Sensitivity of Forecast Errors to Initial Conditions for High-Impact Atmospheric River Events using a Nonlinear Adjoint Method

Adjoint models can provide valuable insight into the practical limitations of our ability to predict weather systems such as atmospheric rivers (ARs), and their associated high-impact weather. An adjoint model can be used for the efficient and rigorous computation of numerical weather prediction forecast sensitivity to changes in the initial state or the earlier forecast state. The sensitivity calculations can help to unravel the contributing factors to high-impact weather predictability barriers influenced by a wide range of scales. Adjoints also can be used to explore the rapid growth of small perturbations that lead to large errors on multiple scales and limit the forecast accuracy of high-impact AR events.

The adjoint, tangent linear, and nonlinear models for the nonhydrostatic COAMPS are applied to the several high-impact precipitation events associated with ARs as part of the Atmospheric Rivers Reconnaissance (AR Recon) program. We focus on two periods of especially high adjoint sensitivity that coincided with multiple extreme precipitation and high-wind events, which occurred in California in January and March 2023, and January 2024. We utilize an iterative adjoint method to minimize the 2-3 day forecast error to estimate analysis errors. This new adjoint method allows for inclusion of nonlinearity into the sensitivity calculation. The adjoint calculations yield an estimate of the portion of analysis errors that are primarily responsible for the short-range forecast errors of ARs. We utilize several different verifying metrics to compute the analysis errors including: i) accumulated rainfall, ii) integrated vapor transport, and iv) potential vorticity (PV). The adjoint sensitivity results underscore the importance of the low- and mid-level moisture distribution, the role of the wave guide extending westward to the Central and Western Pacific, and sensitivity to mid-level PV anomalies, all of which trigger rapid adjoint perturbation growth. We demonstrate that small perturbations of moisture, winds, and temperature in these multi-scale sensitive regions rapidly evolve into disturbances that impact the predictability of downstream high-impact weather associated with the ARs. The results underscore the need for more accurate moisture observations and data assimilation systems that can adequately assimilate these observations in order to reduce the forecast uncertainties for these high-impact events, which is a central goal of the AR Recon program.