<p>I've stumbled across this publication in nature (<a href="https://www.nature.com/articles/s41586-024-07744-y" rel="nofollow noreferrer">Neural general circulation models for weather and climate</a>) where the authors test an AI driven weather forecast model against ECWMF's ensemble forecast. The authors use several goodness of fit criteria. One of them is root mean squared error (<code>RMSE</code>), which is a quite common measure. Then, they use something called root mean squared bias (<code>RMSB</code>), too.</p>
<p>In my understanding, <code>RMSE</code> takes the distance between the simulation and the observation at all points, squares them (to get rid of the sign) and then takes the square root.
To get the bias of a simulation, I would have to calculate the mean error (<code>ME</code>). If <code>ME</code> is not equal 0, my simulation is biased.</p>
<p>Is my understanding correct?</p>
<p>I've never heard of <code>RMSB</code> and I cannot imagine what this is or what could be the difference to <code>RMSE</code>. Unfortunately in the paper, the author do not explain this and they don't cite this, too. Also, I cannot find any information by googling RMSB.</p>

CC BY-SA 4.0
2024-07-24T16:05:11.457Z
Please check [Supplementary Information](https://www.nature.com/articles/s41586-024-07744-y#Sec19) and the linked pdf [Supplementary information **Neural general circulation models for
weather and climate** (p. 20 ff)](https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-024-07744-y/MediaObjects/41586_2024_7744_MOESM1_ESM.pdf) for an explanation.
klanomath
CC BY-SA 4.0
2024-07-25T10:46:55.367Z
Thanks, that explains my question.
smoff
<weather-forecasting><statistics>
What is root mean squared bias?
smoff
# What is root mean squared bias?

(Asked by: username_0 on 2024-07-24)

I've stumbled across this publication in nature ([Neural general circulation models for weather and climate](https://www.nature.com/articles/s41586-024-07744-y)) where the authors test an AI driven weather forecast model against ECWMF's ensemble forecast. The authors use several goodness of fit criteria. One of them is root mean squared error (`RMSE`), which is a quite common measure. Then, they use something called root mean squared bias (`RMSB`), too.

In my understanding, `RMSE` takes the distance between the simulation and the observation at all points, squares them (to get rid of the sign) and then takes the square root.
To get the bias of a simulation, I would have to calculate the mean error (`ME`). If `ME` is not equal 0, my simulation is biased.

Is my understanding correct?

I've never heard of `RMSB` and I cannot imagine what this is or what could be the difference to `RMSE`. Unfortunately in the paper, the author do not explain this and they don't cite this, too. Also, I cannot find any information by googling RMSB.

**Tags:** weather-forecasting, statistics

> **Comments:**
> **username_1**: Please check [Supplementary Information](https://www.nature.com/articles/s41586-024-07744-y#Sec19) and the linked pdf [Supplementary information **Neural general circulation models for weather and climate** (p. 20 ff)](https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-024-07744-y/MediaObjects/41586_2024_7744_MOESM1_ESM.pdf) for an explanation.  
> **username_0**: Thanks, that explains my question.  

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## 0 answers

