Estimating the uncertainty of Australian area-average temperature anomalies

An important metric for communicating the context and impact of climate change is regionally or nationally averaged temperature anomalies. Quantifying the associated uncertainty adds confidence in the reporting of temperature records and trends. For area-averaged temperature anomalies derived from point-source observations we model the uncertainty by a three-step process: (1) observation random error; (2) spatial analysis grid point uncertainty; and (3) area-average uncertainty. Each step should reflect the method used to calculate the area average. For Australian area-average temperature anomalies, the observation random error is modelled as the sum of the sampling uncertainty and the uncertainty in the adjustment process. Daily maximum and minimum temperature time series from the 104 non-urban locations of the Australian Climate Observation Reference Network-Surface Air Temperature (ACORN-SAT) version 2 dataset for 1981-2010 are used to estimate the sampling uncertainty, based on predicted location pair zero-distance correlations having values of less than 1.0. ACORN-SAT version 2 breakpoint information is used to estimate the uncertainty from the selection of reference stations used in the detection and homogenization processes. Monthly area-average temperature uncertainty is estimated for the 1910-2018 period from Monte Carlo simulations using the observation uncertainty and the available ACORN-SAT network for each month. The uncertainty in annual area-average temperature anomalies is then obtained from the monthly uncertainties and inter-month correlations modelled with a periodic auto-regressive model. The +/- 2 sigma annual mean temperature area-average uncertainty is +/- 0.084 degrees C in 2018 and +/- 0.176 degrees C in 1910. The larger value in 1910 is primarily due to decreased ACORN-SAT coverage over areas of inland Australia. The Australian annual mean temperature change and associated uncertainty from ACORN-SAT version 2 over 1910-2018 is found to be 1.42 +/- 0.28 degrees C. This is consistent with global air temperature warming by around 1 degrees C since 1850.