Diagnosing Errors in Climate Forecast Models Using Forced Autoregressive Models

Climate models initialized near the observed state typically drift toward their own climatology as the forecast evolves. This drift is commonly corrected through a lead‐time and start‐month dependent bias adjustment, derived from a hindcast data set. While widely used, this traditional correction has well‐known limitations: it is statistically inefficient, prone to introducing artificial discontinuities, and offers little insight into the underlying causes of forecast error. This paper presents an alternative framework that addresses these limitations and provides a more process‐oriented diagnostic. The proposed method fits separate autoregressive models with exogenous input (ARX models) to both forecasts and observations. Forecast errors are then predicted and removed using the difference between the two ARX models. The method is demonstrated and compared to traditional methods using seasonal forecasts of global mean temperature from the SPEAR model, a contributor to the North American Multi‐Model Ensemble (NMME). The ARX approach outperforms traditional methods in independent data even when traditional approaches include a linear trend correction. The analysis reveals that SPEAR exhibits an exaggerated response to radiative forcing, leading to significant trend errors. Notably, these errors are already present in the first month. These initial trend errors can be reproduced by a one‐dimensional data assimilation system, indicating that they originate from SPEAR's exaggerated response to radiative forcing, which is carried forward into the first‐guess fields used in the data assimilation system.