scholarly journals Fractal Scaling Properties in Rainfall Time Series: A Case of Thiruvallur District, Tamil Nadu, India

2021 ◽  
Author(s):  
Ibrahim Lawal Kane ◽  
Venkatesan Madha Suresh
Keyword(s):  
Time Series ◽  
Fractal Analysis ◽  
Tamil Nadu ◽  
Structure Design ◽  
Rainfall Time Series ◽  
Scaling Properties ◽  
Future Data ◽  
Data Point ◽  
Core Idea ◽  
Red Hills

In the present study, the features of rainfall time series (1971–2016) in 9 meteorological regions of Thiruvallur, Tamil Nadu, India that comprises Thiruvallur, Korattur_Dam, Ponneri, Poondi, Red Hills, Sholingur, Thamaraipakkam, Thiruvottiyur and Vallur Anicut were studied. The evaluation of rainfall time series is one of the approaches for efficient hydrological structure design. Characterising and identifying patterns is one of the main objectives of time series analysis. Rainfall is a complex phenomenon, and the temporal variation of this natural phenomenon has been difficult to characterise and quantify due to its randomness. Such dynamical behaviours are present in multiple domains and it is therefore essential to have tools to model them. To solve this problem, fractal analysis based on Detrended Fluctuation Analysis (DFA) and Rescaled Range (R/S) analysis were employed. The fractal analysis produces estimates of the magnitude of detrended fluctuations at different scales (window sizes) of a time series and assesses the scaling relationship between estimates and time scales. The DFA and (R/S) gives an estimate known as Hurst exponent (H) that assumes self-similarity in the time series. The results of H exponent reveals typical behaviours shown by all the rainfall time series, Thiruvallur and Sholingur rainfall region have H exponent values within 0.5 < H < 1 which is an indication of persistent behaviour or long memory. In this case, a future data point is likely to be followed by a data point preceding it; Ponneri and Poondi have conflicting results based on the two methods, however, their H values are approximately 0.5 showing random walk behaviour in which there is no correlation between any part and a future. Thamaraipakkam, Thiruvottiyur, Vallur Anicut, Korattur Dam and Red Hills have H values less than 0.5 indicating a property called anti-persistent in which an increase will tend to be followed by a decrease or vice versa. Taking into consideration of such features in modelling, rainfall time series could be an exhaustive rainfall model. Finding appropriate models to estimate and predict future rainfalls is the core idea of this study for future research.

Temporal rainfall disaggregation based on scaling properties

1998 ◽  
Vol 37 (11) ◽  
pp. 73-79 ◽  
Author(s):  
J. Olsson ◽  
R. Berndtsson
Keyword(s):  
Time Series ◽  
Daily Rainfall ◽  
Cascade Model ◽  
Rainfall Time Series ◽  
Occurrence Probability ◽  
Southern Sweden ◽  
Scaling Properties ◽  
Time Period ◽  
Rainfall Volume ◽  
Disaggregated Data

The present study concerns disaggregation of daily rainfall time series into higher resolution. For this purpose, the scaling-based cascade model proposed by Olsson (1998) is employed. This model operates by dividing each rainy time period into halves of equal length and distributing the rainfall volume between the halves. For this distribution three possible cases are defined, and the occurrence probability of each case is empirically estimated. Olsson (1998) showed that the model was applicable between the time scales 1 hour and 1 week for rainfall in southern Sweden. In the present study, a daily seasonal (April-June; 3 years) rainfall time series from the same region was disaggregated by the model to 45-min resolution. The disaggregated data was shown to very well reproduce many fundamental characteristics of the observed 45-min data, e.g., the division between rainy and dry periods, the event structure, and the scaling behavior. The results demonstrate the potential of scaling-based approaches in hydrological applications involving rainfall.

Fractal analysis of high-resolution rainfall time series

1993 ◽  
Vol 98 (D12) ◽  
pp. 23265 ◽  
Author(s):  
Jonas Olsson ◽  
Janusz Niemczynowicz ◽  
Ronny Berndtsson
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Fractal Analysis ◽  
Rainfall Time Series

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.

Simulating reference rainfall scenarios for hydrological applications using a multifractal approach

2021 ◽  
Author(s):  
Arun Ramanathan ◽  
Pierre-Antoine Versini ◽  
Daniel Schertzer ◽  
Ioulia Tchiguirinskaia ◽  
Remi Perrin ◽  
...  
Keyword(s):  
Time Series ◽  
Moment Analysis ◽  
Specific Reference ◽  
Rainfall Time Series ◽  
Time Series Dataset ◽  
Hourly Rainfall ◽  
Spatial Dimensions ◽  
Multifractal Theory ◽  
Intensity Duration Frequency ◽  
Hydrological Applications

&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Hydrological applications such as flood design usually deal with and are driven by region-specific reference rainfall regulations, generally expressed as Intensity-Duration-Frequency (IDF) values. The meteorological module of hydro-meteorological models used in such applications should therefore be capable of simulating these reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes such as non-homogeneity (intermittency), scale invariance, and extremal statistics, seems to be an appropriate choice for this purpose. Here we suggest a rather simple discrete-in-scale multifractal cascade based approach. Hourly rainfall time-series datasets (with lengths ranging from around 28 to 35 years) over six cities (Paris, Marseille, Strasbourg, Nantes, Lyon, and Lille) in France that are characterized by different climates and a six-minute rainfall time series dataset (with a length of around 15&amp;#160; years) over Paris were analyzed via spectral analysis and Trace Moment analysis to understand the scaling range over which the universal multifractal theory can be considered valid. Then the Double Trace Moment analysis was performed to estimate the universal multifractal parameters &amp;#945;,C&lt;sub&gt;1&lt;/sub&gt; that are required by the multifractal cascade model for simulating rainfall. A renormalization technique that estimates suitable renormalization constants based on the IDF values of reference rainfall is used to simulate the reference rainfall scenarios. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Keywords&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Stochastic rainfall simulations.&lt;/p&gt;

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals Stationary and Non-Stationary Frameworks for Extreme Rainfall Time Series in Southern Italy

Water ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1477 ◽  
Author(s):  
Davide De Luca ◽  
Luciano Galasso
Keyword(s):  
Time Series ◽  
Climate Models ◽  
Southern Italy ◽  
Regional Climate ◽  
Data Series ◽  
Rainfall Time Series ◽  
Annual Maximum ◽  
Data Set ◽  
Maximum Rainfall ◽  
Rainfall Events

This study tests stationary and non-stationary approaches for modelling data series of hydro-meteorological variables. Specifically, the authors considered annual maximum rainfall accumulations observed in the Calabria region (southern Italy), and attention was focused on time series characterized by heavy rainfall events which occurred from 1 January 2000 in the study area. This choice is justified by the need to check if the recent rainfall events in the new century can be considered as very different or not from the events occurred in the past. In detail, the whole data set of each considered time series (characterized by a sample size N > 40 data) was analyzed, in order to compare recent and past rainfall accumulations, which occurred in a specific site. All the proposed models were based on the Two-Component Extreme Value (TCEV) probability distribution, which is frequently applied for annual maximum time series in Calabria. The authors discussed the possible sources of uncertainty related to each framework and remarked on the crucial role played by ergodicity. In fact, if the process is assumed to be non-stationary, then ergodicity cannot hold, and thus possible trends should be derived from external sources, different from the time series of interest: in this work, Regional Climate Models’ (RCMs) outputs were considered in order to assess possible trends of TCEV parameters. From the obtained results, it does not seem essential to adopt non-stationary models, as significant trends do not appear from the observed data, due to a relevant number of heavy events which also occurred in the central part of the last century.

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