Acknowledgement
AeroVal uses ground based and satellite observations for the evaluation of climate and air quality models.
We would like to thank all the data providers that make this work possible. Before using the data, please check the relevant
data policy networks in their specific websites.
Ground based measurements
- Aerosols Optical Properties (AOD, AE, Scat./Abs. Coef.)
- Aerosols and Gaseous Concentrations (PM, O3, SO2, NO2, CO, ...)
Satellite observations
Statistics
Here is a list of the statistics used for the evaluation of the models.
-
R: The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance
of the
variables divided by the product of their standard deviations. This is the best known and most commonly used type of correlation coefficient; when the term "correlation coefficient" is used without further qualification, it
usually
refers to the Pearson product-moment correlation coefficient.
$$\text{R} = \dfrac{ \sum_{i=1}^{n}(o_i - \overline{o})(m_i - \overline{m}) }{ \sqrt{ \sum_{i=1}^{n}(o_i - \overline{o_i})^2} \sqrt{ \sum_{i=1}^{n}(m_i - \overline{m_i})^2} }$$
-
R Spearman: Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ρ, is a nonparametric measure of rank correlation (statistical dependence
between the
rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function.
$$\rho = 1 - \dfrac{ 6 \sum_{i=1}^{n} (m_i - o_i)^2 }{ n (n^2-1) }$$
-
NMB (Normalized Mean Bias): NMB captures the average deviations between two datasets. On this website it is reported in units of percent. Values near 0 are the best, negative values indicate underestimation and
positive values
indicate overestimation.
$$\text{NMB} = \dfrac{\sum_{i=1}^{n} \left( m_i - o_i \right)}{\sum_{i=1}^{n} o_i} $$
-
MNMB (Modified Normalized Mean Bias): MNMB is a normalisation based on the mean of the observed and forecast value. It ranges between −2 and 2 and when multiplied by 100 %, it can be interpreted as a percentage bias.
$$\text{MNMB} = \dfrac{2}{n} \sum_{i=1}^{n}( \dfrac{m_i - o_i}{m_i + o_i} )$$
-
RMSE / NRMSE (Root Mean Squared Error / Normalized Root Mean Squared Error): RMSE is a commonly used statistical metric that quantifies the average magnitude of the differences between predicted values and actual observed values in a dataset. It's a measure of the accuracy or precision of a prediction or model's performance.
$$\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (o_i - m_i)^2}$$
Normalizing the RMSE facilitates the comparison between datasets or models with different scales.
$$\text{NRMSE} = \dfrac{\sqrt{\frac{1}{n} \sum_{i=1}^{n} (o_i - m_i)^2}}{\overline{o}} $$
-
FGE (Fractionnal Gross Error): FGE is a measure of model error, ranging between 0 and 2 and behaves symmetrically with respect to under- and overestimation, without over emphasizing outliers.
$$\text{FGE} = \dfrac{2}{n} \sum_{i=1}^{n} \left| \dfrac{m_i - o_i}{m_i+o_i} \right|$$
M: Model, O: Observation, n: number of points
