Perturbations Of Initial Conditions Research Articles

Probabilistic Forecasts of Atmospheric River events using the HRRR Ensemble

The nine-member High-Resolution Rapid Refresh Ensemble (HRRRE) is evaluated for its ability to forecast five Atmospheric River (AR) events that impacted California in February–March 2019. Two sets of retrospective HRRRE simulations are conducted, a control with the standard set of perturbations (initial and boundary conditions, stochastic parameters, and physics tendency), and an experiment with initial and boundary perturbations only. Reliability plots suggest the HRRRE control represents the observed Stage IV precipitation frequency well at 6-h to 24-h lead times, and rank histograms suggest the ensemble is slightly underdispersive. The HRRRE overpredicts precipitation frequency at the higher (25 mm) threshold. These results suggest the HRRRE is a useful tool to quantify probabilistic forecasts of AR events in this region. Removing stochastic physics perturbations did not substantially impact probabilistic forecasts, suggesting most of the ensemble spread is from initial and boundary condition perturbations. Spatially, ensemble precipitation coefficient of variance is lower (less forecast uncertainty) over the Sierra Nevada range than other regions, suggesting that these ensemble perturbations have a smaller impact on precipitation processes occurring over the Sierra Nevada range. More work should be conducted to understand the impacts of other model perturbations, such as microphysics, on ensemble performance, and to improve Stage IV accuracy with frozen precipitation in mountainous regions.

Impacts of initial condition perturbation blending in 10- and 40-member convection-allowing ensemble forecasts

Abstract A series of convection-allowing 36-hour ensemble forecasts during the 2018 Spring season are used to better understand the impacts of ensemble configuration and blending different sources of initial condition (IC) perturbation. Ten- and 40-member ensemble configurations are initialized with the multi-scale IC perturbations generated as a product of convective-scale data assimilation (MULTI), and initialized with the MULTI IC perturbations blended with IC perturbations downscaled from coarser resolution ensembles (BLEND). The forecast performance of both precipitation and non-precipitation variables is consistently improved by the larger ensemble size. The benefit of the larger ensemble is largely, but not entirely, due to compensating for under-dispersion in the fixed-physics ensemble configuration. A consistent improvement in precipitation forecast skill results from blending in the 10-member ensemble configuration, corresponding to a reduction in the ensemble calibration error (i.e., reliability component of Brier Score). In the 40-member ensemble configuration, the advantage of blending is limited to the ∼18-22 hour lead times at all precipitation thresholds, and the ∼35-36 hour lead times at the lowest threshold, both corresponding to an improved resolution component of the Brier Score. The advantage of blending in the 40-member ensemble during the diurnal convection maximum of ∼18-22 hour lead times is primarily due to cases with relatively weak synoptic scale forcing while advantages at later lead times beyond ∼30 hours lead time are most prominent on cases with relatively strong synoptic scale forcing. The impacts of blending and ensemble configuration on forecasts of non-precipitation variables is generally consistent with the impacts on the precipitation forecasts.

State estimation of a novel brake-by-wire system based on cascade observer

Pressure regulation is the primary function of the brake-by-wire (BBW) system, and its prerequisite is the precise pressure acquisition. In autonomous vehicles(AVs), a higher fail-safe level is required that a backup pressure source is available when the main pressure source fails. So the use of pressure sensors, like the existing method, for pressure regulation will increase the cost of BBW systems in AVs. To meet the requirement of brake redundancy and the cost limit, a novel BBW system with a redundant pressure supply unit is designed and its electro-mechanical-hydraulic model is analyzed in this research. A time-domain observer (TDO) of motor speed is designed based on the periodic characteristics of motor current to get more system information. Next, the robust observer of pressure is proposed based on the existing current sensor and the derived motor speed. Its computational burden is reduced by calculating the matrices offline. The estimator developed in this paper is verified in typical pressure regulation conditions. Experimental results show that the estimation error of the motor speed is within 3% and has the potential to be improved, and the error of pressure is within 0.1 MPa, and the observer exhibits enough robustness under different initial condition perturbations.

Different Initial Condition Perturbation Methods for Convection-Permitting Ensemble Forecasting over South China during the Rainy Season

Abstract In this study, downscaling, ensemble data assimilation, time lagging, and their combination were used to generate initial condition (IC) perturbations for 12-h convection-permitting ensemble forecasting for heavy-rainfall events over South China during the rainy season in 2013–20. These events were classified as weak- and strong-forcing cases based on synoptic-scale forcing during the presummer rainy season and as landfalling tropical cyclone (TC) cases. This study investigated the impacts of various IC perturbation methods on multiscale characteristics of perturbations and the forecast performance for both nonprecipitation and precipitation variables. These perturbation methods represented different source IC uncertainties and thus differed in multiscale characteristics of perturbations in vertical structures, horizontal distributions, and time evolution. The combination of various IC perturbation methods evidently increased perturbations or spreads of precipitation in both magnitude and location and thus improved the forecast-error estimation. Such an improvement was most and least evident for TC cases during the early and late forecasts, respectively, and was more evident for strong- than weak-forcing cases beyond 6 h. The combination of various IC perturbation methods generally improved both the ensemble-mean and probabilistic forecasts with case-dependent improvements. For heavy rainfall forecasting, 1–6-h improvements were most prominent for TC cases in terms of discrimination and accuracy, while 7–12-h improvements were least prominent for weak-forcing cases in terms of reliability and accuracy. In particular, the improvements in predicting weak-forcing cases increased with spatial errors. In contrast, for strong-forcing cases, the improvements were least and most prominent before and beyond 6 h, respectively. Significance Statement Precipitation forecasting for heavy-rainfall events over South China in the rainy season is still challenging due to large uncertainties. Convection-permitting ensemble forecasting is expected to address such uncertainties to improve forecasts of heavy rainfall. However, it is not yet clear how to optimally design convection-permitting ensembles by implementing perturbations in initial conditions (ICs). This study investigates the impacts of various IC perturbation methods on convection-permitting ensemble forecasting over South China in the rainy season. Various IC perturbation methods show discrepant multiscale characteristics of perturbations, which generally complement each other when these perturbations are combined. The added values of combining various IC perturbation methods in forecasting are confirmed for most variables. However, such values are case dependent, with the largest values for tropical cyclone cases during the early forecasts and for the presummer rainy season cases with strong synoptic-scale forcing during late forecasts. Thus, it is still essential to further improve the combination of various types of IC perturbation methods.

Improving the Forecasting of El Niño Amplitude Based on an Ensemble Forecast Strategy for Westerly Wind Bursts

Abstract The forecasting of El Niño amplitude remains uncertain, with false alarms or underestimations often occurring. It has been suggested that westerly wind bursts (WWBs) are crucial atmospheric stochastic forcing that affects the development, amplitude, and predictability of El Niño. Effectively capturing the influence of WWBs in El Niño forecasting systems to mitigate El Niño forecast uncertainties continues to be a widely discussed topic. In this work, two El Niño ensemble forecast scenarios incorporating WWBs were devised utilizing an intermediate coupled model capable of simulating the rational features of El Niño–Southern Oscillation and a refined WWB parameterization scheme. To start with, both the seasonal variations and the dependence on the oceanic background state were considered to improve the parameterization of WWBs. Furthermore, considering the short intrinsic predictability limit of WWBs with respect to the interannual scale of El Niño evolution, a WWB ensemble forecast strategy was designed to obtain their occurrence probability and the statistical features of their magnitude and central location. With this in mind, an ensemble forecast of El Niño events occurring during 1979–2021 based on a WWB ensemble forecast was established (termed WWB-based). For comparison, a conventional El Niño ensemble forecast based on initial condition (IC) perturbations was also conducted (termed IC-based). Results indicated that the WWB-based approach shows better performance in forecasting the El Niño amplitude than the IC-based one. The present approach suggests that an ensemble forecast with proper consideration of the scale interaction between the fast WWBs and interannual variations is more physically consistent. Significance Statement Westerly wind bursts (WWBs) are believed to influence the growth and amplitude of El Niño events. Unfortunately, the short intrinsic predictability limit of WWBs brings considerable uncertainty to the forecasting of El Niño amplitude. In this study, a refined parameterization scheme for WWBs, along with an ensemble forecast strategy designed to obtain the occurrence probability of WWBs and the statistical features of their magnitude and central location, was employed in an intermediate coupled model to produce an ensemble forecast for the El Niño events occurring during 1979–2021. The results showed that an ensemble forecast of El Niño based on WWB ensemble forecast can fully consider WWBs’ potential impact on the El Niño system and improve El Niño forecasts.

Compressive-sensing model reconstruction of nonlinear systems with multiple attractors

In this study, facing the challenges on model reconstruction for multi-attractor nonlinear systems, the data generation and sparse regression processes in sparse identification method are generalized, referring to compressive sensing, to obtain the accurate description under the least volume of test data set. In the data generation process, we introduce compressive sensing process by an arbitrary initial condition and arbitrary perturbations applied on time domain to transcend the local attractors. In the sparse regression process, the optimum sparse parameter is obtained by bi-optimization criterion according to accuracy and interpretability. Then, accuracy criterion is proposed, and when it discovers the unperceived dynamic behaviors, more dynamic data could be recorded and added into the modeling reconstruction data set by perturbations. It requires less dynamic signals by dynamical compressive sensing with perturbations compared to the previous method with uniform point fetching on the state space. Several numerical cases and two experiments of nonlinear systems with different kinds of multi-attractors are proposed to illustrate the effectiveness of the reconstruction method. In experiment, for the dynamic systems with multi-steady states phenomenon, the most obvious problem is the calibration of the equilibrium at the symmetrical configuration, which cannot be obtained for local dynamic behaviors due to its instability. In applications, this generalized modeling reconstruction method can continuously and compressively sense the dynamic behaviors and the stability of multiple attractors to figure out the accurate governing equations under a small quantity of data. In summary, different from the previous sparse regression algorithm for nonlinear systems with multiple attractors under huge amount of data set assembled offline filling a large enough state space, the proposed model reconstruction process can intelligently sense the dynamic behaviors and give the accurate prediction.

Mediterranean tropical-like cyclone forecasts and analysis using the ECMWF ensemble forecasting system with physical parameterization perturbations

Abstract. Mediterranean tropical-like cyclones, called medicanes, present a multi-scale nature, and their track and intensity have been recognized as highly sensitive to large-scale atmospheric forcing and diabatic heating as represented by the physical parameterizations in numerical weather prediction. Here, we analyse the structure and investigate the predictability of medicanes with the aid of the European Centre for Medium-Range Weather Forecast (ECMWF) Integrated Forecast System (IFS) ensemble forecasting system with 25 perturbed members at 9 km horizontal resolution (compared with the 16 km operational resolution). The IFS ensemble system includes the representation of initial uncertainties from the ensemble data assimilation (EDA) and a recently developed uncertainty representation of the model physics with perturbed parameters (stochastically perturbed parameterizations, SPP). The focus is on three medicanes, Ianos, Zorbas, and Trixie, among the strongest in recent years. In particular, we have carried out separate ensemble simulations with initial perturbations, full physics SPP, with a reduced set of SPP, where only convection is perturbed to highlight the convective nature of medicanes and an operational ensemble combining the SPP and the initial perturbations. It is found that compared with the operational analysis and satellite rainfall data, the forecasts reproduce the tropical-like features of these cyclones. Furthermore, the SPP simulations compare to the initial-condition perturbation ensemble in terms of tracking, intensity, precipitation, and, more generally, in terms of ensemble skill and spread. Moreover, the study confirms that similar processes are at play in the development of the investigated three medicanes, in that the predictability of these cyclones is linked not only to the prediction of the precursor events (namely the deep cutoff low) but also to the interaction of the upper-level advected potential vorticity (PV) streamer with the tropospheric PV anomaly that is diabatically produced by latent heat.

Can Artificial Intelligence‐Based Weather Prediction Models Simulate the Butterfly Effect?

AbstractWe investigate error growth from small‐amplitude initial condition perturbations, simulated with a recent artificial intelligence‐based weather prediction model. From past simulations with standard physically‐based numerical models as well as from theoretical considerations it is expected that such small‐amplitude initial condition perturbations would grow very fast initially. This fast growth then sets a fixed and fundamental limit to the predictability of weather, a phenomenon known as the butterfly effect. We find however, that the AI‐based model completely fails to reproduce the rapid initial growth rates and hence would incorrectly suggest an unlimited predictability of the atmosphere. In contrast, if the initial perturbations are large and comparable to current uncertainties in the estimation of the initial state, the AI‐based model basically agrees with physically‐based simulations, although some deficits are still present.

ENSO Spread Caused by Uncertainties in Initial Condition and High-Frequency Perturbations in the Tropical Pacific

Abstract Uncertainties both in the initial condition (IC) and surface wind high-frequency perturbations (HFPs) contribute to the prediction spread of El Niño–Southern Oscillation (ENSO), yet the relative roles of the two are hard to separate, mostly due to the nonlinearity in ENSO dynamics. In this study, we conducted two ensemble experiments using the CESM model to analyze the source of ENSO spread arising from the tropical Pacific. The HFPs were precluded using an online low-pass-filtering scheme in one experiment. Results showed that the uncertainty in ENSO prediction depends on both the IC and HFPs. By comparing simulations with and without HFPs, it is found that the predicted ENSO spread decreased in magnitude when HFPs are removed, especially in the first four prediction months. At integration time longer than that, the additional impact of HFPs cannot be detected on top of that of the uncertainty in IC. To the ENSO spread anomaly, we found that it is tightly associated with uncertainty in the sea surface temperature and surface wind in the central-eastern equatorial Pacific at the short integration time, and associated with the HFPs in the western equatorial Pacific at the long integration time. When the HFPs are removed, the precursor of the ENSO spread anomaly at the long lead time emerges in the northeastern tropical Pacific, the area where the Pacific meridional mode originates from. Our results indicate that the uncertainty in ENSO prediction depends primarily on IC, and the HFPs in the western equatorial Pacific play the secondary role.

Detectability and global observer design for 2D Navier–Stokes equations with uncertain inputs

We present simulation friendly detectability conditions for 2D Navier–Stokes Equation (NSE) with periodic boundary conditions, and describe a generic class of “detectable” observation operators: it includes pointwise evaluation of NSE’s solution at interpolation nodes, and spatial average measurements. For “detectable” observation operators we design a global infinite-dimensional observer for NSE with uncertain possibly destabilizing inputs: in our numerical experiments we illustrate H1-sensitivity of NSE to small perturbations of initial conditions, yet the observer converges for known and uncertain inputs.

Chaotic van der Pol Oscillator Control Algorithm Comparison

The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the van der Pol oscillator. Deterministic artificial intelligence is a feedforward and feedback control method that leverages the known physics of the van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline.

Initial Condition Convection-Allowing Ensembles with Large Membership for Probabilistic Prediction of Convective Hazards

Abstract Convection-allowing model (CAM) ensemble forecasts provide quantitative probabilistic guidance of convective hazards that forecasters would otherwise qualitatively assess. Various initial condition (IC) strategies can be used to generate CAM probabilistic forecasts, but it is still unclear how different configurations perform. Schwartz et al. verified five 10-member IC CAM ensembles over one month of 0000 UTC initializations with a focus on precipitation. Here, we initialize four 42-member IC CAM ensembles every 12 h over 6 weeks and verify forecasts of precipitation, column maximum reflectivity, and hourly maximum updraft helicity. The Texas Tech University real-time EnKF ensemble and three additional IC ensemble modeling systems are verified. Holding the model configuration constant, additional ICs are generated by downscaling time-lagged Global Ensemble Forecast System (GEFS) members, applying correlated random noise to Global Forecast System (GFS) analyses, and recentering EnKF perturbations about GFS analyses. We found that ensemble ICs constructed with correlated random noise and EnKF perturbations about GFS analyses both produced higher-quality precipitation forecasts than downscaled GEFS and EnKF strategies. However, downscaled GEFS and EnKF perturbations about GFS analyses frequently initialized more skillful forecasts of reflectivity than ICs with random perturbations, suggesting that flow-dependent perturbations are important for forecasting deep convection. Even with a suboptimal EnKF configuration, our findings still echo those of Schwartz et al. We extend their work by exploring 1) verification of additional convective hazards and 2) empirical scaling of IC perturbations as a computationally inexpensive method for improving CAM ensemble forecasts.

SwinVRNN: A Data‐Driven Ensemble Forecasting Model via Learned Distribution Perturbation

AbstractThe data‐driven approaches for medium‐range weather forecasting are recently shown to be extraordinarily promising for ensemble forecasting due to their fast inference speed compared to the traditional numerical weather prediction models. However, their forecast accuracy can hardly match the state‐of‐the‐art operational ECMWF Integrated Forecasting System (IFS) model. Previous data‐driven approaches perform ensemble forecasting using some simple perturbation methods, like the initial condition perturbation and the Monte Carlo dropout. However, their ensemble performance is often limited arguably by the sub‐optimal ways of applying perturbation. We propose a Swin Transformer‐based Variational Recurrent Neural Network (SwinVRNN), which is a stochastic weather forecasting model combining a SwinRNN predictor with a perturbation module. SwinRNN is designed as a Swin Transformer‐based recurrent neural network, which predicts the future states deterministically. Furthermore, to model the stochasticity in the prediction, we design a perturbation module following the Variational Auto‐Encoder paradigm to learn the multivariate Gaussian distributions of a time‐variant stochastic latent variable from the data. Ensemble forecasting can be easily performed by perturbing the model features leveraging the noise sampled from the learned distribution. We also compare four categories of perturbation methods for ensemble forecasting, that is, fixed distribution perturbation, learned distribution perturbation, MC dropout, and multi model ensemble. Comparisons on the WeatherBench data set show that the learned distribution perturbation method using our SwinVRNN model achieves remarkably improved forecasting accuracy and reasonable ensemble spread due to the joint optimization of the two targets. More notably, SwinVRNN surpasses operational IFS on the surface variables of the 2‐m temperature and the 6‐hourly total precipitation at all lead times up to 5 days (Code is available at https://github.com/tpys/wwprediction).

Scale-Dependent Verification of the OU MAP Convection Allowing Ensemble Initialized with Multi-Scale and Large-Scale Perturbations during the 2019 NOAA Hazardous Weather Testbed Spring Forecasting Experiment

Given the large range of resolvable space and time scales in large-domain convection-allowing for ensemble forecasts, there is a need to better understand optimal initial-condition perturbation strategies to sample the forecast uncertainty across these space and time scales. This study investigates two initial-condition perturbation strategies for CONUS-domain ensemble forecasts that extend into the two-day forecast lead time using traditional and object-based verification methods. Initial conditions are perturbed either by downscaling perturbations from a coarser resolution ensemble (i.e., LARGE) or by adopting the analysis perturbations from a convective-scale, EnKF system (i.e., MULTI). It was found that MULTI had more ensemble spread than LARGE across all scales initially, while LARGE’s perturbation energy surpassed that of MULTI after 3 h and continued to maintain a surplus over MULTI for the rest of the 36h forecast period. Impacts on forecast bias were mixed, depending on the forecast lead time and forecast threshold. However, MULTI was found to be significantly more skillful than LARGE at early forecast hours for the meso-gamma and meso-beta scales (1–9h), which is a result of a larger and better-sampled ensemble spread at these scales. Despite having a smaller ensemble spread, MULTI was also significantly more skillful than LARGE on the meso-alpha scale during the 20–24h period due to a better spread-skill relation. MULTI’s performance on the meso-alpha scale was slightly worse than LARGE’s performance during the 6–12h period, as LARGE’s ensemble spread surpassed that of MULTI. The advantages of each method for different forecast aspects suggest that the optimal perturbation strategy may require a combination of both the MULTI and LARGE techniques for perturbing initial conditions in a large-domain, convection-allowing ensemble.

Robust Classification Using Contractive Hamiltonian Neural ODEs

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this letter, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical system is contractive if all solutions with different initial conditions converge to each other exponentially fast. As a consequence, perturbations in initial conditions become less and less relevant over time. Since in NODEs the input data corresponds to the initial condition of dynamical systems, we show contractivity can mitigate the effect of input perturbations. More precisely, inspired by NODEs with Hamiltonian dynamics, we propose a class of contractive Hamiltonian NODEs (CH-NODEs). By properly tuning a scalar parameter, CH-NODEs ensure contractivity by design and can be trained using standard backpropagation. Moreover, CH-NODEs enjoy built-in guarantees of non-exploding gradients, which ensure a well-posed training process. Finally, we demonstrate the robustness of CH-NODEs on the MNIST image classification problem with noisy test data.

A Comparison between 2D and 3D Rescaling Masks of Initial Condition Perturbation in a 3-km Storm-Scale Ensemble Prediction System

Abstract Using a 3-km regional ensemble prediction system (EPS), this study tested a three-dimensional (3D) rescaling mask for initial condition (IC) perturbation. Whether the 3D mask-based EPS improves ensemble forecasts over current two-dimensional (2D) mask-based EPS has been evaluated in three aspects: ensemble mean, spread, and probability. The forecasts of wind, temperature, geopotential height, sea level pressure, and precipitation were examined for a summer month (1–28 July 2018) and a winter month (1–27 February 2019) over a region in North China. The EPS was run twice per day (initiated at 0000 and 1200 UTC) to 36 h in forecast length, providing 56 warm-season forecast cases and 54 cold-season cases for verification. The warm and cold seasons are verified separately for comparison. The study found the following: 1) The vertical profile of IC perturbation becomes closer to that of analysis uncertainty with the 3D rescaling mask. 2) Ensemble performance is significantly improved in all three aspects. The biggest improvement is in the ensemble spread, followed by the probabilistic forecast, and the least improvement is in the ensemble mean forecast. Larger improvements are seen in the warm season than in the cold season. 3) More improvement is in the shorter time range (<24 h) than in the longer range. 4) Surface and lower-level variables are improved more than upper-level ones. 5) The underlying mechanism for the improvement has been investigated. Convective instability is found to be responsible for the spread increment and, thus, overall ensemble forecast improvement. Therefore, using a 3D rescaling mask is recommended for an EPS to increase its utility especially for shorter time range and surface weather elements. Significant Statement A weather prediction model is a complex system that consists of nonlinear differential equations. Small errors in either its inputs or model itself will grow with time during model integration, which will contaminate a forecast. To quantify such contamination (“uncertainty”) of a forecast, the ensemble forecasting technique is used. An ensemble of forecasts is a multiple of model runs at the same time but with slightly “perturbed” inputs or model versions. These small perturbations are supposed to represent true “uncertainty” in inputs or model representation. This study proposed a technique that makes a perturbation’s vertical structure more resemble real uncertainty (intrinsic error) in input data and confirmed that it can significantly improve ensemble forecast quality especially for a shorter time range and lower-level weather elements. It is found that convective instability is responsible for the improvement.

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Engineers strive to realize the goal of control in the best possible way based on a given quality criterion when developing control system. The well-known optimal control problem requires finding a solution as a function of time. Such a function cannot be directly used to control a real object because its application corresponds to an open-loop control system and engineers usually complete it with a feedback stabilization system. Hence, there is an obvious need to reformulate the optimal control problem so that its solution can be directly applied to real objects. The paper presents a new extended statement of the optimal control problem. An additional requirement for the control function is introduced to give the system describing the control object properties that will ensure the stability of solutions. The desired control function must provide for the optimal trajectory given the properties of the attractor in the neighbourhood. The solution to the extended optimal control problem can be directly used to control a real object. The paper presents a computational machine learning approach to solving the extended problem of optimal control based on the application of a synthesized optimal control technique. Examples of the practical solution to the stated problem are given to illustrate the efficiency of the approach, where the solution to the conventional optimal control problem is compared with the proposed extended one in the presence of perturbations in models and initial conditions.

Characterization of ensemble generation strategies: Application to three illustrative examples of Mediterranean high-impact weather

Predictability of high-impact weather constitutes a major challenge. In this study, we contribute to this relevant topic by analyzing the characteristics of multiple ensemble prediction systems aimed at sampling initial and/or model uncertainties for three exemplary heavy precipitation systems that occurred over the western Mediterranean. In particular, initial condition perturbations are generated by (i) directly downscaling the ensemble members from a global ensemble and (ii) creating perturbations by sampling a wide range of scales using an adaptation of the breeding methodology. Model error is sampled by applying stochastic perturbations to physical parameterizations and to microphysics parameters. A positive impact in terms of ensemble diversity is obtained when initial condition perturbations across a broad range of scales are applied, especially at low levels and for cases in which local factors are more relevant. Regarding stochastic model perturbations, they display very localized perturbations with low amplitude, which are insufficient to capture extreme scenarios, except when local factors play a dominant role. However, when combined with initial condition perturbations, they generally increase diversity and perturbation amplitude over areas characterized by deep moist convection. This outcome exhibits the positive impact of sampling both uncertainty sources, even in the extremely nonlinear regime that defines convective-scale phenomena.

The Sensitivity of Downstream Ridge Building Forecasts to Upstream Warm Conveyor Belt Forecast Uncertainty Using MPAS

Abstract One potential way to improve the skill of medium-range weather forecasts is to improve the evolution of Rossby waves, which largely modulate extratropical weather. Recent research has hypothesized that the predictability of downstream Rossby waves may be limited by forecast uncertainty linked to upstream diabatic processes such as latent heat release within the warm conveyor belt (WCB) of extratropical cyclones. This hypothesis is evaluated using Model for Prediction Across Scales (MPAS) ensemble forecasts for two events characterized by highly amplified flow over the North Atlantic associated with cyclogenesis. The source of variability in ridge forecasts is diagnosed using the ensemble-sensitivity technique and a potential vorticity (PV) tendency budget, which quantifies the contribution from individual physical processes toward subsequent ridge amplification. Before the onset of ridge amplitude differences for both events, ensemble forecasts with a more amplified ridge are associated with greater negative PV advection by the irrotational wind. The importance of PV advection by the irrotational wind suggests that PV changes are modulated by diabatic heating, which is confirmed by the sensitivity of ridge amplitude to earlier diabatic heating and lower-tropospheric moisture within an upstream WCB. After the onset of ridge amplitude differences, PV advection by the nondivergent wind becomes the primary driver of downstream forecast differences. Initial condition perturbations within the sensitive areas of the WCB confirm that increasing the initial lower-tropospheric moisture results in a more amplified ridge. This suggests that more accurate initial conditions near the WCB could lead to better downstream forecasts.

Short-Term Convection-Allowing Ensemble Precipitation Forecast Sensitivity to Resolution of Initial Condition Perturbations and Central Initial States

Abstract Nine sets of 36-h, 10-member, convection-allowing ensemble (CAE) forecasts with 3-km horizontal grid spacing were produced over the conterminous United States for a 4-week period. These CAEs had identical configurations except for their initial conditions (ICs), which were constructed to isolate CAE forecast sensitivity to resolution of IC perturbations and central initial states about which IC perturbations were centered. The IC perturbations and central initial states were provided by limited-area ensemble Kalman filter (EnKF) analyses with both 15- and 3-km horizontal grid spacings, as well as from NCEP’s Global Forecast System (GFS) and Global Ensemble Forecast System. Given fixed-resolution IC perturbations, reducing horizontal grid spacing of central initial states improved ∼1–12-h precipitation forecasts. Conversely, for constant-resolution central initial states, reducing horizontal grid spacing of IC perturbations led to comparatively smaller short-term forecast improvements or none at all. Overall, all CAEs initially centered on 3-km EnKF mean analyses produced objectively better ∼1–12-h precipitation forecasts than CAEs initially centered on GFS or 15-km EnKF mean analyses regardless of IC perturbation resolution, strongly suggesting it is more important for central initial states to possess fine-scale structures than IC perturbations for short-term CAE forecasting applications, although fine-scale perturbations could potentially be critical for data assimilation purposes. These findings have important implications for future operational CAE forecast systems and suggest CAE IC development efforts focus on producing the best possible high-resolution deterministic analyses that can serve as central initial states for CAEs. Significance Statement Ensembles of weather model forecasts are composed of different “members” that, when combined, can produce probabilities that specific weather events will occur. Ensemble forecasts begin from specified atmospheric states, called initial conditions. For ensembles where initial conditions differ across members, the initial conditions can be viewed as a set of small perturbations added to a central state provided by a single model field. Our study suggests it is more important to increase horizontal resolution of the central state than resolution of the perturbations when initializing ensemble forecasts with 3-km horizontal grid spacing. These findings suggest a potential for computational savings and a streamlined process for improving high-resolution ensemble initial conditions.