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Journal ArticleDOI

The Applicability of Bipartite Graph Model for Thunderstorms Forecast over Kolkata

31 Dec 2009-Advances in Meteorology (Hindawi)-Vol. 2009, pp 50-61
TL;DR: In this article, a single spectrum bipartite graph connectivity model was developed to forecast thunderstorms over Kolkata during the premonsoon season (April-May) and the statistical distribution of normal probability was observed for temperature, relative humidity, convective available potential energy (CAPE), and convective inhibition energy (CIN) to quantify the threshold values of the parameters for the prevalence of thunderstorms.
Abstract: Single Spectrum Bipartite Graph (SSBG) model is developed to forecast thunderstorms over Kolkata during the premonsoon season (April-May). The statistical distribution of normal probability is observed for temperature, relative humidity, convective available potential energy (CAPE), and convective inhibition energy (CIN) to quantify the threshold values of the parameters for the prevalence of thunderstorms. Method of conditional probability is implemented to ascertain the possibilities of the occurrence of thunderstorms within the ranges of the threshold values. The single spectrum bipartite graph connectivity model developed in this study consists of two sets of vertices; one set includes two time vertices (00UTC, 12UTC) and the other includes four meteorological parameters: temperature, relative humidity, CAPE, and CIN. Three distinct ranges of maximal eigen values are obtained for the three categories of thunderstorms. Maximal eigenvalues for severe, ordinary, and no thunderstorm events are observed to be , , and , respectively. The ranges of the threshold values obtained using ten year data (1997–2006) are considered as the reference range and the result is validated with the IMD (India Meteorological Department) observation, Doppler Weather Radar (DWR) Products, and satellite images of 2007. The result reveals that the model provides 12- to 6-hour forecast (nowcasting) of thunderstorms with 96% to 98% accuracy.

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Citations
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TL;DR: In this paper, the maximum possible value of the terminal Mostar index among all trees of order $n$ is shown to be only attained by the star and not by the whole tree.
Abstract: We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a conjecture on the maximum possible Mostar index of bipartite graphs from (Do\v{s}li\'{c} et al, Journal of Mathematical Chemistry, 2018) and (Ali and Do\v{s}li\'{c}, Applied Mathematics and Computation, 2021). We also correct a result from the latter paper, where they claimed that the maximum possible value of the terminal Mostar index among all trees of order $n$ is $(n-1)(n-2)$. We show that this maximum is $(n-1)(n-3)$ for $n \ge 3$, and that it is only attained by the star. We asymptotically answer another problem on the maximum difference between the Mostar index and the irregularity of trees from (F. Gao et al, On the difference of Mostar index and irregularity of graphs, Bulletin of the Malaysian Mathematical Sciences Society, 2021). We also prove a number of extremal bounds and computational complexity results about the Mostar index, irregularity, and measures of peripherality and centrality. We discuss graphs where the Mostar index is not an accurate measure of peripherality. We construct a general family of graphs with the property that the Mostar index is strictly greater for edges that are closer to the center. We also investigate centrality and peripherality in two graphs which represent the SuperFast and MOZART-4 systems of atmospheric chemical reactions by computing various measures of peripherality and centrality for the vertices and edges in these graphs. For both of these graphs, we find that the Mostar index is closer to a measure of centrality than peripherality of the edges. We also introduce some new indices which perform well as measures of peripherality on the SuperFast and MOZART-4 graphs.

2 citations

01 Feb 2011
TL;DR: In this paper, an attempt has been made to down scale coarse-resolution numerical weather prediction (NWP) based meteorological parameters to fine resolution products for ecological studies at regional scale.
Abstract: A general problem with output from weather forecasting models is that modeled variables often do not compare well with ground-based weather variables and complex downscaling procedures are necessary to convert Numerical Weather Prediction (NWP) weather variables into realistic weather variables on the ground. NWP models have now firmly established as major forecasting tool and there is increasing use of Ensemble Prediction Systems (EPS) based probabilistic information in support of decision-making by forecasters as well as other special users. However, the challenges in down scaling the model forecasts, normally applicable for a grid area commensurable with the model resolution, to a meaningful location-specific product are by no means trivial. An attempt has been made in this study to down scale coarse resolution NWP based meteorological parameters to fine resolution products. The meteorological parameters considered for this study are temperature and downward surface shortwave radiation (DSSR) as important for ecological studies at regional scale. The comparisons have been carried out for the DSSR and temperature from satellite with that of in situ data. The NWP based fine grid data were found to be in good agreement with satellite and in situ data as compared to that of coarse resolution NWP parameters. The variations of these remapped fine grid parameters have also been studied at local and regional scale over India.

2 citations

Journal ArticleDOI
TL;DR: In this paper , it was shown that the Mostar index is closer to a measure of centrality than peripherality of the edges of a graph than of the vertices of the graph.
Abstract: We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a conjecture on the maximum possible Mostar index of bipartite graphs. We asymptotically answer another problem on the maximum difference between the Mostar index and the irregularity of trees. We also prove a number of extremal bounds and computational complexity results about the Mostar index, irregularity, and measures of peripherality and centrality. We discuss graphs where the Mostar index is not an accurate measure of peripherality. We construct a general family of graphs with the property that the Mostar index is strictly greater for edges that are closer to the center. We also investigate centrality and peripherality in two graphs which represent the SuperFast and MOZART-4 systems of atmospheric chemical reactions by computing various measures of peripherality and centrality for the vertices and edges in these graphs. For both of these graphs, we find that the Mostar index is closer to a measure of centrality than peripherality of the edges. We also introduce some new indices which perform well as measures of peripherality on the SuperFast and MOZART-4 graphs.

2 citations

Journal ArticleDOI
TL;DR: In this article, a heuristic equation is proposed which relates the correlation coefficient of atmospheric parameters with the number of hourly incidences of thunderstorms, and four indices are used to compute the indices values from the proposed equation.
Abstract: Prediction of incidences of thunderstorms using different techniques is quite well established. To add to this knowledge, in this paper, a heuristic equation is proposed which relates the correlation coefficient of atmospheric parameters with the number of hourly incidences of thunderstorms. There are four ways to compute the indices values from the proposed heuristic equation. These indices values are used in the classification of the hourly incidences of thunderstorms. The proposed equation and indices work well, as tested on pre-monsoon hourly atmospheric data from 2018 and validated with hourly data from April 2019 and 2020. From the four indices, the first index value is computed with normalized average values of parameters of only hourly incidence of thunderstorms data of 2016-2017 in the month-wise method. The other three indices use optimization techniques namely, the Teaching Learning Based Optimization (TLBO) technique, Differential Evaluation (DE), and Simulated Annealing (SA). TLBO shows better classification of hourly incidences of thunderstorms for 2018 atmospheric data. TLBO is also precisely validating the hourly incidences of thunderstorms for April 2019 and April 2020 hourly atmospheric data. It performed better with 2020 data by 88%. The variations of atmospheric parameters before, after or, during the incidences of thunderstorms are also depicted.

1 citations

Journal Article
TL;DR: In this article, the stability indices that are relevant and useful for convective development are taken to assess the significance in forecasting severe thunderstorms over Kolkata (22° 34'N, 88° 22'E).
Abstract: In the present study the stability indices that are relevant and useful for convective development are taken to assess the significance in forecasting severe thunderstorms over Kolkata (22° 34'N, 88° 22'E). A tree-graph is constructed using the stability indices and the record of severe thunderstorm as vertices. Weights of the edges of different indices are attributed according to two forecast skills. Probability of Detection (POD) and False Alarm Rate (FAR). Two tree-graphs are thus constructed. The most significant and relevant stability indices are obtained using the sub-graph matching analysis. The results reveal that among all the stability indices the lifted index (LI) and the convective inhibition energy (CIN) with the estimated ranges are the most significant stability indices for forecasting severe thunderstorm over Kolkata whereas dew point temperature (Td), convective available potential energy (CAPE) and bulk Richardson number (BRN) are important for indicating the convective development over the region but the occurrence of severe thunderstorms are not assured by these three indices with the estimated ranges.

1 citations

References
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Journal ArticleDOI
TL;DR: In this article, statistical methods in the Atmospheric Sciences are used to estimate the probability of a given event to be a hurricane or tropical cyclone, and the probability is determined by statistical methods.
Abstract: (2007). Statistical Methods in the Atmospheric Sciences. Journal of the American Statistical Association: Vol. 102, No. 477, pp. 380-380.

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"The Applicability of Bipartite Grap..." refers methods in this paper

  • ...The normal probability distribution function [23] is used as the statistical tool to identify the most probable range of values of the selected input parameters (T , Rh, CAPE, CIN) for the occurrence of thunderstorms (Table 1)....

    [...]

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TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
Abstract: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigenvalues and quasi-randomness Expanders and explicit constructions Eigenvalues of symmetrical graphs Eigenvalues of subgraphs with boundary conditions Harnack inequalities Heat kernels Sobolev inequalities Advanced techniques for random walks on graphs Bibliography Index.

6,948 citations


"The Applicability of Bipartite Grap..." refers background in this paper

  • ...Some eigenvalues have been referred to as the algebraic connection patterns of a graph [25]....

    [...]

Book
01 May 1997
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Abstract: Gaph Teory Fourth Edition Th is standard textbook of modern graph theory, now in its fourth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each fi eld by one or two deeper results, again with proofs given in full detail.

6,255 citations


"The Applicability of Bipartite Grap..." refers background in this paper

  • ...There are different lemmas and propositions of spectral graph theory to study the variation characterization of Eigen values, their bounds, and orientations [26]....

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Journal ArticleDOI
TL;DR: This paper presents a general introduction and discussion of recent applications of the multilayer perceptron, one type of artificial neural network, in the atmospheric sciences.

2,389 citations

Journal ArticleDOI
TL;DR: In this article, the preconvective environment on thunderstorm days in Switzerland north of the Alps has been investigated during a 5-yr period (1985-89) using thermodynamic and kinematic parameters calculated from the radiosounding in Payerne (started at 0000 and 1200 UTC) were used to characterize the initiation of convection.
Abstract: The preconvective environment on thunderstorm days in Switzerland north of the Alps has been investigated during a 5-yr period (1985–89). Thermodynamic and kinematic parameters calculated from the radiosounding in Payerne (started at 0000 and 1200 UTC) were used to characterize the initiation of convection. The best parameters were evaluated by using three methods: 1) skill scores, 2) probability distributions, and 3) mean temperature soundings and hodographs. For the decision whether a thunderstorm day was expected or not, the best results were obtained at 0000 UTC with the original Showalter index and at 1200 UTC with the SWEAT index. In addition, to decide whether an isolated or widespread thunderstorm day was expected, the most successful parameter was the modified CAPECCL. Furthermore, the best thermodynamic and kinematic parameters were combined to create new thunderstorm indices, similar to the calculations of the SWEAT index in the United States. The new thunderstorm indices especially de...

130 citations