Oklahoma Tornado Research Articles

Applying the extended parallel process model to understand households' responses to tornado and earthquake risks in Oklahoma.

Oklahoma is a multihazard environment where both natural (e.g., tornadoes) and technological hazards (e.g., induced seismicity) are significant, making Oklahoma a unique setting to better understand how to manage and prepare for multiple hazards. While studies have attempted to understand drivers of hazard adjustments, few have focused on the overall number of adjustments undertaken instead of individual adjustments or adjustments in a multihazard environment. To address these gaps, we employ a survey sample of 866 households in Oklahoma to understand households' danger control responses (protective hazard adjustments) for tornado and earthquake risks in Oklahoma. We apply the extended parallel processing model (EPPM) to categorize respondents according to their relative level of perceived threat and efficacy of protective actions in predicting the number of hazard adjustments they intend to or have adopted in response to tornadoes and induced earthquakes. In line with the EPPM, we found that households have the highest number of danger control responses when their perceived threat and efficacy are both high. Counter to the EPPM literature, we found low threat coupled with high efficacy moved some individuals toward the adoption of danger control responses in response to both tornadoes and earthquakes. When households have high efficacy, threat appraisals matter in tornado danger control responses but not in earthquake danger control responses. This EPPM categorization opens new research approaches for studies of natural and technological hazards. This study also provides information for local officials and emergency managers making mitigation and preparedness investments and policies.

Discriminating between Tornadic and Non-Tornadic Supercells: A New Hodograph Technique

Thompson and Edwards (2000) first noted a prominent hodograph kink separating primarily speed shear from primarily directional shear in the environments of some supercells producing significant tornadoes. Responding to this observation, we compared similar thermodynamic and shear environments between the Moore, Oklahoma tornado of 3 May 1999 and non-tornadic supercell thunderstorms occurring in north Texas on 23 April 2003. The results suggest that certain characteristics of the kink could discriminate between tornadic and non-tornadic supercells. This combination of features consisted of a strong (> 10 m s-1) nearly straight-line hodograph below 500 m above ground level (AGL) and storm-relative inflow orthogonal to the base of this hodograph segment at 10 m, yielding almost purely streamwise storm-relative inflow.
 We evaluated this hypothesis by analyzing 67 severe convective events, 65 of which were supercells, in Oklahoma from 1997-2004, and dividing the events into non-tornadic, weak-tornadic (F0-­F1), and significant-tornadic (F2-­F5) storm classes. The results show improved discrimination between storm classes for 10-­500 m storm-relative helicity and bulk shear magnitude when compared to 10-­1000 m calculations of the same. Also, histograms of the critical angle (defined by the storm-relative inflow vector at 10 m and 10-­500 m shear vector) revealed that the tornadic storms, and in particular the significant tornadic storms, tended to be characterized by angles near 90°, whereas the non-tornadic storms were not. Although the results are based on a relatively small sample, they suggest that a careful consideration of the evolution of the low-level hodograph in both time and space in relation to the storm motion can potentially be a valuable aid in forecasting supercell tornadoes.

Use of Power Transform Mixing Ratios as Hydrometeor Control Variables for Direct Assimilation of Radar Reflectivity in GSI En3DVar and Tests with Five Convective Storm Cases

AbstractWhen directly assimilating radar data within a variational framework using hydrometeor mixing ratios (q) as control variables (CVq), the gradient of the cost function becomes extremely large when background mixing ratio is close to zero. This significantly slows down minimization convergence and makes the assimilation of radial velocity and other observations ineffective because of the dominance of the reflectivity observation term in the cost function gradient. Using logarithmic hydrometeor mixing ratios as control variables (CV logq) can alleviate the problem but the high nonlinearity of logarithmic transformation can introduce spurious analysis increments into mixing ratios. In this study, power transform of hydrometeors is proposed to form new control variables (CVpq) where the nonlinearity of transformation can be adjusted by a tuning exponent or power parameter p. The performance of assimilating radar data using CVpq is compared with those using CVq and CV logq for the analyses and forecasts of five convective storm cases from the spring of 2017. Results show that CVpq with p = 0.4 (CVpq0.4) gives the best reflectivity forecasts in terms of root-mean-square error and equitable threat score. Furthermore, CVpq0.4 has faster convergence of cost function minimization than CVq and produces less spurious analysis increment than CV logq. Compared to CVq and CV logq, CVpq0.4 has better skills of 0–3-h composite reflectivity forecasts, and the updraft helicity tracks for the 16 May 2017 Texas and Oklahoma tornado outbreak case are more consistent with observations when using CVpq0.4.

Memory, risk, and regional identity: Assessing the socio-cultural impacts of tornadoes in Oklahoma, USA

Tornadoes are often seen as a way of life in the Great Plains region of the United States, with many stories of deadly storms originating before the 20th century. Because of this historic connection between people and their environment, residents of states such as Oklahoma develop distinctive sociocultural relationships to extreme weather, particularly associating tornadoes with social memory and regional identity. In this paper, I assert that shared memories of historic tornadoes are impactful to Oklahomans’ regional identity as it relates to residents’ relationships with risk. Multiple qualitative methods, including interview and archival research were used in order to identify the importance of this relationship to Oklahomans as a social group. Much importance is also placed on connecting the present to the past, and many Oklahomans have adopted tornadoes as a symbol of strength. While memories of these tornadic events do not negate the risks of living in a potentially dangerous environment, they also do not imply that risks should be avoided. Rather, facing these risks is seen as a practice in endurance that many Oklahomans believe they were built to face.

Comparisons of Hybrid En3DVar with 3DVar and EnKF for Radar Data Assimilation: Tests with the 10 May 2010 Oklahoma Tornado Outbreak

AbstractIn this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

Tornado loss model of Oklahoma and Kansas, United States, based on the historical tornado data and Monte Carlo simulation

This paper introduces a new tornado loss assessment model for one-family and two-family wood frame residential buildings in the states of Kansas (KS) and Oklahoma (OK), United States. The model belongs to the group of Monte Carlo simulations and consists of five main modules: (1) tornado climatology; (2) tornado intensity and tornado track geometry; (3) exposure map; (4) fragility and vulnerability functions; and (5) financial module that is used to calculate the resulting damages. In addition, two analytical formulations of radial distribution of tangential velocity in tornado vortex were implemented in the tornado intensity module—Rankine Vortex (RV) and Modified Rankine Vortex (MRV) models. Using the MRV tornado model, the resulting mean aggregated annual expected losses for the return period of 1000 years are US$ 392,080,526.8 and US$ 641,281,336.0 for KS and OK, respectively. Although house prices in KS are higher than in OK, the higher occurrence of tornadoes in OK combined with the larger population of OK (i.e., larger density of houses) result in the increased tornado losses for OK. The losses derived using the MRV module are higher than the losses from the RV module due to the RV module underestimating the tornado tangential velocity. Furthermore, the losses predicted by the current model using the MRV formulation are less than the estimated losses from the previous version of the model (Romanic et al., 2016). The model is also tested for the case of a single tornado track positioned over suburban area of Oklahoma City, OK.

Assimilation of Radar Radial Velocity, Reflectivity, and Pseudo–Water Vapor for Convective-Scale NWP in a Variational Framework

Abstract To improve severe thunderstorm prediction, a novel pseudo-observation and assimilation approach involving water vapor mass mixing ratio is proposed to better initialize NWP forecasts at convection-resolving scales. The first step of the algorithm identifies areas of deep moist convection by utilizing the vertically integrated liquid water (VIL) derived from three-dimensional radar reflectivity fields. Once VIL is obtained, pseudo–water vapor observations are derived based on reflectivity thresholds within columns characterized by deep moist convection. Areas of spurious convection also are identified by the algorithm to help reduce their detrimental impact on the forecast. The third step is to assimilate the derived pseudo–water vapor observations into a convection-resolving-scale NWP model along with radar radial velocity and reflectivity fields in a 3DVAR framework during 4-h data assimilation cycles. Finally, 3-h forecasts are launched every hour during that period. The performance of this method is examined for two selected high-impact severe thunderstorm events: namely, the 24 May 2011 Oklahoma and 16 May 2017 Texas and Oklahoma tornado outbreaks. Relative to a control simulation that only assimilated radar data, the analyses and forecasts of these supercells (reflectivity patterns, tracks, and updraft helicity tracks) are qualitatively and quantitatively improved in both cases when the water vapor information is added into the analysis.

The Multiple-Vortex Structure of the El Reno, Oklahoma, Tornado on 31 May 2013

Abstract This study documents the formation and evolution of secondary vortices associated within a large, violent tornado in Oklahoma based on data from a close-range, mobile, polarimetric, rapid-scan, X-band Doppler radar. Secondary vortices were tracked relative to the parent circulation using data collected every 2 s. It was found that most long-lived vortices (those that could be tracked for ≥15 s) formed within the radius of maximum wind (RMW), mainly in the left-rear quadrant (with respect to parent tornado motion), passing around the center of the parent tornado and dissipating closer to the center in the right-forward and left-forward quadrants. Some secondary vortices persisted for at least 1 min. When a Burgers–Rott vortex is fit to the Doppler radar data, and the vortex is assumed to be axisymmetric, the secondary vortices propagated slowly against the mean azimuthal flow; if the vortex is not assumed to be axisymmetric as a result of a strong rear-flank gust front on one side of it, then the secondary vortices moved along approximately with the wind.

Monitoring infrasound from a Tornado in Oklahoma

Tornado-producing storm systems emit infrasound (sound at frequencies below human hearing) up to 2 hours before tornadogenesis. Weak atmospheric attenuation at these frequencies allows them to be detected hundreds of miles away. Hence, passive infrasonic monitoring may be used for long-range study of tornadogenesis as well as characterization of tornado properties if the infrasound can be correlated with flow-field properties. This requires characterization of infrasound during the life of a tornado as well as other background sources. This is being accomplished as part of the Collaboration Leading Operational UAS Development for Meteorology and Atmospheric Physics (CLOUD-MAP) project, a multi-university collaboration focused on the development and implementation of unmanned aerial systems (UAS) and their integration with sensors for atmospheric measurement. The current work focuses on analysis of a small tornado that occurred on May 11, 2017, about 19 km from an infrasonic monitoring station at Oklahoma State University. Results from this tornado will be reported as well as the available radar data.

Demographics and the Dynamics of Recovery: A Latent Class Analysis of Disaster Recovery Priorities after the 2013 Moore, Oklahoma Tornado

Many factors influence decisions made by households impacted by major disasters, including decisions related to rebuilding their homes in situ or relocating to a new home. Our understanding of how recovery priorities play into these decisions, however, is limited, as is our understanding of how these processes vary according to demographic characteristics. This study explored drivers of household residential decision-making after the 2013 Moore, OK, tornado. Using Latent Class Analysis, we examined the dynamic relationship between demographic characteristics, hazard exposure, and recovery priorities, with an emphasis on factors that influenced households to rebuild and remain in their original community. Our results indicate that demographics and hazard exposure dynamically influence the relative importance of several factors households considered in making residential decisions. Implications related to disaster recovery priorities and residential decision-making are discussed, including the potential development of generalizable models for use by emergency managers in predicting housing recovery priorities and prioritizing recovery actions.

Bridging cultures: Nonprofit, church, and emergency management agency collaboration after the May 2013 Oklahoma tornado outbreak.

Community-based organizations, such as nonprofit organizations (NPOs) and churches, play an important role in helping individuals and communities bounce back after a disaster. The nature of disasters requires organizations across sectors to partner together to provide recovery services; however, collaboration is difficult even in times of stability and requires trust and communication to be built through prior collaborative relationships. These prior relationships rarely exist between the majority of the nonprofit sector, churches, and existing emergency management structures. Furthermore, these organizations often have very different cultures, values, and norms that can further hinder successful postdisaster collaboration. The authors use data collected from interviews with nonprofit and church leaders involved in recovery efforts after a series of devastating storms impacted central Oklahoma in 2013 to understand how well nonprofit and church leaders perceive their organizations collaborated with each other and with government and emergency management agencies in response and recovery efforts. Interview data suggest that NPOs and churches without a primary or secondary mission of disaster response and recovery have a difficult time collaborating with organizations involved in existing emergency management structures. The authors suggest that nonprofits with a primary or secondary purpose in disaster response are a potential bridge between other nonprofits and emergency management agencies.

A Severe Weather Quick Observing System Simulation Experiment (QuickOSSE) of Global Navigation Satellite System (GNSS) Radio Occultation (RO) Superconstellations

AbstractGlobal Navigation Satellite System (GNSS) radio occultations (RO) over the last 10 years have proved to be a valuable and essentially unbiased data source for operational global numerical weather prediction. However, the existing sampling coverage is too sparse in both space and time to support forecasting of severe mesoscale weather. In this study, the case study or quick observing system simulation experiment (QuickOSSE) framework is used to quantify the impact of vastly increased numbers of GNSS RO profiles on mesoscale weather analysis and forecasting. The current study focuses on a severe convective weather event that produced both a tornado and flash flooding in Oklahoma on 31 May 2013. The WRF Model is used to compute a realistic and faithful depiction of reality. This 2-km “nature run” (NR) serves as the “truth” in this study. The NR is sampled by two proposed constellations of GNSS RO receivers that would produce 250 thousand and 2.5 million profiles per day globally. These data are then assimilated using WRF and a 24-member, 18-km-resolution, physics-based ensemble Kalman filter. The data assimilation is cycled hourly and makes use of a nonlocal, excess phase observation operator for RO data. The assimilation of greatly increased numbers of RO profiles produces improved analyses, particularly of the lower-tropospheric moisture fields. The forecast results suggest positive impacts on convective initiation. Additional experiments should be conducted for different weather scenarios and with improved OSSE systems.

The Role of Surface Drag in Tornadogenesis within an Idealized Supercell Simulation

Abstract To investigate the effect of surface drag on tornadogenesis, a pair of idealized simulations is conducted with 50-m horizontal grid spacing. In the first experiment (full-wind drag case), surface drag is applied to the full wind; in the second experiment (environmental drag case), drag is applied only to the background environmental wind, with storm-induced perturbations unaffected. The simulations are initialized using a thermal bubble within a horizontally homogeneous background environment that has reached a balance between the pressure gradient, Coriolis, and frictional forces. The environmental sounding is derived from a prior simulation of the 3 May 1999 Oklahoma tornado outbreak but modified to account for near-ground frictional effects. In the full-wind drag experiment, a tornado develops around 25 min into the simulation and persists for more than 10 min; in the environmental-only drag experiment, no tornado occurs. Three distinct mechanisms are identified by which surface drag influences tornadogenesis. The first mechanism is the creation by drag of near-ground vertical wind shear (and associated horizontal vorticity) in the background environment. The second mechanism is generation of near-ground crosswise horizontal vorticity by drag on the storm scale as air accelerates into the low-level mesocyclone; this vorticity is subsequently exchanged into the streamwise direction and eventually tilted into the vertical. The third mechanism is frictional enhancement of horizontal convergence, which strengthens the low-level updraft and stretching of vertical vorticity. The second and third mechanisms are found to work together to produce a tornado, while baroclinic vorticity plays a negligible role.

Simulating the 20 May 2013 Moore, Oklahoma tornado with a 100‐metre grid‐length NWP model

AbstractSince 2013, the Met Office have run a 2.2 km horizontal gridlength version of the Unified Model (MetUM) as part of the National Oceanographic and Atmospheric Administration's Hazardous Weather Testbed Spring Forecasting Experiment. In this study, we perform high resolution MetUM simulations of the 20 May 2013 Oklahoma tornado outbreak at horizontal gridlengths between 2.2 km and 100 m. Here we present results showing that at 2.2 km gridlength the MetUM is able to simulate supercell‐like storms whereas at O(100 m) gridlength it is able to simulate realistic‐looking supercells with tornado‐like vortices. This opens up the opportunity for using such simulations to highlight areas of enhanced tornado risk ahead of time.

Short-Term Probabilistic Forecasts of the 31 May 2013 Oklahoma Tornado and Flash Flood Event Using a Continuous-Update-Cycle Storm-Scale Ensemble System

AbstractA continuous-update-cycle storm-scale ensemble data assimilation (DA) and prediction system using the ARW model and DART software is used to generate retrospective 0–6-h ensemble forecasts of the 31 May 2013 tornado and flash flood event over central Oklahoma, with a focus on the prediction of heavy rainfall. Results indicate that the model-predicted probabilities of strong low-level mesocyclones correspond well with the locations of observed mesocyclones and with the observed damage track. The ensemble-mean quantitative precipitation forecast (QPF) from the radar DA experiments match NCEP’s stage IV analyses reasonably well in terms of location and amount of rainfall, particularly during the 0–3-h forecast period. In contrast, significant displacement errors and lower rainfall totals are evident in a control experiment that withholds radar data during the DA. The ensemble-derived probabilistic QPF (PQPF) from the radar DA experiment is more skillful than the PQPF from the no_radar experiment, based on visual inspection and probabilistic verification metrics. A novel object-based storm-tracking algorithm provides additional insight, suggesting that explicit assimilation and 1–2-h prediction of the dominant supercell is remarkably skillful in the radar experiment. The skill in both experiments is substantially higher during the 0–3-h forecast period than in the 3–6-h period. Furthermore, the difference in skill between the two forecasts decreases sharply during the latter period, indicating that the impact of radar DA is greatest during early forecast hours. Overall, the results demonstrate the potential for a frequently updated, high-resolution ensemble system to extend probabilistic low-level mesocyclone and flash flood forecast lead times and improve accuracy of convective precipitation nowcasting.

Lidar-Based Methodology to Evaluate Fragility Models for Tornado-Induced Roof Damage

AbstractStructural fragility models have been developed to provide probabilistic estimates of building component damage states caused by exposure to differing wind speeds. Limitations in taking accurate measurements and gathering quantitative loss information in the aftermath of tornadoes has not allowed for comparing fragility-based information with actual building-loss data. This paper presents a methodology for extracting damaged building geometry and roof sheathing loss information from three-dimensional (3D) point cloud data collected with laser scanning technology. The observed building component damage states are then compared to fragility model predictions to validate the models. The methodology was tested on 3D data collected after the 2013 Moore, Oklahoma tornado. From this initial study, which was performed on 5 houses having 27 damaged roof surfaces, it was shown that fragility models underestimated the loss in the center of roof planes (Zone 1) and overestimated the loss in the corners of roo...

Central Social Media Actors in Disaster Information Networks

Government agencies and media outlets traditionally have played central roles in disaster information networks. However, their hub status has slightly diminished as social media empowers others to communicate more easily. Little systemic research has identified the key actors in these new information networks. This paper examines Twitter hashtag networks during four disasters, the Boston Marathon bombing; the West, Texas fertilizer plant explosion; the Midwest spring flooding in Peoria, Illinois; and the Moore, Oklahoma tornado. Findings indicate minimal government and nonprofit involvement. While traditional media outlets still played an important role in some networks, others were more heavily shaped by influential private citizens. We examine those networks by identifying key actors and evaluating their message content and conclude by offering an initial typology for hashtag information networks and discuss directions for future research.

Oklahoma tornado risk and variability: A statistical model

This study uses an existing catalog of registered tornadoes over the territory of the United States to construct a numerical model for tornado loss assessment. The model is tested for the state of Oklahoma (OK). The aggregated annual (AGG) tornado losses are modelled as a function of (1) annual frequency of tornadoes, (2) intensity, length and width of tornado tracks, (3) exposure and (4) vulnerability derived using literature information. Three different configurations of input parameters are investigated: (NoVar) all input parameters except for the annual number of tornadoes are derived based on their mean values, (HOV) variability of house prices, track orientation and vulnerability values are included, and (HOVI) variability of tornado intensity along track length and width is introduced. The calculated AGG losses from independent model runs show high level of convergence for 1000 years of simulated tornadoes. The largest differences in the exceedance probability loss curves result from introducing variability in intensity along the tornado tracks (HOVI). We ran proxies for calculating Risk-Based Capital in order to understand the impact of these findings for policy makers and/or the insurance industry. Modelled losses are compared against results from a commercial tornado risk assessment model as well as against the 2013 Moore tornado event. The NoVar and HOV cases predict the 2013 Moore twister to be 1 in 10 and 1 in 12.5 loss event, respectively, whereas the HOVI case estimates the return period of this event at 58 years. Probability of being hit by a tornado in OK is calculated to be 0.039%, which is in accordance with literature. The limitations and uncertainties of developed model are also discussed.

Book Review: Local News from Someplace Else

Local News from Someplace Else. By Maijorie Maddox. Eugene, Ore.: Wipf & Stock, 2013. xii + 92 pp. $14.00 (paper).It is now a commonplace that modem poets tend to embrace, well, commonplace. They don't compose epics about journeys to underworld; they don't rhyme about major historical battles; they avoid supernatural tales. They instead write insightful poems about simple things or everyday objects. Spiral notebooks. Ferns. Wheelbarrows. These are a few of their favorite things.The virtue of this interest in everyday is that it helps us recognize value and significance of things we otherwise take for granted. From a religious perspective, this technique reminds us of God's place in quotidian. But sometimes such poems can make reader yearn for a bigger subject, one with a broader significance and stronger emotional impact.Marjorie Maddox's fourth book of poetry, Local News from Someplace Else, gives us poems about commonplace that also satisfy this desire for something more. On one hand, she writes about events that most of us have never been through: terrorist attacks, deadly storms, armed robberies, plane crashes, school shootings, kidnappings, unsolved deaths, murdered children, hunting accidents, cancer. But these are events that we hear about all too often, if not every day, and Maddox explores how we try to understand pain in distant places.Maddox, a professor of English at Lock Haven University, recognizes that her subjects carry an inherent emotional weight and so avoids melodrama and hyperbole. She uses subtlety and restraint when imagining thoughts of those directly involved with tragedy. Good Mother Hides from Photographers (p. 14) uses metaphors of photography to depict a mothers grief and shame when her daughter commits a crime; Pennsylvania September: The Witnesses, (p. 17) uses distinct voices of three different people to recall crash of United flight 93.Other poems take a more personal (but never solipsistic) approach by meditating on effects that terrible events have on distant observers. In Reoccurring Storms (p. 59), Maddox recounts several weather-related tragedies, including a deadly tornado in Oklahoma from which a family hid in a bathtub. Two boys were killed; father, daughter, and pregnant mother survived. Maddox's moving final stanzas lead us into mind of daughter before casting us back into the ordinary:And in Oklahoma, five-year-old Cathleen,who, amidst hurricane's howl,recognized hope in heartbeatof her unborn sibling:that faint hum in ear;or that sudden surge toward possibilityinto what one day even you and I-after a particularly hard day of ordinary-might discuss as casuallyas weather, as someone else's life. …

Eliminating the major tornado threat in Tornado Alley

The 2013 devastating tornadoes in Oklahoma, Illinois and other states in Tornado Alley raise an important question: Can we do something to eliminate the major tornado threats in Tornado Alley? Violent tornadoes in Tornado Alley start from the clash-between northbound warm air flow and southbound cold air flow. As there is no mountain in Tornado Alley ranging from west to east to weaken or block the air flows, some clashes are violent, creating vortex turbulence called supercells. These supercells are initially in horizontal spinning motion at the lower atmosphere and then tilt as the air turns to rise in the storm's updraft, creating a component of spin around a vertical axis. About 30% of supercells develop into tornadoes, causing tremendous damages. Here we show that if we build three east–west great walls in the American Midwest, 300 m high and 50 m wide, one in North Dakota, one passing Oklahoma to east and the third one in the south Texas and Louisiana, we will weaken or block such air mass clashes and therefore diminish the major tornado threat in the Tornado Alley forever. We may also first build such great walls locally at some areas with frequent devastating tornado outbreaks and then gradually extend them.