Thunderstorm Forecasting Research Articles

On the Predictability of Supercell Thunderstorm Evolution

Abstract Supercell thunderstorms produce a disproportionate amount of the severe weather in the United States, and accurate prediction of their movement and evolution is needed to warn the public of their hazards. This study explores the practical predictability of supercell thunderstorm forecasts in the presence of typical errors in the preconvective environmental conditions. The Advanced Research Weather Research and Forecasting model (ARW-WRF) is run at 1-km grid spacing and a control run of a supercell thunderstorm is produced using a horizontally homogeneous environment. Forecast errors from supercell environments derived from the 13-km Rapid Update Cycle (RUC) valid at 0000 UTC for forecast lead times up to 3 h are used to define the environmental errors, and 100 runs initialized with environmental perturbations characteristic of those errors are produced for each lead time. The simulations are analyzed to determine the spread and practical predictability of supercell thunderstorm forecasts from a storm-scale model, with the control used as truth. Most of the runs perturbed with the environmental forecast errors produce supercell thunderstorms; however, there is much less predictability for storm motion and structure. Results suggest that an upper bound to the practical predictability of storm location with the current environmental uncertainty for a 1-h environmental forecast is about 2 h, with the predictability of the storms decreasing to 1 h as lead time increases. Smaller-scale storm features, such as midlevel mesocyclones and regions of heavy rainfall, display much less predictability than storm location. Mesocyclone location is predictable out to 40 min or less, while heavy 5-min rainfall location is not predictable.

The Study on the Model of Thunderstorm Forecast Based on RS-SVM

The Study on the Model of Thunderstorm Forecast Based on RS-SVM

Kajian pendahuluan analisis peramalan thunderstorm untuk penyusunan indeks dasar adaptasi kegiatan pertambakan (Suatu tinjauan meteorologi di Jakarta)

Abstract. A meteorological prespective to analyze the Thunderstorm forecasting in Jakarta has been done. The principal indices to be adapted in a fishpond were also arranged in the study. Storms in Jakarta, so-called as Ordinary Cell Thunderstorms, are frequently arose in the afternoon, particularly during transition period on March-May and September-November in which many of them are triggered by different in surface heating. The latter emerged to an atmospheric instability and force the air parcel to rise through the atmosphere. RAOB was employed to the forecasting of Thunderstorm. A number of such indices as K and Showalter indices as well as CAPE are produced and applied to forecast the conditional instability of the troposphere. The result showed that the extension of inversion layer in ~500–300 hPa implied the shrink of humidity and might strength the convective instability. In addition, the higher amount of CAPE proved the maximum velocity of updraft which lead to a strong convection and vertical wind shear during Thunderstorm in Jakarta. On the other hand, based on the storm indices, three principal indices adapted in a fishpond were also arranged i.e. normal, moderate and risk condition.Keywords. Thunderstorm, Storm indices, Fishpond adaption

Application of Pattern Recognition Techniques to Predict Severe Thunderstorms

Thunderstorm forecasting is a challenging job. Machine learning techniques are being applied nowadays in meteorological fields for prediction purpose. This study presents the application of different machine learning tools based on multiple correlation, Multi-layer Perceptron (MLP), K-nearest neighbor (K-nn) method, and modified K-nn method to predict seasonal severe thunderstorms associated with squall occurring in Kolkata, North-East India. The models are trained and tested with the radiosonde data recorded in the early morning at 00:00UTC. The predictors are moisture difference and dry adiabatic lapse rate at different geopotential heights of the atmosphere. Our aim in this paper is to find how much correctly one can nowcast 10 to 14 hours before the 'occurrence'/ 'no occurrence' of evening squall-storms by using a few upper air diagnostic predictors. Modified K-nn method is found to yield very promising prognostic information with high prediction accuracy. The results indicate that forecasting can be done correctly up to 82.02% both for 'squall-storm/no storm' events, and up to 91.11% for 'squall-storm' events using modified K-nn based approach. In this article, modified K-nn method is proved as the best method in comparison with the other methods for the squall-storm prediction.

The Impact of Mesoscale Environmental Uncertainty on the Prediction of a Tornadic Supercell Storm Using Ensemble Data Assimilation Approach

Numerical experiments over the past years indicate that incorporating environmental variability is crucial for successful very short-range convective-scale forecasts. To explore the impact of model physics on the creation of environmental variability and its uncertainty, combined mesoscale-convective scale data assimilation experiments are conducted for a tornadic supercell storm. Two 36-member WRF-ARW model-based mesoscale EAKF experiments are conducted to provide background environments using either fixed or multiple physics schemes across the ensemble members. Two 36-member convective-scale ensembles are initialized using background fields from either fixed physics or multiple physics mesoscale ensemble analyses. Radar observations from four operational WSR-88Ds are assimilated into convective-scale ensembles using ARPS model-based 3DVAR system and ensemble forecasts are launched. Results show that the ensemble with background fields from multiple physics ensemble provides more realistic forecasts of significant tornado parameter, dryline structure, and near surface variables than ensemble from fixed physics background fields. The probabilities of strong low-level updraft helicity from multiple physics ensemble correlate better with observed tornado and rotation tracks than probabilities from fixed physics ensemble. This suggests that incorporating physics diversity across the ensemble can be important to successful probabilistic convective-scale forecast of supercell thunderstorms, which is the main goal of NOAA’s Warn-on-Forecast initiative.

Impact of a Diagnostic Pressure Equation Constraint on Tornadic Supercell Thunderstorm Forecasts Initialized Using 3DVAR Radar Data Assimilation

A diagnostic pressure equation constraint has been incorporated into a storm-scale three-dimensional variational (3DVAR) data assimilation system. This diagnostic pressure equation constraint (DPEC) is aimed to improve dynamic consistency among different model variables so as to produce better data assimilation results and improve the subsequent forecasts. Ge et al. (2012) described the development of DPEC and testing of it with idealized experiments. DPEC was also applied to a real supercell case, but only radial velocity was assimilated. In this paper, DPEC is further applied to two real tornadic supercell thunderstorm cases, where both radial velocity and radar reflectivity data are assimilated. The impact of DPEC on radar data assimilation is examined mainly based on the storm forecasts. It is found that the experiments using DPEC generally predict higher low-level vertical vorticity than the experiments not using DPEC near the time of observed tornadoes. Therefore, it is concluded that the use of DPEC improves the forecast of mesocyclone rotation within supercell thunderstorms. The experiments using different weighting coefficients generate similar results. This suggests that DPEC is not very sensitive to the weighting coefficients.

The Second Verification of the Origins of Rotation in Tornadoes Experiment: VORTEX2

The second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2), which had its field phases in May and June of 2009 and 2010, was designed to explore i) the physical processes of tornadogenesis, maintenance, and demise; ii) the relationships among tornadoes, tornadic storms, and the larger-scale environment; iii) numerical weather prediction and forecasting of supercell thunderstorms and tornadoes; and iv) the wind field near the ground in tornadoes. VORTEX2 is by far the largest and most ambitious observational and modeling study of tornadoes and tornadic storms ever undertaken. It employed 13 mobile mesonet–instrumented vehicles, 11 ground-based mobile radars (several of which had dual-polarization capability and two of which were phased-array rapid scan), a mobile Doppler lidar, four mobile balloon sounding systems, 42 deployable in situ observational weather stations, an unmanned aerial system, video and photogrammetric teams, damage survey teams, deployable disdrometers, and other experimental instrumentation as well as extensive modeling studies of tornadic storms. Participants were drawn from more than 15 universities and laboratories and at least five nations, with over 80 students participating in field activities. The VORTEX2 field phases spanned 2 yr in order to increase the probability of intercepting significant tornadoes, which are rare events. The field phase of VORTEX2 collected data in over three dozen tornadic and nontornadic supercell thunderstorms with unprecedented detail and diversity of measurements. Some preliminary data and analyses from the ongoing analysis phase of VORTEX2 are shown.

A composite stability index for dichotomous forecast of thunderstorms

Thunderstorms are the perennial feature of Kolkata (22° 32′ N, 88° 20′ E), India during the premonsoon season (April–May). Precise forecast of these thunderstorms is essential to mitigate the associated catastrophe due to lightning flashes, strong wind gusts, torrential rain, and occasional hail and tornadoes. The present research provides a composite stability index for forecasting thunderstorms. The forecast quality detection parameters are computed with the available indices during the period from 1997 to 2006 to select the most relevant indices with threshold ranges for the prevalence of such thunderstorms. The analyses reveal that the lifted index (LI) within the range of −5 to −12 °C, convective inhibition energy (CIN) within the range of 0–150 J/kg and convective available potential energy (CAPE) within the ranges of 2,000 to 7,000 J/kg are the most pertinent indices for the prevalence thunderstorms over Kolkata during the premonsoon season. A composite stability index, thunderstorm prediction index (TPI) is formulated with LI, CIN, and CAPE. The statistical skill score analyses show that the accuracy in forecasting such thunderstorms with TPI is 99.67 % with lead time less than 12 h during training the index whereas the accuracies are 89.64 % with LI, 60 % with CIN and 49.8 % with CAPE. The performance diagram supports that TPI has better forecast skill than its individual components. The forecast with TPI is validated with the observation of the India Meteorological Department during the period from 2007 to 2009. The real-time forecast of thunderstorms with TPI is provided for the year 2010.

Sharp decrease of attenuation of 183.31 GHz water molecule absorption line associated with Nor’wester over Kolkata – may be one important experimental set-up to forecast Nor’wester

The sharp depletion of attenuation of 183.31GHz signal just before the onset of Nor’wester overKolkata has been studied. Possible explanations of such type of variation are presented. It is concluded that this may betaken as one possible method of forecasting of severe thunderstorms associated with Nor’wester. Physical explanationsbased on the formation and dissipation mechanisms of thunderstorms are also presented.

Evaluation of European Storm Forecast Experiment (ESTOFEX) forecasts

Three years of forecasts of lightning and severe thunderstorms from the European Storm Forecast Experiment (ESTOFEX) have been evaluated. The forecasts exhibit higher quality in summer than in winter and there is some evidence that they have improved over the course of the evaluation. Five individual forecasters made the majority of the forecasts and differences in their forecasts are on the order of the overall variability of the forecast quality. As a result, the forecasts appear to come from a single unit, rather than from a group of individuals. The graphical description of the probability of detection and frequency of hits recently developed by Roebber is a valuable tool for displaying the time series of lightning forecast performance. It also appears that, even though they are not intended for that purpose, using the lightning forecasts as a low-end forecast of severe thunderstorms is potentially useful for decision makers.

Case study of the 20 May 2008 tornadic storm in Hungary — Remote sensing features and NWP simulation

This paper discusses a case study of a tornadic thunderstorm event that occurred over Hungary on 20 May 2008. The paper presents both remote sensing measurements and numerical simulations of the storm system, and the synoptic situation is also described. The pre-convective environment was analyzed using satellite retrieved instability indices and total precipitable water content. The evolution of the convective system was described using 5-minute satellite imagery, 15-minute radar data, and continuous lightning observations. A high resolution MODIS image was also examined. The analysis of cloud top characteristics using satellite imagery revealed numerous cloud top features typically associated with severe storms: cold-ring and cold-U shapes in the infrared images, as well as longer lasting series of strong overshooting tops, gravity waves, above-anvil plumes, and radial cirrus. The cloud top microphysical properties indicated severe updraft — the imagery showed many small ice crystals within the cloud tops. The analysis of retrieved effective radius and brightness temperature profiles also pointed to a strong updraft. Some of the radar images displayed bow echo features often associated with severe storms. Some radar cross-sections showed WER echoes. The total lightning rate was extremely high. The event was simulated using the MM5 non-hydrostatic numeric model, with two goals. First, we wanted to test the model's ability to predict the event. Second, we hoped to improve our knowledge of dynamic processes related to mesocyclogenesis and increased vorticity within this type of thunderstorms. An analysis of the vorticity equation terms indicate that at mid-tropospheric levels vorticity was generated mainly by the tilting of streamwise horizontal vorticity in the thunderstorm updraft. The ambient horizontal vorticity substantially increased near intense thunderstorm cells. At low levels, rotation intensified as a result of vertical acceleration and the stretching of the air column. Overall, the results suggest that in similar conditions (moderate values of CAPE and Storm-Relative Environmental Helicity of the ambient air), explicit numerical forecasts of thunderstorms can warn about the likely development of mesocyclones and other severe weather features such as rear inflow jets.

Probabilistic forecasts of winter thunderstorms around Amsterdam Airport Schiphol

Abstract. The development and verification of a probabilistic forecast system for winter thunderstorms around Amsterdam Airport Schiphol is described. We have used Model Output Statistics (MOS) to develop the probabilistic forecast equations. The MOS system consists of 32 logistic regression equations, i.e. for two forecast periods (0–6 h and 6–12 h), four 90×80 km2 regions around Amsterdam Airport Schiphol, and four 6-h time periods. For the predictand quality-controlled Surveillance et Alerte Foudre par Interférométrie Radioélectrique (SAFIR) total lightning data were used. The potential predictors were calculated from postprocessed output of two numerical weather prediction (NWP) models – i.e. the High-Resolution Limited-Area Model (HIRLAM) and the European Centre for Medium-Range Weather Forecasts (ECMWF) model – and from an ensemble of advected lightning and radar data (0–6 h projections only). The predictors that are selected most often are the HIRLAM Boyden index, the square root of the ECMWF 3-h and 6-h convective precipitation sum, the HIRLAM convective available potential energy (CAPE) and two radar advection predictors. An objective verification was done, from which it can be concluded that the MOS system is skilful. The forecast system runs at the Royal Netherlands Meteorological Institute (KNMI) on an experimental basis, with the primary objective to warn aircraft pilots for potential aircraft induced lightning (AIL) risk during winter.

The Applicability of Bipartite Graph Model for Thunderstorms Forecast over Kolkata

Single Spectrum Bipartite Graph (SSBG) model is developed to forecast thunderstorms over Kolkata(22∘32′N,88∘20′E)during the premonsoon season (April-May). The statistical distribution of normal probability is observed for temperature, relative humidity, convective available potential energy (CAPE), and convective inhibition energy (CIN) to quantify the threshold values of the parameters for the prevalence of thunderstorms. Method of conditional probability is implemented to ascertain the possibilities of the occurrence of thunderstorms within the ranges of the threshold values. The single spectrum bipartite graph connectivity model developed in this study consists of two sets of vertices; one set includes two time vertices (00UTC, 12UTC) and the other includes four meteorological parameters: temperature, relative humidity, CAPE, and CIN. Three distinct ranges of maximal eigen values are obtained for the three categories of thunderstorms. Maximal eigenvalues for severe, ordinary, and no thunderstorm events are observed to be(2.6±0.12),(1.88±0.09), and(1.26±.03), respectively. The ranges of the threshold values obtained using ten year data (1997–2006) are considered as the reference range and the result is validated with the IMD (India Meteorological Department) observation, Doppler Weather Radar (DWR) Products, and satellite images of 2007. The result reveals that the model provides 12- to 6-hour forecast (nowcasting) of thunderstorms with 96% to 98% accuracy.

Probabilistic Forecasts of (Severe) Thunderstorms for the Purpose of Issuing a Weather Alarm in the Netherlands

Abstract The development and verification of a new model output statistics (MOS) system is described; this system is intended to help forecasters decide whether a weather alarm for severe thunderstorms, based on high total lightning intensity, should be issued in the Netherlands. The system consists of logistic regression equations for both the probability of thunderstorms and the conditional probability of severe thunderstorms in the warm half-year (from mid-April to mid-October). These equations have been derived for 12 regions of about 90 km × 80 km each and for projections out to 12 h in advance (with 6-h periods). As a source for the predictands, reprocessed total lightning data from the Surveillance et d’Alerte Foudre par Interférométrie Radioélectrique (SAFIR) network have been used. The potential predictor dataset not only consisted of the combined postprocessed output from two numerical weather prediction (NWP) models, as in previous work by the first three authors, but it also contained an ensemble of advected radar and lightning data for the 0–6-h projections. The NWP model output dataset contained 17 traditional thunderstorm indices, computed from a reforecasting experiment with the High-Resolution Limited-Area Model (HIRLAM) and postprocessed output from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. Brier skill scores and attributes diagrams show that the skill of the MOS thunderstorm forecast system is good and that the severe thunderstorm forecast system generally is also skillful, compared to the 2000–04 climatology, and therefore, the preoperational system was made operational at the Royal Netherlands Meteorological Institute (KNMI) in 2008.

Severe thunderstorm and tornado warnings in Europe

This study summarizes the current severe thunderstorm warning and forecast operations in different European National Hydro-Meteorological Services (NHMSs), and, in doing so, suggests ways for countries developing their own warning service to learn from experiences in other countries, as well as from the warning operations in the United States of America, the longest-lived severe thunderstorm warning operations in the world. This study is based on a questionnaire sent to 39 European NHMSs of which thirty-three (85%) responded. Currently, many European NHMSs are actively developing their severe thunderstorm forecast process and warning services with 26 (79%) of respondent countries issuing severe thunderstorm warnings and 8 (24%) issuing tornado warnings. Both warning criteria and methodologies used in the warning process vary from country to country. Lead-times range from 30 min to 96 h, indicating a range of different warning philosophies for each country. Major challenges toward improving the warning operations include obtaining observations of severe weather for real-time forecasting and post-event verification, educating forecasters, and having access to state-of-the-art forecaster workstations. An additional challenge is in communicating anticipated or ongoing severe thunderstorms, both internationally between NHMSs and nationally with media and emergency authorities.

Forecasting of thunderstorms in pre-monsoon season over northwest India

Early detection and forecasting of thunderstorms is important in safeguarding and prevention of damages resulting from violent thunderstorms. An Expert System for Thunderstorm Forecasting (ESTF) during pre-monsoon season over Delhi the representative location over northwest India has been developed for the first time in India by using technique of approaching the problem “bottom up” by using inductive machine learning techniques to automatically acquire the knowledge about thunderstorm forecasting from the weather development data set consisting of TEMP data of Delhi for the months of May and June for the years from 1995-1999. Only input required is the entry of 0000 UTC TEMP data of Delhi at surface, 850, 700, 500 and 300 hPa levels. The rules are based on stability indices and other thermodynamic parameters evaluated from the said sounding. The system also provides climatological information about thunderstorms over Delhi. To compare the ESTF with the objective techniques, Dynamical-statistical methods for yes or no type thunderstorm occurrence forecast over Delhi during pre-monsoon months of May and June have been developed by using graphical discrimination method and multiple regression method and by using the same development data set i.e., TEMP data of Delhi for the months of May and June for the years from 1995-1999 and by using the same potential predictors as used in development of ESTF. In multiple regression method the parameters were found to be significant by stepwise screening procedure. The three methods developed were tested with independent data sets of May and June for the years from 2000-2001. Comparison of verification parameters of the forecast issued by Graphical Discrimination method, Multiple Regression Technique and by ESTF indicates that results of multiple regression method are better than those of graphical discrimination method. The results obtained by using ESTF were better than those obtained by using dynamical statistical models.

The Operational Mesogamma-Scale Analysis and Forecast System of the U.S. Army Test and Evaluation Command. Part IV: The White Sands Missile Range Auto-Nowcast System

Abstract During the summer months at the U.S. Army Test and Evaluation Command’s (ATEC) White Sands Missile Range (WSMR), forecasting thunderstorm activity is one of the primary duties of the range forecasters. The safety of personnel working on the range and the protection of expensive test equipment depend critically on the quality of forecasts of thunderstorms and associated hazards, including cloud-to-ground lightning, hail, strong winds, heavy rainfall, flash flooding, and tornadoes. The National Center for Atmospheric Research (NCAR) Auto-Nowcast (ANC) system is one of the key forecast tools in the ATEC Four-Dimensional Weather System (4DWX) at WSMR, where its purpose is to aid WSMR meteorologists in their mission of very short term thunderstorm forecasting. Besides monitoring the weather activity throughout the region and warning personnel of potentially hazardous thunderstorms, forecasters play a key role in assisting with the day-to-day planning of test operations on the range by providing guidance with regard to weather conditions favorable to testing. Moreover, based on climatological information about the local weather conditions, forecasters advise their range customers about scheduling tests at WSMR months in advance. This paper reviews the NCAR ANC system, provides examples of the ANC system’s use in thunderstorm forecasting, and describes climatological analyses of WSMR summertime thunderstorm activity relevant for long-range planning of tests. The climatological analysis illustrates that radar-detected convective cells with reflectivity of ≥35 dBZ at WSMR are 1) short lived, with 76% having lifetimes of less than 30 min; 2) small, with 67% occupying areas of less than 25 km2; 3) slow moving, with 79% exhibiting speeds of less than 4 m s−1; 4) moderately intense, with 80% showing reflectivities in excess of 40 dBZ; and 5) deep, with 80% of the storms reaching far enough above the freezing level to be capable of generating lightning.

Short-term forecast of thunderstorms in Argentina

The eastern Andes have been described as a hot spot in severe convection. The damages caused in that particular area by convection are much higher than in other latitudes. In contrast, very few studies have been conducted as yet on the thermodynamic characterization of these events or on their forecasting. This paper assesses pre-convective conditions in south-western Argentina on the basis of radiosonde data of 713 days. Additionally, an objective short-term forecast model for storms has been set up. The linear discriminant analysis provided information about the likelihood of storms in the study zone. The forward stepwise method was used to set up the discriminant equation. Testing the results on a validation sample, the outcome was: Probability of detection (POD) = 0.814, False Alarm Rate (FAR) = 0.200; Heidke Skill Score (HSS) = 0.535. Finally, a forecast model was developed for severe storms too, but the results achieved were not so satisfactory.

Sounding-derived indices for neural network based short-term thunderstorm and rainfall forecasts

A neural network-based scheme to do a multivariate analysis for forecasting the occurrence and intensity of a meteo event is presented. Many sounding-derived indices are combined together to build a short-term forecast of thunderstorm and rainfall events, in the plain of the Friuli Venezia Giulia region (hereafter FVG, NE Italy). For thunderstorm forecasting, sounding, lightning strikes and mesonet station data (rain and wind) from April to November of the years 1995–2002 have been used to train and validate the artificial neural network (hereafter ANN), while the 2003 and 2004 data have been used as an independent test sample. Two kind of ANNs have been developed: the first is a “classification model” ANN and is built for forecasting the thunderstorm occurrence. If this first ANN predicts convective activity, then a second ANN, built as a “regression model”, is used for forecasting the thunderstorm intensity, as defined in a previous article. The classification performances are evaluated with the ROC diagram and some indices derived from the Table of Contingency (like KSS, FAR, Odds Ratio). The regression performances are evaluated using the Mean Square Error and the linear cross correlation coefficient R. A similar approach is applied to the problem of 6 h rainfall forecast in the Friuli Venezia Giulia plain, but in this second case the data cover the period from 1992 to 2004. Also the forecasts of binary events (defined as the occurrence of 5, 20 or 40 mm of maximum rain), made by classification and regression ANN, were compared. Particular emphasis is given to the sounding-derived indices which are chosen in the first places by the predictor forward selection algorithm.

The Use of Sounding-Derived Indices for a Neural Network Short-Term Thunderstorm Forecast

Abstract In this paper several indices derived from atmospheric sounding data are used to develop a short-term thunderstorm forecast tool. The Udine (Italy) sounding (WMO code 16044, taken every 6 h, hereafter 6 h) is used to describe the initial conditions in which a thunderstorm may develop in the Friuli Venezia Giulia region. The tool forecasts the convective activity in the 6 h after the sounding is launched. Sounding, lightning, and mesonet station data, from April to September of the years 1995–2002, were used to train and validate artificial neural networks (ANNs) and the data of 2003 were used as an independent test sample. Special emphasis was given to avoid one of the major ANN problems, that of data overfitting, which requires limiting the possible complexity of the ANN, that is, the total number of inputs (predictors) and of hidden neurons. To select the best input set, the training–validation mechanism was repeated in eight different ways. Two types of ANNs were developed: the first is a classification model and is built for forecasting the thunderstorm occurrence, defined as the report of at least one cloud-to-ground lightning strike. If this first ANN forecasts convective activity, then a second ANN, built as a regression model, is used for forecasting the thunderstorm intensity. The relative operating characteristic (ROC) diagram and some parameters derived from a contingency table were used to compare the different classification performances. The linear cross-correlation coefficient, R2, was used to assess the performance of the regression ANNs. The ANN inputs were not the only “raw” sounding-derived index values; in addition, two derived sets of variables, corresponding to the z scores and the “posterior probability” transformed data, were used as preprocessing methods. The last method yields the best results. The tool reported on here has been used operationally since 2001 in the regional meteorological office of the Friuli Venezia Giulia region [Osservatorio Meteorologico Regionale/Agenzia Regionale per la Protezione dell’Ambiente (OSMER/ARPA)].