Optimizing the spatial resolution for urban CO2 flux studies using the Shannon entropy

Abstract

The 'Hestia Project' uses a bottom-up approach to quantify fossil fuel CO2 (FFCO2) emissions spatially at the building/street level and temporally at the hourly level. Hestia FFCO2 emissions are provided in the form of a group of sector-specific vector layers with point, line, and polygon sources to support carbon cycle science and climate policy. Application to carbon cycle science, in particular, requires regular gridded data in order to link surface carbon fluxes to atmospheric transport models. However, the heterogeneity and complexity of FFCO2 sources within regular grids is sensitive to spatial resolution. From the perspective of a data provider, we need to find a balance between resolution and data volume so that the gridded data product retains the maximum amount of information content while maintaining an efficient data volume. The Shannon entropy determines the minimum bits that are needed to encode an information source and can serve as a metric for the effective information content. In this paper, we present an analysis of the Shannon entropy of gridded FFCO2 emissions with varying resolutions in four Hestia study areas, and find: (1) the Shannon entropy increases with smaller grid resolution until it reaches a maximum value (the max-entropy resolution); (2) total emissions (the sum of several sector-specific emission fields) show a finer max-entropy resolution than each of the sector-specific fields; (3) the residential emissions show a finer max-entropy resolution than the commercial emissions; (4) the max-entropy resolution of the onroad emissions grid is closely correlated to the density of the road network. These findings suggest that the Shannon entropy can detect the information effectiveness of the spatial resolution of gridded FFCO2 emissions. Hence, the resolution-entropy relationship can be used to assist in determining an appropriate spatial resolution for urban CO2 flux studies. We conclude that the optimal spatial resolution for providing Hestia total FFCO2 emissions products is centered around 100 m, at which the FFCO2 emissions data can not only fully meet the requirement of urban flux integration, but also be effectively used in understanding the relationships between FFCO2 emissions and various social-economic variables at the U.S. census block group level.