To address the effect of stratiform latent heating on meso- to large scale circulations, an enhanced implementation of the Multiscale Coherent Structure Parameterization (MCSP) is developed for the Met Office Unified Model. MCSP represents the top-heavy stratiform latent heating from under-resolved organized convection in general circulation models. We couple the MCSP with a mass-flux convection scheme (CoMorph-A) to improve storm lifecycle continuity. The improved MCSP trigger is specifically designed for mixed-phase deep convective cloud, combined with a background vertical wind shear, both known to be crucial for stratiform development. We also test a cloud top temperature dependent convective-stratiform heating partitioning, in contrast to the earlier fixed partitioning. Assessments from ensemble weather forecasts and decadal simulations demonstrate that MCSP directly reduces cloud deepening and precipitation areas by moderating mesoscale circulations. Indirectly, it amends tropical precipitation biases, notably correcting dry and wet biases over India and the Indian Ocean, respectively. Remarkably, the scheme outperforms a climate model ensemble by improving seasonal precipitation cycle predictions in these regions. This enhancement is partly due to the scheme’s refinement of Madden-Julian Oscillation (MJO) spectra, achieving better alignment with reanalysis data by intensifying MJO events and maintaining their eastward propagation after passing the Maritime Continent. However, the scheme also increases precipitation overestimation over the Western Pacific. Shifting from fixed to temperature-dependent convective-stratiform partitioning reduces the Pacific precipitation overestimation but also lessens the improvements of seasonal cycle in India. Spatially correlated biases highlight the necessity for advancements beyond deterministic approaches to align MCSP with environmental conditions.

The ‘signal-to-noise paradox’ for seasonal forecasts of the winter NAO is often described as an ‘underconfident’ forecast and measured using the ratio-of-predictable components metric (RPC). However, comparison of RPC with other measures of forecast confidence, such as spread-error ratios, can give conflicting impressions, challenging this informal description. We show, using a linear statistical model, that the ‘paradox’ is equivalent to a situation where the reliability diagram of any percentile forecast has a slope exceeding 1. The relationship with spread-error ratios is shown to be far less direct. We furthermore compute reliability diagrams of winter NAO forecasts using seasonal hindcasts from the European Centre for Medium-range Weather Forecasts and the UK Meteorological Office. While these broadly exhibit slopes exceeding 1, there is evidence of asymmetry between upper and lower terciles, indicating a potential violation of linearity/Gaussianity. The limitations and benefits of reliability diagrams as a diagnostic tool are discussed.

The Madden–Julian Oscillation (MJO) is the dominant source of sub-seasonal variability in the tropics. It consists of an Eastward moving region of enhanced convection coupled to changes in zonal winds. It is not possible to predict the precise evolution of the MJO, so sub-seasonal forecasts are generally probabilistic. We present a deep convolutional neural network (CNN) that produces skilful state-dependent probabilistic MJO forecasts. Importantly, the CNN’s forecast uncertainty varies depending on the instantaneous predictability of the MJO. The CNN accounts for intrinsic chaotic uncertainty by predicting the standard deviation about the mean, and model uncertainty using Monte-Carlo dropout. Interpretation of the CNN mean forecasts highlights known MJO mechanisms, providing confidence in the model. Interpretation of forecast uncertainty indicates mechanisms governing MJO predictability. In particular, we find an initially stronger MJO signal is associated with more uncertainty, and that MJO predictability is affected by the state of the Walker Circulation.

Continuous Structural Parameterization (CSP) is a method for approximating different numerical model parameterizations of the same process as functions of the same gridscale variables. This allows systematic comparison of parameterizations with each other and observations or resolved simulations of the same process. Using the example of two convection schemes running in the Met Office Unified Model (UM), we show that a CSP is able to capture concisely the broad behavior of the two schemes, and differences between the parameterizations and resolved convection simulated by a high resolution simulation. When the original convection schemes are replaced with their CSP emulators within the UM, basic features of the original model climate and some features of climate change are reproduced, demonstrating that CSP can capture much of the important behavior of the schemes. Our results open the possibility that future work will estimate uncertainty in model projections of climate change from estimates of uncertainty in simulation of the relevant physical processes.