# Monthly smoothed total sunspot number

Time range: 1/1749 - last elapsed month (provisional values)

Data description:

The 13-month smoothed monthly sunspot number is derived by a "tapered-boxcar" running mean of monthly sunspot numbers over 13 months centered on the corresponding month (Smoothing function: equal weights = 1, except for first and last elements (-6 and +6 months) = 0.5, Normalization by 1/12 factor). There are no smoothed values for the first 6 months and last 6 months of the data series: columns 4, 5 and 6 are set to -1 (no data).

Choice of smoothing:

This 13-month smoothed series is provided only for backward compatibility with a large number of past publications and methods resting on this smoothed series. It has thus become a base standard (e.g. for the conventional definition of the times of minima and maxima of solar cycles).

However, a wide range of other smoothing functions can be used, often with better low-pass filtering and anti-aliasing properties. As the optimal filter choice depends on the application, we thus invite users to start from the monthly mean Sunspot Numbers and apply the smoothing function that is most appropriate for their analyses. The classical smoothed series included here should only be used when direct comparisons with past published analyses must be made.

Error values:

The standard deviations in this files are obtained from the weighted mean of the variances of the 13 months in the running mean value:

sigma(ms)=sqrt(SUM(weigth(M)*sigma(M)^2)/SUM(weight(M))

where sigma(M) is the standard deviation for a single month, weight(M) is 1 or 0.5 and M=13 in this case.

As successive monthly means are highly correlated, the standard error on the smoothed values can be estimated by the same formula as for a single month: sigma/sqrt(N) where sigma is the listed standard deviation and N the total number of observations in the month.

The number of observations given in column 6 is the number of observations of the corresponding (middle) month: same value SUM N(d) as in the monthly mean file.

This thus gives a smoothed mean of monthly standard deviations, i.e. with the samme low-pass filtering as the data value itself. Further autocorrelation analyses will be needed to derive a conversion of this standard deviation to a standard error of the 13-month smoothed number.

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TXT

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Filename: SN_ms_tot_V2.0.txt

Format: plain ASCII text

Contents:

Column 1-2: Gregorian calendar date

- Year

- Month

Column 3: Date in fraction of year for the middle of the corresponding month

Column 4: Monthly smoothed total sunspot number.

Column 5: Monthly mean standard deviation of the input sunspot numbers.

Column 6: Number of observations used to compute the corresponding monthly mean total sunspot number.

Column 7: Definitive/provisional marker. A blank indicates that the value is definitive. A '*' symbol indicates that the monthly value is still provisional and is subject to a possible revision (Usually the last 3 to 6 months)

Line format [character position]:

- [1-4] Year

- [6-7] Month

- [9-16] Decimal date

- [19-23] Smoothed total sunspot number

- [25-29] Standard deviation

- [32-35] Number of observations

- [37] Definitive/provisional indicator

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CSV

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Filename: SN_ms_tot_V2.0.csv

Format: Comma Separated values (adapted for import e.g. in MS Excel)

Contents:

Column 1-2: Gregorian calendar date

- Year

- Month

Column 3: Date in fraction of year

Column 4: Monthly smoothed total sunspot number.

Column 5: Monthly mean standard deviation of the input sunspot numbers.

Column 6: Number of observations used to compute the corresponding monthly mean total sunspot number.

Column 7: Definitive/provisional marker.'1' indicates that the value is definitive. '0' indicates that the value is still provisional.