Bayesian maximum entropy mapping and the soft data problem in urban climate research

The pressing problem of Phoenix's urban heat island (UHI) has spawned numerous academic studies of the spatiotemporal nature of this physical process and its relationship to energy and water use, urban design features, and ecosystem processes. Critical to these studies is an accurate representation of the UHI over space and time. This article is concerned chiefly with representing the UHI by using the Bayesian Maximum Entropy (BME) method of modern geostatistics to account for data uncertainty from missing records. We apply BME to the UHI in Phoenix by retrieving and mapping minimum temperature observations over time from historical weather station networks, then testing our mapping accuracy compared to traditional maps that do not account for data uncertainty. The results demonstrate that BME leads to increases of mapping accuracy (up to 35.28 percent over traditional linear kriging analysis). A subsequent synthetic case study confirms that substantial increases in mapping accuracy occur when there are many cases of missing or uncertain data. Use of BME reduces the need for costly sampling protocols and produces UHI maps that can be integrated with other data about human and environmental processes in future studies of urban sustainability.