## 3 Underlying Terminology and Concepts
### Validation Metrics  
The provision of uncertainty for both the reference and satellite data is a prerequisite in order to have a rigorous and meaningful validation. As a matter of fact, the validation problem, in its basic form, consists in verifying whether the two independent measurements of the same measurand are statistically consistent at a given significance level within their combined standard uncertainties. This translates, under the assumption of normally distributed uncertainties, to the following statistical test [47]:  
\[\left|y_{\text{Sat}}-y_{\text{Ref}}\right|<\text{k}\sqrt{\text{u}_{\text{Sat }}^{2}+\text{u}_{\text{Ref}}^{2}} \tag{1}\]  
where \(\text{y}_{\text{Sat}}\) and \(\text{y}_{\text{Ref}}\) are the satellite and reference measurements, \(\text{u}_{\text{Sat}}\) and \(\text{u}_{\text{Ref}}\) are their respective uncertainties and \(\text{k}\) is the so-called coverage factor. Equation (1) provides a mean to quantitatively assess the consistency between the two independent measurements for different values of the coverage factor. Following the frequently used terminology [47], we can state that two measurements are \"consistent\" if they agree within \(\text{k}=1\), while, if they agree within \(\text{k}=2\), they are in \"statistical agreement\" to 4.5% significance level. This test can also be used to assess the quality of the uncertainty estimates. For instance, if a large number of data are compared and a fraction, much larger than 4.5%, of this data is significantly different (i.e., the consistency test is false for \(\text{k}=2\)), then the provided uncertainties are likely to be underestimated [47]. Equation (1) was further elaborated by [PERSON] et al. [48], introducing an additional uncertainty component, which is induced by the different spatiotemporal representativeness of the satellite and reference measurements. In this formulation, the statistical test takes the form of [48]:  
\[\left|y_{\text{Sat}}-y_{\text{Ref}}\right|<\text{k}\sqrt{\text{u}_{\text{Sat }}^{2}+\text{u}_{\text{Ref}}^{2}+\Sigma_{\text{mismatch}}^{2}}, \tag{2}\]  
where the term \(\Sigma\), is the collocation mismatch error, which is supposed, in this expression, to be fully uncorrelated from the uncertainties of the satellite and reference measurements. Equation (2) provides a more comprehensive test, which is highly suitable to the validation of satellite-based EO products, owing to the intrinsic spatial and temporal scale mismatch between the measurements acquired from a space-borne and ground-based platform. This issue is of particular relevance for land bio-geophysical products, as further discussed in the next paragraph.  
In most of the cases however, uncertainties are not provided as part of the space-borne or ground-based EO data, so the rigorous application of Equation (1) is not viable. In such cases, the general approach consists in using standard statistical metrics to quantify the pairwise agreement of the two datasets. The most commonly used methods are the correlation coefficient, the bias and the root-mean-square deviation (RMSD) [48]. In the land community, widely used metrics include the accuracy, expressed in terms of mean bias, the precision, representative of the repeatability of the measurements and computed as standard deviation of the estimates around the true values, and the uncertainty, which is a measure of the actual statistical deviation of the estimate from the truth and is expressed as RMSD [49]. This latter terminology is consistent with the generic uncertainty definition provided in the previous paragraph, since it represents a statistical method for evaluating uncertainties, namely a Type A evaluation, in metrological terms [38]. The validity of such statistical approaches increases as long as the population of the ensemble of satellite and ground-truth collocated data increase in size and spatiotemporal representativeness.