Summarizing multiple aspects of triple collocation analysis in a single diagram - Siu, Leong Wai; Zeng, Xubin; Sorooshian, Armin; Cairns, Brian; Ferrare, Richard A.; Hair, Johnathan W.; Hostetler, Chris A.; Painemal, David; Schlosser, Joseph S. (Frontiers in Remote Sensing, 2024)
With our ever-growing global observation network, it is expected that we shall routinely analyze records of geophysical variables such as temperature from multiple collocated instruments.Validating datasets in this situation is not a trivial task because every observing system has its own bias and noise. Triple collocation is a general statistical framework to estimate the error characteristics in three or more observational-based datasets. In a triple colocation analysis, several metrics are routinely reported but it becomes unwieldy when the analysis gets complicated.A new formula of error variance is derived for connecting the key terms in the triple collocation theory. A diagram based on this formula is devised to facilitate triple collocation analysis of any data from observations, as illustrated using three aerosol optical depth datasets from the recent Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). An observational-based skill score is also derived to evaluate the quality of three datasets by taking into account of both error variance and correlation coefficient. Several applications are discussed and sample plotting routines are provided.