- Research
- Open Access

# GIS-based regression modeling of the extreme weather patterns in Arkansas, USA

- Kyle W. Rowden
^{1}and - Mohamed H. Aly
^{1}Email author

**Received:**28 December 2017**Accepted:**12 March 2018**Published:**27 March 2018

## Abstract

### Background

Investigating the extreme weather patterns (EWP) in Arkansas can help policy makers and the Arkansas Department of Emergency Management in establishing polices and making informed decisions regarding hazard mitigation. Previous studies have posed a question whether local topography and landcover control EWP in Arkansas. Therefore, the main aim of this study is to characterize factors influencing EWP in a Geographic Information System (GIS) and provide a statistically justifiable means for improving building codes and establishing public storm shelters in disaster-prone areas in the State of Arkansas. The extreme weather events including tornadoes, derechos, and hail that have occurred during 1955–2015 are considered in this study.

### Results

Our GIS-based regression analysis provides statistically robust indications that explanatory variables (elevation, topographic protection, landcover, time of day, month, and mobile homes) strongly influence EWP in Arkansas, with the caveat that hazardous weather frequency is congruent to magnitude.

### Conclusions

Results indicate a crucial need for raising standards of building codes in high severity regions in Arkansas. Topography and landcover are directly influencing EWP, consequently they make future events a question of “when” not “where” they will reoccur.

## Keywords

- Extreme weather
- GIS
- Regression modeling
- Risk assessment
- Arkansas

## Background

A common misconception propagates an axiom through rural communities that tornadoes do not occur in mountainous terrains, but this is just a myth (Lyza and Knupp 2013). Fujita (1971) first observed that tornadoes have a tendency to strengthen on the down-slope of their storm track. More researchers have followed Fujita’s footprints pursuing the relationship between topography and severe weather events (e.g. LaPenta et al. 2005; Bosart et al. 2006; Frame and Markowski 2006; Markowski and Dotzek 2011; Gaffin 2012; Karstens et al. 2013; Lyza and Knupp 2013). Forbes et al. (1998) and Forbes & Bluestein (2001) provided more insightful observations: (1) widths of destructive swaths contract on down slopes, (2) intense swirls are most likely occurring at the base of mountains or along the down slope path, (3) intensity of a tornado is likely to decrease on the upward slope, and (4) tornadoes are likely to weaken on a jump from one hill top to another and strengthen upon touching down on the adjacent hill. Lewellen (2012) elaborated on these observations and questioned whether topography might statistically provide zones of safety from severe weather. Other explanatory variables (EV) influencing damage include concentrations of mobile homes, often referred to as “trailer parks”. Kellner and Niyogi (2013) examined the phenomenon of tornado attraction to mobile home communities and determined that these communities do not attract strong weather events as much as these communities are constructed in the undesirable hinterlands that are heavily prone to severe weather patterns.

### Study area

Along with tornadoes, Arkansas is prone to powerful supercell thunderstorms that can produce large magnitude hail storms and deadlier derechos (also known as “straight-line winds” or “micro-bursts”), which are strong wind events with gusts exceeding 50 knots. Historically, the highest injury and fatality counts related to severe weather in Arkansas and the rest of USA predate the 1950’s when the first weather forecasting station was installed at Tinker Air Force Base in Oklahoma, coinciding with President Harry Truman’s signing of the Civil Defense Act (CDA) in 1950 (Galway 1985; Bradford 1999 l;2001; Coleman et al. 2011). The CDA mandated installation of warning sirens across the USA, which became the saving grace for countless Americans from severe weather strikes.

Arkansas has three main population centers located in unique regions across the state. These being the Little Rock metropolitan area that includes Little Rock, Jacksonville, Cabot, Benton, Maumelle, and Conway located in the geographic center of the state; northwest Arkansas (NWA) which includes Fayetteville, Springdale, Rodgers, and Bentonville; and lastly Jonesboro in northeastern Arkansas. All these regions are vital socio-economic hubs for the state and the USA and unfortunately are prone to the most violent episodes of hazardous weather.

The city of Little Rock (Pulaski County) houses the State Capital along with all major state agency headquarters as well as large private sector corporations such as Dillard’s, a fortune 500 company headquartered in Little Rock (Fortune 2017). Little Rock’s population is ~ 200,000 people. When taking into consideration the counties adjacent to Pulaski County, there are over 700,000 residents with even more working in this region daily (U.S. Census 2016). Central Arkansas is consistently hit with the highest frequency and magnitude events annually. For an instance, on April 27, 2014, the Mayflower Tornado touched down about 25 km northwest of Little Rock carving a 70-km path of destruction. This tornado remained on the ground for over 60 min, reaching a maximum width of ~ 1 km, killed 16 lives and injured over 120 people. This was the second deadliest single tornadic event in Arkansas in the past 50 years.

NWA is the second most populated area in the state with the two counties (Benton and Washington) having a combined total of 500,000 residents (U.S. Census 2016). The University of Arkansas located in Fayetteville is the largest university in the state with a current enrollment of ~ 28,000 students in fall of 2017 (UA 2017). Multiple fortune 500 companies are headquartered in NWA, these being Walmart (#1 biggest company in the world), Tyson Foods, J.B. Hunt Transportation (Fortune 2017) along with the ancillary business these companies drawn in. Walmart, and its related U.S. distribution, is anchored in Arkansas with 6 of Arkansas’ 10 distribution centers, supporting the billion-dollar corporation being located in NWA. Although not immediately in Arkansas, the May 22, 2011, EF-5 Joplin Tornado was one of the most powerful and deadliest tornadoes in U.S. history and was responsible for 158 fatalities, over 1150 injuries, and $2.8 billion dollars’ worth of damage (Kuligowski et al. 2014). It is conceivable that a tornado of this magnitude could strike NWA.

Lastly, Jonesboro, the county seat for Craighead County has a population of more than 100,000 residents and supports the second largest university in the state; Arkansas State University with 25,000+ enrollments (ASU website 2017). Although this region of Arkansas doesn’t have the quantity of people as the aforementioned regions, Jonesboro serves as the agricultural center for Arkansas as well as much of the USA. Arkansas is the number-1 rice producing state in the USA by raising more than 50% of domestic rice. Billion dollars agriculture companies, such as Riceland Foods, Inc., operate out of this region and export more than 60% of Arkansas rice (ARFB 2017) to the international market.

The Mississippi Alluvial Plain (MAP) often referred to as the Arkansas Delta is a flat lowland physiographic region nearly void of any topographic relief apart from Crowley’s Ridge just west of Jonesboro. This type of landscape is particularly favorable for agriculture but meanwhile it is also proper for broad sweeping weather patterns with the capability of inundating the region with heavily rains. For instance, a hail event occurred in May 2015 in close proximity to Walnut Ridge (45 km northwest of Jonesboro) produced hail up to 5 in. in diameter. Hail of this size is large enough to kill people and livestock, as well as destroy roofs of houses. Fortunately, this event missed a direct hit on Walnut Ridge and occurred across the agricultural land adjacent to the town. Derechos frequently strike this region accounting for 30% of all derechos in the state. Single microburst can cause millions of dollars in damage such as the event on May 12 of 1990 that was responsible for $6 million dollar in property loss. Derechos’ magnitudes may exceed 100 knots, such as the recent event on January 22, 2012. The same weather system also spawned 7 tornadoes and blanketed the MAP region with hail up to 3 in., emphasizing the interconnectedness of all three severe-weather types within a single storm. Event details and weather-related statistics are extracted from the GIS metadata that are publicly available through NOAA and NWS geodata as part of the Storm Prediction Center’s Severe GIS (SVRGIS) data repository.

## Methods

### Gridding and standardizing input data

Fishnetting allows storm tracts to be standardized into grids, supporting field summing, as well as later analysis of original attributes. Grid size is standardized to 10 × 10 km in this study. A 1-arc sec digital elevation model (DEM) for the state is classified into ten classes using an interval of 82.66 m that closely mirrored a stretch classification method. These respective elevation attributes are then joined to the 10 × 10 km grid. Primary alchemy applied to this analysis revolves around the spatial join tool available in ArcGIS release 5.10.1, presenting two valuable options: (1) one-to-one, where a 1:1 ratio is maintained and the choice to sum totals is used to get sums of attributes for each respective cell and (2) one-to-many, which allows user selected attributes from a line, representing a storm track, intersecting multiple grid cell to be added. The one-to-many spatial join has been used in this study to model event frequencies for each respective weather hazard.

### Creating severity indices

*SSI*is the statewide severity index,

*TS*is the tornado severity,

*DS*is the derecho severity, and

*HS*is the hail severity.

### Exploratory regression

Regression analyses provide a means for exploratory data trends, offering statistical scrutiny of influential spatio-patterns. The exploratory regression (ER) tool in ArcGIS (5.10.1) provides a simplistic means for trial and error experimentation, allowing the analyst a to narrow down factors that may be influencing the dependent variable model. ER is employed in this study as a first step investigation to conduct an OLS regression on the most influential variables. Explanatory variables (EV) considered in this analysis are found to be: trailer parks, elevation, topographic protection, physiographic ecological sub regions. These variables are chosen based on results from previous studies (e.g. LaPenta et al. 2005; Bosart et al. 2006; Frame and Markowski 2006; Markowski and Dotzek 2011; Gaffin 2012; Karstens et al. 2013; Lyza and Knupp 2013) that show strong correlations between topography, elevation, land cover features, and windward aspects of topographic features to directly influence strength and subsequent severity of weather events. Several statistical properties are used to determine the strength of EV.

*Adjusted R*

^{ 2 }and evaluated by Steel and Torries (1960) as:

*k*, denotes the quantity of coefficients implemented in the regression,

*n*, the number of variables,

*SSError*, the sum for standard error and

*SSTotal*is the total sum of squares.

*t-test*developed by Gosset (1908) can be simplified as:

*X*

_{ 1 }

*, X*

_{ 2 }

*,…. X*

_{ n }, out of a size

*n*, which follows a natural tendency of normal distribution between the variance in

*σ*

^{2}and

*μ,*with

*μ*denoting mean population, and

*σ*being the standard deviation in the population.

*LM*is a Lagrange Multiplier,

*N*denotes the number of observations, n the sample size, \( {\widehat{u}}_t^2 \) are the dependent gamma residuals, \( {\widehat{\sigma}}^2 \)is the estimated residual variance in observations.

*k*denoting the number of parameters and

*n*, the sample size (e.g. Burnham and Anderson 2002; Konishi and Kitagawa 2008).

*S*is skewness in the dataset,

*C*is the sample’s kurtosis,

*n*the number of observations, and

*k*represents the quantity regressors (e.g. Jarque and Bera 1980, 1981; and 1987).

*i*th variable is 1 less, the proportion of variance which is \( {R}_i^2 \) (O’brien 2007).

*I*value based on Tobler’s (1970) Law to calculate p-scores and z-scores. P-scores designate probability percentages that range from 0.10 to < 0.01 (weak), null, and 0.10 to < 0.01 (strong). Z-scores represent standard deviations, when combined with a strong corresponding p-scores indicate robust confidence. Ranges for Z-scores are (weak) < − 2.58 up to (strong) > 2.58. Moran’s

*I*is defined by ESRI (2016) as:

*I*, from mean (

*x*

_{ i }−

*X*) is

*z*

_{ i },

*n*denotes total feature count

*,*spatial weighting between (

*i*,

*j*) becomes

*W*

_{ i },

*j*, and lastly the amalgamation of these spatial weights is

*S*

_{0}:

_{I}-scores are calculated with:

### Ordinary least squares

*y*is the dependent variable which is the variable that is predicting or explaining the model and is a function of

*X*, which are coefficients representing EVs that, together, help answer

*y*.

*β*are regression coefficients that are calculated through algorithms running in the GIS background and

*β*

_{ 0 }is the regression intercept and represents an expected outcome for

*y*and

*ε*are the residual random error terms.

As part of the OLS process, we run a SA utilizing Global Moran’s I, which determines the likeliness of randomly chosen EVs relative to their spatial distribution and impact. Other statistical outputs included in the final OLS include: (1) *StdError* and (2) *Robust*_{
SE
}, which are errors in standard deviation; (3) t-Statistic and (4) *Robust*_{
t
} which are ratios between an estimated value of a parameter and a hypothesized value relative to standard error; (Akaike, 1973) probability and (Akaike, 1974) *robust probability* (_{
Pr
}), which are the statistically significant coefficients (*p* < 0.01); should initial probability values possess a significant (Akaike, 2011) *Koenker* statistic, then (*pr)* is used to determine significance of coefficient; (Arkansas Farm Bureau, 2017) *VIF* factors (> 7.5) that are indicative of redundancy; (Arkansas State University, 2016) *Joint Wald* statistic, which help determine model’s overall significance if *Koenker* value is significant; and finally (Amemiya, 1985) *AICc* and (Belsley et al., 1980) *R*^{
2
}, which are measures of model’s overall fit and performance.

### Quantile classification

Quantile classification is used for the symbology of all choropleth maps. Quantile is chosen as the appropriate means for classification because it creates classes based on equal division of units in each class (e.g. Cromley 1996; Brewer and Pickle 2002; Burnham and Anderson 2002; Xiao et al. 2007, Sun et al. 2015). Quantile classification most closely represents the input data trends that are poorly represented using other classification methods, such as Jenks-Natural breaks, equal interval, standard deviation, and geometric classifications.

## Results and discussion

Ordinary Least Squares results for tornadoes

Variable | Coefficient | StdError | t-Statistic | Probability | Robust_SE | Robust_t | Robust_Pr | VIF | |
---|---|---|---|---|---|---|---|---|---|

Event | Intercept | 2.9560 | 0.2807 | 10.5299 | 0.000000* | 0.2917 | 10.1329 | 0.000000* | – |

Month | 0.0279 | 0.0059 | 4.7338 | 0.000003* | 0.0058 | 4.8383 | 0.000002* | 1.0391 | |

ADJ_TIME | 0.0246 | 0.0035 | 7.0107 | 0.000000* | 0.0031 | 7.8801 | 0.000000* | 1.1056 | |

SUM_MAG | 0.4708 | 0.0042 | 112.0444 | 0.000000* | 0.0049 | 96.6009 | 0.000000* | 1.1092 | |

AR_ECO_ID | −0.0021 | 0.0002 | −13.1645 | 0.000000* | 0.0002 | −11.4925 | 0.000000* | 1.0497 | |

Protection | 0.1328 | 0.0517 | 2.5702 | 0.010193* | 0.0403 | 3.2951 | 0.001009* | 1.0600 | |

Magnitude | Intercept | −6.3259 | 0.5174 | −12.2254 | 0.000000* | 0.4869 | −12.9926 | 0.000000* | – |

Month | −0.0274 | 0.0109 | −2.5071 | 0.012203* | 0.0107 | −2.5624 | 0.010423* | 1.0452 | |

ADJ_TIME | 0.0096 | 0.0065 | 1.4702 | 0.141599 | 0.0057 | 1.6650 | 0.096012 | 1.1194 | |

Event (Sum) | 1.6066 | 0.0145 | 111.0131 | 0.000000* | 0.0173 | 92.6609 | 0.000000* | 1.1401 | |

Elevation | −0.0011 | 0.0004 | −3.0899 | 0.002030* | 0.0004 | −3.0349 | 0.002434* | 1.9239 | |

Trailer Parks | −0.0411 | 0.0080 | −5.1587 | 0.000001* | 0.0082 | −5.0265 | 0.000001* | 1.1378 | |

AR_ECO_ID | 0.0054 | 0.0004 | 15.1201 | 0.000000* | 0.0004 | 13.6639 | 0.000000* | 1.5146 | |

Protection | 0.0552 | 0.1118 | 0.4935 | 0.621665 | 0.0894 | 0.6170 | 0.537257 | 1.4571 | |

Joint Wald | Jarque-Bera | Koenker (BP) Statistic | AICc | Adjusted R2 | |||||

11,822.594 | 254.1233 | 1002.2988 | 13,317.7251 | 0.78686 |

Ordinary Least Square results for derechos

Variable | Coefficient | StdError | t-Statistic | Probability | Robust_SE | Robust_t | Robust_Pr | VIF | |
---|---|---|---|---|---|---|---|---|---|

Event | Intercept | −32.346 | 2.3571 | −13.7229 | 0.000000* | 1.9912 | −16.2441 | 0.000000* | – |

Elevation | 0.001 | 0.0016 | 0.6341 | 0.5260 | 0.0013 | 0.7589 | 0.4479 | 1.7764 | |

Month | 0.407 | 0.0650 | 6.2605 | 0.000000* | 0.0620 | 6.5668 | 0.000000* | 1.0309 | |

TIME_ADJ | 0.128 | 0.0258 | 4.9677 | 0.000001* | 0.0248 | 5.1690 | 0.000001* | 1.0270 | |

AR_ECO_ID | 0.024 | 0.0016 | 15.1470 | 0.000000* | 0.0015 | 15.3767 | 0.000000* | 1.3115 | |

Protection | 4.716 | 0.4971 | 9.4886 | 0.000000* | 0.3091 | 15.2565 | 0.000000* | 1.4236 | |

Magnitude | Intercept | −423.667 | 41.0222 | −10.3278 | 0.000000* | 33.5516 | −12.6273 | 0.000000* | – |

Trailer Parks | 2.423 | 0.5258 | 4.6078 | 0.000006* | 0.5302 | 4.5697 | 0.000007* | 1.1736 | |

Event (Sum) | 39.873 | 0.1577 | 252.7619 | 0.000000* | 0.1959 | 203.5371 | 0.000000* | 1.1379 | |

Elevation | −0.425 | 0.0281 | −15.1447 | 0.000000* | 0.0255 | −16.6968 | 0.000000* | 1.8430 | |

Month | 4.531 | 1.1255 | 4.0255 | 0.000065* | 1.0887 | 4.1618 | 0.000037* | 1.0340 | |

TIME_ADJ | 1.603 | 0.4466 | 3.5889 | 0.000348* | 0.4341 | 3.6920 | 0.000237* | 1.0294 | |

AR_ECO_ID | 0.340 | 0.0284 | 11.9668 | 0.000000* | 0.0272 | 12.5045 | 0.000000* | 1.4518 | |

Protection | 61.355 | 8.6204 | 7.1175 | 0.000000* | 6.3061 | 9.7296 | 0.000000* | 1.4340 | |

Joint Wald | Jarque-Bera | Koenker (BP) Statistic | AICc | Adjusted R2 | |||||

409,245.6 | 5144.80 | 3643.4876 | 74,204.573 | 0.9857 |

Ordinary Least Squares results for hail

Variable | Coefficient | StdError | t-Statistic | Probability | Robust_SE | Robust_t | Robust_Pr | VIF | |
---|---|---|---|---|---|---|---|---|---|

Event | Intercept | −0.0296 | 0.2200 | −0.1346 | 0.8929 | 0.2050 | −0.1444 | 0.8852 | – |

SUM_MAG | 0.8729 | 0.0009 | 1023.3266 | 0.000000* | 0.0016 | 561.5929 | 0.000000* | 1.0212 | |

MO | 0.0409 | 0.0076 | 5.3547 | 0.000000* | 0.0078 | 5.2433 | 0.000000* | 1.0241 | |

HAIL_TIM_2 | −0.0082 | 0.0033 | −2.4808 | 0.013107* | 0.0033 | −2.4926 | 0.012680* | 1.0196 | |

ELEVATION | 0.0015 | 0.0001 | 10.8536 | 0.000000* | 0.0001 | 12.5462 | 0.000000* | 1.2704 | |

AR_ECO_ID | −0.0004 | 0.0002 | −2.1620 | 0.030620* | 0.0002 | −2.2770 | 0.022785* | 1.2861 | |

Magnitude | Intercept | −0.2115 | 0.2501 | −0.8456 | 0.3978 | 0.2248 | −0.9406 | 0.3469 | – |

SUM_EVENT | 1.1281 | 0.0011 | 1023.3266 | 0.000000* | 0.0021 | 533.7691 | 0.000000* | 1.0215 | |

MO | −0.0422 | 0.0087 | −4.8542 | 0.000002* | 0.0088 | −4.7753 | 0.000003* | 1.0244 | |

HAIL_TIM_2 | 0.0115 | 0.0037 | 3.0678 | 0.002173* | 0.0037 | 3.0856 | 0.002049* | 1.0194 | |

ELEVATION | −0.0018 | 0.0002 | −11.2164 | 0.000000* | 0.0001 | −12.8938 | 0.000000* | 1.2698 | |

AR_ECO_ID | 0.0008 | 0.0002 | 4.1671 | 0.000037* | 0.0002 | 4.5625 | 0.000007* | 1.2851 | |

Joint Wald | Jarque-Bera | Koenker (BP) Statistic | AICc | Adjusted R2 | |||||

47,365.25 | 2445.7748 | 1057.0264 | 190,276.91 | 0.84911 |

*p*-values in Table 1. OLS output has ±2 standard deviations of residuals from best prediction indicating that EVs predict ~ 80% of the model as determined from residual

*R*

^{ 2 }value of 0.78686. Std output shown in Fig. 7 displays a dominant ±1 std for over-prediction/under-prediction of the final model. These results are reliable being within the accepted ±2 std of error.

Lyza and Knupp (2013) noted four common modes of behavior with tornadoes that can help explain the high magnitude and frequency in central Arkansas along with the protected zones in the Ouachita and Boston Mountain region immediately north of the Arkansas River Valley. Mode 1: where tornadic strength deteriorates on the up slopes, proved to be consistent in the findings of Selvam et al. (2014) with the Mayflower Tornado. Mode 2: tornado whirl pattern intensifies on plateaus but weakens as the whirl moves of the plateau, potentially helping to explain the central Boston Mountain low severity zone. Mode 3: tornado tracts tend to follow valleys like a hallway, once again related to the Ouachita Mountains which are systematically folded long linear ridges and valleys helping funnel wind driven weather patterns from west to east into Little Rock. Mode 4: tornadoes have a tendency to trace the edges of ridges and plateaus. That has been also observed by Selvam et al. (2014) in Mayflower and can explain the strong tendency of EF-3 and EF-4 tornadoes to trend along the eastern boundary that the Ouachita Mountains makes with the Mississippi Embayment (refer back to Fig. 1 for physiographic provinces of Arkansas).

*p*< 0.01) coefficients, except for elevation, which is not found to be a good EV for event frequency although patterns are observed at specific elevations previously mentioned. Outside of these tight elevation windows, random patterns are observed. Table 2 shows the OLS outputs for the regression analysis. The

*R*

^{ 2 }of 0.9857 has a strong indication that the EVs chosen are sufficient at explaining the dependent variables. OLS shows that all explanatory inputs have VIF values below 2, where VIF values > 7.5 indicate redundancy of EVs.

*p*-values < 0.01, implying a robust model for explanation of historical hail patterns. OLS outputs in Table 3 provide ancillary validation for

*R*

^{ 2 }values of 0.84911, indicating the respective EVs chosen are sufficient at explaining ~ 85% of dependent variables. Applying EVs (time, month, elevation, topographic protection, sum of magnitudes, sum of events, concentration of mobile homes) to OLS regression analysis for events and magnitude (Fig. 11) shows that these EVs perform well at explaining most of the events but as with tornadoes and derechos still struggled at fully explaining the highest frequency and magnitude of events found in central Arkansas. This being said, even the outliers fall within ±2 stds of error.

The summed severity map shows a strong correlation between high severity and major population centers. A similar observation has been documented by Kellner and Niyogi (2013) where they spatially calculated touchdown points in Indiana to find that 61% of EF0-EF5 tornadoes touchdown within 1–3 km of urban landuse area bordering landcover classified as forest. Areas surrounding Little Rock in central Arkansas, which have had the highest incidence of tornadic and derecho activity, suffer from not only topographic terrain influence in the Ouachita Mountains to the immediate west, but also a wind corridor effect through the Arkansas River Valley, as well as flat topography with land surface heterogeneity.

## Conclusions

Complacency is a deadly human tendency that overcomes residents, especially when weather-related disasters have not occurred in recent years. Severe weather events sometimes occur simultaneously during the largest and most powerful storm system such as the example of the January 22, 2012, which impacted the entire Arkansas Delta. Robust and viable statistics can help re-enforce the imperative need for storm shelters and higher building codes to better prepare for such extreme weather events. Better understanding of severe weather patterns and preferential tendency for storms to frequent certain cities, regions, or trajectories is the first step in mitigating risk by minimizing exposure and vulnerability in these highest severity regions.

Analysis of the severe weather events from 1955 to 2015 reveals a very strong positive correlation with time of the day, in association with the three weather types under consideration. The extreme weather events are found to most likely occur between 2:00 and 10:00 pm local time. This is of vital importance because line-of-sight is reduced to near zero visibility at night, thus residents in most of fall and winter months must rely on National Weather Service warnings. Raising public awareness to the frequency and likelihood of such geoenvironmental risks occurring in evening hours may help bolster residents taking advantage of FEMA funding for building residential shelters in rural areas and community shelters in more urban settings.

Our findings in this study provide statistically robust evidence for variables that respond to Lewellen’s (2012) question regarding whether it is statistically possible to prove that topography might influence regional weather patterns. Along with topographic influence, this study also found that other physiographic features such as elevation, physiographic provincial sub regions, and most importantly the windward protection afforded to leeward sides of physiographic features are statistically significant EV in predicting severe weather patterns.

The explanatory variables of time of day, month, elevation, physiographic region (subclass), topographic protection, elevation, and concentration of trailer parks are not only effective at forecasting severe weather patterns but also have been found to be statistically robust through OLS regression analysis. Susceptibility models based on these variables may provide substantially higher precision for spatio-temporal patterns, which in turn can be used by ADEM and FEMA as well as other first responding agencies, and residents to better access risk beyond the broad umbrella of previous county-wide assessments. The developed methodology can be applied to a broad spectrum of severe weather around the globe to improve hazard mitigation and help with preparedness for geoenvironmental disasters.

## Declarations

### Acknowledgements

This study has been conducted using the research facilities in the InSAR Lab, which is part of the Center for Advanced Spatial Technologies and the Department of Geosciences at the University of Arkansas. Thanks are due to the three anonymous reviewers and the Editor, Fawu Wang, for their thorough reviews, comments, and suggestions.

### Funding

NASA EPSCoR RID, grant #24203116UAF, awarded to Mohamed H. Aly.

### Availability of data and materials

All weather and mobile home concentration data are publicly available from NOAA/NWS Geodata as part of the Storm Prediction Center’s SVRGIS. Arkansas GIS data are publicly available from www.spc.noaa.gov/gis/svrgis/ and https://gis.arkansas.gov.

### Authors’ contributions

Both authors developed the research methodology, wrote the manuscript, and improved the revised version of the paper. Both authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- Ahmed N, Selvam RP (2015a) Tornado-Hill interaction: Damage and sheltering observations. Inter. J. App. Earth Observ. and Geoinfo. Str.Google Scholar
- Ahmed N, Selvam RP (2015b) Topography effects on tornado path deviation. University of Arkansas Computer Mechanics lab Internal Paper, 1-31.Google Scholar
- Ahmed N, and Selvam RP (2015c) Ridge effects on tornado path deviation.
*Int. J. Civil Str. Eng. Res*3 (1): 273–294.Google Scholar - Ahmed, N. 2016 Field observations and computer modeling of tornado-terrain interaction and its effects on tornado damage and path. Thesis, University of Arkansas.Google Scholar
- Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle, in Petrov, B.N.; Csáki, F., 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, USSR, September 2-8, 1971, Budapest. Akadémiai Kiadó, 267–281.Google Scholar
- Akaike, H. 1974. A new look at the statistical model identification.
*IEEE Transactions on Automatic Control*19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.View ArticleGoogle Scholar - Akaike, H. 2011. Akaike’s information criterion.
*Int. Encyc. Stat. Sci*2: 1–25. https://doi.org/10.1007/978-3-642-04898-2_110.Google Scholar - Amemiya, T. 1985.
*Advanced economics*. Massachusetts: Harvard University Press.Google Scholar - Arkansas Farm Bureau (2017) Agriculture facts, http://www.arfb.com/pages/education/ag-facts/.Accessed 22 November 2017.Google Scholar
- Arkansas State University (2016) The Arkansas State University system 2015–2016 factbook, Office of Institutional Research and Planning. 1–91.Google Scholar
- Belsley, D.A. 1984. Demeaning conditioning diagnostics through centering.
*The American Statistician*38: 73–82. https://doi.org/10.1080/00031305.1984.10483169.Google Scholar - Belsley, D.A., E. Kuh, and R.E. Welsch. 1980.
*Regression diagnostics: Identifying influential data and sources of collinearity*. New York: Wiley.View ArticleGoogle Scholar - Bosart, L.F., A. Seimon, K.D. LaPenta, and M.J. Dickinson. 2006. Supercell tornadogenesis over complex terrain: The Great Barrington, Massachusetts, tornado on 29 may 1995.
*Wea. Forecasting*21: 897–922.View ArticleGoogle Scholar - Bradford, M. 1999. Historical roots of modern tornado forecasts and warnings.
*Wea. Forecasting*14: 484–491. https://doi.org/10.1175/1520-0434(1999)014<0484:HROMTF>2.0.CO;2.View ArticleGoogle Scholar - Bradford, M. 2001. Scanning the skies: A history of tornado forecasting, 220. University of Oklahoma Press.Google Scholar
- Breusch, T.S., and A.R. Pagan. 1979. A simple test for heteroscedasticity and random coefficient variation.
*Econometrica*47: 1287–1294. https://doi.org/10.2307/1911963.View ArticleGoogle Scholar - Brewer, C.A., and L. Pickle. 2002. Evaluation of methods for classifying epidemiological data on choropleth maps in series.
*Ann. Assoc. Am. Geog*92: 662–681.View ArticleGoogle Scholar - Burnham, K.P., and D.R. Anderson. 2002.
*Model selection and multimodel inference: A practical information-theoretic approach*. 2nd ed. New York: Springer-Verlag.Google Scholar - Coleman, T.A., K.R. Knupp, J. Spann, J.B. Elliott, and B.E. Peters. 2011. The history (and future) of tornado warning dissemination in the United States.
*Am. Meteor. Soc*567-582. https://doi.org/10.1175/2010BAMS3062.1. - Crichton, D. 1999. The risk triangle, natural disaster management. Ingleton, J., (ed), Tudor rose London.Google Scholar
- Cromley, R.G. 1996. A comparison of optimal classification strategies for choroplethic displays of spatially aggregated data.
*Inter. J. Geog. Infor. Sci*10 (4): 405–424. https://doi.org/10.1080/02693799608902087.View ArticleGoogle Scholar - Edwards R (2017) The online tornado FAQ: Frequently asked questions about tornadoes. National Oceanic and Atmospheric Administration Storm Prevention Center. www.spc.ncep.noaa.gov/faq/tornado. Accessed 27 October 2017.
- ESRI (2016) ArcGIS10.4.1 desktop help. http://resources.arcgis.com/en/help/. Accessed 15 June 2017.
- FEMA (2002) Community wind shelters: background and research. http://www.fema.gov/plan/prevent/bestpractices/casestudies.shtm. Accessed 12 Oct 2017.
- FEMA (2008) Arkansas’ tornado shelter initiative for residences and schools: Mitigation case studies.Google Scholar
- Forbes, G.S., and H.B. Bluestein. 2001. Tornadoes, tornadic thunderstorms, and photogrammetry: A review of the contributions by T.
*T. Fujita. Bull. Amer. Meteor. Soc*82 (1): 73–96. https://doi.org/10.1175/1520-0477.View ArticleGoogle Scholar - Forbes, G.S., M.L. Pearce, T.E. Dunham, and R.H. Grumm. 1998. Downbursts and gustnadoes from mini-bow echoes and affiliated mesoscale cyclones over Central Pennsylvania. Preprints. In 16th Conf. On weather analysis and forecasting, Phoenix, AZ, Amer, 295–297. Meteor. Soc.Google Scholar
- Fortune. 2017.
*The global 500: The world’s largest companies*. New York City: Time.Google Scholar - Frame, J., and P. Markowski. 2006. The interaction of simulated squall lines with idealized mountain ridges.
*Mon. Wea. Rev*134: 1919–1941. https://doi.org/10.1175/MWR3157.1.View ArticleGoogle Scholar - Fujita TT (1971) Proposed characterization of tornadoes and hurricanes by area and intensity. SMRP research paper 91, University of Chicago, 42 pp.Google Scholar
- Fujita, TT. 1989. The Teton-Yellowstone tornado of 21 July 1987. Mon. Wea. Rev., 117(9):1913–1940. https://doi.org/10.1175/1520-0493(1989)117<1913:TTYTOJ>2.0.CO;2
- Gaffin, D.M. 2012. The influence of terrain during the 27 April 2011 super tornado outbreak and 5 July 2012 derecho around the great Smoky Mountains National Park. Preprints, 26th conference on severe local storms, Nashville, TN. Amer. Meteor. Soc.Google Scholar
- Galway, J.G. 1985. J.P. Finley: The first severe storms forecaster.
*Bull. Amer. Meteor. Soc*66: 1389–1395. https://doi.org/10.1175/1520-0477(1985)066<1389:JFTFSS>2.0.CO;2.View ArticleGoogle Scholar - Gosset, W.S. 1908. The probable error of a mean.
*Biometrika*6 (1): 1–25.View ArticleGoogle Scholar - Jarque, C.M., and A.K. Bera. 1980. Efficient tests for normality, homoscedasticity and serial independence of regression residuals.
*Economics Letters*6 (3): 255–259. https://doi.org/10.1016/0165-1765(80)90024-5.View ArticleGoogle Scholar - Jarque, C.M., and A.K. Bera. 1981. Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence.
*Econ. Let*7 (4): 313–318. https://doi.org/10.1016/0165-1765(81)90035-5.View ArticleGoogle Scholar - Jarque, C.M., and A.K. Bera. 1987. A test for normality of observations and regression residuals.
*Inter. Stat. Rev*55 (2): 163–172.View ArticleGoogle Scholar - Karstens, C.D., W.A. Gallus, B.D. Lee, and C.A. Finley. 2013. Analysis of tornado-induced tree fall using aerial photography from the Joplin, Missouri, and Tuscaloosa–Birmingham, Alabama, tornadoes of 2011.
*J. Appl. Meteor. Climatol*52: 1049–1068. https://doi.org/10.1175/JAMC-D_12_0206.1.View ArticleGoogle Scholar - Kellner, O., and D. Niyogi. 2013. Land-surface heterogeneity signature in tornado climatology: An illustrative analysis over Indiana 1950-2012. Earth Inter.,18(10):1-32. https://doi.org/10.1175/2013EI000548.1.
- Koenker, R. 1981. A note on studentizing a test for heteroscedasticity.
*Journal of Econometrics*17 (1): 107–112. https://doi.org/10.1016/0304-4076(81)90062-2.View ArticleGoogle Scholar - Konishi, S., and G. Kitagawa. 2008.
*Information criteria and statistical modeling*. New York: Springer.View ArticleGoogle Scholar - Kuligowski, E.D., F.T. Lombardo, L.T. Phan, M.L. Levitan, and D.P. Jorgensen. 2014. Final report, National Institute of Standards and Technology (NIST) technical investigation of the may 22, 2011, tornado in Joplin, Missouri. Nat. Const. Safety team act rep.
*NIST NCSTAR*3: 1–428. https://doi.org/10.6028/NIST.NCSTAR.3.Google Scholar - LaPenta, K.D., L.F. Bosart, T.J. Galarneau, and M.J. Dickinson. 2005. A multiscale examination of the 31 may 1998 Mechanicville, New York, tornado, weather and forecasting.
*Am. Meteor. Soc*20 (1): 494–516. https://doi.org/10.1175/WAD875.1.Google Scholar - Lewellen, D.C. 2012. Effects of topography on tornado dynamics: a simulation study. 26th Conference on Severe Local Storms (5–8 November 2012) Nashville, TN, am.
*Meteor. Soc*. https://ams.confex.com/ams/26SLS/webprogram/Paper211460.html Accessed 6 Nov 2017. - Lyza AW, Knupp KR (2013) An observational analysis of potential terrain influences on tornado behavior. Severe Weather Institute and Radar & Lightening Laboratories (SWIRLL), University of Alabama, Huntsville. Internal Paper. 1–7.Google Scholar
- Markowski, P.M., and N. Dotzek. 2011. A numerical study of the effects of orography on supercells.
*J. Atmos. Res.*100: 457–478. https://doi.org/10.1016/j.atmosres.2010.12.027.View ArticleGoogle Scholar - National Climatic Data Center (2013) U.S. tornado climatology. https://www.ncdc.noaa.gov/climate-information/extreme-events/us-tornado-climatology. Accessed 22 Nov 2017.
- NOAA (2017a) Converting traditional hail size descriptions, storm prediction center, http://www.spc.noaa.gov/misc/tables/hailsize.htm. Accessed 22 Nov 22, 2017.
- NOAA (2017b) SPC tornado, hail, and wind database format specification (for .csv output). http://www.spc.noaa.gov/wcm/#data. Accessed 15 Sept 2017.
- O’Brien, R.M. 2007. A caution in regarding rules of thumb for variance inflation factors.
*Quality & Quantity*41: 673–690. https://doi.org/10.1007/s11135-006-9018-6.View ArticleGoogle Scholar - Safeguard (2009) Safeguard storm shelters - Fujita Scale. http://www.safeguardshelters.com/fujitascale.php. Accessed 21 Oct 2017.Google Scholar
- Selvam RP, Ahmed NS, Yousof MA, Strasser M, Costa A (2015) RAPID: Documentation of tornado track of mayflower tornado in hilly terrain.Google Scholar
- Selvam RP, Ahmed NS, Yousof MA, Strasser M, Ragan Q (2014) Study of tornado terrain interaction from damage documentation of April 27, 2014 mayflower, AR tornado. Department of Civil Engineering, University of Arkansas, Fayetteville, AR 72701.Google Scholar
- Steel, R.D.G., and J.H. Torrie. 1960. Principles and procedures of statistics with special reference to the biological sciences. McGraw Hill.Google Scholar
- Sun, M., D.W. Wong, and B.J. Kronenfeld. 2015. A classification method for choropleth maps incorporating data reliability information.
*The Professional Geographer*67 (1): 72–83. https://doi.org/10.1080/00330124.2014.888627.View ArticleGoogle Scholar - Tobler, WR. 1970. A Computer Movie Simulating Urban Growth in the Detroit Region.
*Econ. Geogr.*46:234. http://www.jstor.org/stable/143141 - United States Census Bureau. 2016.
*Annual estimates of the resident population: April 1, 2010 to July 1, 2016*. U.S.: Census Bureau Population Division https://factfinder.census.gov. Accessed 22 Nov 2017.Google Scholar - University of Arkansas (2017) Fall 2017 11th day enrollment report, Office of Institutional Research and Assessment, https://oir.uark.edu/students/enrollment-report.php, Accessed 22 Nov 2017.
- Xiao, N., C.A. Calder, and M.P. Armstrong. 2007. Assessing the effect of attribute uncertainty on the robustness of choropleth map classification.
*Int. J. Geog. Inf. Sci*21 (2): 121–144. https://doi.org/10.1080/13658810600894307.View ArticleGoogle Scholar