The inter-annual variability of boreal summer intra-seasonal oscillation (BSISO) propagation from the Indian Ocean (IO) to the western Pacific (WP) is investigated for the boreal summers (May to September) of 1979–2018. It is shown that the interannual variability of BSISO mainly happens in its evolution, not in its strength over the IO. Here, we classify four distinctive modes for inter-annual variability of BSISO propagation: (i) northeast mode, propagating from the IO to the western equatorial Pacific (WEP) and the western North Pacific (WNP); (ii) north-only mode, only propagating to the WNP; (iii) east-only mode, only propagating to the WEP; and (iv) stationary mode, propagating to neither the WEP nor the WNP. It is found that the Maritime Continent (MC) and WEP are two key regions determining these four modes concerning mean state moisture and vertical motion. Associated with central equatorial Pacific cooling, the BSISO of northeast and north-only modes can reach the WP by passing over the MC due to positive mean moisture anomalies and upward mean motion anomalies over the MC. The strong negative mean moisture anomalies and downward mean motion anomalies over the WEP, related to strong central Pacific cooling, prevents the development of BSISO there, resulting in north-only mode. For the east-only and stationary modes associated with the central Pacific warming, their BSISO can hardly pass the MC due to negative mean moisture anomalies and downward mean motion anomalies. The positive mean moisture anomalies and upward mean motion anomalies over the WEP related to strong central Pacific warming, however, will reinitiate the BSISO in the WEP for the east-only mode.

Estimation of anthropogenic carbon dioxide (CO₂) emission sources and natural sinks (i.e., CO₂ fluxes) is essential for the development of climate policies. Satellite observations provide an opportunity for top-down inversion of CO₂ fluxes, which can be used to improve the results of bottom-up estimation. This study proposes to develop a new top-down CO₂ flux estimation method based on deep learning, as well as satellite observations, and an atmospheric chemical transport model. This method utilizes two deep learning models: the concentration correction model and the concentration–flux inversion model. The former optimizes the GEOS-Chem-simulated CO₂ concentration using Orbiting Carbon Observatory-2 (OCO-2) satellite observations, while the latter establishes the complicated relationship between CO₂ concentration and CO₂ flux. Results showed that both deep learning models demonstrated excellent prediction performance, with a mean bias of 0.461 ppm for the concentration correction model and an annual mean correlation coefficient of 0.920 for the concentration–flux inversion model. A posterior CO₂ flux was obtained through a two-step optimization process using these well-trained models. Our findings indicate that the posterior estimations of CO₂ flux sources in eastern China and northern Europe have been significantly reduced compared to the prior estimations. This study provides a new perspective on top-down CO₂ flux inversion using satellite observation. With advancements in deep learning algorithms and increased satellite observations, this method may become an effective approach for CO₂ flux inversion in the future.

The observed convective adjustment time (CAT) associated with Madden–Julian Oscillation (MJO) precipitation is found to vary significantly in space. Here, we investigate the effect of different spatial distributions of CAT on MJO precipitation based on the frictional coupled dynamics moisture (FCDM) model. The results show that a large value of CAT tends to decrease the frequency and growth rate of eastward-propagating MJO-like mode in the FCDM model, delaying the occurrence of MJO deep convection and slowing down its eastward propagation. A large phase lag between circulation and convection decreases convective available potential energy (CAPE). In the observations, a small background vertical moisture gradient (BVMG) tends to increase the frequency associated with cold sea surface temperature (SST), while a large value of CAT tends to decrease the frequency. Due to their competing effect, the simulated frequency and phase speed remain the same when the convection moves from a warm to a cold SST region. The convection is heavily suppressed over the cold SST region due to the decreasing growth rate of unstable wavenumber-one mode with smaller BVMG and longer CAT. This theoretical finding should improve our understanding of MJO dynamics and simulation.

Deep-learning-based convection schemes have garnered significant attention for their notable improvements in simulating precipitation distribution and tropical convection in Earth system models. However, these schemes struggle to capture the stochastic nature of moist physics, which can degrade the simulation of large-scale circulations, climate means, and variability. To address this issue, a stochastic parameterization scheme called DIFF-MP, based on a probabilistic diffusion model, is developed. Cloud-resolving data are coarse-grained into resolved-scale variables and subgrid contributions, which serve as conditional inputs and outputs for DIFF-MP. The performance of DIFF-MP is compared with that of generative adversarial networks and variational autoencoders. The results demonstrate that DIFF-MP consistently outperforms these models in terms of prediction error, coverage ratio, and spread–skill correlation. Furthermore, the standard deviation, skewness, and kurtosis of the subgrid contributions generated by DIFF-MP more closely match the test data than those produced by the other models. Interpretability experiments confirm that DIFF-MP’s parameterization of moist physics is physically consistent.

Deep-learning-based convection schemes receive wide attention due to its impressive im-provement on precipitation distribution and tropical convections of earth system simulation. But they cannot represent the stochasticity of moist physics, which will degrade the simulation of large-scale circulations, climate mean, and variability. To solve this problem, a stochastic pa-rameterization scheme based on probabilistic diffusion model named DIFF-MP is developed. The cloud-resolving data from GRIST model is coarse-grained into resolved-scale variables and sub-grid contributions due to moist physics to form the training data. DIFF-MP’s performance is compared against generative adversarial network and variational autoencoder. Results show that DIFF-MP is consistently better than the other two models on prediction error, coverage ratio, and spread-skill correlation. The standard deviation, skewness, and kurtosis of subgrid contributions generated by DIFF-MP is also closer to the testing data than the others. Interpretability experiment shows that DIFF-MP’s parameterization of moist physics is physically reasonable.