Modeling of Sunspot Numbers by a Modified Binary Mixture of Laplace Distribution Functions

Sabarinath, A.; Anilkumar, A. K.

doi:10.1007/s11207-008-9209-5

Cited by 19 publications

(12 citation statements)

References 7 publications

(5 reference statements)

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“…The functions used by Du (2011) and Sabarinath & Anilkumar (2008; the latter takes into account the double peak feature of the solar cycle) led to results that are comparable to those obtained with Eq. (1).…”

Section: Number Of Sunspot Groupssupporting

confidence: 68%

Spot cycle reconstruction: an empirical tool

Santos

Cunha

Avelino

et al. 2015

A&A

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Context. The increasing interest in understanding stellar magnetic activity cycles is a strong motivation for the development of parameterized starspot models which can be constrained observationally. Aims. In this work we develop an empirical tool for the stochastic reconstruction of sunspot cycles, using the average solar properties as a reference. Methods. The synthetic sunspot cycle is compared with the sunspot data extracted from the National Geophysical Data Center, in particular using the Kolmogorov-Smirnov test. This tool yields synthetic spot group records, including date, area, latitude, longitude, rotation rate of the solar surface at the group's latitude, and an identification number. Results. Comparison of the stochastic reconstructions with the daily sunspot records confirms that our empirical model is able to successfully reproduce the main properties of the solar sunspot cycle. As a by-product of this work, we show that the GnevyshevWaldmeier rule, which describes the spots' area-lifetime relation, is not adequate for small groups and we propose an effective correction to that relation which leads to a closer agreement between the synthetic sunspot cycle and the observations.

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Section: Number Of Sunspot Groupssupporting

confidence: 68%

Spot cycle reconstruction: an empirical tool

Santos

Cunha

Avelino

et al. 2015

A&A

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“…where R i is the monthly averaged sunspot number, f i is the functional fit value, s i is the standard deviation for the monthly averaged sunspot number, N is the number of months in the cycle. The analysis provided in Sabarinath and Anilkumar (2008) shows that the BMLD model gives the best fit with minimum error (within the 0.47 standard deviation of the data points) when comparing with various other models available. By considering these aspects, we propose the BMLD function to model the sunspot number cycle.…”

Section: Prediction Improvementmentioning

confidence: 77%

“…The deviation of the prediction from the actual observed data can be improved through the following method. Here an improvement on the proposed prediction technique is by the predicted peak amplitude from a shape model as proposed in Sabarinath and Anilkumar (2008). Here we consider the prediction from the shape model derived from BMLD function.…”

Section: Prediction Improvementmentioning

confidence: 99%

“…Since sunspot number data is available for the last three centuries, model building and analysis can be carried out for sunspot numbers. In the present study, an attempt is being made to predict the sunspot number cycle in a long term as well as in a short term manner using a combination of two models, one derived from a multivariate regression and another one derived from the binary mixture of Laplace distribution (BMLD) function (Sabarinath and Anilkumar 2008). Before developing this hybrid model, in the subsequent section we review the various techniques already available in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Sunspot cycle prediction using multivariate regression and binary mixture of Laplace distribution model

Sabarinath

Anilkumar

2018

J Earth Syst Sci

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Prediction of sunspot cycle is a vital activity in space mission planning and various engineering decision making. In the present study, the sunspot cycle prediction has been carried out by a hybrid model which employs multivariate regression technique and the binary mixture of Laplace distribution (BMLD) function. The Expectation Maximization (EM) algorithm is being applied to the multivariate regression analysis to obtain a robust prediction of the sunspot cycle. Sunspot cycle 24 has been predicted using this technique. Multivariate regression model has been derived based on the available cycles 1 to 23. This model could predict cycle 24 as an average of previous cycles. Prediction from this model has been refined to capture the cycle characteristics such as bimodal peak at the high solar activity period by incorporating a predicted peak sunspot number from the BMLD model. This revised prediction has shown more accuracy in forecasting the major discrete features of sunspot cycle like maximum amplitude, the Gnevyshev gap, time duration from peak to peak amplitude, and the epoch of peak amplitude. This refined prediction shows that cycle 24 will be having a peak amplitude of 78 with an uncertainty of ±25. Moreover, the present forecast says that, cycle 24 will be having double peak with a strong second peak compared to the first peak. This hypothesis is found to be true with the realized data of cycle 24. Further, this techniques have been validated by predicting sunspot cycles 22 and 23. A preliminary level prediction of sunspot cycle 25 also been carried out using the technique presented here. Present study predicts that, cycle 25 also will be a modest cycle like the present cycle 24, and the peak amplitude may vary in a band of 75-95.

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“…When extracting cycle length, rising time, and amplitude information from SSN data, we adopt an approach similar to the two-parameter curve fitting of Hathaway et al (1994; see also Sabarinath andAnilkumar, 2008, andVolobuev, 2009, who propose other functional forms). For cycle i, suppose t (i) 0 is the starting time, t (i) max is the time of the cycle maximum, t (i) 1 is the end time, c i is the amplitude, and U t is a parameter that captures the "average solar activity level" at time t. We postulate that…”

Section: Stage One: Modeling the Cyclesmentioning

confidence: 99%

A Bayesian Analysis of the Correlations Among Sunspot Cycles

Dyk

Kashyap

et al. 2012

Sol Phys

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Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97 +- 15, to occur in January--February 2014 +- 6 months.Comment: Accepted for publication in Solar Physic

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Modeling of Sunspot Numbers by a Modified Binary Mixture of Laplace Distribution Functions

Cited by 19 publications

References 7 publications

Spot cycle reconstruction: an empirical tool

Spot cycle reconstruction: an empirical tool

Sunspot cycle prediction using multivariate regression and binary mixture of Laplace distribution model

A Bayesian Analysis of the Correlations Among Sunspot Cycles

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