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Biased, incomplete numerical models are often used for forecasting states of complex dynamical systems by mapping an estimate of a “true” initial state into model phase space, making a forecast, and then mapping back to the “true” space. While advances have been made to reduce errors associated with model initialization and model forecasts, we lack a general framework for discovering optimal mappings between “true” dynamical systems and model phase spaces. Here, we propose using a data‐driven approach to infer these maps. Our approach consistently reduces errors in the Lorenz‐96 system with an imperfect model constructed to produce significant model errors compared to a reference configuration. Optimal pre‐ and post‐processing transforms leverage “shocks” and “drifts” in the imperfect model to make more skillful forecasts of the reference system. The implemented machine learning architecture using neural networks constructed with a custom analog‐adjoint layer makes the approach generalizable across applications. Plain Language Summary Modeling and forecasting natural systems, such as Earth's oceans and atmosphere, is difficult due to their inherent unpredictability, our incomplete understanding of their dynamics, and their vastness and complexity. One way to improve forecasts is by improving physical representations within numerical models. However, models will always have shortcomings. The alternative approach explored here is to maximize the utility of available imperfect or incomplete models by revising how the model is used and how its forecast is interpreted. Here, we employ machine learning to learn pre‐ and post‐processing operators, called cross‐attractor transforms (CATs), which reduce the overall forecast errors from imperfect models. We demonstrate the framework's efficacy by using a simplified dynamical model as an imperfect representation of a higher‐dimensional chaotic dynamical system, analogous to using a simple pendulum to forecast the behavior of a double pendulum. In addition to improving forecasts, CATs offer insights into how the two systems evolve in time. The approach is generalizable across dynamical systems and disciplines. Key Points Forecasts from imperfect models are improved using optimized pre‐ and post‐processing operators Neural networks trained on imperfect models and reference truth forecasts efficiently derive these operators Forecasts from this hybrid machine‐learning approach are more accurate than purely data‐driven methods when applied to an idealized system

Forecasts of numerical weather prediction models unavoidably contain errors, and it is a common practice to post-process the model output and correct the error for the proper use of the forecasts. This study develops a grid-to-multipoint (G2N) model output error correction scheme which extracts model spatial features and corrects multistation forecasts simultaneously. The model was tested for an operational high-resolution model system, the precision rapid update forecasting system (PRUFS) model, running for East China at 3 km grid intervals. The variables studied include 2 m temperature, 2 m relative humidity, and 10 m wind speed at 311 standard ground-based weather stations. The dataset for training G2N is a year of historical PRUFS model outputs and the surface observations of the same period and the assessment of the G2N performance are based on the output of two months of real-time G2N. The verification of the real-time results shows that G2N reduced RMSEs of the 2 m temperature, 2 m relative humidity, and 10 m wind speed forecast errors of the PRUFS model by 19%, 24%, and 42%, respectively. Sensitivity analysis reveals that increasing the number of the target stations for simultaneous correction helps to improve the model performance and reduces the computational cost as well indicating that enhancing the loss function with spatial regional meteorological structure is helpful. On the other hand, adequately selecting the size of influencing grid areas of the model input is also important for G2N to incorporate enough spatial features of model forecasts but not to include the information from the grids far from the correcting areas. G2N is a highly efficient and effective tool that can be readily implemented for real-time regional NWP models.

Tropical cyclone (TC) Doksuri (2023) exhibited a sudden northward turn over the northeastern part of the South China Sea (SCS). However, most global models failed to capture such track change. The US National Centers for Environmental Prediction Final Analysis (FNL) data and The International Grand Global Ensemble (TIGGE) data were therefore used to study the underlying mechanisms for the sudden track change and the factors leading to the track forecast errors of different global models so as to give some insight for the forecasters in predicting such TC track change and global model developers in modifying the model physics. The non‐linear advection of the vorticity of the asymmetric winds associated with the monsoon trough over the SCS and that of the symmetric wind of the TC resulted in the sudden northward turn of the TC track. However, the strength and the eastward extension of the monsoon trough were underpredicted, leading to a westward‐moving track without a sharp northward turn. On the contrary, if the strength of the monsoon trough was overpredicted, the environmental steering was over‐altered, resulting in an early northward turn. The intensity and outer wind structure of the TC also played important roles in the monsoonal interaction and thus the track forecast errors. Global numerical models failed to predict the track of tropical cyclone (TC) Doksuri (2023) with a large forecast spread. This paper is to find out the underlying reasons for the erroneous track forecast and gives insight for the forecasters and model developers for reducing the track forecast error.

Statistical predictions of storm surge are critical for guiding evacuation and emergency response/preparedness decisions during landfalling storms. The probabilistic characteristics of these predictions are formulated by utilizing historical forecast errors to quantify relevant uncertainties in the National Hurricane Center advisories. This ultimately leads to the description of probability distributions quantifying the deviation from the nominal advisory for four different storm features: intensity, size, cross-track variability and along-track variability. Propagation of the uncertainty in these four storm features, serving as input to a numerical model for calculating storm surge, leads to the definition of the statistical surge estimates. This work investigates the application of variance-based global sensitivity analysis (GSA), quantified through the estimation of Sobol' indices, to explore the importance of the forecast errors in the peak storm surge predictions. This GSA can assist in better understanding the impact of the different forecast errors for typical storms, and can also offer important insights for a specific storm, regarding the characteristics that influence the probabilistic surge predictions across its different advisories, as the storm comes closer to landfall. An efficient GSA implementation is presented here to address two key challenges of the specific problem: (i) the need to perform the GSA for a multi-dimensional output, corresponding to the surge for multiple locations within the geographic domain of interest that will be affected by a specific storm, and (ii) the restriction to use only a small number of hydrodynamic numerical simulations, since the associated computational burden of such simulations is significant. For addressing these challenges, dimensionality reduction through Principal Component Analysis (PCA) and a probability-based estimation of the variance of conditional expectations are combined to provide the necessary efficiency in the proposed GSA framework. The development of aggregated importance indices across the entire geographic domain is also discussed, incorporating the importance of the surge for each separate location (within this domain) using a variance-based weighting. This formulation is compared with an alternative, computationally efficient, definition of the aggregated importance, based on the readily available PCA information. A demonstration of this framework’s utility considering different historical storms (using National Weather Service advisories and forecast errors for past events) is provided, establishing comparisons across them and across multiple advisories for each storm.

It is often argued that numerical weather prediction models remain deficient in forecasting specific weather features and that such deficiencies contribute significantly to overall forecast errors. To clarify these claims, we quantify how cyclones, fronts, upper tropospheric jets, moisture transport axes (MTAs), and cold‐air outbreaks (CAOs) contribute to short‐term (12‐h) forecast errors and biases in the ERA5 reanalysis dataset from 1979 to 2022. Employing a feature‐based attribution method, we evaluate errors globally, focusing particularly on temperature, moisture, and wind fields, and examine regional and seasonal variations during winter (DJF) and summer (JJA). The presence of weather features is generally associated with increased forecast errors (RMSEs) compared to feature‐free conditions. RMSEs are especially pronounced for moisture fields in conjunction with fronts and MTAs, where errors in total column water vapor can be twice as large. Cyclone‐related errors are more pronounced in the low‐level wind field. During CAOs, on the other hand, errors are reduced. In terms of systematic biases, wind speeds and moisture are underestimated along western boundary currents, together with insufficient moisture transport along MTAs. Wintertime temperature biases over the Northern Hemisphere oceans have stronger associations with fronts and MTAs than those over the Southern Hemisphere oceans. A persistence analysis confirms that for some features and specific variables, forecasts yield less added value relative to non‐feature conditions. Cyclones are the most notable example, where forecasts provide less added value in most cases. In contrast, jets and CAOs are features where forecasts consistently add more added value. The identified feature‐based error diagnostics can aid targeted efforts to improve numerical weather prediction systems. We systematically attribute 12‐h forecast errors to five key synoptic features using ERA5, revealing that their contributions vary significantly across variables, regions, and seasons. During winter, for example, fronts over midlatitude oceans double forecast errors in moisture (left panel), whereas cyclones nearly double the errors in low‐level wind, particularly along the western boundary currents (right panel).

It is fundamental and useful to investigate how deep learning forecasting models (DLMs) perform compared to operational oceanography forecast systems (OFSs). However, few studies have intercompared their performances using an identical reference. In this study, three physically reasonable DLMs are implemented for the forecasting of the sea surface temperature (SST), sea level anomaly (SLA), and sea surface velocity in the South China Sea. The DLMs are validated against both the testing dataset and the “OceanPredict” Class 4 dataset. Results show that the DLMs’ RMSEs against the latter increase by 44%, 245%, 302%, and 109% for SST, SLA, current speed, and direction, respectively, compared to those against the former. Therefore, different references have significant influences on the validation, and it is necessary to use an identical and independent reference to intercompare the DLMs and OFSs. Against the Class 4 dataset, the DLMs present significantly better performance for SLA than the OFSs, and slightly better performances for other variables. The error patterns of the DLMs and OFSs show a high degree of similarity, which is reasonable from the viewpoint of predictability, facilitating further applications of the DLMs. For extreme events, the DLMs and OFSs both present large but similar forecast errors for SLA and current speed, while the DLMs are likely to give larger errors for SST and current direction. This study provides an evaluation of the forecast skills of commonly used DLMs and provides an example to objectively intercompare different DLMs.

Tropical cyclone (TC) track forecasting provides essential guidance for coastal communities. However, track forecast errors still occur, highlighting the need for continued research into error sources. Piecewise potential vorticity (PV) inversion is used systematically to quantitatively diagnose errors in track forecasts in four models during the 2017 Atlantic hurricane season. The deep layer mean steering flow (DLMSF) provides a sufficient proxy for hurricane movement, and DLMSF errors are correlated with TC track errors. Analysis of track forecasts for Hurricanes Harvey, Irma, and Maria reveals that their track errors are attributed to steering errors caused by misrepresentations of specific pressure systems. Harvey's westward track error in the GFS resulted from zonal wind errors from the Continental High, while Irma's northward track error in the SHiELD gfsIC resulted from meridional wind errors in the Bermuda High and Continental High. Maria's southward track error in the IFS resulted from meridional wind errors in the Bermuda High and a misrepresentation of Jose to Maria's northwest. The mean absolute error of the DLMSF shows that the Bermuda High contributed the most to steering flow errors in the cases examined. Our results show that piecewise PV inversion can identify the sources of biases in TC track forecasts. The correction of these biases may lead to improved track forecasts. Quantitative diagnostics presented here provide useful information for future model development. Plain Language Summary A tropical cyclone typically moves with the environmental wind, which is generated by several large‐scale pressure systems (e.g., Bermuda High, Continental High) in the atmosphere. Weather models can predict the path of tropical cyclones, but these forecasts have errors. Tropical cyclones often bring devastation along their path, so it is important to mitigate track errors to provide better warnings for impacted communities. Here, we use a diagnostic technique called “piecewise potential vorticity inversion” to understand how the environmental wind causes errors in tropical cyclone tracks. In three different examples of hurricane track forecasts, we show that errors in the predicted track are caused by errors in the environmental wind from specific pressure systems. By considering numerous cases, we can also identify model biases, or errors that are consistent throughout many forecasts. These errors are a result of errors in the models themselves. Overall, our results show that piecewise potential vorticity inversion is a useful diagnostic tool that has the potential to improve track forecasts through the identification of model biases. Key Points Contributions to tropical cyclone movement from individual synoptic systems are quantified using piecewise potential vorticity inversion Forecast errors of the deep layer mean steering flow are the main source of the track errors for Hurricanes Harvey, Irma, and Maria (2017) Forecast errors of the Bermuda High dominated the steering flow errors for the 2017 hurricane season

Weather manifests in spatiotemporally coherent structures. Weather forecasts hence are affected by both positional and structural or amplitude errors. This has been long recognized by practicing forecasters (cf., e.g., Tropical Cyclone track and intensity errors). Despite the emergence in recent decades of various objective methods for the diagnosis of positional forecast errors, most routine verification or statistical post-processing methods implicitly assume that forecasts have no positional error. The Forecast Error Decomposition (FED) method proposed in this study uses the Field Alignment technique which aligns a gridded forecast with its verifying analysis field. The total error is then partitioned into three orthogonal components: (a) large scale positional, (b) large scale structural, and (c) small scale error variance. The use of FED is demonstrated over a month-long MSLP data set. As expected, positional errors are often characterized by dipole patterns related to the displacement of features, while structural errors appear with single extrema, indicative of magnitude problems. The most important result of this study is that over the test period, more than 50% of the total mean sea level pressure forecast error variance is associated with large scale positional error. The importance of positional error in forecasts of other variables and over different time periods remain to be explored.

Using the observational data and the forecast and reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) during 2015–2018, the temporal and spatial distribution characteristics of the 2 m temperature forecast errors of ECMWF in China, as well as their attribution to upper-level circulation, are analyzed. Results show that positive 2 m temperature forecast errors mainly occur in northwestern, northern and northeastern China, and gradually increase from January to December. This kind of error is attributed to the circulation errors associated with the circumfluence of the low-level differential winds along the Mongolian Plateau, and influenced by the changes in the mid-latitude trough and ridge with the seasons. In contrast, the negative 2 m temperature forecast errors mainly occur in the southeastern part of the Qinghai-Tibet Plateau, with the largest errors around March and October, and the smallest errors around June and December. This kind of error is associated with a series of cyclonic and anticyclonic differential circulations generated by the detouring of the mid-level differential winds along the terrain near the south side of the Plateau. The positions and intensity of these differential circulations are also influenced by the variation in the mid-level circulation with the seasons.

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic (or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii (GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach 2 with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.