Risk of a road accident in rainy weather

Accid. Anal. & Prev. Vol. 20. No. 3. pp. 161-176, Printed in Great Britam.

RISK OF A ROAD Department

$3.a)+ .@I Ocol-4575/t% 0 1988 Pergsmon Press plc

1988

ACCIDENT

IN RAINY

WEATHER

HAROLD BRODSKY of Geography, University of Maryland, College Park, MD 20742, U.S.A. and A. SHALOM HAKKERT Road Safety Center. Technion, Haifa, Israel (Received 27 June 1986; in revised form 23 April 1987)

Abstract-A number of methods have been proposed for measuring the added risk of a road accident during rainy weather. These methods are reviewed here, and two of them are applied, with adjustments, to data from Israel and the United States. Their accuracy, however, is limited because surrogates have to be used for traffic exposure to rain. Nevertheless, results do indicate that the added risk of an injury accident in rainy conditions can be substantial: two to three times greater than in dry weather. And when a rain follows a dry spell the hazard could be even greater.

INTRODUCTION

Rain and wet roads are hazardous to driving. Most people sense this and generally traffic slows down. Despite these precautions accidents occur. But how many were actually related to the weather? Measuring the added risk during rainy weather has presented a challenging statistical problem and a number of methods have been proposed. These methods will be reviewed here, and suggestions will be made for improving their accuracy. Two methods will be examined in detail and applied to accident data from Israel where a Mediterranean-type climate prevails; and then to accident data taken from an east coast region of the United States where a maritime influence on rainfall is strong. Involved in these measurements are issues frequently encountered in accident analysis when surrogates for exposure are used to estimate risk. Objective estimations of relative risk are important, even though political considerations and intangible values may weigh heavily in decisions involving priorities for safety expenditures. The concept of risk, however, is by no means easily conveyed in any one mathematical formulation. In a concluding discussion, results will be expressed in several ways to allow for differences in interpretation when used within the context of risk management.

RAIN

AS A HAZARD

Substantial theoretical and common sense reasons can be offered to explain why rain can be hazardous to traffic. The friction of the road surface in contact with the tires of a vehicle is reduced on a wet surface [OECD, 19761 and [Barzelay and Lacy, 19841. Consequently at any speed a greater stopping distance is required. The surface is also more slippery on curves, or when making certain maneuvers, especially at higher speeds. Visibility, especially at night, may be reduced by the glare and distraction of wet shining surfaces. Therefore, it is easier for a driver to lose control over a vehicle in rainy weather than in bright weather. One can forestall the effect of rain by driving slower and with greater caution. Good windshield wipers and quality tires with unworn treads will help, along with a well maintained vehicle braking system. During a heavy downpour one can pull off to the side of the road and wait until conditions have improved. One can refrain from going out at all in rainy weather, particularly when a trip is discretionary. Road conditions 161

162

II. RROIXKI

and A. S. I-f~mxR7

can be made safer with better warning signs and lighting, better road geometry. and better paved surfaces with well maintained striping. A statistically derived ratio of relative risk between wet and dry weather will. therefore, be specific to existing circumstances, and to precautions that have already been taken. To be meaningful, however. such a measurement of risk has to be substantially independent of variations in exposure. In the case of added risk due to rainy weather, exposure is determined by traffic volume, traffic pattern, and duration of rainfall. These variables of exposure are, in a sense, extraneous and need to be cancelled out. A somewhat paradoxical, but possible situation, may illustrate the importance of standardization for exposure. The number of pedestrians usually declines in the rain. This decline may lead to fewer pedestrian accidents than might normally occur in bright weather. Nevertheless, for those that do venture out into the ram, the risk of an accident may be substantially higher than in bright weather. As ;I measure of risk the absolute number of accidents during the rainy period would bc misleading. Oni!~ :I rnC>rsure standardized for exposure would rcvcnl the true dimensions of the hazard. The absolute number of accidents in the rain may be misle~~ding for other reasons. From year to year the occurrence and duration of rainfall may vary. Therefore, a higher or lower number of accidents in the rain. over time, may have more to do with variations in climate than relative change in risk. Nor can a simple ratio of rain to total accidents indicate relative risk. Just because an accident occurs in the rain does not necessarily mean that the accident might not have happened anyway. regardless of the weather. Therefore. a way has to be found, statistically. to determine how many accidents can actually be attributed to rainy conditions: this requires standardization for exposure. For highway accidents traffic volume is normally used to measure vehicular travel exposure [Wolfe, 19821; one would, in addition, have to know how much of this travel was under rainy conditions. Rain and traffic exposure, however, vary temporally and geographically and therein lies a measureinent problem.

Studies of wet weather accidents do not always use the same type of data, and therefore results may not always appear to be comparable. Some investigators place emphasis on the effect of falling rain on accidents, whereas others may be concerned exclusively with wet pavement conditions. Some studies apply to road accidents in general, while others narrow interest to injury accidents. or even more specifically, to vehicle injury accidents (excluding pedestrians), or to accidents in which at least one fatality occurs. While it may have been the intent of some investigators to limit analysis to specific conditions, it is also likely that choice of data was at least partly influenced by statistical requirements, or by the relative availability of sources. For example, to insure an adequate sample size, data on all types of accidents grouped together may be used. Over a large region. however. it is easier to obtain and process data on fatal accidents. The joint effect of failing rain and wet pavements may be of greater concern for safety than the effect of wet pavement alone, but these two effects are not easily separable. Depending on the technique of analysis used one may find it easier to obtain results from data coded by pavement condition than by atmospheric condition. For a particular purpose the consequences of using one data set, or another, may only necessitate a shift in interpretation. For comparative studies, it would be best to have more consistency, but even here some accommodation can be made based on reasonable assumptions. More fundamental are differences in the way exposure to wet weather may be measured. Some studies rely entirely on data from a police accident file. Others require, in addition, precipitation data taken from climatological records. Regardless of method used, however, statistical problems can be found which suggests a limit to their accuracy. A method applied by Smeed 11953, 19773 used data taken exclusively from an accident file. Number of wet and dry accidents per day were plotted as Y and Xvariabies on a scatter diagram and a least squares regression line was fit to these data. Smeed

Risk of a road accident in rainy weather

163

found that the slope of this line indicated an increase in number of accidents as exposure to rain increased. Relative risk of an accident in the rain was measured by projecting the regression line to both Y and X zero intercepts. These intercepts represented days when only wet or only dry accidents occurred. The ratio of the expected number of accidents on wet days, divided by the number on dry days, was taken as an indication of the relative risk of an accident in wet weather. Applied to adult pedestrian accidents in Great Britain, an increased risk of 1.06 was estimated during the daylight, and an increased risk of 2.05 during darkness [Smeed, 19771. Smeed’s choice of dependent (Y-axis) variable, however, appears to have been arbitrary. The X and Y variables could just as logically have been switched. In least squares regression, however, a reversal of X and Y variables will lead to a different numerical solution unless the association is zero, or perfect. In a study of wet weather accidents in California, Satterthwaite [1976] also used data from an accident file to measure exposure. Accidents were cross tabulated by day and by type of weather. Days with at least one accident in the rain were grouped into categories of wet, very wet, and extremely wet, depending on percentage of total accidents in the rain. Ratios were calculated for each of these groups by comparing the number of accidents on wet, very wet, and extremely wet days with the number of accidents on days when no accidents were reported in the rain. These ratios correspondingly went from 1.01 to 1.29 to 2.23. This latter figure (2.23) approaches, but does not reach a measure of relative risk. Only if all accidents during extremely wet days are in the rain can this ratio measure relative risk. In contrast to studies that rely entirely on data within accident records, are those which use climatological records to measure exposure to precipitation. Perhaps one of the earliest published references to use precipitation data can be found in Campbell [1971]. This method has been used by a number of state highway departments and in several studies on skidding accidents published by the Transportation Research Board in 1976 (TRB 622, 623, 624). It was also reviewed and used by the National Transportation Safety Board [1980] in a study of wet pavement fatal accidents by state throughout the United States. This method requires hourly precipitation data along with estimates of average pavement drying time after a rain to measure exposure. For the United States as a whole, the Safety Board estimated that wet pavements occurred 3.0% to 3.5% of the time over a period of two years (1976-1977). During this same period, 13.5% of fatal accidents were on wet pavements. The Safety Board reasoned, therefore, that the risk of a fatal accident, nationwide, was about 3.9 to 4.5 times greater on a wet than on a dry pavement. As will be pointed out later, however, this ratio mathematically underestimates risk and therefore requires a correction. Also this ratio is subject to random error and a possible bias in the measurement of drying time. A study of Codling [1974] also used precipitation data for exposure, but differently than the wet pavement method. Time of precipitation was linked with time of accident to obtain matched samples. Periods of time during which some traffic was exposed to rain could then be compared to equivalent periods when no rainfall occurred. By this method Codling estimated that, at selected urban places in Great Britain, accidents increased by an average of 50% during rainy periods. Codling also checked for the possible effect of rain on a reduction of vehicular traffic. This reduction should be least on weekdays especially during the winter when vehicular travel tends to be dominated by work or business trips, which usually cannot be put off or postponed. During such periods, in London, a 2% decline in traffic (and therefore exposure) was estimated. A variation of the matched sample design was also used to measure the relationship between rainfall and traffic accidents for seven southern Illinois cities [Sherretz & Farhar, 19781. Ratios between hours of the day when some rain fell versus corresponding periods of no rain, varied from a high of 2.88 to a low of 1.65, with all results significant at the 5% level. A similar design was used by Bertness [1980] in a study on the impact of rain on transportation activities in the Chicago area, and by Smith [1982] in a study of road accidents in Glasgow. But as indicated by Bertness this method probably underestimates

164

H. HRODSKY

and A. S.

HAKKERT

risk because the effect is measured over a period of time (an hour, or a day) during which some rain fell, but not necessarily all of the time. To measure the risk of rain accurately one would have to compare a period of dry weather, with an equivalent period, when traffic was exposed to the rain all of the time. Such a measurement may be difficult to obtain directly, for reasons that will be illustrated below. SOURCES

OF DATA

In this study, accident data were obtained from two independent sources: the traffic injury (fatal and non-fatal) accident file in Israel (1979-3981), and the U.S. fatal accident (FARS) file (1983-1984). The analysis was done first on the Israeli data, partly because the seasonality of Israel’s rain provided an obvious means for checking a long held (but statistically unexamined) hypothesis that the rains following dry weather are especially hazardous. To broaden the scope of this study, however, we also used similar techniques to examine rainfall patterns that are less seasonal, as in the eastern United States. To estimate the added risk of an accident during the rainy season we tried, at first, to apply the matched sample technique, using the city of Haifa as an example. Plots of the data, however, indicated that a matched sample design in this city would be difficult to use accurately (Fig. 1). Frequent discrepancies occurred between the reported time of accidents in the rain, and the recorded time of precipitation at a station, probably because the rainfall patterns in this city are varied and change within short distances [Soffer and Kipnis, 19801. One would, therefore, require here a close net of continuously recorded precipitation data to estimate traffic exposure to rain accurately. Also the accident record itself, is none too precise. Accidents are recorded as occurring in rainy, or non-rainy weather, but the time of crash may be approximated to the nearest quarter or half hour by whomever fills out the accident form. More uniform climatic conditions and better accident data would, therefore. be needed to make accurate use of a matched sample method in a specific area. Over broad regional areas some of the variability inherent in accident and rainfall data can be smoothed out. In the process one loses geographic detail, but insights can also be obtained from regional generalizations. The regression method of Smeed 119533 and the relative ratio method of Satterthwaite [1976] were, therefore, re-examined for possible use in estimating risk in Israel as a whole. Difficulties in Smeed’s regression method can be partly overcome by redefining the Y and X variables. The Y variable can be taken as the number of daily accidents. (More specifically, in this example, daylight. vehicle injury accidents, during the months of December through February for Israel as a whole.) The X variable can be taken as an index of exposure based on percentage of accidents in the rain (as Satterthwaite did). By redefining the variables in this way, a positive result was obtained. As expected the number of daily accidents increased as the index of exposure to rain increased (Fig. 2). It is not essential to this regression analysis that the index (percentage of accidents in the rain) be strictly proportional to exposure. Only two assumptions about this index need to be made: that Y is a linear function of X, and that X is monotonically related to exposure. In fact, according to the results of this linear regression, the percentage of accidents in the rain cannot be strictly proportional to exposure. Embedded in the transformation of the data to percentages one can derive a relationship that more directly expresses exposure to rain-the difference between expected number of accidents at 0% exposure (12.5, the horizontal line), and the number of accidents occurring in non-rainy weather (the irregular curved line). (The number of accidents in non-rainy weather can be determined mathematically, or estimated visually from the graph, Fig. 2.) The curvature of the line separating rainy from non-rainy accidents implies that at small daily exposures to rain (perhaps in scattered or intermittent episodes) the risk of an accident may be higher than average, even though the number of accidents affected by the rain are likely to be lower than average. For example, at a daily exposure of 20% accidents in the rain, the risk ratio (total rainy weather accidents divided by the expected number of accidents in rainy weather) is 3.46; substantially more than the 1.93 risk ratio measured at the hypothetical exposure of 100% accidents per day in rainy weather.

165

Risk of a road accident in rainy weather

s n . .

+ + +

++ +

3

1'46!11'4B!N

sinoq

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elsw!xoJddv

I

+I

I

166

H. BRODSKY and A. S. HAKKERT

1

EFFECTOF RAIN ON ACCIDENTS

. /’ Number

ofpredrcted

.fl’,

acadents

Y=l246+0.1156(x)~58

r2=2o.r0

Exoess

Accidents /

10-

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in

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Number of erp%d acudenls I” bught weather

5-

Numberof acndents m bnghf weather

0

/ 10

I

I

20

30

1 40

/ 50

1 60

1 70

60

I 90

‘,. 10000

PERCENTAGE OFTOTAL ACCIDENTS IN RAINY WEATHER

Fig, 2. Regression of number of daily accidents against percentage occurring in rainy weather (an index for exposure). Accidents are personal injury involving a vehicle only, during daylight. December through February, 1979-1981. Accidents in rainy weather can be subdivided into expected (would have happened anyway), and excess (attributed to the rain). An allocation of decreasing risk with increasing exposure is made by this regression.

Some caution, however, is needed in interpreting these results. The sliding risk ratio may only be an artifact of the linear form of the equation. Still, a variable risk rate is consistent with suggestions that brief exposures to rain (in the form of intermittent, or scattered showers) are likely to be riskier per unit of time than more widespread and persistent rains. Regardless of interpretation, however, the fact remains that this regression provides a range of risk ratios, while what is needed, is one single overall average as a summary measure. A mean risk ratio can be found on the regression line at the intersection of the mean X and Y values, but more directly, having verified that an increase in dosage (rain) leads to an increase in response (accidents), one can now and use a simplier difference-of-means dispense with regression and its assumptions, analysis to compare risk between rainy and non-rainy conditions. Difference-of-means method Accidents in rainy weather can be separated into the two categories that were noted in the regression analysis: excess accidents (attributed to the influence of rainy weather); and expected accidents (events that would have happened anyway, even if it had not been raining). A single ratio of relative risk can be calculated by dividing total rainy

Risk of a road accident

167

in rainy weather

accidents by expected accidents. The denominator (expected accidents), relates only to rainy conditions and therefore indicates traffic exposure to rain alone. During December through February, 1979-1981 there were 82 days when no vehicle injury accidents were reported in rainy weather. The mean number of accidents during these days can be compared with the mean number on the 122 days when one or more accidents were in rainy weather. One would anticipate a higher mean on rainy, than on non-rainy days. The recorded difference, in fact, was 3.5 additional accidents per day on rainy days (Fig. 3A, and Table 1). Not all of the accidents on rainy days were in the rain, however. The proportion was 6.4 accidents in the rain, for every 10.0 non-rainy accidents (for a daily rainy day total mean of 16.4 accidents, Table 2). Of the 6.4 rainy accidents, 3.5 are excess (additional accidents on rainy days) and therefore can be attributed to the effect of rainy weather. The remaining 2.9 rainy accidents are expected, and can be considered accidents that would have happened anyway, even without rain. The added risk of an accident in rainy weather, therefore, can be estimated as the ratio of total rainy accidents to exposure (measured by expected accidents), (6.4/2.9 = 2.2), Fig. 3B, and Table 2. The risk ratio of 2.2 is subject to sampling error. The standard error of the difference between the two means (non-rainy days and rainy days) is kO.746. At the 95% confidence level the mean difference in number of accidents could be as low as 2.01 or as high as 4.99. Correspondingly the risk ratio could be as low as 1.5 or as high as 4.5 (Table 2). In addition to normal error, however, sources of possible bias have to be considered because when a surrogate is used for exposure of traffic to rain a number of potentially influential factors cannot be isolated for control. The most serious of these factors may be biases due to changes in traffic during rainy weather. An underestimation of risk will occur if traffic decreased during rainy periods. If travel is only delayed until after the rain has stopped, this bias will be partly offset, but if the trip is cancelled for the day, or postponed until a bright day, the difference-of-means test will provide a conservative estimate of risk, perhaps seriously so (Fig. 4). There is some reason to believe, however, that daylight weekday vehicular traffic is only reduced slightly in the rain [Codling, 19741, but the same may not be as true for nighttime and pedestrian traffic. weather

Other circumstances The preceding difference-of-means analysis was applied to daylight vehicle accidents in the winter months. With a large enough sample, however, one can also apply this method to other aggregations of data involving different types of accidents and circum-

( A) Difference of Means

(B)

Risk Ratio

ZO-

= lo-

0:

2.2 morexc/dents ramy weather expected

I

I

Brlghl

day

m than

I

Rmy

day

, Fig. 3. Difference in means is used to measure mean number of accidents on rairiy days attributed the effect of rain (A). Risk ratio is formed by using expected accidents as a surrogate for exposure

to (B).

16X Table

1. Difference

H. BRODSKY and A. S. HAKKERT in means bright and rainy days, Israel,

Bright Type and Period I. Vehicle 1. Daylight Dec.-Feb. 2. Nightlight Dec.-Feb. 3. Daylight Nov. and March 4. Nightlight Nov. and March II. Pedestrian 5. Daylight Dec.-Feb. 6. Nightlight Dec.-Feb.

Days

Number

Rainy

X

S.D.

82

12.91

3.87

105

5.29

85

1979-1981*

Dayst

Number

Difference

X

S.D.

X,,,

S.E.

I

112

16.41

6.46

3.50

0.75

4.7

2.26

90

7.18

2.87

1.89

0.37

5.0

13.12

4.20

45

19.13

7.97

6.01

1.27

4.7

93

4.75

2.27

37

7.27

2.98

2.52

0.54

4.6

112

8.96

3.37

82

9.23

2.91

0.27

0.37

0.7

124

3.25

1.69

71

5.32

2.96

2.07

0.38

5.4

*Personal injury accidents, weekdays (Sunday-Thursday). tRainy day had one or more accidents occurring in rainy weather. Source: Israel Police Accident File Computer Tape, 1979-1981.

stances. In particular, in Israel, one can contrast risks during transitional months, prior to and after, the major winter rainy seasons. During the transitional months of November and March the rains tend to be sporadic, between spells of dry weather. By contrasting transitional and winter months one can examine, from a somewhat different perspective, the previous suggestion that sporadic or intermittent rains are more likely to be riskier than widespread, persistent rains. Daylight risk ratios for November and March were, in fact measured as 11.2: far higher than the ratio of 2.2 for the winter months (Table 2). Perhaps a more meaningful numerical comparison can be made with percentages. During the winter months about 55% of the accidents in rainy weather could be attributed to rain, but during November and March virtually all accidents in rainy weather (91%) could be attributed to the rain [(3.50/6.40) x 100 = 55%, (6.01/6.60) x 100 = 91% (Table 2)]. Table 2. Risk ratio,

Type and Period I. Vehicle 1. Daylight Dec.-Feb. 2. Nightlight Dec.-Feb. 3. Daylight Nov. and March 4. Nightlight Nov. and March II. Pedestrian 5. Daylight Dec.-Feb. 6. Nightlight Dec.-Feb.

total number

(A) Differencein-Means (Excess Accidents)

of rainy weather accidents 1979-1981 (B) Mean Rainy Weather Accidents per Rainy Day

relative

(C) Expected Rainy Weather Accidents (B)-(A)

to expected

number,

Israel,

Risk Ratio 95% Confidence Limits Risk Ratio (B)/(C)

Low

High

3.50

6.40

2.90

2.21

1.46

4.48

1.89

3.58

1.69

2.12

1.48

3.73

6.01

6.60

0.59

11.19

5.00

*

2.52

3.27

0.75

4.36

2.41

*

0.27

3.45

3.18

1.08t

2.07

3.17

1.10

2.88

*All accidents in rain attributed tNot significant at 5%. -Not Estimated. Source: Same as Table 1.

to rain.

1.72

2.81

Risk of a road accident in rainy weather

169

________ ---------Possible Effect of Travel Reduction

20

F

a

I

Rarny wealher

accdmts

.

_----_

------

0 Brlghl

d.ly

Rmy

day

(A)

(B)

Fig. 4. A reduction in travel in rainy weather may cause risk to be underestimated (A). However, if travel is only delayed until the rain has stopped the bias may be partly offset (B). (A) and (B) are hypothetical examples.

Other hypotheses concerning the varying effects of rain on accidents, were also examined, but with results that were somewhat less clear. In an analysis of nighttime accidents we tested the effect suggested both by Smeed [1953] and Codling [1974] that rain at night is especially hazardous (more so than during the day) because visibility problems are exacerbated. Our results however, failed to confirm this hypothesis and, in fact, showed a slightly lower risk ratio (2.1 at night compared to 2.2 during the day). Since it is unlikely that the hazard of rain could actually be less at night, the reason must lie elsewhere. A plausible explanation may be that nighttime travel is more discretionary than daytime because it may include a greater proportion of social and recreational trips. A decline in travel on rainy nights may lead to an underestimation of risk. In November and March, the relative risk at night was also less than the day (4.4 versus 11.2). Again one suspects that the ratio is an underestimate due to a reduction in travel on rainy nights. Contributing to this lower estimated ratio in the transitional months may be the shorter length of nighttime which may reduce the commuter (nondiscretionary) component of travel in favor of a higher proportion of social and recreational travel (more discretionary). Pedestrian accidents are more difficult to evaluate using a difference-of-means method. Pedestrian movement is far more sensitive to rain than vehicular travel. In particular, weather may be selective. Children at play, or the elderly (groups most prone to pedestrian accidents) may be more reluctant to venture out in rainy weather. To the extent that exposure declines and becomes selective, the risk ratio will be underestimated. For daytime pedestrian accidents, a small nonsignificant statistical difference between non-rainy and rainy days was derived and the relative risk ratio was only 1.08. A somewhat higher ratio of 2.88 for night pedestrians was calculated. The nighttime ratio seems more reasonable than the daytime ratio because children and the elderly normally go out less frequently at night-even in brighter weather. Still, some reduction in pedestrian travel can be expected in rainy weather, and to that extent even the nighttime ratio may be conservative (Tables 1 and 2). Wet pavement accident index method

As an alternative to the difference-of-means method of measuring relative risk one can also apply the technique used by the Safety Board: the wet pavement accident index method. This method, however, requires hourly precipitation data from a fairly extensive sampling of weather stations. In the United States it is possible to obtain such data, in summary form, from computer tapes. In Israel, however, this data has to be hand copied

170

H. BRODSKY and A. S. HAKKERT

from original records. As a result our data on precipitation in Israel are limited to only three stations: Jerusalem, Haifa, and Tel-Aviv. Consequently, our calculations are subject to the uncertainties involved in using a small sample. The wet pavement accident index is the ratio of proportion of wet pavement accidents to proportion of wet pavement time [National Transportation Safety, Board, 19801. If the proportion of wet pavement accidents were the same as the proportion of wet time then the ratio would be 1 (an indication that wet pavements had no affect on wet accidents). Any ratio above 1. therefore, was taken by the Safety Board to measure the added relative risk of an accident on wet pavement. From a strictly mathematical view, however, a correction is needed. Wet pavement accidents are composed of: excess wet accidents (accidents due to wet pavement) and expected wet accidents (accidents on wet pavement due to exposure). The ratio used by the Safety Board assumes that the number of expected accidents equals the total number of accidents times the proportion of wet time. More accurately, however, the number of expected accidents equals total accidents, minus excess accidents, times the proportion of wet time. To correct for this difference one needs to know the number of excess accidents. This can be found algebraically by manipulation of the variables involved, or the following formula can be used to find excess accidents (X), on the basis of wet pavement accidents ( W), total number of accidents (T). and the ratio of wet time (r): X = (W -

rT)l(l

A corrected index (CZ) can then be found by expected accidents (W - X): CI = W/(W

-

r).

by dividing

-

wet pavement

accidents

(W)

X)

This corrected index will always be larger than the index used by the Safety Board. The Safety Board also used the wet pavement accident index as a descriptive statistic which may convey a sense of accuracy that is unwarranted. If one considers the random nature of the timing of accidents. then this index must be subject to random error. As a model for this chance element one can use the binomial probability distribution. For large enough samples normal probability approximates the standard error of the proportion. In our calculations of wet accidents for Israel, we used a corrected index, and expressed our results stochastically. For the three month winter rainy season (December through February), wet pavement was estimated to occur 5.6% of the time. Wet pavement, during the two transitional months (November and March), occurred only 2.8% of the time. Vehicle accidents in rainy weather were 25.4% of the total in the rainy season months, and 15.6% of the total in the transitional months. Using the corrected wet accident method the risk ratio was calculated as 5.7 during the rainy winter season (with a 95% confidence limit from 5.0 to 6.7). The transitional months registered a higher ratio of 6.4 (with 95% confidence limits between 5.2 and 8.5) (Table 3). Discrepancies between the two methods of measuring relative risk (wet pavement accident index versus difference-of-means) can be ascribed to a number of sources of measurement error. Of special importance is the assumption concerning drying time. To estimate wet pavement time the Safety Board assumed 30 minutes of drying time after precipitation had ended. In the winter season, in Israel, however, roads may remain visibly wet an hour or more after a rain. In which case, the wet accident index would overestimate risk, perhaps grossly. Neither method adjusts for the possible error due to changes in traffic during rainy weather. This problem has a greater impact on the difference-of-means method, than on the wet accident index method. In the difference-of-means method a decline in traffic will lead to an overestimation of exposure, and an underestimation of risk (Fig. 4). In

Vehicular-Day Vehicular-Night Pedestrian-Day Pedestrian-Night Vehicular-All Day Pedestrians-All Day

2.2 2.1 1.1 2.9 5.7 4.2

Risk Ratio 1.5-4.5 1.5-3.7 i 1.7-2.8 5.0-6.7 3.6-4.9

95% Confidence

December-February

6.4 2.7

11.2 4.4 -

Risk Ratio

S.O-* 2.4-* 5.2-8.5 2.1-3.7

95% Confidence

November and March

*All accidents in rain attributed to the influence of rain. tNot significant at 5% level. -Not estimated. Source: Same as Table 1. Precipitation data used in the wet pavement index were obtained from records at the Israel Meterological Service, Bet Dagon.

II. Corrected Wet Pavement Accident Index

I. Differencein-Means

Method

Type and Period

Table 3. Comparison of methods, Israel, 1979-1981

172

H. BRODSKY and A. S. HAKKERT

the wet accident index a decline in traffic only affects number of wet accidents, but has no effect at all on estimation of exposure (wet time). Considering measurement bias, and the margin of random error, particularly in the wet pavement accident index, one may question the utility of these results. However, bias in the difference-of-means estimate is generally toward lower than expected risks, while bias in the wet accident index appears to be toward higher than expected risks. The actual relative risk ratio may, therefore, lie between the ranges of these two estimates. COMPARISON

WITH

U.S.

DATA

The difference-of-means method is a general technique for adjusting for exposure, and therefore is not necessarily limited in use to Mediterranean climates, or to injury (fatal and non-fatal) accidents. It can also be used to measure risk for fatal accidents on wet pavements. When applied, however, special consideration has to be given to sample size. Fatal accidents occur less frequently than general injury accidents. Since daily accidents are the basis of comparison, the sample size has to be sufficiently large so that an unambiguous classification can be made: either as dry pavement days, or as days when one or more accidents occurred on wet pavement. One way to avoid this problem is to aggregate data by similar geographic units to obtain a larger daily sample. To illustrate this point, and to provide another comparison of these two methods of analysis (difference-of-means and wet pavement accident) we examined an east coast region of the United States consisting of Delaware, the District of Columbia, Maryland, and Virginia, for two years, 1983-1984, taken together. We applied the difference-of-means method and compared these results with the wet pavement fatal accident index based on the Safety Board’s data. Although this comparison is not exact (the Safety Board data are for 1977-1978, ours are for 19831984), it appears that as in Israel, the difference-in-means method also provides a lower estimate of risk than the wet pavement accident index (2.18 versus 3.75) (Table 4). As in the Israeli data, there are indications in the U.S. data that sporadic episodes of rain may be riskier to traffic than more persistent rains. For example, the DE-DCMD-VA region has a lower index of risk than the United States as a whole. This region also has a higher proportion of wet time than the nation as a whole (Table 4). Further, using all of the state data published by the Safety Board we found a significant negative association between the index of risk, and wet time (r’ = 0.36, t = -5.2). Possibly states with less wet time also have more sporadic rains and this might account for their generally higher indices of relative risk. Technically it is possible to obtain direct exposure data by a careful monitoring of rain and vehicle travel, and in some special experiments this may have been done, but it is expensive to obtain such data over a broad area and over time. By their very nature, the use of surrogates introduces error since surrogates are indirect measures based on assumptions that can only be partly correct. To the extent that measurement errors are random, they can be expressed in probabilistic terms. Systematic errors leading to a bias are always possible since not all relevant factors can be controlled. Detection of such errors depends upon a knowledge of the subject. Evaluation of such errors is a matter of professional judgment. The difference-of-means method used here is sensitive to variations in traffic that might be systematically related to weather. These variations may include quantitative as well as qualitative changes in type of travel. The wet pavement accident index method, in addition, is based on the assumption that if any precipitation is recorded during an hour, then the entire hour may be considered wet time. This assumption may be correct if, on the average, it rains for 30 minutes during any hour when precipitation is recorded, and if the remaining 30 minutes of the hour are made of pavement drying time. In other words, wet time is calculated by assuming both an average of 30 minutes of rain, and 30 minutes of drying time, during any hour when measurable precipitation occurs. The assumption of an average of 30 minutes of pavement drying time after rain is questionable.

83,466 83,466

13.5 13.5

16.6 14.1

3.5 3.0

4.2

-

% Wet Time B

% Wet Pavement Accidents

*Data sources: Wet pavement fataf accident index, National Transportation Safety Board, 1980; Difference of means, FARS Tapes, 1983 and 1984, Department of Transportation. tWet pavement fatal accident index was corrected upwards from the figure given by the Safety Board. The regional index was obtained by using number of accidents per state to obtain weights that were then applied to wet time, by state. $Confidence limits were computed by assuming a normal error in proportion of wet-time based on sample size. Upper and lower limits were computed in a ratio, which accounts for the lack of symmetry about the expected ratio. The formula for weighted standard deviations was used to obtain the confidence limits for the DE-DC-MD-VA region. 8% wet time is the percentage of hours during the two year period when some measurabIe precipitation occurred. Source is National Transportation Safety Board, 1980. -Nat estimated.

4.15-4.47 4.85-526

U.S.A. as a Whole 1976-1977 4.30 1976-1977 5.05

Index or Ratio 3,249 3,446

Year Delaware, D.C., Maryland, and Virginia Region 1983-1984 2.18 1.36-13.81 19761977 3.75 2.93-5.52

Corrected Wet Pavement Fatal Lower Estimate Accident Indext Higher Estimate

Difference of Means Corrected Wet Pavement Fatal Accident Index?

Method

Number of Fatal Accidents

95% Confidence Limits*

TabIe 4. Comparison of methods, selected states and U.S.A.*

174

H. BRODSKY and A. S. HAKKEKI

Scientific measurements of pavement drying time are rarely done, and usually only for special engineering purposes. In one such study [Blackburn, Harwood, St. John, et al..19781 pavement drying time was reported as averaging 30 minutes. However, it is not clear whether this refers to daytime or nighttime conditions or whether this refers to a particular season or region (the report mentions Ohio and Louisiana as locations where observations were made). However, what is clear is that the 30 minutes refer specifically to “observed drying time for wheel paths” (p. 38) and not necessarily to the general appearance of the road surface. Wheel paths can be expected to dry faster than the rest of a road surface because of the squeegee effect of tires, and the turbulent air movement over these paths. The condition of wheel paths may be relevant to skidding accidents (for which purpose they were measured) but they are less relevant to the determination of exposure to wet pavement. A wet pavement accident will be classified as such by whomever fills out the accident report. It is likely that the general appearance of the road surface. rather than wheel paths influence how the accident is classified. Consequently a 30 minute drying time is probably an underestimation in some areas. An underestimation of wet time will lead to an overestimation of accident risk. The sensitivity of both the difference-in-means method and the wet pavement accident method to possible error in the measurement of exposure can be tested by stimulating various conditions. Here, wc will use the data from eastern United States to examine how a 5”; reduction in travel during rainy days might affect results from the difference-of-mean\ method. We have already noted that Codling measured a 2% reduction in vehicular traffic during weekdays during the rain. Since our data includes weekend and pedestrian accidents, a somewhat higher figure of 5% is possible. If so, then on days classified as rainy, one can increase the number of accidents by 5%. This would bring the number of accidents up to a hypothetical level that might be expected if there were no reduction in travel in the rain. This supposition raises the average daily number of fatal accidents on rainy days from 5.25 to 5.52. Differences between rainy and non-rainy days increase from I. 1 I to 1.37. Since there were 263 days with wet pavement accidents, the total number of excess wet pavement accidents would increase from (1.11 x 263) = 291 to (1.37 x 263) = 360. During these two years there were 538 wet pavement accidents, so that the relative risk ratio would increase from our previous estimate of (538/(53X - 291)] = 2.18. to a new estimate of (538/(538 - 360)] = 3.02. Correspondingly one can look at the wet pavement accident index and test its sensitivity to what is probably its major (but not only) source of possible measurement bias. Let us assume for the sake of discussion, that average wet time is 45 minutes, only 15 minutes more than the Safety Board’s estimates. If pavement appears wet for an average of 45 minutes after rain stops then wet time has to be increased by a multiple of 1.25. The expected number of accidents on wet pavement correspondingly increases, so that excess accidents on wet pavement is less. The risk index then drops from 3.75 to 2.Y5. But a more exact comparison with the difference-of-means method also requires an adjustment upward for a 5% reduction in travel during the rain. This effect is less on the wet pavement index than on the difference-of-means ratio, since the wet accident index only increases from 2.95 to 3.03. The result of applying these two plausible changes in assumptions is to bring the two measurements into virtual agreement, at a ratio of about three fatal accidents on wet pavement for every accident on dry pavement. Such a resolution of the discrepancy between the two methods, however, may not be entirely reassuring and we do not intend it to be. Although the adjustments made are plausible, they are based on supposition, not empirical evidence. The obvious sensitivity of the two methods to modest changes in the measurement of exposure also adds uncertainty. With more reliable local data, however. such an adjustment could be used to provide more exact estimates. SUMMARY

AND

CONCLUSIONS

Unless new methods are developed. any progress toward a more reliable and usable measurement of relative risk will depend upon research into the effect of rain on traffic

Risk of a road accident

in rainy weather

175

volume and average pavement drying time. Other sources of error appear to be less important but would also enter into a refined estimation of risk, particulary for a small area. An unadjusted difference-of-means analysis will underestimate risk if traffic decreases during rainy weather. An unadjusted wet pavement accident index will overestimate risk where pavement drying time exceeds 30 minutes. Where feasible, analysts may want to use both methods to estimate risk. Since they are independent of each other they may provide a range for estimating the upper and lower bounds of true risk. Better yet, both methods are capable of refinement and possible reconciliation if detailed information can be obtained about local climatic and traffic conditions. Given fairly large random errors, refinements will have to be incorporated in order to use relative risk ratios for monitoring change and determining relative hazards in small geographic areas. The results of using either method seems to substantiate a widely held opinion that rain is riskier when it follows a dry spell. In Israel the risk of an accident in rainy weather does appear to be higher during the occasional rains of the transitional months than during the more persistent rains of the winter season. Similarily, in the United States, those states with a higher proportion of wet time do tend to have lower indices of risk. These trends are consistent with a suggestion that during intervening dry periods pavement grime tends to accumulate on road surfaces which may be especially slippery when wetted by the first rain. However, other factors may have a bearing on this matter so that further study is needed. On a yearly basis, rainy weather may contribute to about 6% of weekday vehicular injury accidents in Israel (Table 5). During a five month period, however, rainy conditions may be responsible for upwards of 14%) or one out of every seven injury accidents. But even in the winter rainy season, rain is highly sporadic, so that during a fraction of the day rain may claim an inordinate number of injury accidents, at least twice as much, possibly more, than otherwise. The National Transportation Safety Board in it special study in 1980 found that the risk of a fatal accident in the United States as a whole was 3.9 to 4.5 times greater on wet than on dry pavements. As a consequence of its findings the Safety Board issued an alert to state and county public officials concerning the magnitude of this hazard. In making its assessment and recommendations the Safety Board was acting upon the best Table 5. Effect

Type and Period I. Vehicle 1. Daylight Dec.-Feb 2. Nightlight Dec.-Feb. 3. Daylight Nov. and March 4. Nightlight Nov. and March Sum of 5 months Sum of 12 months II. Pedestrian 5. Daylight Dec.-Feb 6. Nighlight Dec.-Feb

of rainy weather

(A) Total Number of Accidents

(B) Total Number of Rain Accidents

on injury

accidents,

1979-1981*

(C) Number of Accidents Attributed to the Rain

Attributed as a % of Total (C)I(A) x 100

Attributed as a % of all Rain (C)/(B) x 100

2,897

717

392

13.5

54.7

1,201

322

170

14.2

52.8

1,976

297

270

13.7

90.9

711

121

93

13.1

76.9

6,785 16,737

1,457

925 925

13.6 5.5

63.5 -

1,761

283

781

225

t

145

*All estimates are based on the difference of means method conservative. tAbout 10% of rainy weather vehicle accidents occur outside analyzed. -Not estimated. AAP 20:3-B

Israel,

18.6

and therefore the 5 month

64.4

may be considered season

but were not

176

H. BRODSKY and A. S. HAKKERT

information then available and a method of analysis that had appeared in the scientific literature and had been in use for about a decade. A re-examination of the wet pavement accident index indicates that a mathematical correction is needed to avoid underestimating risk, but that if average pavement drying time exceeds 30 minutes, then an adjustment is needed to prevent an overestimation of risk. Further, there is a substantial random error that should be considered in evaluating this risk ratio. Our estimates of relative risk, for certain east coast states, therefore, differ from those of the Safety Board. Based on the results of both the difference-of-means, and the wet pavement accident methods, a relative risk of about three seems most likely. The Safety Board indicated a risk factor of almost three and a half for this same region. Given our appraisal, one may wish to scale down the estimates of the Safety Board somewhat. But even if wet pavement contributed to only half of the fatalities attributed to it by the Safety Board, that would still involve an annual loss in the United States of two to three thousand lives. In the arena of risk management, action often has to be taken on the basis of crude estimates, and with a realization that, with further research, revisions will be likely. Thus far, all indications are that the hazards of wet pavement and rain are of a magnitude to justify a continued search for countermeasures. REFERENCES Barzelay M. E. and Lacy G. W. Scientific Automobile Accident Reconstruction, Vol. 1. Matthew Bender, New York, 1984. Bertness J. Rain-related impacts on selected transportation activities and utility services in the Chicago area. .I. of Appl. Meteorology 19, 545-556, 1980. Blackburn R. R., Harwood A. D.. St. John A. D. and Sharp M. C. Effectiveness ofAIternate Skid Reduction Measures, Vol. I. Report No. FHWA-RD-79-22, Federal Highway Administration, Washington, D.C., 1978. Campbell M. E. The wet-pavement accident problem: Breaking through. Traffic Quart. 15,209-214, 1971. Codling P.J. Weather and road accidents. Climatic Resources and Economic Activity, David and Charles Holding (Eds.), Chap. 11, pp. 205-222. Newton Abbot, London, 1974. National Transportation Safety Board. Fatal Highway Accidents on Wet Pavement-The Magnitude, Location, and Characteristics, HTSB-HSS-80-1. National Technical Information Service. Springfield, VA, 1980. OECD. Adverse Weather, Reduced Visibility and Road Safety. Organization for Economic Co-Operation and Development, Paris, 1976. Satterthwaite S. P. An assessment of seasonal and weather effects on the frequency of road accidents in California. Accid. Anal. & Prev. 8, 87-96. 1976. Sherretz L. A. and Farhar B. C. An analysis of the relationship between rainfall and occurrence of traffic accidents. J. of Appl. Meteorology 17, 711-715, 1978. Smeed R. J. Some factors affecting visibility from a driver’s seat and their effect on road safety. L3r. J. of Physiol. Optics 10,63-85, 1953. Smeed R. .I. Pedestrian accidents. In A. S. Hakkert (Ed.). Proceedings of the Internutional Conference on Pedestrian Safety, Volume 2, pp. 7-21. Michlol, Haifa. 1977. Smith K. How seasonal and weather conditions influence road accidents in Glasgow. Scottish Geographical Magazine 98, 103-114, 1982. Soffer A. and Kipnis B. (Eds.), Atlas of Haifa and the Carmel. University of Haifa Ltd., Haifa, Israel, 1980. Wolfe A. C. The concept of exposure to the risk of a road traffic accident and an overview of exposure data collection methods. Accid. Anal. & Prev. 14, 337-340, 1982.