Scaling regimes of composite rainfall time series

1993 ◽  
Vol 45 (4) ◽  
pp. 289-298 ◽  
Author(s):  
KLAUS FRAEDRICH ◽  
CHRIS LARNDER
Keyword(s):  
Time Series ◽  
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

<p><strong>Abstract</strong></p><p>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  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 α,C<sub>1</sub> 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.</p><p><strong>Keywords</strong></p><p>Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Stochastic rainfall simulations.</p>

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.

scholarly journals A copula-based assessment of Bartlett–Lewis type of rainfall models for preserving drought statistics

2013 ◽  
Vol 10 (6) ◽  
pp. 7469-7516 ◽  
Author(s):  
M. T. Pham ◽  
W. J. Vanhaute ◽  
S. Vandenberghe ◽  
B. De Baets ◽  
N. E. C. Verhoest
Keyword(s):  
Time Series ◽  
Important Variable ◽  
Drought Severity ◽  
Test Case ◽  
Rainfall Time Series ◽  
Climate Data ◽  
Drought Duration ◽  
Environmental Consequences ◽  
Stochastic Point Process ◽  
The Impact

Abstract. Of all natural disasters, the economic and environmental consequences of droughts are among the highest because of their longevity and widespread spatial extent. Because of their extreme behaviour, studying droughts generally requires long time series of historical climate data. Rainfall is a very important variable for calculating drought statistics, for quantifying historical droughts or for assessing the impact on other hydrological (e.g. water stage in rivers) or agricultural (e.g. irrigation requirements) variables. Unfortunately, time series of historical observations are often too short for such assessments. To circumvent this, one may rely on the synthetic rainfall time series from stochastic point process rainfall models, such as Bartlett–Lewis models. The present study investigates whether drought statistics are preserved when simulating rainfall with Bartlett–Lewis models. Therefore, a 105 yr 10 min rainfall time series obtained at Uccle, Belgium is used as test case. First, drought events were identified on the basis of the Effective Drought Index (EDI), and each event was characterized by two variables, i.e. drought duration (D) and drought severity (S). As both parameters are interdependent, a multivariate distribution function, which makes use of a copula, was fitted. Based on the copula, four types of drought return periods are calculated for observed as well as simulated droughts and are used to evaluate the ability of the rainfall models to simulate drought events with the appropriate characteristics. Overall, all Bartlett–Lewis type of models studied fail in preserving extreme drought statistics, which is attributed to the model structure and to the model stationarity caused by maintaining the same parameter set during the whole simulation period.

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution and a simple representation of the rainfall process

2010 ◽  
Vol 7 (4) ◽  
pp. 4957-4994 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which is able to describe zero and non zero values of rainfall time series by assuring a perfect overlapping with the GPD fitted on the exceedances of any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it will only reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest on the exceedances of a wide range of thresholds using again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

Congo Basin's Shrinking Watersheds

2020 ◽  
pp. 1452-1468
Author(s):  
Bila-Isia Inogwabini
Keyword(s):  
Time Series ◽  
Regression Analysis ◽  
Time Series Data ◽  
Democratic Republic Of Congo ◽  
Congo Basin ◽  
Series Data ◽  
Water Volume ◽  
Rainfall Time Series ◽  
Aquatic Resources ◽  
Basin Water

Rainfall time series data from three sites (Kinshasa, Luki, and Mabali) in the western Democratic Republic of Congo were analyzed using regression analysis; rainfall intensities decreased in all three sites. The Congo Basin waters will follow the equation y = -20894x + 5483.16; R2 = 0.7945. The model suggests 18%-loss of the Congo Basin water volume and 7%-decrease for fish biomasses by 2025. Financial incomes generated by fishing will decrease by 11% by 2040 compared with 1998 levels. About 51% of women (N= 408,173) from the Lake Tumba Landscape fish; their revenues decreased by 11% between 2005 and 2010. If this trend continues, women's revenues will decrease by 59% by 2040. Decreased waters will severely impact women (e.g. increasing walking distances to clean waters). Increasing populations and decreasing waters will lead to immigrations to this region because water resources will remain available and highly likely ignite social conflicts over aquatic resources.

Sign in / Sign up

Export Citation Format

Share Document