Calculating Uncertainty of Aquired Evaporation Rate

[Hanatwork]

Hi! I am Calculating the uncertainty in an Evaporation Rate i obtained from measurements around a lake using E=C.U(ess-ea)/P where C is constant 135mm/day at 1.5m above lake surface, U is average wind speed, P air pressure hPa, ess saturation vapour pressure @lake surface temp (Ave), ea is air vapour pressure =11.65 hPa.
E= 2.48mm/day. The uncertainty is to be found from an obtained uncertainty in the vapour pressures (ea1-ea2/ea1= 4.47%) and the standard deviation of the wind speed observations:

U= 2.12 +/- 1.26 m/s
Im unsure on how to use the standard deviation of wind speed data (1.26) and the previous obtained vapour P uncertainty (0.0447) to obtain an uncertainty for E?

I thought it might be calculating E at max and min U (by standard deviation) and finding the difference, and then maybe multiplying that by the uncertainty of vapour pressures (4.47%)? but this felt wrong as just a guess.
CAN ANYONE PLEASE OFFER SOME ADVICE ON HOW I FIND THE ANSWER? Thanks heaps for any help! :)

 

[nate808]

Hello! It sounds like you are on the right track in your approach to calculating the uncertainty in your evaporation rate. To incorporate the uncertainty in wind speed and vapor pressure, you can use the propagation of uncertainty method.

First, calculate the uncertainty in E due to the uncertainty in wind speed. This can be done by calculating E at the maximum and minimum wind speeds (2.12 + 1.26 = 3.38 m/s and 2.12 - 1.26 = 0.86 m/s). Then, find the difference between the two E values (3.38 mm/day - 0.86 mm/day = 2.52 mm/day). This difference represents the range of uncertainty in E due to wind speed.

Next, calculate the uncertainty in E due to the uncertainty in vapor pressure. To do this, you can use the equation you provided: (ea1 - ea2)/ea1 = 4.47%. This represents the percent difference in vapor pressure, which can be applied to E as well. So, you can calculate E at ea1 and ea2 (using the same equation you provided) and find the difference between them. This difference represents the range of uncertainty in E due to vapor pressure.

Finally, to find the total uncertainty in E, you can combine the two ranges of uncertainty by adding them. So, the total uncertainty in E would be 2.52 mm/day + (4.47% of E) = 2.52 mm/day + (0.0447 x 2.48 mm/day) = 2.53 mm/day. This means that your final result for E would be 2.48 +/- 2.53 mm/day.

I hope this helps! Please let me know if you have any further questions. Good luck with your calculations!