---
tags: Showcase, Notes
---
# Hidden Forcing
[](https://hackmd.io/@engeir/SJPvH8Ecj)
[](https://github.com/engeir/hack-md-notes/blob/main/hidden-linear-forcing.md)
> How do the different forcings relate to the temperature, and does any of them have a
> linear relationship with temperature?
With this, we want to look at how close the different forcings come to forming a linear
relationship with the temperature signal.
## Temperature
Let us first have a look at the temperature response as a deviation from the equilibrium
for three different volcanic eruption strengths.
## Forcings
Now, let us create an equivalent plot for the three different forcing time series;
aerosol optical depth, total injected sulphate and top of the atmosphere radiation
imbalance.
![Aerosol optical depth for three different volcanic
eruptions](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/aod-which-forcing.png>
"Aerosol optical depth for three different volcanic eruptions" =33%x) ![Total injected
sulphate for three different volcanic
eruptions](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/injected-which-forcing.png>
"Total injected sulphate for three different volcanic eruptions" =32%x) ![Radiation
imbalance for three different volcanic
eruptions](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/raddiff-which-forcing.png>
"Radiation imbalance for three different volcanic eruptions" =33%x)
## Comparison
Now, let us use the peak values, marked in each plot above with red, horizontal lines,
and plot forcing peaks against temperature peaks.
![Aerosol optical depth versus
temperature](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/aod-trefht-which-forcing.png>
"Aerosol optical depth versus temperature" =33%x) ![Total injected sulphate versus
temperature](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/injected-trefht-which-forcing.png>
"Total injected sulphate versus temperature" =32%x) ![Radiation imbalance versus
temperature](<https://raw.githubusercontent.com/engeir/hack-md-notes/23da90d9caad1afbb1cf9ebe5dda0b137c550a85/assets/pic/hidden-linear-forcing/raddiff-trefht-which-forcing.png>
"Radiation imbalance versus temperature" =33%x)
## CESM LME
But in the above, we have only three data points to compare, which are many too few. Let
us instead try to plot all non-zero values in the CESM LME forcing time series and the
corresponding temperature value at that element. There will be significant noise to
consider especially for the smallest eruptions, and some eruptions that follow close may
get unrealistically large temperature values, but maybe numerous events will clear
things up. We may also use the deconvolution algorithm to get a response function
estimate that we subsequently use to estimate the temperature, thus reducing the noise
(not shown here).
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