The first case study consists of satellite measurements of the Normalized Vegetation Difference Index (NDVI) carried out from 1 October 2013 to 31 May 2014 on North-West Africa. The spatial resolution is 1 km and the temporal resolution is a decade (a decade is a period resulting from the division of each calendar month into 3 parts, which can therefore take values of 8, 9, 10 or 11 days). The data is obtained from two different instruments on board two different satellite platforms: SPOT-VEGETATION and PROBA-V (these are called VT and PV for simplicity). Photovoltaic data is available via the Copernicus Global Land24 service portal, while VT archive data is provided with the kind permission of the JRC MARSOP25 project. Although the geometric and spectral characteristics of the satellites and the data processing chains are as close as possible, differences between the products can nevertheless be expected, as the instruments are not equal. The interest here is to quantify where, in the region, the time series do not coincide. Since there is no reason to say that one reference should be better than the other, a symmetric correspondence index should be applied to each pair of time series, resulting in values that can be represented in space. Index symmetry is an important feature in the conformity assessment of all data. Unlike validation or calibration exercises, which compare some model estimates to reference values considered error-free (usually observations of the quantity involved), there may not be a reference in comparative studies. Since two sets of data compared present a certain uncertainty, often unknown or poorly characterized, there is a priori no set of data “better” than the other.
Therefore, a conformity assessment index between data series X and Y should correspond to the index calculated between Y and X, a symmetry requirement often not met by validation measures. Other aspects to consider are the possibility of reformulating indices (1) to show their relationship with more well-known metrics such as r or RMSE10,11; and (2) to disentangle the systematics of the non-systematic random difference in the over-representation of data6. The systematic component can be interpreted as a regularized distortion due to known or identifiable factors, while the non-systematic element is a random component caused by noise or unknown factors. The distinction between the two is interesting, because the systematic difference can in principle be eliminated by regression analysis. Another common approach is to take into account that a statistical model can be adapted to the data. In this case, a conformity measure can be deduced from the coefficient of determination which indicates how well the data correspond to the chosen model. . . .