A novel spatial statistical method called Single Point Area Estimation (SPA) was developed to estimate an area value based on the observations at a single point. The method is applicable to estimate an area value when establishing observation stations are too expensive, or records are rare in ancient time or in remote areas.
The principle of SPA is that the value at the single point was weighted to estimate the true value of a large area, with an objective function of unbiased and the least variance of the estimation. After a mathematical derivation, the weight and the error of the estimation are found to be the functions of spatial auto correlation, and the correlation between the single point value and the entire area value. The correlation coefficients can be approximated by that of an auxiliary variable. The auxiliary variable should be spatiotemporally correlated with the target variable, and should fully coverage the study area and easy to be acquired.
SPA was used to estimate the daily value of citywide PM2.5 concentration in Beijing, based on daily PM2.5 observations at a single point in the US Embassy to Beijing, with an auxiliary variable of PM10 observed at 18 evenly distributed stations in the city. Cross validation R2 is between 0.76-0.97, the most are greater than 0.90.
The related research results have been published in the PLoS ONE.