# Propagation of errors in a rainfall equation

#### confusedwitherrors

Hello guys! I am having some trouble calculating propagation errors for this equation:

P=9T^2 + 296T + 645
where P=precipitation (mm a-1 ) , T=5.68 +/- 1.5°C

My thought process was to calculate the error for '296T' using the multiplication by constant rule. Then, calculate the error for 9T^2 using the power rule. Finally, I would use the sum rule to combine these errors. However, this article states that "the errors being propagated must be uncorrelated". So now I am totally confused on how to get the error for this equation.

To add more complexity, there is a standard error on the above equation of +/- 200mm a-1 and I am unsure on how to factor this in.
Can anyone point me in the right direction on how I should treat this error analysis? I would be so grateful!

#### studiot

~~~Well if you differentiate your expression and set dP equal to the error, there is your answer in relation to the error in T

$$\displaystyle \frac{{dP}}{{dT}} = \frac{d}{{dT}}\left( {9{T^2} + 296T + 645} \right)$$

error = $$\displaystyle dP = \left( {18T + 296} \right)dT$$

• topsquark

#### confusedwitherrors

God it seems so simple now! Thank you very much for your reply, it has helped me greatly.