Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

Model for forecasting expressway surface temperature in snowy areas
Masafumi Horii* and Takayuki Hayami*** Department of Civil Engineering, College of Engineering, Nihon University** Saku Office, Nexco-Maintenance Kanto Company Ltd.

(Received: May. 20, 2016 Accepted :Sept. 28, 2016 )ABSTRACT
We proposed a forecast model that uses a neural network to predict what the winter road surface temperature will be after three hours in order to increase the efficiency of anti-icing programs. In order toestablish the forecast model, learning models of the road surface temperature using three sets of input variables at a specific site were created. These learning models were then applied to other sites along an expressway, and the correct classification of the road surface temperature was examined. The results of thepresent study revealed that the road surface temperature along an expressway can be predicted three hours
in advance more than 76% of the time by applying a learning model to the time series variation of the roadsurface temperature and other variables, such as the hourly traffic volume and the effect of spreading antiicing chemicals.
Keywords: forecast of road surface temperature, neural network, discriminant analysis

1. Introduction
In snowy areas, highway maintenance authorities often spread chemicals such as sodium chloride (salt) on
the road surface in order to increase safety during winter conditions. However, these chemicals damage
the soil, plants, vehicles, and roadside structures. The amount of salt used has increased yearly, increasing
the financial burden for these services. Therefore, a forecast model of the road surface temperature thatenables salt to be spread before the road surface freezes would be beneficial. The model should be simple
and easy to apply in daily route-based road maintenance using only existing basic sensor measurements.
However, no such practical forecast model has been established.
Several studies on forecast models of the road surface temperature have been conducted. Thesestudies can be classified into two types: 1) methods using heat balance models and 2) statistical methods.
Heat balance models have been reported by Rayer (1987), Shao et al. (1993), and Voldborg (1993), andthese models have improved the accuracy of the road surface temperature prediction. However, these models are difficult to apply in all locations for which effective winter road maintenance is needed because theyrequire several types of equipment for the observation of meteorological variables, such as solar radiation,
radiation balance, and albedo.
With respect to statistical methods, Suzuki et al. (1993) constructed a forecast model of the roadsurface temperature that uses multiple regression analysis and reported that a fairly accurate forecast model
could be obtained. Shao (1998) and Almkvist and Walter (2006) investigated the forecasting of the roadsurface temperature using a neural network model. These methods also require several types of equipment
for measuring meteorological variables.
Under these conditions, we proposed a forecast model that uses a neural network to predict roadsurface temperatures three hours in advance at a specific site on an expressway based on measurements49

M.HORII, T.HAYAMI
using existing basic sensors and obtained acceptably accurate results. Moreover, we confirmed that theneural network model has an accuracy similar to that of multiple regression models (Suzuki et al., 1993) bycomparing the results (Horii and Fukuda, 2000). Furthermore, Horii (2013) applied a forecast model tosites on a national highway and established a route-based forecast model having sufficient accuracy forpractical application. In our previous studies, we constructed the model by inputting the times series datafor only one variable, that is, road surface temperature. In the present paper, however, we apply the proposed model (Horii, 2013) to an expressway by changing the input variables. We examine the effect of the
input variables of the forecast model and evaluate the difference in precision between the various sets of
input variables of the route-based model in order to increase the efficiency of anti-icing programs (Horiiand Hayami, 2015).

2. Forecast model
Artificial neural networks are computer models that are inspired by components of the human brain and are
powerful tools that can be used to solve complex problems. The neural network used in the present study
is a multilayer network, as shown in Fig. 1. A neural network consists of three layers: an input layer, ahidden layer, and an output layer. The input neurons receive signals from outside the model and send their
outputs to the hidden neurons. The output neurons receive signals from the hidden neurons and produce thefinal outputs.

wjil

wkju

i

j

k

Input layer

Hidden layer

Output layer

Figure 1. Multilayered neural network
The outputs of the hidden and output neurons, denoted by oj and yk, respectively, are given by Iloj = f (uj ) = f 
w ji xi  i =1

(1)

 J

u
yk = f ( zk ) = f 
w oj 
 j =1 kj




( 2)

∑

∑

where uj is the input to the jth neuron in the hidden layer, zk is the input to the kth neuron in the output layer,
wjil is the connection weight between the jth neuron in the hidden layer and the ith neuron in the input layer,

50

Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

wkju is the connection weight between the kth neuron in the output layer and the jth neuron in the hidden
layer, xi is the input to the ith neuron in the input layer, and I and J are the numbers of neurons in the input
and the hidden layer, respectively. The most commonly used activation function is a sigmoid function:f (x ) =1
1 + e−x(3)

Neural networks can be trained by adjusting the connection weights in order to abstract the relationships between the input data and the output data. This learning procedure can be achieved by minimizing
the error between the desired outputs and the actual outputs:
1 K( yk − ydk )2
2 k =1

∑

E=

( 4)

where ydk is the desired output signal of the kth neuron in the output layer, and K is the number of neurons
in the output layer. In general, the error backpropagation algorithm is applied in order to minimize thiserror function. However, the backpropagation learning algorithm has some problems. The backpropagation
process requires too many learning cycles to converge to the correct weights, and the learning process
becomes stuck at a local minimum of the error.
In the present paper, a learning algorithm that is based on an extended Kalman filter has been introduced (Murase et al., 1994). We assume the following nonlinear state model (Katayama, 1983):

wt +1 = f t (wt ) + vt

(5)yt = ht (wt ) + nt

(6)where wt is the n-dimensional state vector at time t, yt is the p-dimensional observation vector, ft(wt) andht(wt) are the n- and p-dimensional nonlinear vector functions, respectively, vt is the zero-mean m-dimensional plant noise, and nt is the zero-mean p-dimensional observation noise with covariance matrices(

 v  T
E  t  vτ
 n t nτT) = Q0

t





0
δ tτ
Rt 

(7 )

in which Qt is a matrix of size m × m, Rt is a matrix of size p × p, and δtτ is the Kronecker delta.
Here, since the connection weights are the elements of the state vector and are assumed to be timeinvariant, the plant noise is not taken into consideration. Therefore, in place of Equation 5, the state equation can be expressed as follows:

wt +1 = Iwt(8)

where I is the identity matrix.
Since ht(wt) is a nonlinear function, this function is linearized around the estimate of the state as
follows:

ˆ t / t −1 ) + H t (wt − w
ˆ t / t −1 )ht (wt ) = ht ( w

51

(9)

M.HORII, T.HAYAMI
Then, an extended Kalman filter algorithm can be applied to the estimates of the states. By substituting Equation 9 into Equation 6, we can derive the following expression to replace Equation 6:

η t = H t wt + nt

(10)

where

ˆ t / t −1 ) + H t w
ˆ t / t −1
ηt = yt − ht ( w(11)and Ht is the gradient matrix that results from linearizing the network and is defined as follows: ∂ht H t =  ∂wt  w= wˆ t / t −1

(12)

Using the state and observation equations, a method for updating the estimators of the system can bederived. The updated equations areˆt /t = w
ˆ t / t −1 + K t [ yt − ht (wˆ t / t −1 )]w

ˆ t +1 / t = w
ˆt /tw
K t = Pt / t −1 H t

T

(H P
t

t / t −1

(14)
H t + RtT

Pt / t = Pt / t −1 − K t H t Pt / t −1

Pt +1/ t = Pt / t

(13)

)

−1

(15)

(16)

(17)

ˆ t / t is the Kalman filter estimate of the state at time t based on its one-step prediction, Kt is thewhere w
Kalman gain, and Pt/t is an estimation error covariance matrix.
3. Application
3.1. Learning model of road surface temperature
We applied a neural network model based on the extended Kalman filter to forecast road surface temperatures at three sites of the Ban-Etsu expressway in Fukushima prefecture. Site A (99.1 kp, altitude: 512.6
meters) and Site C (121.5 kp, altitude: 190.4 meters) are located in embankment sections, and Site B (105.3
kp, altitude: 570.8 meters) is located in a cut section. Here, kp refers to kilo-posts and indicates the distancefrom the origin of a route.
Observation data from December 2013 to March 2014 were provided by the Tohoku Regional Head
Office of the East Nippon Expressway Company (NEXCO East, 2013-2014). These data consist of air
temperature, road surface temperature, temperatures at 5 and 10 centimeters underground, wind velocity,
amounts of rainfall and snowfall per hour, traffic volume, and reports on operations of spreading anti-icing
chemicals. Furthermore, the grid point value (GPV) data at the nearest point of three sites at 37.6 degrees
north latitude and 140.0 degrees east longitude were collected. The GPV data were provided by the Japan
Meteorological Agency and were calculated using the Global Spectral Model.

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Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

The model structure is a three-layer network, as shown in Fig. 2. We used the time series variationof data as inputs to the input neurons and the road surface temperatures after three hours as outputs to the
output neurons. Three hours corresponds to the amount of time required for a salt spreader to depart froma snow removal station and complete the spreading operation.

Present
inputs
Inputs of 1
hour
beforeInputs of 2
hours
beforeInputs of 3
hours
beforeOutputs of
3 hoursahead

Inputs of 4
hours
beforeFigure 2. Basic architecture for forecasting road surface temperatures
In the present paper, we selected three sets of input variables: 1) road surface temperature, 2) roadsurface temperature, hourly traffic volume, and effectiveness of spreading anti-icing chemicals, and 3) selected variables by stepwise discriminant analysis. The stepwise discriminant analysis for variable was carried out by adding and deleting variables from the equation according to the partial F values in order to findthe appropriate discriminant equation. Refer to, for example, Afifi and Clark (1984) for details. Here, thedata on the effectiveness of spreading anti-icing chemicals can be represented by a dummy variable thattakes one of two values: 1, indicating chemicals on a road surface are effective, and 0, indicating otherwise.
We assume anti-icing chemicals on a road surface to be effective for three hours after salt spreader operation.
The selection of the model structure was based on the learning and testing results. Here, the data set
for learning was a period of 31 days, from January 1 to January 31 of 2014, and the data set for testing wasa period of 90 days, from December 1 to December 31 of 2013 and from February 1 to March 31 of 2014.
Firstly, we constructed the learning model by varying the input neurons and hidden neurons for each input
variable. We then predicted the outputs of these models using the testing data set, which had not beenpreviously presented to the models. Finally, we decided the forecast model structure of the road surface
temperature with the best classification results of the learning and testing. The number of iterations forlearning was fixed at 100, for the sake of practicality (Horii and Fukuda, 2000).
At the same time, discriminant analysis was used to examine whether the road surface temperatures
could be adequately predicted by the neural network model. Discriminant analysis was used to assign a new
sample belonging to two or more groups in order to minimize the probability of misclassification.
Evaluation of the classification results was conducted in terms of 1) total correct classification, including correct classification of the road surface temperatures for above-zero and below-zero conditions,and 2) critical correct classification for dangerous road conditions, that is, below-zero road surface temperatures.
Tables 1 and 2 show the best results of the correct classification for the learning and testing dataobtained using the first set of input variables at Site A. In this case, the input variables are the time series

53

M.HORII, T.HAYAMI
variation of the road surface temperature for six hours, and the number of hidden neurons is nine. Tables 3
and 4 show the same results obtained using the second set of input variables, which are the time series
variation of the road surface temperature for six hours, the hourly traffic volume, and the effectiveness of
spreading anti-icing chemicals for three hours, at Site A. The number of hidden neurons in this case is againnine. In both cases, the percentages of overall correct classification for the learning and testing data werehigh: 88.4% (first set, learning), 84.1% (first set, testing), 89.2% (second set, learning), and 77.6%. (second
set, testing).
Table 1. Learning results for road surface temperature using the first set of input variables(January of 2014, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
496
38
46
145
91.5%

79.2%

Correctclassification
92.9%
75.9%
88.4%

Table 2. Tasting results for road surface temperature using the first set of input variables(Other three months, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
964
123
213
815
81.9%

86.9%

Correctclassification
88.7%
79.3%
84.1%

Table 3. Learning results for road surface temperature using the second set of input variables(January of 2014, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
496
38
40
151
92.5%

79.9%

54

Correctclassification
92.9%
79.1%
89.2%

Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

Table 4. Tasting results for road surface temperature using the second set of input variables(Other three months, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
982
105
368
660
72.7%

Correctclassification
90.3%
64.2%

86.3%

77.6%

Table 5 shows the discriminant functions for two groups of data: data for below-zero road surface
temperatures and data for above-zero road surface temperatures. The predictor variables in this table wereselected based on the results of the stepwise discriminant analysis. A new sample is assigned to the groupwith the higher discriminant function score.
Table 5. Discriminant functions

Predictor
variables
Road surface
temperature
Hourly traffic
volumeSurfacetemperature(GPV)
Relative
humidity at 500hPa (GPV)
Constant

Coefficients of
discriminantfunctions
Below
Above
zero
zero

Partial F
value-0.2090.727

1275.7

0.017

0.030

708.3

-1.037-0.710

496.0

0.089

0.077

374.5

-5.127-6.536

Tables 6 and 7 show the results of correct classification for the learning and testing data obtainedusing the third set of input variables, which consists of the time series variation of the road surface temperature for eight hours, the hourly traffic volume for three hours, the surface temperature for two hours, andthe relative humidity at 500 hPa for one hour, all at Site A. In this case, the number of hidden neurons isseven. We obtained fairly high percentages of overall correct classification for the learning (93.4%) andtesting data (84.7%). The three forecast model structures are summarized in Table 8.

55

M.HORII, T.HAYAMI
Table 6. Learning results for road surface temperature using the third set of input variables(January of 2014, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
502
32
16
175
96.9%

Correctclassification
94.0%
91.6%

84.5%

93.4%

Table 7. Tasting results for road surface temperature using the third set of input variables(Other three months, Site A).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
933
154
169
859
84.7%

Correctclassification

84.8%

85.8%
83.6%
84.7%

Table 8. Summary of forecast model structures
Set No. of input
variablesFirst set
Second set

Third set

Input neurons
Variable name
Road surface temperature
Road surface temperature
Hourly traffic volume
Spreading results of anti-icing chemicals
Road surface temperature
Hourly traffic volume
Surface temperature (GPV)
Relative humidity at 500 hPa (GPV)

hours
6
6
3
3
8
3
2
1

Number of hidden neurons
997

Figures 3 and 4 show the learning and testing results, respectively, obtained using the first set of input
variables for Site A. Figures 5 and 6 show the same results obtained using the second set of input variables,
and Figs. 7 and 8 show the same results obtained using the third set of input variables. In every case, thepredicted values follow the observed values. Therefore, we can obtain three models that enable high-precision learning and testing.

56

Road surface temperature（℃）

Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

30

Observed values( Site A)

Predicted values

20
10
0
-10

Date

Road surface temperaure（℃）

Figure 3. Learning results for road surface temperatures using the first set of input variables(December of 2014, Site A)

30

Observed values( Site A)

Predicted values

20
10
0
-10

Date

Figure 4. Testing results for road surface temperatures using the first set of input variables(December of 2013, Site A)

57

Raod surface temperatute（℃）

M.HORII, T.HAYAMI

30

Observed values( Site A)

Predicted values

20
10
0
-10

Road surface temperature（℃）

Date
Figure 5. Learning results for road surface temperatures using the second set of input variables(January of 2014, Site A)

30

Observed values( Site A)

Predicted values

20
10
0
-10

Date
Figure 6. Testing results for road surface temperatures using the second set of input variables(December of 2013, Site A)58

Raod surface temperature（℃）

Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

30( Site A)

Observed values

Predicted values

20
10
0
-10

Date
Figure 7. Learning results for road surface temperatures using the third set of input variables(January of 2014, Site A)

Road syrface temperature（℃）( Site A)

Observed values

Predicted values

30
20
10
0
-10

Date

Figure 8. Testing results for road surface temperatures using the third set of input variables(December of 2013, Site A)

3.2. Forecasting road surface temperature for other sites along the expressway
Next, we examined the possibility of forecasting road surface temperatures at other sites along the expressway using the learning model of the road surface temperature at Site A (99.1 kp).

59

M.HORII, T.HAYAMI
Tables 9, 10, and 11 show the forecast results obtained using the time series variation of the first,
second, and third sets of input variables, respectively, at Site B, which is located 6.2 kilometers from Site
A. Tables 12, 13, and 14 show the same results for Site C, which is located 22.4 kilometers from Site A.
For the two sites, the percentages of critical correct classification results obtained using the first set of input
variables and the third set of input variables were 94.5% (Site B, first set), 93.3% (Site B, third set), 89.6%(Site C, first set), and 91.0% (Site C, third set), which are extremely high for below-zero conditions. Furthermore, the percentages of correct classification results obtained using the second set of input variables
were 85.6% (Site B, second set) and 86.4% (Site C, second set). These percentages are considerably highfor overall prediction. Therefore, when considering the correct classification for overall prediction, we
should use the second set of input variables, and when considering the correct classification for criticalcondition, that is, below-zero road surface temperatures, we should use the first or third set of input variables. Thus, the expressway maintenance authorities would select the forecast model according to the traffic
volume, weather conditions, and financial burden for these services.
Table 9. Forecast results for road surface temperature using the first set of input variables(four months, Site B).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
1299
76
456
1009
74.0%

93.0%

Correctclassification
94.5%
68.9%
81.3%

Table 10. Forecast results for road surface temperature using the second set of input variables(four months, Site B).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
1160
215
194
1271
85.7%

85.5%

60

Correctclassification
84.4%
86.8%
85.6%

Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

Table 11. Forecast results for road surface temperature using the third set of input variables(four months, Site B).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
1283
92
585
1191
68.7%

90.5%

Correctclassification
93.3%
60.1%
76.2%

Table 12. Forecast results for road surface temperature using the first set of input variables(four months, Site C).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
972
113
420
1335
69.8%

92.2%

Correctclassification
89.6%
76.1%
81.2%

Table 13. Forecast results for road surface temperature using the second set of input variables(four months, Site C).

Measuredconditions
Below zero
Above zero
Correctclassification

Predicted
conditions
Below
Above
zero
zero
888
197
189
18566
82.5%

88.8%

61

Correctclassification
81.8%
89.2%
86.4%

M.HORII, T.HAYAMI
Table 14. Forecast results for road surface temperature using the third set of input variables(four months, Site C).
Predicted
conditions
MeasuredCorrect
conditionsclassification
Below
Above
zero
zero
Below zero
987
98
91.0%
Above zero
565
1190
67.8%
Correct
63.6%
92.4%
76.7%
classification
Figures 9 and 10 show the forecast results for the road surface temperature at Sites B and C obtainedusing the learning model for Site A and the observations of time series variation of the third set of input
variables at Sites B and C, which has extremely high percentages of correct classification for below-zeroconditions. In both cases, the predicted road surface temperatures follow the observed values for near-zeroconditions. In contrast, larger errors occur at higher road surface temperatures. However, this is not problematic, because this temperature range is not subject to ice formation.
Observed values

Road surface temperature（℃）

40

Predicted values( Site B)

30

20

10

0

-10

Date

Figure 9. Forecast results for road surface temperature using the third set of input variables(four months, Site B).

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Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp49-64

Observed values( Site C)

Predicted values

Road surface temperature（℃）

40

30

20

10

0

-10

Date

Figure 10. Forecast results for road surface temperature using the third set of input variables(four months, Site C).

4. Conclusion
In the present paper, we attempted to establish a forecast model of the road surface temperature along an
expressway.
The results are as follows:
1. The neural network model has the ability to forecast road surface temperature with high precision.
2. We examined the ability of the learning model to forecast the road surface temperature at other sites
along the expressway, i.e., route-based forecasting of the road surface temperature.
3. We obtained three models that have the ability to forecast road surface temperatures for overall conditions
or road surface temperatures in below-zero conditions along the expressway using different input variables.
For expressway maintenance in winter, it is of particular importance to carefully maintain safe roadsurface conditions by using an appropriate forecast model of the road surface temperature when below-zeroconditions might exist.
We hope to establish a route-based forecast model for the road surface conditions by combining the
proposed model and a model for detecting water on road surfaces. This model uses a discriminant analysis
and a neural network to predict dry versus other road surface conditions three hours in advance (Horii and
Fukuda, 2001).

Acknowledgments
The present research was supported in part by a Grant from the Ministry of Education, Culture, Sports,
Science, and Technology (No. 26350490). We are grateful to the staff of Koriyama and Aizu Office ofEast Nippon Expressway Company.

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