<p>The effective sunspot number $R_{\text{eff}}$ is calculated through a mix of observations and model calculations. It focuses primarily on some parameter called the frequency of the <a href="https://en.wikipedia.org/wiki/F_region" rel="nofollow">ionosphere F2 layer</a>, denoted $\text{foF2}$, the highest frequency of electromagnetic radiation which can be reflected off the F2 layer; it can be observed as well as computed based on a certain model (real-time observational data from stations around the world is available <a href="http://www.ngdc.noaa.gov/stp/IONO/rt-iono/realtime/RealTime_foF2.html" rel="nofollow">here</a>). More information on $\text{foF2}$ can be found on <a href="https://spawx.nwra.com/spawx/fof2/fof2.html" rel="nofollow">this page</a>.</p>

<p>The mean-squared error between the observational value $\text{foF2}_{\text{obs}}$ and the calculated value $\text{foF2}_{\text{calc}}$ over observations by $n$ stations is
$$\Delta=\frac{1}{n}\sum_{i=1}^n\left(\text{foF2}_{\text{obs},i}-\text{foF2}_{\text{calc},i}\right)^2$$
where $_i$ denotes the value at station $i$. $R_\text{eff}$ is defined to be that chosen sunspot number such that $\Delta$ is minimized.</p>

<p>This is just an application of a <a href="https://en.wikipedia.org/wiki/Least_squares" rel="nofollow">least squares</a> method to fit a model framework to match observations. An example of this using the Simplified Ionospheric Regional Model (SIRM) is <a href="http://onlinelibrary.wiley.com/doi/10.1029/2003RS002936/pdf" rel="nofollow">Zolesi et al. (2004)</a>, although the procedure for calculating $R_\text{eff}$ was first proposed by <a href="http://adsabs.harvard.edu/abs/1993JEEEA..13...99H" rel="nofollow">Houminer et al. (1993)</a>. This was introduced to augment or replace something called the 12-month smoothed sunspot number, $R_{12}$, which is entirely based on observations. Zolesi et al. write</p>

<blockquote>
  <p>It is therefore expected that during periods of relative ionospheric quietness, when the observed $\text{foF2}$ value is much closer to the model predicted median values, the $R_{\text{eff}}$ does not differ much from the $R_{12}$. On the contrary, during periods of ionospheric activity, the $R_{\text{eff}}$ should have large difference form [sic] $R_{12}$. </p>
</blockquote>

CC BY-SA 3.0
2016-10-19T00:37:25.157Z
2016-10-19T15:51:56.137Z
2016-10-19T15:51:56.137Z
HDE 226868
<p>I am doing research on SSN-like parameters. As I can see, effective SSN is a parameter that is derived from SSN or other parameters. Do anyone know how to calculate effective SSN?</p>

<p>For example, <a href="ftp://ftp.swpc.noaa.gov/pub/latest/DSD.txt" rel="nofollow">this file</a> has some parameters. See also <a href="http://spawx.nwra.com/spawx/ssne.html" rel="nofollow">this page</a>.</p>

<the-sun>
Calculating effective SSN (sunspot number)
lsc
# Calculating effective SSN (sunspot number)

(Asked by: username_0 on 2015-06-10)

I am doing research on SSN-like parameters. As I can see, effective SSN is a parameter that is derived from SSN or other parameters. Do anyone know how to calculate effective SSN?

For example, [this file](ftp://ftp.swpc.noaa.gov/pub/latest/DSD.txt) has some parameters. See also [this page](http://spawx.nwra.com/spawx/ssne.html).

**Tags:** the-sun

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## 1 answers

### Answer by username_1 on 2016-10-19. Score: 2

The effective sunspot number $R\_{\text{eff}}$ is calculated through a mix of observations and model calculations. It focuses primarily on some parameter called the frequency of the [ionosphere F2 layer](https://en.wikipedia.org/wiki/F_region), denoted $\text{foF2}$, the highest frequency of electromagnetic radiation which can be reflected off the F2 layer; it can be observed as well as computed based on a certain model (real-time observational data from stations around the world is available [here](http://www.ngdc.noaa.gov/stp/IONO/rt-iono/realtime/RealTime_foF2.html)). More information on $\text{foF2}$ can be found on [this page](https://spawx.nwra.com/spawx/fof2/fof2.html).

The mean-squared error between the observational value $\text{foF2}\_{\text{obs}}$ and the calculated value $\text{foF2}\_{\text{calc}}$ over observations by $n$ stations is
$$\Delta=\frac{1}{n}\sum\_{i=1}^n\left(\text{foF2}\_{\text{obs},i}-\text{foF2}\_{\text{calc},i}\right)^2$$
where $\_i$ denotes the value at station $i$. $R\_\text{eff}$ is defined to be that chosen sunspot number such that $\Delta$ is minimized.

This is just an application of a [least squares](https://en.wikipedia.org/wiki/Least_squares) method to fit a model framework to match observations. An example of this using the Simplified Ionospheric Regional Model (SIRM) is [Zolesi et al. (2004)](http://onlinelibrary.wiley.com/doi/10.1029/2003RS002936/pdf), although the procedure for calculating $R\_\text{eff}$ was first proposed by [Houminer et al. (1993)](http://adsabs.harvard.edu/abs/1993JEEEA..13...99H). This was introduced to augment or replace something called the 12-month smoothed sunspot number, $R\_{12}$, which is entirely based on observations. Zolesi et al. write

> It is therefore expected that during periods of relative ionospheric quietness, when the observed $\text{foF2}$ value is much closer to the model predicted median values, the $R\_{\text{eff}}$ does not differ much from the $R\_{12}$. On the contrary, during periods of ionospheric activity, the $R\_{\text{eff}}$ should have large difference form [sic] $R\_{12}$.


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