  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 Auto-regressive Moving Average
(ARMA)(1, 1) model. The model was developed for observed annual mean
temperature anomaly X(t) which is a combination of 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 decomposed to Land Surface Temperature (LST)
uncertainty, Sea Surface Temperature (SST) uncertainty, and the corresponding
source of uncertainty. The ARMA model was analyzed and compared with
Auto-regressive (AR), and Auto-regressive integrated moving average (ARIMA) for
the data taken from NASA, Goddard Institute for space studies Surface
Temperature Analysis. The statistical analysis of the Auto-correlation function
(ACF), Partial auto-correlation function (PACF), Normal quantile-quantile
(Normal Q-Q) plot, the density of the residuals, and variance of normal
variable w(t) show that ARMA(1, 1)is better than AR(1) and ARIMA(1, d, 1) for d
= 1, 2.
