Prediction Beyond the Medium Range with an Atmosphere-Ocean Model that Combines Physics-based Modeling and Machine Learning

TL;DR

The hybrid model used for the forecast experiments of the paper is based on the low‐resolution, simplified parameterization atmospheric general circulation model SPEEDY, which has skill in predicting the El Niño cycle and its global teleconnections with precipitation for 3–7 months depending on the season.

Abstract

This paper explores the potential of a hybrid modeling approach that combines machine learning (ML) with conventional physics-based modeling for weather prediction beyond the medium range. It extends the work of Arcomano et al. (2022), which tested the approach for short- and medium-range weather prediction, and the work of Arcomano et al. (2023), which investigated its potential for climate modeling. The hybrid model used for the forecast experiments of the paper is based on the low-resolution, simplified parameterization atmospheric general circulation model SPEEDY. In addition to the hybridized prognostic variables of SPEEDY, the model has three purely ML-based prognostic variables: the 6h cumulative precipitation, the sea surface temperature, and the heat content of the top 300m deep layer of the ocean (a new addition compared to the model used in Arcomano et al., 2023). The model has skill in predicting the El Nino cycle and its global teleconnections with precipitation for 3-7 months depending on the season. The model captures equatorial variability of the precipitation associated with Kelvin and Rossby waves and MJO. Predictions of the precipitation in the equatorial region have skill for 15 days in the East Pacific and 11.5 days in the West Pacific. Though the model has low spatial resolution, for these tasks it has prediction skill comparable to what has been published for high-resolution, purely physics-based, conventional, operational forecast models.

Figures (10)

• Figure 1: Schematic of the model setup during (a) training and (b) prediction. The atmospheric model component and ocean model component are trained independently as shown in (a), but coupled during prediction as shown in (b). We take the atmospheric (oceanic) model state $\mathbf{u}_G(t)$ ($\mathbf{v}_G(t)$) to be $\mathbf{u}_G^a(t)$ ($\mathbf{v}_G^a(t)$) during training and $\mathbf{u}_G^H(t)$ ($\mathbf{v}_G^M(t)$) during prediction. The super-script $a$ denotes the observation-based analysis atmospheric or oceanic states, and the super-script $H$ ($M$) denotes the states predicted by the hybrid atmospheric (ML-only oceanic) model component. Since the time step $\Delta t$ of the atmospheric model component is taken to be smaller than the time step $\Delta t'$ of the oceanic model component (i.e., $\Delta t'{=}n\Delta t$), the atmospheric model component variables used as input to the oceanic model component are time-averaged over a trailing $n\Delta t$ time window. In a similar fashion, the oceanic model component variables fed to the atmospheric model component are interpolated in time to produce the $\Delta t$ time step of the oceanic input to the atmospheric model component. See Appendix A for more details.
• Figure 2: Illustration of the geographic domain decomposition for a local input vector $\mathbf{u}^{(in)}_l$ (with grid points enclosed by a red box), and a local output vector $\mathbf{u}^{(out)}_l$ (with grid points enclosed by a blue box). The black dots correspond to grid points of the SPEEDY model.
• Figure 3: Illustration of the dependence of the skill of the hybrid model in predicting the Niño 3.4 Index on the forecast lead time. Shown are the (a) RMSE (b) PCC (c) forecast bias, and (d) standard deviation of forecast errors for (thick solid blue) the hybrid model and (thin solid various colors) various state-of-the-art conventional physics-based models. For reference, black dashes show the RMSE for the climate based forecasts in (a) and the PCC=$0.5$ line in (b). Also shown is (e) the dependence of the PCC for the hybrid model on the (x-axis) forecast lead time and (y-axis) month of the start of the forecast.
• Figure 4: The skill of the seasonal hybrid model forecasts in capturing the teleconnection between the Niño 3.4 Index and the global SST anomalies. Shown are the (top) concurrent correlations and (bottom) lagged correlations with a 3-month lag for the SST anomalies for the (left) hybrid model and (right) ERA5 reanalyses. Black dots indicate locations where the PCC is statistically significant at the $95\%$ confidence level.
• Figure 5: The skill of the seasonal hybrid model forecasts in capturing the teleconnections between the El Niño cycle and the precipitation anomalies around the globe. Shown are the concurrent PCC for the Niño 3.4 Index and the seasonal precipitation anomalies for the (left) 3-month lead time hybrid model forecasts and (right) ERA5 reanalyses. The verification times of the forecasts fall in the (from top to bottom) DJF, MAM, JJA, and SON season. Black dots indicate the locations where the PCC is significant at the $95\%$ level.