Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

Benavides-Bravo, Francisco Gerardo; Almaguer, F-Javier; Soto-Villalobos, Roberto; Tercero-Gómez, Víctor G.; Morales-Castillo, Javier

doi:10.1155/2015/629254

Cited by 5 publications

(6 citation statements)

References 28 publications

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“…Let a rainfall time series {X t , t ≥ 0} (in mm); we define the variogram γ(h) as in [21,34] (they defined the variogram without the square root):…”

Section: Experimental Variogramsmentioning

confidence: 99%

“…The scale is then defined by h; from the minimal distance value, increasing h allows the quantitative representation of long-term variations in the hydrological series. A critical remark is that Equation (5) works on the average of the differences (X(t + h) − X(t)), so that it only depends on the interval h. Consequently , for a given times series located at a fixed point in the space, the trend or the persistence of such series is only characterized by h. Now, the discrete version of Equation ( 5) can be written as [34]:…”

Section: Experimental Variogramsmentioning

confidence: 99%

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A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

et al. 2021

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Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

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“…Let a rainfall time series {X t , t ≥ 0} (in mm); we define the variogram γ(h) as in [21,34] (they defined the variogram without the square root):…”

Section: Experimental Variogramsmentioning

confidence: 99%

Section: Experimental Variogramsmentioning

confidence: 99%

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

et al. 2021

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“…. , d, have a length of m. Then, according to [36,37], the following steps are carried out for each subseries:…”

Section: Hurst Exponent (Hrs)mentioning

confidence: 99%

“…, k} is the interval time of that subseries, and k max is the total number of subseries used. In this work, we used k max = 8, which is a significant number about an intermediate value between the Köppen classification by semesters [35] and the annual periodicity of the phenomenon in the region [37]. In addition, we carried out the calculation of HFD with several k max , obtaining that k max = 8 gave the best relation between HFD and climate in terms of better limits between clusters, see Table A1 in Appendix A.…”

Section: Higuchi Fractal Dimension (Hfd)mentioning

confidence: 99%

A Climate-Mathematical Clustering of Rainfall Stations in the Río Bravo-San Juan Basin (Mexico) by Using the Higuchi Fractal Dimension and the Hurst Exponent

et al. 2021

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When conducting an analysis of nature’s time series, such as meteorological ones, an important matter is a long-range dependence to quantify the global behavior of the series and connect it with other physical characteristics of the region of study. In this paper, we applied the Higuchi fractal dimension and the Hurst exponent (rescaled range) to quantify the relative trend underlying the time series of historical data from 17 of the 34 weather stations located in the Río Bravo-San Juan Basin, Mexico; these data were provided by the National Water Commission CONAGUA) in Mexico. In this way, this work aims to perform a comparative study about the level of persistency obtained by using the Higuchi fractal dimension and Hurst exponent for each station of the basin. The comparison is supported by a climate clustering of the stations, according to the Köppen classification. Results showed a better fitting between the climate of each station and its Higuchi fractal dimension obtained than when using the Hurst exponent. In fact, we found that the more the aridity of the zone the more the persistency of rainfall, according to Higuchi’s values. In turn, we found more relation between the Hurst exponent and the accumulated amount of rainfall. These are relations between the climate and the long-term persistency of rainfall in the basin that could help to better understand and complete the climatological models of the study region. Trends between the fractal exponents used and the accumulated annual rainfall were also analyzed.

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“…This analysis should reveal the differences in the selected clusters for streamflow. The combination of such a clustering method and information measures can be a useful tool for time series modeling, interpolation, and data mining; delineation of homogeneous hydrometeorological regions; catchment classification; regionalization of catchments for flood frequency analysis and prediction in ungauged basins; and hydrological modeling, flood forecasting, and estimation of predictive uncertainty [ 5 , 6 , 7 , 8 , 9 ]; among others. In the agglomerative hierarchical approach, we define each data point as a cluster and combine existing clusters at each step.…”

Section: Introductionmentioning

confidence: 99%

The Choice of an Appropriate Information Dissimilarity Measure for Hierarchical Clustering of River Streamflow Time Series, Based on Calculated Lyapunov Exponent and Kolmogorov Measures

Mihailoviĉ

Nikolić-Đorić

Malinović-Milićević

et al. 2019

Entropy

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The purpose of this paper was to choose an appropriate information dissimilarity measure for hierarchical clustering of daily streamflow discharge data, from twelve gauging stations on the Brazos River in Texas (USA), for the period 1989–2016. For that purpose, we selected and compared the average-linkage clustering hierarchical algorithm based on the compression-based dissimilarity measure (NCD), permutation distribution dissimilarity measure (PDDM), and Kolmogorov distance (KD). The algorithm was also compared with K-means clustering based on Kolmogorov complexity (KC), the highest value of Kolmogorov complexity spectrum (KCM), and the largest Lyapunov exponent (LLE). Using a dissimilarity matrix based on NCD, PDDM, and KD for daily streamflow, the agglomerative average-linkage hierarchical algorithm was applied. The key findings of this study are that: (i) The KD clustering algorithm is the most suitable among others; (ii) ANOVA analysis shows that there exist highly significant differences between mean values of four clusters, confirming that the choice of the number of clusters was suitably done; and (iii) from the clustering we found that the predictability of streamflow data of the Brazos River given by the Lyapunov time (LT), corrected for randomness by Kolmogorov time (KT) in days, lies in the interval from two to five days.

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Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

Cited by 5 publications

References 28 publications

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

A Climate-Mathematical Clustering of Rainfall Stations in the Río Bravo-San Juan Basin (Mexico) by Using the Higuchi Fractal Dimension and the Hurst Exponent

The Choice of an Appropriate Information Dissimilarity Measure for Hierarchical Clustering of River Streamflow Time Series, Based on Calculated Lyapunov Exponent and Kolmogorov Measures

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