Propagation of temperature difference

lartemperature

## Propagation of temperature difference

$$E^\text{(corr)}_{\text{year}} = E_{\text{year}} / (1 + \alpha_{\text{year}})$$

we want

$$E^\text{(corr)}_{\text{2012}} = E^\text{(corr)}_{\text{2015}} $$

and we know (temperature effect):

$$E_{2015} = (1 + x) E_{2012}$$

where $x=E_{2015}/E_{2012} - 1$ is your last but one column. Define:

$$\Delta\alpha = \alpha_{2015} - \alpha_{2012}$$

then:

$$ E_{\text{2012}} / (1 + \alpha_{\text{2012}}) = E_{\text{2015}} / (1 + \alpha_{\text{2015}})$$

$$ (1 + \alpha_{\text{2015}}) / (1 + \alpha_{\text{2012}}) = (1+x)$$

$$ (1 + \alpha_{\text{2012}} + \Delta\alpha)  = (1+x)  (1 + \alpha_{\text{2012}}) = 1 +x + \alpha_{2012} + x\alpha_{2012}$$

$$ \Delta\alpha  = x + x\alpha_{2012}\simeq x$$