A weak-constraint four-dimensional variational analysis system in the stratosphere

A weak-constraint four-dimensional variational (4D-Var) analysis system designed to correct stratospheric model errors has been evaluated. Verifications against upper-level radiosonde temperature observations and Stratospheric Sounding Unit (SSU) radiance data show that the addition of a weak constraint in the stratosphere can greatly reduce analysis bias. Both single-observation analysis experiments and extended assimilations have been performed to help us understand the impact of the model error covariance specifications required for the weak-constraint formulation. It is found that the use of multivariate balance constraints similar to those implemented in background-error covariances can be problematic.