ARMA model development and analysis for global temperature uncertainty

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time-series temperature uncertainty model, which is the autoregressive moving average (ARMA) (1,1) model. The model was developed for an observed annual mean temperature anomaly X ( t ), which is a combination of a true (latent) global anomaly Y ( t ) for a year ( t ) and normal variable w ( t ). The uncertainty is taken as the variance of w ( t ), which was divided into land surface temperature (LST) uncertainty, sea surface temperature (SST) uncertainty, and the corresponding source of uncertainty. The ARMA model was analyzed and compared with autoregressive (AR) and autoregressive integrated moving average (ARIMA) for the data obtained from the NASA Goddard Institute for Space Studies Surface Temperature (GISTEMP) Analysis. The statistical analysis of the autocorrelation function (ACF), partial autocorrelation function (PACF), normal quantile–quantile (normal Q-Q) plot, density of the residuals, and variance of normal variable w ( t ) shows that ARMA (1,1) fits better than AR (1) and ARIMA (1, d , 1) for d = 1, 2.