In recent years, deep learning methods have been increasingly applied in atmospheric and oceanic forecasting, showing superior forecast skills. Unlike time-stepping numerical models, deep learning forecasting models (DLMs) typically adopt a "multi-time-slice input" structure. This structure breaks the deterministic causality in the time dimension that exists in the numerical models. In this case, the forecast errors in DLMs should be attributed to all input slices, rather than any single one. This fundamental difference limits the applicability of the classical conditional nonlinear optimal perturbation (CNOP) method, as CNOP is defined at a single time slice, specifically, the initial time.
Recently, researchers have extended the CNOP method in the time dimension and proposed the CNOP-DL method. Designed specifically for DLMs with multi-time-slice inputs, CNOP-DL includes perturbations across multiple times of the inputs, revealing the sensitivity of forecast errors to input errors in both time and space dimensions. The new method is published in Advances in Atmospheric Sciences .
"CNOP-DL is useful in the targeted observation studies, as it allows us to identify not only where, but also when additional observations should be deployed to reduce the input errors, ultimately to significantly mitigate the forecast errors," said Dr. Ziqing Zu from National Marine Environmental Forecasting Center of China, the lead author of the study. "This is especially valuable for improving the forecasts of rapidly developing systems such as typhoons and mesoscale eddies, where observational resources are often limited."
To demonstrate the utility of the method, they applied CNOP-DL to a case study of sea surface temperature (SST) forecasting in the South China Sea. The CNOP-DL included six time slices in the time dimension. Therefore, the optimal time can be identified according to the temporal structure of the perturbation energies. Furthermore, the results revealed that forecast errors are more sensitive to the time of the input perturbations than to the location. In other words, determining when to deploy additional observations can be more critical than determining where.
"In conventional targeted observation studies, the focus is typically on identifying the optimal locations for targeted observations at the initial time. By extending CNOP in the time dimension, CNOP-DL can identify which time steps in the inputs are more critical, thereby broadening the scope of conventional targeted observation studies." said Professor Mu Mu from Fudan University, the corresponding author of the study. "By highlighting the importance of time sensitivity, CNOP-DL holds the potential for guiding practical field campaigns that optimize both spatial and temporal deployment of observational platforms such as moored buoys, gliders, and research vessels."
CNOP-DL is also useful in predictability studies. The authors demonstrate that there are significant differences between CNOP-DL and CNOP, and that CNOP-DL can lead to larger forecast errors, thereby providing a more accurate estimate of the upper bound of forecast uncertainty. This is because, essentially, CNOP searches for the optimal solution within a subset of the CNOP-DL space; thus, CNOP can be regarded as a special case of CNOP-DL.
Next, the authors plan to calculate CNOP-DL for a lot of forecast cases, and then conduct composite analyses of CNOP-DL results. By identifying common patterns in sensitive regions and key time windows, they aim to design an optimal observational network in the South China Sea, particularly for moored buoy arrays. Such a system could provide valuable observations to improve significantly operational forecasts, using limited observational resources.
Other contributors include Jiangjiang Xia from Key Laboratory of Regional Climate-Environment for Temperate East Asia at CAS IAP in Beijing, China and Qiang Wang from College of Oceanography, Hohai University in Nanjing, China.
