scholarly journals A Nonparametric Procedure to Assess the Accuracy of the Normality Assumption for Annual Rainfall Totals, Based on the Marginal Statistics of Daily Rainfall: An Application to the NOAA/NCDC Rainfall Database

2021 ◽  
Vol 60 (4) ◽  
pp. 595-605
Author(s):  
Dario Ruggiu ◽  
Francesco Viola ◽  
Andreas Langousis
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Random Search ◽  
Daily Rainfall ◽  
Annual Rainfall ◽  
Rainfall Time Series ◽  
Normality Assumption ◽  
Normal Shape ◽  
Nonparametric Procedure ◽  
Rain Rates

AbstractWe develop a nonparametric procedure to assess the accuracy of the normality assumption for annual rainfall totals (ART), based on the marginal statistics of daily rainfall. The procedure is addressed to practitioners and hydrologists that operate in data-poor regions. To do so we use 1) goodness-of-fit metrics to conclude on the approximate convergence of the empirical distribution of annual rainfall totals to a normal shape and classify 3007 daily rainfall time series from the NOAA/NCDC Global Historical Climatology Network database, with at least 30 years of recordings, into Gaussian (G) and non-Gaussian (NG) groups; 2) logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification; and 3) a random-search algorithm to conclude on a set of constraints that allows classification of ART samples on the basis of the marginal statistics of daily rain rates. The analysis shows that the Anderson–Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer–Von Mises and Lilliefors’s version of Kolmogorov–Smirnov) and that daily rainfall time series with fraction of wet days fwd < 0.1 and daily skewness coefficient of positive rain rates skwd > 5.92 deviate significantly from the normal shape. In addition, we find that continental climate (type D) exhibits the highest fraction of Gaussian distributed ART samples (i.e., 74.45%; AD test at α = 5% significance level), followed by warm temperate (type C; 72.80%), equatorial (type A; 68.83%), polar (type E; 62.96%), and arid (type B; 60.29%) climates.

scholarly journals A non-parametric procedure to assess the accuracy of the normality assumption for annual rainfall totals, based on the marginal statistics of daily rainfall: An application to NOAA-NCDC rainfall database

2020 ◽  
Author(s):  
Dario Ruggiu ◽  
Francesco Viola ◽  
Andreas Langousis
Keyword(s):  
Goodness Of Fit ◽  
Search Algorithm ◽  
Random Search ◽  
Daily Rainfall ◽  
Annual Rainfall ◽  
Test Statistic ◽  
Statistical Tool ◽  
Normality Assumption ◽  
Normal Shape ◽  
Non Parametric

&lt;p&gt;In an effort to assess the accuracy of the normality assumption for annual rainfall totals (ART) in data-poor regions, we develop a non-parametric procedure based on the marginal statistics of daily rainfall. In doing so we start by using three goodness-of-fit metrics to conclude on the approximate convergence of the empirical ART distribution to a normal shape, and classify daily rainfall timeseries into Gaussian (G) and non-Gaussian (NG) groups. At a second step, we apply logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification. In the third and final step, we use a random-search algorithm to conclude on a set of constraints to classify ART samples based on the marginal statistics of daily rainrates. The analysis is conducted using 3007 daily rainfall timeseries from the NOAA-NCDC Global Historical Climatology Network (GHCN) database, and aims at developing a statistical tool towards informed decision making for water management purposes. The conducted analysis highlights that the Anderson-Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer-Von Mises and Kolmogorov-Smirnov), while daily rainfall timeseries with fraction of dry days in excess of 90% and skewness coefficient of positive rainrates that exceeds 5.92 deviate significantly from the normal shape. Further, our results indicate that continental climate exhibits the highest fraction of Gaussian distributed ART samples, followed by warm temperate, equatorial, polar, and arid climates.&lt;/p&gt;

Spatial Variability of the Hurst Exponent for the Daily Scale Rainfall Series in the State of Zacatecas, Mexico

2013 ◽  
Vol 52 (12) ◽  
pp. 2771-2780 ◽  
Author(s):  
M. A. Velásquez Valle ◽  
G. Medina García ◽  
Ignacio Sánchez Cohen ◽  
L. Klaudia Oleschko ◽  
J. A. Ruiz Corral ◽  
...  
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
Fractal Theory ◽  
Daily Rainfall ◽  
The State ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Rainfall Time Series ◽  
Wavelet Techniques ◽  
Hurst Exponents

AbstractThe structural pattern of rainfall data exhibits random fluctuations over time and space. Utilizing concepts of fractal theory, it has been possible to identify characteristics of rainfall data beyond simple statistical indicators of their randomness. The objective of this research was to identify the spatial variation of the Hurst exponent, extracted through standard wavelet techniques from time series of daily rainfall data in the state of Zacatecas, Mexico. The Hurst exponent was extracted for 26 locations using the reference techniques for auto-affine traces—in particular, the wavelets method. Results have shown that the Hurst exponents of rainfall time series are negatively influenced by altitude; thus, stations located at higher altitudes were characterized by Hurst exponents indicating more nonpersistent behavior. The trends among geographical variables (west longitude and latitude) and climatic parameters (annual rainfall and number of rainy days) and their relationship with the Hurst exponent were also analyzed.

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.

scholarly journals Modelling of monsoon rainfall for a mesoscale catchment in North-West India II: stochastic rainfall simulations

2006 ◽  
Vol 10 (6) ◽  
pp. 807-815 ◽  
Author(s):  
E. Zehe ◽  
A. K. Singh ◽  
A. Bárdossy
Keyword(s):  
Time Series ◽  
Meteorological Data ◽  
Daily Rainfall ◽  
Time Variability ◽  
Western India ◽  
Data Sets ◽  
Rainfall Time Series ◽  
North West ◽  
Monthly Scale ◽  
Circulation Patterns

Abstract. Within this study we present a robust method for generating precipitation time series for the Anas catchment in North Western India. The method employs a multivariate stochastic simulation model that is driven by a time series of objectively classified circulation patterns (CPs). In a companion study (Zehe et al., 2006) it was already shown that CPs classified from the 500 or 700 Hpa levels are suitable to explain space-time variability of precipitation in that area. The model is calibrated using observed rainfall time series for the period 1985–1992 for two different CP time series, one from the 500 Hpa level and the over from the 700 Hpa level, and 200 realizations of daily rainfall are simulated for the period 85–94. Simulations using the CPs from the 500 Hpa level as input yield a good match of the observed averages and standard deviations of daily rainfall. They show furthermore good performance at the monthly scale. When used with the 700 Hpa level CPs as inputs the model clearly underestimates the standard deviation and performs much worse at the monthly scale, especially in the validation period 93–94. The presented results give evidence that CPs from the 500 Hpa, level in combination with a multivariate stochastic model, make up a suitable tool for reducing the sparsity of precipitation data in developing regions with sparse hydro-meteorological data sets.

Hybrid of ARIMA-GARCH Modeling in Rainfall Time Series

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Fadhilah Yusof ◽  
Ibrahim Lawal Kane ◽  
Zulkifli Yusop
Keyword(s):  
Time Series ◽  
Daily Rainfall ◽  
Rainfall Series ◽  
Empirical Modeling ◽  
Dependence Structure ◽  
Rainfall Time Series ◽  
Arima Models ◽  
Starting Point ◽  
Garch Modeling ◽  
Squared Residuals

The dependence structure of rainfall is usually very complex both in time and space. It is shown in this paper that the daily rainfall series of Ipoh and Alorsetar are affected by nonlinear characteristics of the variance often referred to as variance clustering or volatility, where large changes tend to follow large changes and small changes tend to follow small changes. In most empirical modeling of hydrological time series, the focus was on modeling and predicting the mean behavior of the time series through conventional methods of an Autoregressive Moving Average (ARMA) modeling proposed by the Box Jenkins methodology. The conventional models operate under the assumption that the series is stationary that is: constant mean and either constant variance or season-dependent variances, however, does not take into account the second order moment or conditional variance, but they form a good starting point for time series analysis. The residuals from preliminary ARIMA models derived from the daily rainfall time series were tested for ARCH behavior. The autocorrelation structure of the residuals and the squared residuals were inspected, the residuals are uncorrelated but the squared residuals show autocorrelation, the Ljung-Box test confirmed the results. McLeod-Li test and a test based on the Lagrange multiplier (LM) principle were applied to the squared residuals from ARIMA models. The results of these auxiliary tests show clear evidence to reject the null hypothesis of no ARCH effect. Hence indicates that GARCH modeling is necessary. Therefore the composite ARIMA-GARCH model captures the dynamics of the daily rainfall series in study areas more precisely. On the other hand, Seasonal ARIMA model became a suitable model for the monthly average rainfall series of the same locations treated.

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series

2010 ◽  
Vol 14 (12) ◽  
pp. 2559-2575 ◽  
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 assures a perfect overlapping with the GPD fitted on the exceedances over any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it is expected to 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 by using exceedances over a wide range of thresholds applying 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 and with a significative percentage of heavily quantized data. 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.

scholarly journals Variability and Trend Analysis of Rainfall Data of Shillong and Agartala Stations of North East India

2020 ◽  
pp. 134-142
Author(s):  
Mirbana Lusick K. Sangma ◽  
Hamtoiti Reang ◽  
G. T. Patle ◽  
P. P. Dabral
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Winter Season ◽  
Summer Season ◽  
Annual Rainfall ◽  
Rainfall Time Series ◽  
North East ◽  
South West ◽  
Total Annual Rainfall ◽  
Sw Monsoon

This paper discusses the variability in rainfall and trend analysis of annual and seasonal rainfall time series of Shillong and Agartala stations located in the north-east region of India. Commonly used non-parametric statistical methods namely Mann-Kendall and Sen’s slope estimator was used to analyse the seasonal and annual rainfall time series. Statistical analysis showed less variation in annual and south-west monsoon rainfall for both Shillong and Agartala stations. In the total annual rainfall, the share of south-west (SW) monsoon, north-east (NE) monsoon, winter season and summer season rainfall was observed 64.60%, 13.22%, 1.40% and 20.80%, respectively for Shillong station of Meghalaya state. However, the contribution of SW monsoon, NE monsoon, winter season and summer season rainfall in the total annual rainfall was 59.59%, 9.55%, 1.14% and 29.72%, respectively for Agartala station of Tripura state. Non-significant increasing trends of rainfall was observed by 4.54 mm/year, 2.80 mm/year and 2.54 mm/year for annual, SW monsoon, and summer season, whereas, non-significant decreasing trends in rainfall for NE monsoon and winter season was observed with a magnitude of 1.83 mm/year and 1.63 mm/year for Shillong, Meghalaya during 1992 to 2017. Results also revealed that rainfall increased by 1.07 mm/year and 0.18 mm/year in SW monsoon and winter season whereas, rainfall decreased by 7.64 mm/year, 2.58 mm/year and 1.29 mm/year during annual, NE monsoon and summer season non-significantly during 1995 to 2019 in case of Agartala. The findings of present study will be useful for water management and crop planning in hill agriculture of Meghalaya and Tripura state of India.

scholarly journals A stochastic design rainfall generator based on copulas and mass curves

2010 ◽  
Vol 7 (3) ◽  
pp. 3613-3648 ◽  
Author(s):  
S. Vandenberghe ◽  
N. E. C. Verhoest ◽  
E. Buyse ◽  
B. De Baets
Keyword(s):  
Time Series ◽  
Return Period ◽  
Goodness Of Fit ◽  
Rainfall Time Series ◽  
Return Periods ◽  
Rainfall Runoff ◽  
Design Studies ◽  
Design Storm ◽  
Practical Usefulness ◽  
Storm Duration

Abstract. The use of design storms can be very useful in many hydrological and hydraulic practices. In this study, the concept of a copula-based secondary return period in combination with the concept of mass curves is used to generate design storms. The analysis is based on storms selected from the 105 year rainfall time series with a 10 min resolution, measured at Uccle, Belgium. In first instance, bivariate copulas and secondary return periods are explained, together with a focus on which couple of storm variables is of highest interest for the analysis and a discussion of how the results might be affected by the goodness-of-fit of the copula. Subsequently, the fitted copula is used to sample storms with a predefined secondary return period for which characteristic variables such as storm duration and total storm depth can be derived. In order to construct design storms with a realistic storm structure, mass curves of 1st, 2nd, 3rd and 4th quartile storms are developed. An analysis shows that the assumption of independence between the secondary return period and the internal storm structure could be made. Based on the mass curves, a technique is developed to randomly generate an intrastorm structure. The coupling of both techniques eventually results in a methodology for stochastic design storm generation. Finally, its practical usefulness for design studies is illustrated based on the generation of design storm ensembles and rainfall-runoff modelling.

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