The Centrality of Mathematics in the History of Western Thought

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields

Validation of methane and carbon monoxide from Sentinel-5 Precursor using TCCON and NDACC-IRWG stations

The Sentinel-5 Precursor (S5P) mission with the TROPOspheric Monitoring Instrument (TROPOMI) on board has been measuring solar radiation backscattered by the Earth\u27s atmosphere and surface since its launch on 13 October 2017. In this paper, we present for the first time the S5P operational methane (CH4) and carbon monoxide (CO) products\u27 validation results covering a period of about 3 years using global Total Carbon Column Observing Network (TCCON) and Infrared Working Group of the Network for the Detection of Atmospheric Composition Change (NDACC-IRWG) network data, accounting for a priori alignment and smoothing uncertainties in the validation, and testing the sensitivity of validation results towards the application of advanced co-location criteria. We found that the S5P standard and bias-corrected CH4 data over land surface for the recommended quality filtering fulfil the mission requirements. The systematic difference of the bias-corrected total column-averaged dry air mole fraction of methane (XCH4) data with respect to TCCON data is −0.26±0.56 % in comparison to −0.68±0.74 % for the standard XCH4 data, with a correlation of 0.6 for most stations. The bias shows a seasonal dependence. We found that the S5P CO data over all surfaces for the recommended quality filtering generally fulfil the missions requirements, with a few exceptions, which are mostly due to co-location mismatches and limited availability of data. The systematic difference between the S5P total column-averaged dry air mole fraction of carbon monoxide (XCO) and the TCCON data is on average 9.22±3.45 % (standard TCCON XCO) and 2.45±3.38 % (unscaled TCCON XCO). We found that the systematic difference between the S5P CO column and NDACC CO column (excluding two outlier stations) is on average 6.5±3.54 %. We found a correlation of above 0.9 for most TCCON and NDACC stations. The study shows the high quality of S5P CH4 and CO data by validating the products against reference global TCCON and NDACC stations covering a wide range of latitudinal bands, atmospheric conditions and surface conditions

Comparisons between SCIAMACHY and ground-based FTIR data for total columns of CO, CH4, CO2 and N2O

Total column amounts of CO, CH4, CO2 and N2O retrieved from SCIAMACHY nadir observations in its near-infrared channels have been compared to data from a ground-based quasi-global network of Fourier-transform infrared ( FTIR) spectrometers. The SCIAMACHY data considered here have been produced by three different retrieval algorithms, WFM-DOAS (version 0.5 for CO and CH4 and version 0.4 for CO2 and N2O), IMAP- DOAS ( version 1.1 and 0.9 (for CO)) and IMLM (version 6.3) and cover the January to December 2003 time period. Comparisons have been made for individual data, as well as for monthly averages. To maximize the number of reliable coincidences that satisfy the temporal and spatial collocation criteria, the SCIAMACHY data have been compared with a temporal 3rd order polynomial interpolation of the ground-based data. Particular attention has been given to the question whether SCIAMACHY observes correctly the seasonal and latitudinal variability of the target species. The present results indicate that the individual SCIAMACHY data obtained with the actual versions of the algorithms have been significantly improved, but that the quality requirements, for estimating emissions on regional scales, are not yet met. Nevertheless, possible directions for further algorithm upgrades have been identified which should result in more reliable data products in a near future