A Kalman Filter Technique for Improving Medium-Term Predictions of the Sunspot Number

Podladchikova, Tatiana; Linden, Ruud van der

doi:10.1007/s11207-011-9899-y

Cited by 19 publications

(14 citation statements)

References 10 publications

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“…A large number of methods are based on finding a particular sunspot number precursor in the past, which can serve as an indicator for the amplitude of the upcoming solar cycle (e.g. Waldmeier 1935;Ramaswamy 1977;Macpherson et al 1995;Conway 1998;Sello 2001;Lantos 2006;Cameron & Schüssler 2008;Podladchikova et al 2008Podladchikova et al , 2017Aguirre et al 2008;Brajša et al 2009;Podladchikova & Van der Linden 2011;Kakad et al 2020). Other types of precursor methods are based on the polar magnetic fields (e.g.…”

Section: Discussionmentioning

confidence: 99%

Hemispheric sunspot numbers 1874–2020

Veronig

Jain

Podladchikova

et al. 2021

A&A

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Context. Previous studies show significant north-south asymmetries for various features and indicators of solar activity. These findings suggest some decoupling between the two hemispheres over the solar cycle evolution, which is in agreement with dynamo theories. For the most important solar activity index, the sunspot numbers, so far only limited data are available for the two hemispheres independently. Aims. The aim of this study is to create a continuous series of daily and monthly hemispheric sunspot numbers (HSNs) from 1874 to 2020, which will be continuously expanded in the future with the HSNs provided by SILSO. Methods. Based on the available daily measurements of hemispheric sunspot areas from 1874 to 2016 from Greenwich Royal Observatory and National Oceanic and Atmospheric Administration (NOAA), we derive the relative fractions of the northern and southern activity. These fractions are applied to the international sunspot number (ISN) to derive the HSNs. This method and obtained data are validated against published HSNs for the period 1945-2004 and those provided by SILSO for 1992 to 2016. Results. We provide a continuous data series and catalogue of daily, monthly mean, and 13-month smoothed monthly mean HSNs for the time range 1874-2020 -fully covering solar cycles 12 to 24-that are consistent with the newly calibrated ISN (Clette et al. 2014). Validation of the reconstructed HSNs against the direct data available since 1945 reveals a high level of consistency, with Pearson correlation coefficients of r = 0.94 (0.97) for the daily (monthly mean) data. The cumulative hemispheric asymmetries for cycles 12-24 give a mean value of 16%, with no obvious pattern in north-south predominance over the cycle evolution. The strongest asymmetry occurs for cycle no. 19, in which the northern hemisphere shows a cumulated predominance of 42%. The phase shift between the peaks of solar activity in the two hemispheres may be up to 28 months, with a mean absolute value over cycles 12-24 of 16.4 months. The phase shifts reveal an overall asymmetry of the northern hemisphere reaching its cycle maximum earlier (in 10 out of 13 cases), with a mean signed phase shift of −7.6 months. Relating the ISN and HSN peak growth rates during the cycle rise phase with the cycle amplitude reveals higher correlations when considering the two hemispheres individually, with r ≈ 0.9. Conclusions. Our findings provide further evidence that to some degree the solar cycle evolves independently in the two hemispheres, and demonstrate that empirical solar cycle prediction methods can be improved by investigating the solar cycle dynamics in terms of the HSN evolution.

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Section: Discussionmentioning

confidence: 99%

Hemispheric sunspot numbers 1874–2020

Veronig

Jain

Podladchikova

et al. 2021

A&A

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“…In our previous studies (Podladchikova et al 2008), we demonstrated the importance of sunspot number variability during the declining phase of the sunspot cycle to predict the peak of the ensuing cycle. The analysis revealed that a slow decline and short-term rise of the sunspot number during the declining phase, can be viewed as a presage to a stronger peak of the following cycle.…”

Section: Introductionmentioning

confidence: 88%

Sunspot Number Second Differences as a Precursor of the Following 11-year Sunspot Cycle

Podladchikova

Linden²,

Veronig

2017

ApJ

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Forecasting the strength of the sunspot cycle is highly important for many space weather applications. Our previous studies have shown the importance of sunspot number variability in the declining phase of the current 11-year sunspot cycle to predict the strength of the next cycle when the minimum of the current cycle has been observed. In this study we continue this approach and show that we can remove the limitation of having to know the minimum epoch of the current cycle, and that we can already provide a forecast of the following cycle strength in the early stage of the declining phase of the current cycle. We introduce a method to reliably calculate sunspot number second differences (SNSD) in order to quantify the short-term variations of sunspot activity. We demonstrate a steady relationship between the SNSD dynamics in the early stage of the declining phase of a given cycle and the strength of the following sunspot cycle. This finding may bear physical implications on the underlying dynamo at work. From this relation, a relevant indicator is constructed that distinguishes whether the next cycle will be stronger or weaker compared to the current one. We demonstrate that within 24-31 months after reaching the maximum of the cycle, it can be decided with high probability (0.96) whether the next cycle will be weaker or stronger. We predict that sunspot cycle 25 will be weaker than the current cycle 24.

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“…We develop this approach to noise statistics identification for a nonstationary dynamical system disturbed by white noise with unknown biased mathematical expectation of model noise. Most recently, Podladchikova and Van der Linden [] used the same approach to estimate unknown noise statistics of the model describing the 11 year sunspot cycle.…”

Section: The Essence Of Proposed Approachmentioning

confidence: 99%

Noise statistics identification for Kalman filtering of the electron radiation belt observations I: Model errors

et al. 2014

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In this study we present a first attempt to identify errors of the 1-D radial diffusion model for relativistic electron phase space density (PSD). In practice, the model error and characteristics of satellite observations are poorly known, which may cause failure of a Kalman filter algorithm. Correct specification of model errors statistics is necessary for the development of the next generation of radiation belt specification models providing the effective PSD reconstruction and hence the prediction and mitigation of space weather effects in the hazardous space environment. The proposed approach to the identification of errors statistics is based on estimating the unknown bias and the covariance matrix of model errors from the sparse CRRES observations over a period of 441 days, from 28 July 1990 to 11 October 1991. With our technique we demonstrate that model errors are biased. Neglecting the bias when applying a data assimilation algorithm to radiation belt electrons can cause significant errors of the PSD estimate during data gaps. Both the identified bias and the covariance matrix of model errors increase with increase of L shell. Sensitivity of the PSD reconstruction to model errors statistics and advances of the improved physical-based model based on the model errors identification are illustrated by a number of representative examples of the PSD reanalysis. Identification of satellite observations characteristics, and filtration and smoothing algorithms are discussed in the companion paper.

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A Kalman Filter Technique for Improving Medium-Term Predictions of the Sunspot Number

Cited by 19 publications

References 10 publications

Hemispheric sunspot numbers 1874–2020

Hemispheric sunspot numbers 1874–2020

Sunspot Number Second Differences as a Precursor of the Following 11-year Sunspot Cycle

Noise statistics identification for Kalman filtering of the electron radiation belt observations I: Model errors

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