minimizing storage and transmission burdens is a key role of the autocorrelation function.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

scholarly journals Sensitivity Analysis of Sentinel-1 Backscatter to Oil Palm Plantations at Pluriannual Scale: A Case Study in Gabon, Africa

2021 ◽  
Vol 13 (11) ◽  
pp. 2075
Author(s):  
J. David Ballester-Berman ◽  
Maria Rastoll-Gimenez
Keyword(s):  
Time Series ◽  
Sensitivity Analysis ◽  
Oil Palm ◽  
Time Interval ◽  
Potential Candidate ◽  
Initial Growth ◽  
Natural Forests ◽  
Wet Season ◽  
Radar Signatures ◽  
The Times

The present paper focuses on a sensitivity analysis of Sentinel-1 backscattering signatures from oil palm canopies cultivated in Gabon, Africa. We employed one Sentinel-1 image per year during the 2015–2021 period creating two separated time series for both the wet and dry seasons. The first images were almost simultaneously acquired to the initial growth stage of oil palm plants. The VH and VV backscattering signatures were analysed in terms of their corresponding statistics for each date and compared to the ones corresponding to tropical forests. The times series for the wet season showed that, in a time interval of 2–3 years after oil palm plantation, the VV/VH ratio in oil palm parcels increases above the one for forests. Backscattering and VV/VH ratio time series for the dry season exhibit similar patterns as for the wet season but with a more stable behaviour. The separability of oil palm and forest classes was also quantitatively addressed by means of the Jeffries–Matusita distance, which seems to point to the C-band VV/VH ratio as a potential candidate for discrimination between oil palms and natural forests, although further analysis must still be carried out. In addition, issues related to the effect of the number of samples in this particular scenario were also analysed. Overall, the outcomes presented here can contribute to the understanding of the radar signatures from this scenario and to potentially improve the accuracy of mapping techniques for this type of ecosystems by using remote sensing. Nevertheless, further research is still to be done as no classification method was performed due to the lack of the required geocoded reference map. In particular, a statistical assessment of the radar signatures should be carried out to statistically characterise the observed trends.

scholarly journals SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 602
Author(s):  
Luisa Martínez-Acosta ◽  
Juan Pablo Medrano-Barboza ◽  
Álvaro López-Ramos ◽  
John Freddy Remolina López ◽  
Álvaro Alberto López-Lambraño
Keyword(s):  
Time Series ◽  
Water Resources ◽  
Autocorrelation Function ◽  
Information Criterion ◽  
Monthly Rainfall ◽  
Statistical Characteristics ◽  
Rainfall Time Series ◽  
River Watershed ◽  
Statistical Measures ◽  
Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

scholarly journals Spatial and Temporal Spread of the COVID-19 Pandemic Using Self Organizing Neural Networks and a Fuzzy Fractal Approach

2021 ◽  
Vol 13 (15) ◽  
pp. 8295
Author(s):  
Patricia Melin ◽  
Oscar Castillo
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Temporal Trends ◽  
Main Idea ◽  
Temporal Analysis ◽  
Virus Propagation ◽  
Self Organizing Maps ◽  
Fractal Approach ◽  
The Times ◽  
Self Organizing

In this article, the evolution in both space and time of the COVID-19 pandemic is studied by utilizing a neural network with a self-organizing nature for the spatial analysis of data, and a fuzzy fractal method for capturing the temporal trends of the time series of the countries considered in this study. Self-organizing neural networks possess the capability to cluster countries in the space domain based on their similar characteristics, with respect to their COVID-19 cases. This form enables the finding of countries that have a similar behavior, and thus can benefit from utilizing the same methods in fighting the virus propagation. In order to validate the approach, publicly available datasets of COVID-19 cases worldwide have been used. In addition, a fuzzy fractal approach is utilized for the temporal analysis of the time series of the countries considered in this study. Then, a hybrid combination, using fuzzy rules, of both the self-organizing maps and the fuzzy fractal approach is proposed for efficient coronavirus disease 2019 (COVID-19) forecasting of the countries. Relevant conclusions have emerged from this study that may be of great help in putting forward the best possible strategies in fighting the virus pandemic. Many of the existing works concerned with COVID-19 look at the problem mostly from a temporal viewpoint, which is of course relevant, but we strongly believe that the combination of both aspects of the problem is relevant for improving the forecasting ability. The main idea of this article is combining neural networks with a self-organizing nature for clustering countries with a high similarity and the fuzzy fractal approach for being able to forecast the times series. Simulation results of COVID-19 data from countries around the world show the ability of the proposed approach to first spatially cluster the countries and then to accurately predict in time the COVID-19 data for different countries with a fuzzy fractal approach.

scholarly journals Priors for Macroeconomic Time Series and Their Application

1994 ◽  
Vol 10 (3-4) ◽  
pp. 609-632 ◽  
Author(s):  
John Geweke
Keyword(s):  
Time Series ◽  
Prior Distribution ◽  
Odds Ratio ◽  
General Trend ◽  
Stationary Model ◽  
Posterior Odds ◽  
Posterior Odds Ratio ◽  
The Family ◽  
Macroeconomic Time Series ◽  
Posterior Moments

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson–Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and they indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

scholarly journals A forecasting the consumer price index using time series model

2021 ◽  
Vol 107 ◽  
pp. 10002
Author(s):  
Volodymyr Shinkarenko ◽  
Alexey Hostryk ◽  
Larysa Shynkarenko ◽  
Leonid Dolinskyi
Keyword(s):  
Time Series ◽  
Price Index ◽  
Consumer Price Index ◽  
Exponential Smoothing ◽  
Time Series Model ◽  
Initial Time ◽  
Autocorrelation Functions ◽  
Minimum Error ◽  
Initial Time Series

This article examines the behavior of the consumer price index in Ukraine for the period from January 2010 to September 2020. The characteristics of the initial time series, the analysis of autocorrelation functions made it possible to reveal the tendency of their development and the presence of annual seasonality. To model the behavior of the consumer price index and forecast for the next months, two types of models were used: the additive ARIMA*ARIMAS model, better known as the model of Box-Jenkins and the exponential smoothing model with the seasonality estimate of Holt-Winters. As a result of using the STATISTICA package, the most adequate models were built, reflecting the monthly dynamics of the consumer price index in Ukraine. The inflation forecast was carried out on the basis of the Holt-Winters model, which has a minimum error.

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