Scalable Bias Correction Techniques Investigated with a Low-dimensional Dynamical Model

Biased observations present a pervasive and highly individualized challenge for performing data assimilation within numerical weather prediction systems. Consequently, bias correction of observations is crucial for the accuracy of analyses, especially for remotely sensed measurements such as satellite radiances. In the absence of model bias, bias correction schemes that correct observations to a model background state, such as variational bias correction techniques commonly used in practice, would work nearly perfectly. However, when undiagnosed model bias is present, such schemes are subject to bias reinforcement. We aim to develop a strategy for independently correcting model and observation bias, to avoid bias reinforcement while considering the computational limitations of operational data assimilation systems. We explore this new methodology using Model III of Lorenz (2005), an idealized chaotic dynamical model that simulates the evolution of a scalar field based on advection, diffusion, and constant forcing at two distinct scales of motion. For our experiments, we induce controllable amounts of observation and model bias to simulate known challenges for operational modeling. We then use analysis increment and innovation statistics collected over a training period to independently correct for sources of bias in observation or model space. By treating these biases separately and sequentially, model and observation biases are decoupled, resulting in a bias correction scheme that provides accurate results over successive data assimilation cycles.