Abstract This paper investigates the performance of a unique proof-of-concept hybrid model in a cycling data assimilation scheme. This previously published model combines the Simplified Parameterization, Primitive Equation Dynamics (SPEEDY) model with a machine learning (ML)-based component that itself is capable of modeling the global atmospheric dynamics. Analysis and forecast experiments are carried out assuming that ERA5 reanalyses, interpolated to the model grid, represent the “true” spatiotemporal evolution of the atmosphere. Six-hourly simulated observations are generated for a 30-yr training period and a 1-yr testing period by randomly perturbing the true states. To investigate the effect of the training data on the model performance, the model is trained on different datasets in the different experiments: The training data are either ERA5 reanalyses, analyses prepared using SPEEDY for cycling, or analyses prepared using the hybrid model for cycling. The simulated observations are assimilated with a local ensemble transform Kalman filter (LETKF), and the length of the ensuing forecasts is 10 days in all experiments. The cycled LETKF remains stable for the entire testing period in all experiments. When the hybrid model is trained on ERA5 reanalyses, the biases of the analyses are negligible and the variance of the analysis error is greatly reduced compared to the experiment in which SPEEDY rather than the hybrid model is used for cycling. The gains in analysis accuracy are more modest when the hybrid model is trained on analyses obtained with SPEEDY or a prior trained version of the model. All forecasts with the hybrid model are more accurate than with SPEEDY. Significance Statement This is the first study to investigate the performance of a unique proof-of-concept hybrid model in a cycling data assimilation scheme. This previously published model combines a physics-based model using its original physical parameterization schemes with a machine learning (ML)-based component that itself is capable of modeling the global atmospheric dynamics.

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.

The hybrid model combines the physics-based primitive-equations model SPEEDY with a machine learning-based (ML-based) model component, while ERA5 reanalyses provide the presumed true states of the atmosphere. Six-hourly simulated noisy observations are generated for a 30-year ML training period and a one-year testing period. These observations are assimilated with a Local Ensemble Transform Kalman Filter (LETKF), and a 10-day deterministic forecast is also started from each ensemble mean analysis of the testing period. In the first experiment, the physics-based model provides the background ensemble members and the 10-day deterministic forecasts. In the other three experiments, the hybrid model plays the same role as the physics-based model in the first experiment, but it is trained on a different data set in each experiment. These training data sets are analyses obtained by using the physics-based model (second experiment), the hybrid model of the previous experiment (third experiment), and for comparison, ERA5 reanalyses (fourth experiment). The results of the experiments show that hybridizing the model can substantially improve the accuracy of the analyses and forecasts. When the model is trained on ERA5 reanalyses, the biases of the analyses are negligible and the magnitude of the flow-dependent part of the analysis errors is greatly reduced. While the gains in analysis accuracy are distinctly more modest in the other two hybrid model experiments, the gains in forecast accuracy tend to be larger in those experiments after 1-3 forecast days. However, these extra gains of forecast accuracy are achieved, in part, by a modest gradual reduction of the spatial variability of the forecasts.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Corresponding author: Jerald A. Brotzge, jerald.brotzge@wku.edu

It is shown that a recently developed hybrid modeling approach that combines machine learning (ML) with an atmospheric global circulation model (AGCM) can serve as a basis for capturing atmospheric processes not captured by the AGCM. This power of the approach is illustrated by three examples from a decades‐long climate simulation experiment. The first example demonstrates that the hybrid model can produce sudden stratospheric warming, a dynamical process of nature not resolved by the low resolution AGCM component of the hybrid model. The second and third example show that introducing 6‐hr cumulative precipitation and sea surface temperature (SST) as ML‐based prognostic variables improves the precipitation climatology and leads to a realistic ENSO signal in the SST and atmospheric surface pressure.

This paper describes an implementation of the combined hybrid‐parallel prediction (CHyPP) approach of Wikner et al. (2020), https://doi.org/10.1063/5.0005541 on a low‐resolution atmospheric global circulation model (AGCM). The CHyPP approach combines a physics‐based numerical model of a dynamical system (e.g., the atmosphere) with a computationally efficient type of machine learning (ML) called reservoir computing to construct a hybrid model. This hybrid atmospheric model produces more accurate forecasts of most atmospheric state variables than the host AGCM for the first 7–8 forecast days, and for even longer times for the temperature and humidity near the earth's surface. It also produces more accurate forecasts than a model based only on ML, or a model that combines linear regression, rather than ML, with the AGCM. The potential of the CHyPP approach for climate research is demonstrated by a 10‐year long hybrid model simulation of the atmospheric general circulation, which shows that the hybrid model can simulate the general circulation with substantially smaller systematic errors and more realistic variability than the host AGCM.

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data are in the form of noisy partial measurements of the past and present state of the dynamical system. Recently, there have been several promising data-driven approaches to forecasting of chaotic dynamical systems using machine learning. Particularly promising among these are hybrid approaches that combine machine learning with a knowledge-based model, where a machine-learning technique is used to correct the imperfections in the knowledge-based model. Such imperfections may be due to incomplete understanding and/or limited resolution of the physical processes in the underlying dynamical system, e.g., the atmosphere or the ocean. Previously proposed data-driven forecasting approaches tend to require, for training, measurements of all the variables that are intended to be forecast. We describe a way to relax this assumption by combining data assimilation with machine learning. We demonstrate this technique using the Ensemble Transform Kalman Filter to assimilate synthetic data for the three-variable Lorenz 1963 system and for the Kuramoto-Sivashinsky system, simulating a model error in each case by a misspecified parameter value. We show that by using partial measurements of the state of the dynamical system, we can train a machine-learning model to improve predictions made by an imperfect knowledge-based model.

Abstract This study further evaluates the modeling approach of Jia et al. (2019), https://doi.org/10.1029/2019gl081960 (JEA19) to investigate the potential effects of mesoscale sea surface temperature (SST) variability on the atmospheric circulation. The approach employs a global atmospheric circulation model coupled to a slab ocean model to produce two ensembles of simulations: one in which the SST exhibits realistic mesoscale variability, and another in which the mesoscale SST variability is suppressed. The results of the present study suggest that the modeling approach yields the desired SST differences between the two ensembles at the mesoscales. They also show, however, that the approach can lead to undesirable SST differences at the large scales, if the prescribed pair of oceanic heat flux fields have large scale differences. In the experiments of JEA19, such forced, large scale SST differences dominate over the large scale differences that may develop in response to changes in the large scale atmospheric circulation by nonlinear interactions with the SST. This result suggests that finding a proper pair of estimates of the oceanic heat flux fields is necessary for the investigation of the potential upscale impact of mesoscale SST variability on the atmosphere by the approach of JEA19. The paper concludes with proposing a potential improved strategy to obtain such a pair of estimates.

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics (subgrid-scale closure).

In their comment, Žagar and Szunyogh raised concerns about a recent study by Zhang et al. that examined the predictability limit of midlatitude weather using two up-to-date global models. Zhang et al. showed that deterministic weather forecast may, at best, be extended by 5 days, assuming we could achieve minimal initial-condition uncertainty (e.g., 10% of current operational value) with a nearly perfect model. Žagar and Szunyogh questioned the methodology and the experiments of Zhang et al. Specifically, Žagar and Szunyogh raised issues regarding the effects of model error on the growth of the forecast uncertainty. They also suggested that estimates of the predictability limit could be obtained using a simple parametric model. This reply clarifies the misunderstandings in Žagar and Szunyogh and demonstrates that experiments conducted by Zhang et al. are reasonable. In our view, the model error concern in Žagar and Szunyogh does not apply to the intrinsic predictability limit, which is the key focus of Zhang et al. and the simple parametric model described in Žagar and Szunyogh does not serve the purpose of Zhang et al.

In this talk we use the data from an operational ensemble prediction system to investigate recent developments in practical predictability across scales. Furthermore, we separate the estimated forecast error data into components representing the two dominant regimes in the atmosphere, the Rossby and inertia-gravity regimes. The latter is used to discuss aspects of tropical predictability. We define the practical predictability limit of a meteorological field (e.g., meridional wind at 500 hPa) or of a variability mode (e.g., the equatorial Kelvin wave) by the forecast time at which the root mean square (rms) forecast error normalized by its saturation value reaches a prescribed threshold value (e.g., 60%). The investigative technique fits a parametric function to the curve that describes the growth of the rms error of the forecasts with forecast time for a sample of forecasts. The parametric model describes the functional dependence of the magnitude of the forecast error on the magnitude of the initial error. Thus, it can be used for the estimation of the forecast error reduction that can be achieved by reducing the magnitude of the analysis error by a presumed percentage. Likewise, it can be used for the quantitative attribution of the forecast improvements between the years to analysis or model improvements. The calculations are carried out for the different spatial scales and the two regimes separately.

The paper investigates the applicability of machine learning (ML) to weather prediction by building a reservoir computing-based, low-resolution, global prediction model. The model is designed to take advantage of the massively parallel architecture of a modern supercomputer. The forecast performance of the model is assessed by comparing it to that of daily climatology, persistence, and a numerical (physics-based) model of identical prognostic state variables and resolution. Hourly resolution 20-day forecasts with the model predict realistic values of the atmospheric state variables at all forecast times for the entire globe. The ML model outperforms both climatology and persistence for the first three forecast days in the midlatitudes, but not in the tropics. Compared to the numerical model, the ML model performs best for the state variables most affected by parameterized processes in the numerical model.

An efficient modeling strategy is proposed for the investigation of the effect of the sea surface temperature (SST) mesoscale variability on atmospheric dynamics. Two ensembles of numerical simulations are generated with a high-resolution atmospheric global circulation model coupled to a slab ocean model. The two ensembles differ only in the treatment of the SST data used for the specification of the SST initial conditions and the estimation of the oceanic heat transport: one of the ensembles is generated by retaining, while the other by filtering, the mesoscale SST variability. The effect of mesoscale SST variability is assessed by comparing the two ensembles. The strategy is illustrated by simulation experiments with the Community Earth System Model, with a focus on the processes of the NH midlatitudes. The results suggest that ocean mesoscale variability has a significant effect on the jet streams, large-scale flow, and midlatitude storm tracks.

A pair of morphing-based ensemble forecast diagnostics is proposed for the verification of the location of precipitation events. The diagnostics are applied to operational global ensemble forecasts of winter storms in the United States in the winters of 2014/2015 and 2015/2016. A slowly developing systematic error is found to lead to an unrealistically fast eastward propagation of the storms in the week-two forecasts. Apart from this systematic error, the forecasts predict the uncertainty in the location of the precipitation events reliably. They, however, also grossly underestimate the uncertainty of the amount of precipitation in the short (shorter than 5 days) forecast range.

A regionally enhanced global (REG) data assimilation (DA) method is proposed. The technique blends high-resolution model information from a single or multiple limited-area model domains with global model and observational information to create a regionally enhanced analysis of the global atmospheric state. This single analysis provides initial conditions for both the global and limited-area model forecasts. The potential benefits of the approach for operational data assimilation are (i) reduced development cost, (ii) reduced overall computational cost, (iii) improved limited-area forecast performance from the use of global information about the atmospheric flow, and (iv) improved global forecast performance from the use of more accurate model information in the limited-area domains. The method is tested by an implementation on the U.S. Navy’s four-dimensional variational global data assimilation system and global and limited-area numerical weather prediction models. The results of the monthlong forecast experiments suggest that the REG DA approach has the potential to deliver the desired benefits.