Validation metrics summary

Definitions

Assume that we have a model \(m\) and observations \(o\) of the same size \(N\).

Root mean square deviation (RMSD)

\[ \text{RMSD}(m, o) = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (m_i - o_i)^2} \]

Bias

\[ \text{Bias}(m, o) = \frac{1}{N} \sum_{i=1}^N (m_i - o_i) \]

Pearson correlation coefficient

\[ \text{Corr}(m, o) = \frac{\sum_{i=1}^N (m_i - \bar{m})(o_i - \bar{o})}{\sqrt{\sum_{i=1}^N (m_i - \bar{m})^2 \sum_{i=1}^N (o_i - \bar{o})^2}} \]

where \(\bar{m}\) and \(\bar{o}\) are the mean values of \(m\) and \(o\) respectively.

Software used

Models were matched up with observational data using the Python package nctoolkit. Plots were created using the Python package nctoolkit, and the R package ggplot2. Data analysis was performed using the Python packages pandas, nctoolkit, and statsmodels.