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 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 Cascade Rainfall Disaggregation Application in U.S. Central Plains

2017 ◽  
Vol 7 (4) ◽  
pp. 30 ◽  
Author(s):  
Jurgen D. Garbrecht ◽  
Rabi Gyawali ◽  
Robert W. Malone ◽  
John C. Zhang
Keyword(s):  
Time Series ◽  
Model Performance ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Rainfall Time Series ◽  
Random Component ◽  
Rainfall Characteristics ◽  
Hourly Rainfall ◽  
Replicated Observations

Long-term observations of daily rainfall are common and routinely available for a variety of hydrologic applications. In contrast, observations of 10 or more years of continuous hourly rainfall are rare. Yet, sub-daily rainfall data are required in rainfall-runoff models. Rainfall disaggregation can generate sub-daily time-series from available long term daily observations. Herein, the performance of Multiplicative Random Cascade (MRC) model at disaggregating daily-to-hourly rainfall was investigated. The MRC model was parameterized and validated with 15 years of continuous observed daily and hourly rainfall data at three weather stations in Oklahoma. Model performance, or degree to which the disaggregated rainfall time series replicated observations, was assessed using 46 variables of hourly rainfall characteristics, such as longest wet spell duration, average number of rainfall hours per year, and largest hourly rainfall. Findings include: a) average-type hourly rainfall characteristics were better replicated than single value characteristics such as longest, maximum, or peak hourly rainfall; b) the large number of sub-trace hourly rainfall values (<0.254 mm h-1) generated by the MRC model were not supported by observations; c) the random component of the MRC model led to a variation under 15% of the average value for most rainfall characteristics with the exceptions of the “longest wet spell duration” and “maximum hourly rainfall”; and d) the MRC model produced fewer persistent rainfall events compared to those in the observed rainfall record. The large number of generated trace rainfall values and difficulties to replicate reliably extreme rainfall characteristics, reduces the number of potential hydrologic applications that could take advantage of the MRC disaggregated hourly rainfall. Nevertheless, in most cases, the disaggregated rainfall generated by the MRC model replicated observed average-type rainfall characteristics well.

Disaggregation of Daily Rainfall into Hourly Rainfall in an Ungauged Urban Catchment

2021 ◽  
Author(s):  
Ashutosh Pati ◽  
Ravindra Kale ◽  
Bhabagrahi Sahoo
Keyword(s):  
Time Series ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Rainfall Time Series ◽  
Urban Flooding ◽  
Validation Period ◽  
Calibration And Validation ◽  
Method Of Fragments ◽  
Hourly Rainfall ◽  
Daily Scale

&lt;p&gt;Nowadays, most of the urban cities and their surrounding ambiances are facing increasing flooding issues. Many times, the cause of urban flooding is improper drainage under increasing rainfall intensity. To properly monitor and manage the drainage system in urban areas, high-resolution rainfall data is required to model the flooding scenarios a priori. However, the high-resolution rainfall data in urban regions to address the urban flooding issues are rarely available, especially in developing countries. To overcome this problem, many studies suggest the use of hourly scale IMERG-FR (Integrated Multi-satellitE Retrievals for GPM-Final Run) data which exhibits good agreement with the ground-truth rainfall measurements. Therefore, this study attempts to utilize area-averaged IMERG-FR hourly data over Bhubaneswar, a data-scarce urban area of eastern India as a benchmark for assessing the performance of six parametric (Bartlett-Lewis Model, BL) and a nonparametric (Method of Fragments, MOF) approaches disaggregating daily scale IMD (India Meteorological Department) rainfall data into hourly scale data. The performance of the considered approaches is evaluated by disaggregating the monsoon months (June-October) rainfall timeseries data for the period 2001-2015 by adopting performance criteria such as root mean square error (RMSE) and percent bias (PBIAS). The rainfall time series data from 2001-2010 and 2011-2015 were used for calibration and validation of the proposed approaches, respectively.&lt;/p&gt;&lt;p&gt;The obtained RMSE values in the case of the BL approach during calibration and validation period were 2.53 mm and 2.04 mm, respectively. Similarly, RMSE values in the case of the MOF approach during the calibration and validation period were 2.5 mm and 1.87 mm, respectively. This comparison suggests the both of these approaches exhibit nearly the same performance during the calibration period whereas the MOF approach was slightly better than BL during the validation period. The PBIAS estimates for the MOF approach were around -6.6% and 17.3% during the calibration and validation period, respectively, whereas the PBIAS estimates for the BL approach were around 11.25% for calibration and -11.25% for the validation period. From the present evaluation, it could be concluded that though the MOF approach exhibits slightly better performance in terms of RMSE, the BL approach can provide a more balanced performance in terms of PBIAS. As the MOF is a non-parametric approach, it can be applied to a lesser length of daily rainfall time series for disaggregation whereas the BL approach can perform well when its parameters are derived using a good length of rainfall series. Conclusively, this study summarizes the applicability of the BL and MOF approaches for disaggregating course resolution daily scale rainfall to hourly rainfall for the monsoon months in Bhubaneswar using IMERG-FR hourly rainfall data as a benchmark.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Keywords: &lt;/strong&gt;Rainfall; Rainfall disaggregation; Bartlett-Lewis Model (BL); Method of Fragments (MOF); IMERG-FR; IMD.&lt;/p&gt;

scholarly journals Performance of TRMM TMPA 3B42 V7 in Replicating Daily Rainfall and Regional Rainfall Regimes in the Amazon Basin (1998–2013)

2018 ◽  
Vol 10 (12) ◽  
pp. 1879 ◽  
Author(s):  
Véronique Michot ◽  
Daniel Vila ◽  
Damien Arvor ◽  
Thomas Corpetti ◽  
Josyane Ronchail ◽  
...  
Keyword(s):  
Amazon Basin ◽  
Daily Rainfall ◽  
Rain Gauge ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Spatial Coverage ◽  
Rainfall Regimes ◽  
Trmm 3B42 ◽  
Good Agreement

Knowledge and studies on precipitation in the Amazon Basin (AB) are determinant for environmental aspects such as hydrology, ecology, as well as for social aspects like agriculture, food security, or health issues. Availability of rainfall data at high spatio-temporal resolution is thus crucial for these purposes. Remote sensing techniques provide extensive spatial coverage compared to ground-based rainfall data but it is imperative to assess the quality of the estimates. Previous studies underline at regional scale in the AB, and for some years, the efficiency of the Tropical Rainfall Measurement Mission (TRMM) 3B42 Version 7 (V7) (hereafter 3B42) daily product data, to provide a good view of the rainfall time variability which is important to understand the impacts of El Nino Southern Oscilation. Then our study aims to enhance the knowledge about the quality of this product on the entire AB and provide a useful understanding about his capacity to reproduce the annual rainfall regimes. For that purpose we compared 3B42 against 205 quality-controlled rain gauge measurements for the period from March 1998 to July 2013, with the aim to know whether 3B42 is reliable for climate studies. Analysis of quantitative (Bias, Relative RMSE) and categorical statistics (POD, FAR) for the whole period show a more accurate spatial distribution of mean daily rainfall estimations in the lowlands than in the Andean regions. In the latter, the location of a rain gauge and its exposure seem to be more relevant to explain mismatches with 3B42 rather than its elevation. In general, a good agreement is observed between rain gauge derived regimes and those from 3B42; however, performance is better in the rainy period. Finally, an original way to validate the estimations is by taking into account the interannual variability of rainfall regimes (i.e., the presence of sub-regimes): four sub-regimes in the northeast AB defined from rain gauges and 3B42 were found to be in good agreement. Furthermore, this work examined whether TRMM 3B42 V7 rainfall estimates for all the grid points in the AB, outgoing longwave radiation (OLR) and water vapor flux patterns are consistent in the northeast of AB.

scholarly journals Architecture of Artificial Neural Network in Identification of Internal Dynamics and Prediction of Dynamic System Rainfall Data Time Series

2012 ◽  
pp. 34-42
Author(s):  
Sanjeev Karmakar ◽  
Manoj Kumar Kowar ◽  
Pulak Guhathakurta
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Dynamic System ◽  
Long Range ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Global Minima ◽  
Internal Dynamics ◽  
Artificial Neural

The objective of this study is to expand and evaluate the back-propagation artificial neural network (BPANN) and to apply in the identification of internal dynamics of very high dynamic system such long-range total rainfall data time series. This objective is considered via comprehensive review of literature (1978-2011). It is found that, detail of discussion concerning the architecture of ANN for the same is rarely visible in the literature; however various applications of ANN are available. The detail architecture of BPANN with its parameters, i.e., learning rate, number of hidden layers, number of neurons in hidden layers, number of input vectors in input layer, initial and optimized weights etc., designed learning algorithm, observations of local and global minima, and results have been discussed. It is observed that obtaining global minima is almost complicated and always a temporal nervousness. However, achievement of global minima for the period of the training has been discussed. It is found that, the application of the BPANN on identification for internal dynamics and prediction for the long-range total annual rainfall has produced good results. The results are explained through the strong association between rainfall predictors i.e., climate parameter (independent parameter) and total annual rainfall (dependent parameter) are presented in this paper as well.

scholarly journals Bayesian Time Series Modelling of the Italian Daily Rainfall Data using Mixed Distribution

2019 ◽  
Vol 8 (4) ◽  
pp. 2279-2288
Keyword(s):  
Time Series ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Seasonal Effects ◽  
Model Parameters ◽  
Daily Rainfall Data ◽  
Mixed Distribution ◽  
Time Series Modelling ◽  
Bayesian Time Series ◽  
The Ideal

A combination of continuous and discrete elements is referred to as a mixed distribution. For example, daily rainfall data consist of zero and positive values. We aim to develop a Bayesian time series model that captures the evolution of the daily rainfall data in Italy, focussing on directly linking the amount and occurrence of rainfall. Two gamma (G1 and G2) distributions with different parameterisations and lognormal distribution were investigated to identify the ideal distribution representing the amount process. Truncated Fourier series was used to incorporate the seasonal effects which captures the variability in daily rainfall amounts throughout the year. A first-order Markov chain was used to model rainfall occurrence conditional on the presence or absence of rainfall on the previous day. We also built a hierarchical prior structure to represent our subjective beliefs and capture the initial uncertainties of the unknown model parameters for both amount and occurrence processes. The daily rainfall data from Urbino rain gauge station in Italy were then used to demonstrate the applicability of our proposed methods. Residual analysis and posterior predictive checking method were utilised to assess the adequacy of model fit. In conclusion, we clearly found that our proposed method satisfactorily and accurately fits the Italian daily rainfall data. The gamma distribution was found to be the ideal probability density function to represent the amount of daily rainfall.

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.

scholarly journals Validation of Daily Rainfall Based on Global Satellite Mapping of Precipitation (GSMAP) Data of Bali and Nusa Tenggara Region

2018 ◽  
Vol 19 (1) ◽  
pp. 12
Author(s):  
Sanjaya Natadiredja ◽  
I Ketut Sukarasa ◽  
Gusti Ngurah Sutapa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Satellite Data ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Observation Data ◽  
Similar Data ◽  
Strong Positive Correlation ◽  
Cause Analysis ◽  
Satellite Rainfall

Limitations of observation data cause analysis and prediction of precipitation is difficult. One way to overcome such limitations is the use of satellite data such as GSMaP, but satellite data needs to be validated before use. This study aims to validate GSMaP rainfall data on observation data in Bali and Nusa Tenggara. Through monthly time series analysis, GSMaP rainfall data tend to have smaller value than observation data, but it has similar data pattern in each region with rain pattern that occurs in November to March (NDJFM). While validation between GSMaP satellite rainfall data and observation using Pearson and RMSE correlation and MBE at each location showed strong positive correlation value (> 0.5), correlation value obtained from each location from 0.82 to 0.93 with RMSE value from 2.08 to 5.51 and MBE values ??from 0.23 to 0.89, this indicates that GSMaP satellite data is valid and can be used to fill in empty data especially in 5 observation areas ie Denpasar, Ampenan, Sumbawa Besar, Bima and Kupang.

Sign in / Sign up

Export Citation Format

Share Document