Ensemble-based Sensitivity Analysis Research Articles

Ensemble-based analysis of heavy rainfall–snowfall associated with mesoscale precipitation bands within an extratropical cyclone over northeastern China

This paper investigates the key synoptic-scale factors that affected the forecasting of mesoscale rainfall and snowfall and their associated uncertainties in a heavy rain–snow event in northeastern China on 18–20 November 2020, using ensemble-based sensitivity analysis based on global ensemble forecasts from the European Centre for Medium-Range Weather Forecasts. The heavy precipitation event was attributed to an extratropical cyclone and experienced two stages, with the snowfall stage having a better precipitation forecast skill than the rainfall stage. The mesoscale rainfall and snowfall were caused by a mesoscale rainband over Liaoning Province and two mesoscale snowbands over Heilongjiang Province, respectively, and they showed some differences with respect to their forecast skill and related key synoptic-scale factors contributing to the precipitation centers. The precipitation amount in the two different stages was correlated significantly with the midlevel trough and sensitive to the location and intensity of the low-level vortex (surface cyclone), and particularly the low-level jets and the associated water vapor transport. However, some differences were confirmed in the two different stages: the weaker midlevel trough and accompanying weaker low-level temperature trough in the rainfall stage were related to increased precipitation because the midlevel trough was far away from the control area, while the stronger midlevel trough and accompanying stronger low-level temperature trough were associated with increased precipitation in the snowfall stage. In addition to the synoptic-scale low-level jet (SLLJ), the precipitation in the rainfall stage was also affected by a boundary layer jet (BLJ) over the ocean, while only SLLJs were present in the snowfall stage. The uncertainty of the precipitation forecast was derived mainly from the uncertainty in the strength and location of the SLLJs and BLJ. Notably, the intensity of northeasterly winds west of the low-level vortex may affect the predictability of heavy snowfall.

Ensemble-based sensitivity analysis and predictability of an extreme rainfall event over northern Taiwan in the Mei-yu season: The 2 June 2017 case

In the present study, an ensemble-based sensitivity analysis (ESA) on the extreme-rainfall event along the northern coast of Taiwan on 2 June 2017 in the Mei-yu season is performed using the results from 45 forecast members with a grid size of 2.5–5 km. An quasi-stationary rainband associated with the front produced localized rainfall up to 635 mm in 12 h (0000–1200 LST 2 June), causing serious flooding and inundation near the northern tip of Taiwan. With a relatively large spread (i.e., standard deviation or σ), small ensemble mean (~130 mm), and low probability of heavy rainfall in northern Taiwan, the ensemble indicates a lower predictability there, compared to the topographic rainfall over the mountains. However, the ESA allows for identification of several contributing factors to heavy rainfall in northern Taiwan in a quantitative manner as given below.With their impact given in change of (areal-mean) 6-h rainfall amount per one σ increase, these factors include: (1) surface frontal position and moving speed (−16.00 mm per 5 km h−1), (2) position of 700-hPa wind-shift line (+12.59 mm per 0.4° latitude), (3) environmental moisture amount near the surface front (+11.73 mm per 0.92 g kg−1 in mixing ratio), (4) timing and location of frontal low-pressure disturbance (+11.03 mm per 1.38° longitude), and (5) frontal intensity (+9.58 mm per 3 K in equivalent potential temperature difference across 0.5°). While many of the factors identified are interconnected, they tend to increase the local rainfall through lengthening the duration and enhancing near-surface convergence along the northwestern coast of Taiwan over the area immediately upstream.

Ensemble sensitivity analysis of an extreme rainfall event over the Himalayas in June 2013

Forecast Sensitivity of an extreme rainfall event over the Uttarakhand state located in the Western Himalayas is investigated through Ensemble-based Sensitivity Analysis (ESA). ESA enables the assessment of forecast errors and its relation to the flow fields through linear regression approach. The ensembles are initialized from an Ensemble Kalman Filter (EnKF) Data Assimilation in Weather Research and Forecast (WRF) model. ESA is then applied to evaluate the dynamics and predictability at two different days of the extreme precipitation episode. Results indicate that the precipitation forecast over Uttarakhand is sensitive to the mid-tropospheric trough and moisture fields for both the days, in general. The day 1 precipitation shows negative sensitivity to the trough over upstream regions of the storm location while in day 2, the sensitive region is found to be located over the southward intruded branch of the mid–tropospheric trough. Perturbations introduced in the initial conditions (IC) over the most sensitive region over the west of the storm location indicate significant variations in the forecast location of precipitation. IC perturbed experiments show that the perturbation amplitude is correlated linearly with predicted change in precipitation, which becomes nonlinear as the forecast length increases. ESA performed on convection-permitting ensembles show that precipitation over the Uttarakhand is mostly non-convective. However, when the location of the response function box is moved north-westward of the Uttarakhand, the sensitivity patterns show signs of convection.

Neural network ensemble-based sensitivity analysis in structural engineering: Comparison of selected methods and the influence of statistical correlation

Surrogate model-based sensitivity analysis, especially framed by neural network ensemble (NNE), is an attractive but unresolved issue in structural reliability assessment. In this paper, differing from existing studies, an overview and assessment of typical methods for surrogate model-based parameter sensitivity analysis, namely the input perturbation method, the local analysis of variance, the connection weight method, the non-parametric Spearman rank-order correlation method, and the Sobol indices method, are performed and demonstrated on three illustrative cases of increasing complexity: a simple theoretical instance, an engineering case of midspan deflection of a simply-supported beam, and a real-world practical application of shear failing in a precast concrete girder. Through comprehensive comparisons, several findings are obtained as follows: (i) the NNE is testified a superior surrogate model for sensitivity analysis to a single artificial neural network; (ii) robustness and accuracy of an NNE in sensitivity analysis are demonstrated; (iii) the properties of these parameter sensitivity analysis methods are fully clarified with distinguished merits and limitations; (iv) mechanism of local- and global- sensitivity analysis methods is revealed; and (v) the strategy for sensitivity analysis of correlated descriptive variables are elaborated to address the impact of correlation among random variables in engineering systems.

Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces

Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

The Tornadic Supercell on the Kanto Plain on 6 May 2012: Polarimetric Radar and Surface Data Assimilation with EnKF and Ensemble-Based Sensitivity Analysis

A tornadic supercell and associated low-level mesocyclone (LMC) observed on the Kanto Plain, Japan, on 6 May 2012 were predicted with a nonhydrostatic mesoscale model with a horizontal resolution of 350 m through assimilation of surface meteorological data (horizontal wind, temperature, and relative humidity) of high spatial density and C-band Doppler radar data (radial velocity and rainwater estimated from reflectivity and specific differential phase) with a local ensemble transform Kalman filter. With assimilation of both surface and radar data, a strong LMC was successfully predicted near the path of the actual tornado. When either surface or radar data were not assimilated, however, the LMC was not predicted. Therefore, both surface and radar data were essential for successful LMC forecasts. The factors controlling the strength of the predicted LMC, defined as a low-level maximum vertical vorticity, were clarified by an ensemble-based sensitivity analysis (ESA), which is a new approach for analyzing LMC intensification. The ESA showed that the strength of the LMC was sensitive to low-level convergence forward of the storm and to low-level relative humidity in the rear of the storm. Therefore, the correction of these low-level variables by assimilation of dense observations was found to be particularly important for forecasting and monitoring the LMC in the present case.

Bootstrapped-ensemble-based Sensitivity Analysis of a trace thermal-hydraulic model based on a limited number of PWR large break loca simulations

The safety verification of nuclear systems can be done by analyzing the outputs of Best-Estimate Thermal-Hydraulic (BE-TH) codes, which allow predicting the system response under safe and accidental conditions with greater realism as compared to conservative TH codes. In this case, it is necessary to quantify and control the uncertainties in the analysis, which affect the estimated safety margins. This can be achieved by Sensitivity Analysis (SA) and Uncertainty Analysis (UA) techniques tailored to handle the large computational costs of TH codes. This work presents an Ensemble-Based Sensitivity Analysis (EBSA) based on Finite Mixture Model (FMM) as an effective solution to keep low the code runs and handle the uncertainty in the SA methods. The approach proposed is challenged against a situation of a very low number of code runs: the Bootstrap method is, then, used in support. Three different strategies based on EBSA and Bootstrap are set forth (i.e., bottom-up, all-out and filter strategies). An application is provided with respect to a Large Break Loss of Coolant Accident (LBLOCA) simulated by a TRACE model of the Zion 1 Nuclear Power Plant (NPP).

Invariant methods for an ensemble-based sensitivity analysis of a passive containment cooling system of an AP1000 nuclear power plant

Sensitivity Analysis (SA) is performed to gain fundamental insights on a system behavior that is usually reproduced by a model and to identify the most relevant input variables whose variations affect the system model functional response. For the reliability analysis of passive safety systems of Nuclear Power Plants (NPPs), models are Best Estimate (BE) Thermal Hydraulic (TH) codes, that predict the system functional response in normal and accidental conditions and, in this paper, an ensemble of three alternative invariant SA methods is innovatively set up for a SA on the TH code input variables. The ensemble aggregates the input variables raking orders provided by Pearson correlation ratio, Delta method and Beta method. The capability of the ensemble is shown on a BE–TH code of the Passive Containment Cooling System (PCCS) of an Advanced Pressurized water reactor AP1000, during a Loss Of Coolant Accident (LOCA), whose output probability density function (pdf) is approximated by a Finite Mixture Model (FMM), on the basis of a limited number of simulations.

Ensemble-based sensitivity analysis of a Best Estimate Thermal Hydraulics model: Application to a Passive Containment Cooling System of an AP1000 Nuclear Power Plant

The reliability analysis of a Nuclear Power Plant (NPP) passive safety system requires to quantify its functional failure probability, using a Best Estimate (BE) Thermal Hydraulic (TH) code to predict the behavior in normal and accidental conditions. To effectively do this, sensitivity analysis (SA) is performed to identify the relevant, important input variables whose variations affect the system functional response (calculated as output of the BE-TH code). In this paper, we propose a novel framework for the sensitivity analysis (SA) of a BE-TH code and apply it to the analysis of the Passive Containment Cooling System (PCCS) of an Advanced Pressurized reactor AP1000 during a Loss Of Coolant Accident (LOCA). We build Finite Mixture Models (FMMs) for approximating the probability density function (pdf) of the pressure reached by the PCCS during the LOCA, on the basis of a limited number of simulations. Then, an ensemble of three alternative SA methods is innovatively set up for identifying the input variables that most affect the TH code output: input saliency, Hellinger distance and Kullback–Leibler divergence. The capability of the ensemble is shown on a numerical case study.

Observing Strategy and Observation Targeting for Tropical Cyclones Using Ensemble-Based Sensitivity Analysis and Data Assimilation

Abstract An ensemble Kalman filter data assimilation system for the Weather Research and Forecasting Model is used with ensemble-based sensitivity analysis to explore observing strategies and observation targeting for tropical cyclones. The case selected for this study is Typhoon Morakot (2009), a western Pacific storm that brought record-breaking rainfall to Taiwan. Forty-eight hours prior to making landfall, ensemble sensitivity analysis using a 50-member convection-permitting ensemble predicts that dropsonde observations located in the southwest quadrant of the typhoon will have the highest impact on reducing the forecast uncertainty of the track, intensity, and rainfall of Morakot. A series of observing system simulation experiments (OSSEs) demonstrate that assimilating synthetic dropsonde observations located in regions with higher predicted observation impacts will, on average, lead to a better rainfall forecast than in regions with smaller predicted impacts. However, these OSSEs also suggest that the effectiveness of the current-generation ensemble-based tropical cyclone targeting strategies may be limited. The limitations may be due to strong nonlinearity in the governing dynamics of the typhoon (e.g., moist convection), the accuracy of the ensemble background covariance, and the projection of individual dropsonde observations to the complicated targeted sensitivity vectors from the ensemble.

Predictability of an Atmospheric Blocking Event that Occurred on 15 December 2005

AbstractAtmospheric blocking occurred over the Rocky Mountains at 1200 UTC 15 December 2005. The operational medium-range ensemble forecasts of the Canadian Meteorological Center (CMC), the Japan Meteorological Agency (JMA), and the National Centers for Environmental Prediction (NCEP), as initialized at 1200 UTC 10 December 2005, showed remarkable differences regarding this event. All of the NCEP members failed to predict the correct location of the blocking, whereas almost all of the JMA members and most of the CMC members were successful in predicting the correct location. The present study investigated the factors that caused NCEP to incorrectly predict the blocking location, based on an ensemble-based sensitivity analysis and the JMA global spectral model (GSM) multianalysis ensemble forecasts with NCEP, regionally amplified NCEP, and globally amplified NCEP analyses.A sensitive area for the blocking formation was detected over the central North Pacific. In this area, the NCEP control analysis experienced problems in the handling of a cutoff cyclone, and the NCEP initial perturbations were ineffective in reducing uncertainties in the NCEP control analysis. The JMA GSM multianalysis ensemble forecasts revealed that regional amplification of initial perturbations over the sensitive area could lead to further improvements in forecasts over the blocking region without degradation of forecasts over the Northern Hemisphere (NH), whereas the global amplification of initial perturbations could lead to improved forecasts over the blocking region and degraded forecasts over the NH. This finding may suggest that excessive amplification of initial perturbations over nonsensitive areas is undesirable, and that case-dependent rescaling of initial perturbations may be of value compared with climatology-based rescaling, which is widely used in current operational ensemble prediction systems.

Ensemble-Based Sensitivity Analysis Applied to African Easterly Waves

Abstract An ensemble Kalman filter (EnKF) coupled to the Advanced Research version of the Weather Research and Forecasting (WRF) model is used to generate ensemble analyses and forecasts of a strong African easterly wave (AEW) during the African Monsoon Multidisciplinary Analysis field campaign. Ensemble sensitivity analysis is then used to evaluate the impacts of initial condition errors on AEW amplitude and position forecasts at two different initialization times. WRF forecasts initialized at 0000 UTC 8 September 2006, prior to the amplification of the AEW, are characterized by large variability in evolution as compared to forecasts initialized 48 h later when the AEW is within a denser observation network. Short-lead-time amplitude forecasts are most sensitive to the midtropospheric meridional winds, while at longer lead times, midtropospheric θe errors have equal or larger impacts. For AEW longitude forecasts, the largest sensitivities are associated with the θe downstream of the AEW and, to a lesser extent, the meridional winds. Ensemble predictions of how initial condition errors impact the AEW amplitude and position compare qualitatively well with perturbed integrations of the WRF model. Much of the precipitation associated with the AEW is generated by the Kain–Fritsch cumulus parameterization, thus the initial-condition sensitivities are also computed for ensemble forecasts that employ the Betts–Miller–Janjić and Grell cumulus parameterization schemes, and for a high-resolution nested domain with explicit convection, but with the same initial conditions. While the 12-h AEW amplitude forecast is characterized by consistent initial-condition sensitivity among the different schemes, there is greater variability among methods beyond 24 h. In contrast, the AEW longitude forecast is sensitive to the downstream thermodynamic profile with all cumulus schemes.

Initial Condition Sensitivity of Western Pacific Extratropical Transitions Determined Using Ensemble-Based Sensitivity Analysis

Abstract An ensemble Kalman filter based on the Weather Research and Forecasting (WRF) model is used to generate ensemble analyses and forecasts for the extratropical transition (ET) events associated with Typhoons Tokage (2004) and Nabi (2005). Ensemble sensitivity analysis is then used to evaluate the relationship between forecast errors and initial condition errors at the onset of transition, and to objectively determine the observations having the largest impact on forecasts of these storms. Observations from rawinsondes, surface stations, aircraft, cloud winds, and cyclone best-track position are assimilated every 6 h for a period before, during, and after transition. Ensemble forecasts initialized at the onset of transition exhibit skill similar to the operational Global Forecast System (GFS) forecast and to a WRF forecast initialized from the GFS analysis. WRF ensemble forecasts of Tokage (Nabi) are characterized by relatively large (small) ensemble variance and greater (smaller) sensitivity to the initial conditions. In both cases, the 48-h forecast of cyclone minimum SLP and the RMS forecast error in SLP are most sensitive to the tropical cyclone position and to midlatitude troughs that interact with the tropical cyclone during ET. Diagnostic perturbations added to the initial conditions based on ensemble sensitivity reduce the error in the storm minimum SLP forecast by 50%. Observation impact calculations indicate that assimilating approximately 40 observations in regions of greatest initial condition sensitivity produces a large, statistically significant impact on the 48-h cyclone minimum SLP forecast. For the Tokage forecast, assimilating the single highest impact observation, an upper-tropospheric zonal wind observation from a Mongolian rawinsonde, yields 48-h forecast perturbations in excess of 10 hPa and 60 m in SLP and 500-hPa height, respectively.

Ensemble Synoptic Analysis

Abstract Synoptic and mesoscale meteorology underwent a revolution in the 1940s and 1950s with the widespread deployment of novel weather observations, such as the radiosonde network and the advent of weather radar. These observations provoked a rapid increase in our understanding of the structure and dynamics of the atmosphere by pioneering analysts such as Fred Sanders. The authors argue that we may be approaching an analogous revolution in our ability to study the structure and dynamics of atmospheric phenomena with the advent of probabilistic objective analyses. These probabilistic analyses provide not only best estimates of the state of the atmosphere (e.g., the expected value) and the uncertainty about this state (e.g., the variance), but also the relationships between all locations and all variables at that instant in time. Up until now, these relationships have been determined by sampling in time by, for example, case studies, composites, and time-series analysis. Here the authors propose a new approach, ensemble synoptic analysis, which exploits the information contained in probabilistic samples of analyses at one or more instants in time. One source of probabilistic analyses is ensemble-based state-estimation methods, such as ensemble-based Kalman filters. Analyses from such a filter may be used to study atmospheric phenomena and the relationships between fields and locations at one or more instants in time. After a brief overview of a research-based ensemble Kalman filter, illustrative examples of ensemble synoptic analysis are given for an extratropical cyclone, including relationships between the cyclone minimum sea level pressure and other synoptic features, statistically determined operators for potential-vorticity inversion, and ensemble-based sensitivity analysis.