# The protection of roads from blizzards

Tatiana Samodurovaª, Olga Gladysheva, Jurij Baklanov and Konstantin Panferov

Voronezh State University of Architecture and Civil Engineering, Russia

**Abstract.** The problems of snow protection designing of roads from blizzards snow were studied. The classification of snow protection was given. The type of snow protection depends on the blizzards parameters: blizzards intensity and duration, snow transfer volume and snowbring volume to the road. The mathematical models to determine the blizzards parameters for problem solving of protecting and cleaning the roads from snow were proposed. The meteorological data are used for calculations. The method of statistical processing was given. The study proposes to calculate the snowbring volume to the road for the winter period and for the single blizzard to design of snow protection. It is also recommended to take into account the losses of snow volume from evaporation and melting during thaw. The modeling results were verified by experiments on separate road sections. The comparison of modeling results with special snow surveys showed a high resemblance. The calculation results are presented in a series of road climatic maps. The realization of the study results by using GIS technology was proposed.

## 1 Introduction

Snowdrifts often form on the roads of Russia after blizzards in winter. Snowdrifts reduce the vehicle speed, worsening traffic conditions. Traffic interruptions occur during the intense and prolonged blizzards. In order to conduct effective snow-related maintenance of roads, it is necessary to know the estimated blizzards parameters (blizzards intensity and duration, volumes of snow drifting and snow accumulation on the roads)

The presented paper is focused on the systematic approach to the definition of estimated blizzards parameters, using the meteorological data necessary for the determination of estimated blizzards parameters. Mathematical models for the calculation and statistical processing of modeling results are carried out. Calculation results are presented in the form of climatic road maps, the practical work maps is possible with the use of GIS technology.

## 2 The variants of snow protection

Snowdrifts form on the roads after snowfalls and blizzards. Snowdrifts after snowfalls often have a height of 5-10 cm, rarely 15 cm, and even more rarely up to 35 cm. Snowdrifts after blizzards may have a greater height more than 1 meter. The amount of snowdrifts depends on the snow accumulation volume.

All measures to ensure the absence of drifts on the roads during a blizzard are based on the forecast of the possible snow accumulation volumes to the road sections in the winter or in a single blizzard and possible snow deposits volume at the end of winter or a blizzard.

The defense of roads from snowdrifts is done using permanent or temporary snow protection. The snow protective belts and fences are permanent snow protection. The snow boards, snow trenches and shafts are temporary snow protection.

The snow protection is divided on the basis of the windsnow flow impact:

- The snow protection with the accumulation effect. In this case the snow protection works on the principle of the detention of snow on the side of the road,

- The snow protection with the blown out effect. In this case the snow protection increases the speed of the windsnow flow and helps to transfer the snow across the road,

- The snow protection that completely insulates the road from snow.

- The snow protection with the accumulation effect are more common on the roads.

- To make a decision about what type of snow protection to use it is necessary to define:

- The estimated snow accumulation volume to the left side and right side of road in the winter,

- The estimated snow accumulation volume at the snow protection at the end of winter,

- The estimated parameters of blizzard: the snow accumulation volume and duration,

- The snow drifts volume after estimated snowfall.

## 3 The estimated blizzards parameters and models for calculation

### 3.1. The estimated blizzards parameters

The main blizzard parameters were determined using the study results conducted by the authors and other researchers. Their characteristics are given in Table 1 [1-5]. The parameters in the table describe blizzards in the region of an auto road. The observation data from meteorological stations is needed to determine the parameters.

Data selection from the tables performed under the following constraints that correspond to the physical processes of snow drifting during a blizzard: atmospheric phenomena – snow, sleet, all types of blizzards; wind speed – more than 5 m/s; air temperature – below 0º C. The wind direction in the calculation is taken by 16 rhumbs.

<figure><img src="image_583.png" /></figure>

<footnote>ª Corresponding author: [samodurova@vgasu.vrn.ru](mailto:samodurova@vgasu.vrn.ru)</footnote>
<table><caption>**Table 1.** The estimated blizzards parameters</caption><thead><tr><td>Parameter name</td><td>Parameter physical characteristic and effect for winter road maintenance</td></tr></thead><tbody><tr><td>Blizzard duration</td><td>Time of an actual snowfall and snowdrift (choice of snow plowing technology; number of cycles for snow plowing (work of snowplows))</td></tr><tr><td>Wind speed</td><td>Determines the snowdrift intensity (intensity of snow accumulation on the road; time between cycles of snow removal)</td></tr><tr><td>Wind direction</td><td>Determines the snowdrift direction (defining the road sections with possible snow drifts)</td></tr><tr><td>Intensity of snowdrift</td><td>Amount of a snowdrift per unit time per unit area during a blizzard which is perpendicular to the wind snow flow stream (intensity of snow accumulation on the road; time between cycles of snow removal)</td></tr><tr><td>Volume of snowdrift</td><td>Amount of a snowdrift through the front unit length which is perpendicular to the wind direction at the time of a blizzard (amount of snow removal)</td></tr><tr><td>Snow accumulation volume for the winter period</td><td>Snow amount which is brought to one side of the road during the entire winter period (amount of snow which need to be kept away by using the snow protective structures)</td></tr><tr><td>Snow accumulation volume for a single blizzard</td><td>Snow amount which is brought to one side of the road during a single blizzard (number of cycles for snow plowing (work of snowplows); amount of cleaned snow)</td></tr><tr><td>Estimated snow accumulation volume</td><td>Snow accumulation volume with the exceeding probability obtained as a result of the statistical processing of snow accumulation volumes data (selecting the type of snow; protection (permanent or temporary))</td></tr></tbody></table>

Data selection is made no less than for 15 years of observation. The meteorological data is used to conduct the special calculations.

## 3.2 The models for calculation of snow accumulation volumes

For the detection of snow accumulation volumes the method of the summarized snow transfer suggested by D.M. Melnik is used [6]. The method takes into consideration the intensity of snow transfer, which depends on the wind speed and the time of a snowdrift with the given intensity.

The volume of snow transfer in winter period ($W_i$) is calculated by the formula:

$$W_i = \frac{t}{m} \sum_{i=1, (V>5)}^{m} C \cdot V_i^3 = I_c \cdot t, \quad (1)$$

where $t$ is the summary duration of blizzards for winter period, hour; $m$ is the number of measurements of the wind speed during blizzards (at speeds over 5 m/sec); $C$ is an empiric factor which is equal to 0,00046, when the

average density of the fresh brought snow is 0,17 m³/m; $V_i$ is the wind speed during blizzards, m/sec; $I_c$ is the average intensity of blizzards during the entire winter period (m³/m hour).

Collecting the data provided by the meteorological stations, the winds with the speed less than 5 m/sec are not taken into consideration, because their energy is not sufficient for snow transfer.

The dependency between the average intensity of horizontal snow drifting and the wind speed at the weathercock height is expressed by the following formula:

$$I = C \cdot V^3, \quad (2)$$

where $I$ is the intensity of horizontal snow transfer, m³/m h; $C$ is the proportionality factor which depends on density the snow; $V$ is the wind speed at the weathercock height, m/sec.

The volume of the snow accumulation on an auto road at the end of the winter period from one direction ($W_{sb}$) is calculated according to the formula:

$$W_{sb} = W_i \cdot \sin(\alpha_r - \alpha_i), \quad (3)$$

where $\alpha_r$ is the direction of the auto road, degree; $\alpha_i$ is the direction of the wind, degree.

The volume of the snow accumulation at one side of the auto road in winter ($W_b$) is calculated according to the formula:

$$W_b = \sum_{i=1}^{7} W_{sb,i} \cdot \sin(\alpha_o - \alpha_i), \quad (4)$$

where $W_b$ is the amount of snow brought to one side of the road (m³/m); $W_{sb,i}$ is the snow drifting volume by one compass point (m³/m); $\alpha_i$ is the azimuth of compass points, degree; $\alpha_r$ is road azimuth, degree.

For each road direction the number of compass points in which the snowdrift is calculated equals 7. Counting the volume of snow transfer, winds blowing at an angle less than 30° are not taken into consideration. Figure 1 gives the scheme of calculating of directions from which the snow is brought to one side of the auto road directed northward. The zone of each direction (at 16 compass points) is determined by the sector with the arc of 22,5°.

## 3.3 The models for calculation of estimated blizzards parameters

To estimate the blizzards parameters the statistical analysis of the modeling results is carried out. The method of Federal Service for Hydrometeorology and Environmental is used for statistical processing [7]. Based on the calculation results the descending series of parameters are compiled.

For each series unit the empirical probability of exceeding is calculated:
<figure><img src="image_584.png" /><figcaption>Figure 1. Scheme of the calculation of snowdrift on the road directed northward.</figcaption></figure>

$$p_3 = \frac{m}{n+1} \cdot 100\%, \qquad (5)$$

where m is the serial number of series unit; n is the length of series (number of observation years).

The three-parameter gamma-distribution is taken for smoothing of empirical data and extrapolation of calculated parameters [7].

The integral curve characterizes the probability of exceeding the existing values of parameter and represents the integral of binomial distribution curve of continuous random variables:

$$P(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} \int_{x_0}^{\infty} \bar{x}^{\alpha-1} \cdot e^{-\beta \cdot x} \cdot dx, \qquad (6)$$

where $\Gamma(\alpha)$ is the gamma function or Euler integral of the second kind:

$$\Gamma(\alpha) = \int_{0}^{\infty} z^{\alpha-1} \cdot e^{-z} \cdot dz, \qquad (7)$$

where $\bar{x}$ is an average long-term value of the parameter of estimated blizzard:

$$\bar{x} = \sum_{i=1}^{n} x_i / n, \qquad (8)$$

where $x_i$ is the parameter value for the i year.

where $\alpha$ and $\beta$ are parameters of the law which are expressed by means of central moments:

$$\alpha = \frac{4m_2^3}{m_3^2}, \quad \beta = \frac{2m_2}{m_3}, \qquad (9)$$

where $m_2, m_3$ are the second and the third moments of the distribution curve:

$$m_2 = C_v^2, \quad m_3 = C_s \cdot C_v^3, \qquad (10)$$

where $C_v$ is the variation coefficient, $C_s$ is the asymmetry coefficient.

Statistical processing resulted in acquisition of the parameters of estimated blizzard were obtained, i.e. the snow accumulation volume on a section of an auto road, the blizzard duration with a different probability of exceeding, and the snow accumulation volume during the winter period.

## 3.4 The models for calculation of coefficient of snow losses from melting and evaporation

The winter seasons in Russia are characterized by the alternation of the air temperatures over zero degrees, thus the snow volume near roads depends on the air temperature change.

For the account of snow volume change it is proposed to calculate the “Coefficient of snow losses from melting and evaporation”. The definition of this parameter is done according to the data observation of the snow cover characteristics, i.e. the snow height and density.

A snow mass per 1 m² (Q) is calculated by the formula:

$$Q = h \cdot \delta, \qquad (11)$$

where h is snow cover height, m; $\delta$ is the snow cover density, g/m³.

Reduction of the snow mass in the time period between blizzards:

$$P_i = Q_{\max} - Q_{\min}, \qquad (12)$$

where $P_i$ is the decrease of the snow mass, g/m²; $Q_{\max}$ is the maximum of the snow mass per unit area (g/m²); $Q_{\min}$ is the minimum of the snow mass per unit area (g/m²).

The total reduction of the snow mass during the winter period is equal to the sum:

$$P = \sum_{i=1}^{m} P_i, \qquad (13)$$

where m is the number of periods between blizzards during the winter period.

The coefficient of snow losses from melting and evaporation for the entire winter is calculated by the formula:

$$K_p = \frac{P}{Q_{\max}}. \qquad (14)$$

The average long-term value of the coefficient is determined for practical calculations.
The volume of snow accumulations for the entire winter, considering the decrease of the snow mass, is calculated by the formula:

$$Q = W_{sb} \cdot (1 - K_p) \cdot \frac{\delta_s}{\delta_{av}}, \quad (15)$$

where $\delta_s$ is average density of new snow, $\delta_s=0,17$ g/cm³; $\delta_{av}$ is average density of the snow cover (g/cm³).

The average annual snow density can be found, using the meteorological station data about the density changes during the winter, by the formula:

$$\delta_{av} = \frac{\sum_{i=1}^{k} \delta_{i}}{T_{s}}, \quad (16)$$

where $\delta_i$ is the density of snow accumulation in one test (g/m³); k is the number of density estimations during the entire winter; $T_s$ is the number of observation years.

The proposed models allow to calculate the blizzards parameters which are essential parameters for snow protection maintenance and design on the roads of Russia.

The computer program «Blizzards» was specially developed for that kind of calculations [8]. The initial data and the calculation results are stored in the databases with specific structures. This allows using the data in other calculations and receiving the reports of various forms.

## 4 The experimental verification of the models

The experimental verification of the models has been done for the three seasoned road sections. During the experimental work adequateness of the models was tested according to the snow volume measurements.

The snow survey methodology provides the determination of the actual snow volume on the embankments subgrade according to the snow cover height and snow length parameters on the basis of their geometric parameters [9]. Tachometry has been conducted to determine the embankments geometrical parameters at selected seasoned road sections. Determined marks: subgrade verge, the bottom cuvette and land marks in field at a distance of 15-20 m from the cuvette embankment. In winter, with the leveling rods, the snowdrift height in the typical points of the land cross-sections and in the points of snowdrift shape and height change were measured, snow shafts was measured on the verge. Simultaneously, the snow density detection in snow accumulation zones was done using the cutting ring.

The cross sections on experimental open roadways and snow accumulation profiles were used for the calculation of the actual snow volume by their geometric shapes [9].

Snowdrift measurements were performed after the intense blizzard or in the late winter. If the snowdrift

measurements were made in late winter with taking into account the determining of the snowdrift volume, the snow losses from melting and evaporation during thaws affected the changes in snowdrift density.

The convergence of the calculated and actual data on snowdrift volume is about 88% in average [9]. Therefore, we can conclude about the possibility of applying the model for solving tasks of winter road maintenance.

## 5 The road maps with blizzards parameters

The calculation results for one selected territory in Russia are shown in Figure 2.

<figure><img src="image_585.png" /><figcaption>Figure 2. Distribution of snow drifting volumes to 16 directions for Nizhny Novgorod region.</figcaption></figure>

Diagrams of the snow transfer volumes according to 16 rhumbs were placed in the locations of the State Meteorological Stations. The analysis of the diagrams shows a significant change of blizzards parameters within a single region. Therefore, for solving the practical problems the most convenient way of submitting the calculations results are in the form of maps form with isolines representing the estimated blizzards parameters. The calculation of isolines and drawing them on the map was automated by using the methods of creation of the digital terrain models. To calculate the program complex “CREDO Roads” from joint venture “Credo-Dialogue” was used.

Models are created in the following sequence:

- Bitmapped substrate is created in the program TRANSFORM, i.e. a map of the auto roads network and location of the weather observation points (e.g. State Meteorological Observation Network),
– Bitmapped substrate is exported to the program "CREDO Roads" to digitize.

The locations of meteorological stations served as control points for the digitizing maps. Numerical values of climatic parameters are given in control points. The layers are created for the construction of climatic models.

The model of one climatic parameter is constructed in each layer. This allows to observe simultaneously the change in the parameters distribution on the given territory and application of the additional data on the generated model.

The closed contour is created to build the model. Three-dimensional surface and its two-dimensional image in the lines interpolation (isolines) form are constructed inside of the contour. Isolines represent the equal parametrical values in the different points of the terrain (in the first approximation). Isolines increment can vary for different layers. Its value depends on the variability of climatic factors, accuracy of its calculation, and given tasks.

The program "CREDO Roads" allows to build 2D models in the form of cuts (sections) along road axis and to display any parameter distribution on the road as a line graph. The map fragment with the estimated snow accumulating volume for roads towards the north (left), to the south (right) is shown in Figure 3.

<figure><img src="image_586.png" /><figcaption>Figure 3. The distribution map of estimated snow accumulation volumes for roads towards the north (left) to the south (right)</figcaption></figure>

The information on the map allows to reveal the prevailing direction of snow transfer and to estimate the possibility of snow drifts formation in separate road sections with the given road direction.

The maps with the blizzard parameters can be used to solve the following problems: detection of road sites with possible snow drifts; designing different variants of snow protection (forest belts, fences, etc.); planning snow removal (snow plowing); calculation of resources (equipment, anti-icing materials) for winter road maintenance.

The method of creation of digital terrain models and displaying of the information on maps makes possible the use of the results in the form of GIS technology. The calculations results in the program «CREDO Roads» can be exported into a GIS system. The calculation results in the program «CREDO Roads» after their export into a GIS system and automatic conversion of the calculation

results allow to display the data in the Earth surface coordinates and put them together with the data from roads.

## 6 Conclusion

The estimated blizzards parameters influencing the road reliability and traffic safety during the winter period were determined using the system approach basis. The meteorological data necessary for calculating of estimated blizzards parameters was determined. The mathematical models for the calculation and statistical processing of the modeling results were presented. The results are presented in the form of maps which can be used in special GIS projects for the winter road maintenance.

The permanent snow protection should be designed on the estimated snow deposits volume at the end of winter or the estimated blizzard with a snow accumulation volume greater than the snow deposits volume at the end of winter. The snow drifts volume after snowfall must be taken into account in the calculations. It is also recommended to take into account the losses of snow volume from evaporation and melting during thaw.

The temporary snow protection should be designed for the estimated blizzard because after work of temporary snow protection it needs recovery.

## References

[1] O.V. Gladysheva, Estimation amount of snow deposit on the road, *14th International road Weather Conference*, Prague, Czech Republic, 19 (2008)

[2] T.V. Samodurova, O.V. Gladysheva, Determination amount of snow deposit on the road, *H. Ed. In. Pr. Construction*, 8, 94 (2003)

[3] O.V. Gladysheva, Considering the dynamics of snow accumulation on the roads, *H. Ed. In. Pr. Construction*, 7, 77 (2006)

[4] A.K. Djunin, *Road winter maintenance*, Publishing house «Transport», Moscow, Russia, (1966)

[5] R.D. Tabler, Controlling blowing and drifting snow with snow fences and road design, *Tabler and associates, Niwot, Colorao*, (2003)

[6] D.M. Melnik, About laws of snow transport and their use in snow-drift control, *Technics of railways*, 11 (1952)

[7] A.V.Rozhdestvensky, A.I. Chebotarev, *Statistical methods in hydrology*, Gidrometeoizdat, Moscow, (1974).

[8] T.V. Samodurova, O.V. Gladysheva, Blizzards: OFAP № 2063, № гос reg. 50200200397, *Comp. Teach. Pr. and In.*, 3, 10 (2003)

[9] T.V. Samodurova, O.V. Gladysheva, N.Y. Alimova, S.M. Shiryayeva, Verification the adequacy of models to estimate of snow deposits on the roads, *Scientific Bulletin of the Voronezh State University of Architecture and Civil Engineering, Construction and architecture*, 1, 66 (2013)
# Influence of sunshine hours in fine weather on the rate of wintry accidents

Akira Saida¹,ª, Masayuki Hirasawa¹, Naoto Takahashi¹ and Tateki Ishida¹

¹ Civil Engineering Research Institute for Cold Region, Public Works Research Institute, National Research and Development Agency, Japan

**Abstract.** This study examined the relationship between sunshine hours, which are considered to greatly affect road surface conditions in winter, and the rate of wintry accidents on a national highway in Hokkaido. As a result, mostly in mountainous areas, a negative correlation was found between sunshine hours and the rate of wintry accidents. Also shown was the trend that, at sections with short sunshine hours, the rate of wintry (i.e., accidents per hundred million vehicle kilometers on a given road section) greatly increases if other danger factors such as sharp bends exist.

## 1 Background of the study

The basic plan in traffic safety of Japanese Government sets the goal to realize the world's safest road traffic. Its objective is to decrease the number of annual fatalities who are killed within 24 hours after traffic accident below 2,500 by 2018, compared to the 4,113 fatalities in 2014. Further actions are necessary as the pace of decreasing traffic accidents has been slower.

Snowy cold regions account for 60% of Japan's land area. These regions see many traffic accidents that stem from weather conditions peculiar to winter (hereinafter: "wintry accidents"). Typical examples include skidding accidents on snow-covered or icy roads and run-off-the-road accidents involving snowstorm-induced poor visibility. Approximately 80% of wintry accidents are skidding accidents, occurring when the road becomes very slippery[1]. Therefore, in taking measures against wintry accidents, it is highly useful to clarify how traffic accidents are influenced by sunshine hours and the intensity of solar radiation, both of which greatly affect the road surface conditions.

To this end, this study aimed to analyze the relationship between the distribution of sunshine hours on a route and the situations where wintry accidents occur on the route by using digital topography data and data on the injury/fatal accidents.

## 2 Literature review

There are many studies on the influence of weather conditions on traffic accidents. Such studies include Kojima and Takubo[2], which surveyed the number of accidents on the National Highway 13 in Akita Prefecture to indicate that the number of injury accidents decrease in winter while the property-damage-only accidents increase. Also, Hirasawa and Asano[1] reviewed how temperature variation affect the occurrence of accidents in Hokkaido and found that the accidents occur the most frequently when the daily mean temperature drops to approximately -4°C. Other studies similarly explore the influence of winter weather conditions on road traffic, showing that the number of accidents are likely to increase by adverse weather in winter.

However, there are few studies or analyses made to reveal the influence of sunshine hours and the intensity of solar radiation on traffic accidents, though these factors are considered to have a significant impact on road surface conditions. One of the few studies includes Iwasaki and Katahira[3] which examined the relationship between sunshine hours measured at Fukushima Local Meteorological Observatory and the number of traffic accidents occurring in the jurisdiction of Fukushima Police Station. Sunshine hours vary by topography and structures alongside the road. This may lead to the view that a location with shorter sunshine hours raises the risk in accidents. Unfortunately, there are no studies on how sunshine hours cause impact on traffic accidents by taking into account the topography and structures alongside the road.

## 3 Study method

For this study, we surveyed sunshine hours on sunny days in winter ("sunshine hours"), and compared the data to the rate of wintry accidents. The study details are shown in the following sections.

### 3.1 Estimation on Sunshine Hours

#### 3.1.1 Estimating the Location of the Sun

The location of the sun is expressed by azimuth $\theta$ and sun's altitude $\alpha$. $\theta$ is expressed between 0 (indicating due north) and 360 degree in a clockwise direction. $\alpha$ is an angle-off between the accident location-sun segment and horizon plane. It is 90 degree when the sun stays at the zenith, while it is 0 degree when the sun stays on the horizon.

$\theta$ and $\alpha$ are expressed by the following equations:

$$ \cos \alpha = \sin \delta \sin \phi + \cos \delta \cos \phi \cos t \quad (1) $$

$$ \tan \theta = \frac{-\cos \delta \sin t}{\sin \delta \sin \phi - \cos \delta \sin \phi \cos t} \quad (2) $$

<figure><img src="image_587.png" /></figure>

<footnote>ª Corresponding author: saida-a@ceri.go.jp</footnote>
where $\delta$: declination of the sun, $\phi$: the latitude of the location subject to sunshine hours calculation, $t$: the hour angle of the sun on the location where sunshine hours are estimated.

$\delta$ is expressed by the following equation:

$$ \sin \delta = \sin \lambda_s \cos e \quad (3) $$

where $\lambda_s$: the longitude of the sun and $e$: ecliptic angle of tilt. $\lambda_s$ is given by the equation proposed by Nagasawa[4].

$$ \begin{aligned} \lambda_s = & 280.4603 + 360.007697T \\ & + (1.9146 - 0.00005T) \\ & \times \sin(357.538 + 359.991T) \\ & + 0.0200\sin(355.05 + 719.981T) \\ & + 0.0048\sin(234.95 + 19.341T) \\ & + 0.0020\sin(247.10 + 329.640T) \\ & + 0.0018\sin(297.80 + 4452.670T) \\ & + 0.0018\sin(251.30 + 0.200T) \\ & + 0.0015\sin(343.20 + 450.37T) \\ & + 0.0013\sin(81.40 + 225.18T) \\ & + 0.0008\sin(132.50 + 659.29T) \\ & + 0.0007\sin(153.30 + 90.38T) \\ & + 0.0007\sin(206.80 + 30.35T) \\ & + 0.0006\sin(29.80 + 337.18T) \\ & + 0.0005\sin(207.40 + 1.50T) \\ & + 0.0005\sin(291.20 + 22.81T) \\ & + 0.0004\sin(234.90 + 315.56T) \end{aligned} \quad (4) $$

where $T$: time variable.

When the elapsed time since the noon January 1, 2000 is referred to as $K$, $T$ is given by the following equation:

$$ T = K/365.25 \quad (5) $$

$t$ is given by the following equation:

<figure><img src="image_588.png" /><figcaption>Figure 1. Method for determining sunlight shielding</figcaption></figure>

$$ t = \Theta - \beta \quad (6) $$

where $\Theta$: sidereal time, and $\beta$: right ascension of the sun.

$\beta$ is expressed by the following equation:

$$ \tan \beta = \tan \lambda_s \cos e \quad (7) $$

Near the surface of the ground, $\alpha$ is likely to be greater than the values estimated by equations (1) - (7). In consideration of its retraction through the air, the altitude of the sun, $\alpha'$, is given by the following equation:

$$ \alpha' = \alpha + r \quad (8) $$

$$ r = \frac{0.0167}{\tan(\alpha + 8.6/(\alpha + 4.4))} \quad (9) $$

### 3.1.2 Determination of Sunlight Shielding

Sunlight shielding at locations where the sunshine hours are estimated ("the locations") is determined by using the digital terrain data. Figure 1 shows the method of sunlight shielding determination. In this study, the topography around the locations as well as the shapes of structures are expressed as a set of triangular elements. Sunlight shielding is determined by looking at whether the segments which connects the sun and the locations are crossed with any triangular elements. If crossing is recognized, it is determined that the sunlight shielding occurs. This method is referred to in detail in References [5] and [6].

### 3.1.3 Computation of Sunshine Hour Distribution on the Route

By using the method mentioned in 3.1.2, the sunshine hour distribution of each location of the route was estimated through a 24-hour observation of hourly sunlight shielding. The locations were set every 10 minutes along the observed section. From the obtained results, the average sunshine hours were estimated every 1 km across the section.

## 3.2 Calculation of the Rate of Wintry Accidents

The Hokkaido Prefectural Police categorizes traffic accidents occurred under wintry weather or road conditions and resulted in injury or death as "wintry accidents", and adds this category to its traffic accident record slip. In this study, we calculated the rate of such wintry accidents by using the data obtained at the observed route. The rate of wintry accidents is given by the following equation:

$$ R_j = \frac{10^8 f_j}{365.25 \text{PL}_j Q} \quad (10) $$
where $R_j$: the rate of wintry accidents at Section *j*
(case/hundred million vehicle-km), $f_j$: the number of
wintry accident cases at Section *j* (case), *P*: analysis
period (year), $L_j$: distance of Section *j* (km), *Q*: annual
average traffic (vehicle/day).

4 Verification Conditions

This study computed the distribution of sunshine hours in
fine weather in wintertime. The subject section was
National Highway 230 between KP1.0 in Sapporo City
and KP60.0 in Kimobetsu Town, Hokkaido prefecture
(Figure 2). As the road condition varied by section,
KP1.0 - KP18.0 were categorized as the urban section
and KP18.0 - KP60.0 as the mountainous section, for
both of which the relation between sunshine hours and
the rate of wintry accidents was examined. In estimating
sunshine hours, the digital altitude data from the base
map information of the Geospatial Information Authority
of Japan (spatial resolution of 10m) was used as
topography data, and a digital housing map issued by
Zenrin Co., Ltd. was used for data of building shapes.

In calculating the rate of wintry accidents, the data of
20-year traffic accident record slips between January 1,
1993 and December 31 2012 was used as the data of
wintry accident locations, and the road traffic census data
2005 was used as the traffic volume data.

Additionally, the relation between air temperature and
the rate of wintry accidents was investigated, in that the
air temperature is considered as one of the factors for
accidents. For the air temperature distribution data, the
measurements of KP 1.0 - 45.0 at 3:00, 4:00, 8:00 and
10:00 on weekdays from December 2012 to February
2013.

<figure><img src="image_589.png" /><figcaption>Figure 2. Map of the subject route</figcaption></figure>

5 Results and Discussion

Figure 3 shows the average sunshine hours in winter (wave line), average air temperatures (dashed line) and the rate of wintry accidents on the subject route (solid line).

<figure><img src="image_590.png" /><figcaption>Figure 3. Sunshine hours and distribution of the rate of wintry accidents of the subject route</figcaption></figure>
<figure><img src="image_591.png" /><figcaption>**Figure 4.** Alignment of road and topography around KP30.0, National Highway 230</figcaption></figure>

<figure><img src="image_592.png" /><figcaption>**Figure 6.** Alignment of road and topography around KP157.0, National Highway 274</figcaption></figure>

Sunshine hours significantly vary by section: average sunshine hours at mountainous sections, at KP23.0 - KP24.0 and KP36.0 - KP38.0, were shorter than 2 hours because those sections were faced with mountain on the south of the road. In urban sections, KP1.0 - KP4.0 also recorded shorter sunshine hours than neighboring sections, because surrounding structures were higher at KP1.0 - KP4.0 than in others, causing sunlight shielding. Air temperature became lower as the altitude rose, and it was the lowest at KP45.0.

The rate of wintry accidents was considerably high at KP36.0 - KP37.0; the rate increased threefold compared to other sections. The rate was also likely to increase at KP25.0 - KP26.0 and KP49.0 - KP51.0.

Any significant relation between air temperature and the rate of wintry accidents was not recognized in mountainous sections (correlation coefficient: 0.08, p = 0.581). With regards to the relation between sunshine hours and the rate of wintry accidents in mountainous sections, the sections with shorter sunshine hours more likely caused wintry accidents. This indicates a negative correlation between sunshine hours and the rate of wintry accidents (correlation coefficient: 0.45, p = 0.002).

<figure><img src="image_593.png" /><figcaption>**Figure 5.** Alignment of road and topography around KP36.0, National Highway 230</figcaption></figure>

<figure><img src="image_594.png" /><figcaption>**Figure 7.** Alignment of road and topography around KP91.0, National Highway 39</figcaption></figure>

With regards to the relation between sunshine hours and the rate of wintry accidents in urban sections, it is suggested that a closer verification is necessary by including more urban routes/roads in further studies, as the studied distance was too short to verify the hypothesis.

It is noted that there were several sections, such as KP30.0 - KP31.0, with shorter sunshine hours and the rate of wintry accidents. This may suggest that wintry accidents may be subject to other factors than sunshine hours. We then focused on the alignment of road, which is considered as another accident factor, to additionally verify the relation between the road alignment and the rate of wintry accidents.

Comparing the road alignment of KP30.0 - KP31.0 to that of KP36.0 - KP38.0, it was found that KP30.0 - KP31.0 was a straight lane (Figure 4) and KP36.0 - KP38.0 consisted of several 150-km radius curves (Figure 5). In the straight lines, sections with shorter sunshine hours caused fewer wintry traffic accidents. Similarly as KP36.0 - KP38.0 of the subject route, National Highway 274's KP157.0 - KP169.0 (Figure 6; East of Nissho Pass, Shimizu-cho, Hokkaido Prefecture) and National Highway 39's KP91.0 - KP97.0 (Figure 7;
East of Sekihoku Pass, Kitami City, Hokkaido Prefecture) consist of curved lines and long sunshine hours. With regards to the relation between sunshine hours and the rate of wintry accidents, the rate of wintry accidents were 3.7 cases/billion vehicle-km for the former section and 6.6 cases/billion vehicle-km for the latter section. Both figures were smaller than that for KP36.0 - KP38.0 of National Highway 230. From this, it was suggested that curved line sections with longer sunshine hours may cause fewer wintry traffic accidents.

In summary, the occurrence of wintry accidents may be influenced by sunshine hours, as well as by other factors such as the alignment of road. A combination of these factors may likely cause a soaring rate of wintry accidents.

## 6 Conclusion

This study aimed to clarify the influence of sunshine hours on the rate of wintry accidents. Towards this goal, we measured sunshine hours of KP1.0 - KP60.0 of National Highway 230 in fine weather of mid winter, and compared the measurements to the rate of wintry accidents across the sections. The findings are as follows:

1. Sunshine hours at National Highway 230 greatly vary by section. Sunshine hours are likely to be short at sections facing mountains on the south of the road and the center of urban area.

2. For mountainous sections, a negative correlation was identified between sunshine hours and the rate of wintry accidents. For urban sections, however, no specific relationship, such as found in the data for mountainous sections, was identified between sunshine hours and the rate of wintry accidents, due to the insufficient amount of data.

3. The rate of wintry accidents is influenced not only by sunshine hours but by the horizontal alignment of the road. The sections with several risk factors (such as sharp curves and short sunshine hours) are likely to greatly increase the wintry accident rate.

Detailed examinations of the relationship between sunshine hours and situations in which accidents occurred in urban areas in winter will be conducted, with the addition of data on property damage accidents to the data on injurious/fatal traffic accidents.

## References

[1] Masayuki Hirasawa and Motoki Asano: Characteristic of Traffic Accidents in Hokkaido During Last Decade, Monthly Report of Civil Engineering Research Institute of Hokkaido, Vol. 576, pp. 13-21 (2001)

[2] Yukio Kojima and Nobuaki Takubo: Influence of weather factors on safe driving of motor vehicles. 3. Snowfall and snow- or ice-covered pavement, Research on traffic safety and regulation, Reports of the National Research Institute of Police Science, Vol. 30, No. 1, pp. 115-132 (1989)

[3] Shoichi Iwasaki and Kiyoaki Katahira: Correlational analyses between meteorological factors and traffic accidents, Ergonomics, Vol. 30, pp. 384-385 (1994)

[4] Ko Nagasawa: Computations of Sunrise and Sunset, Chijin Shokan Co., Ltd. (1999)

[5] Akira Saida, Akihiro Fujimoto and Teruyuki Fukuhara: Forecasting Model of Road Surface Temperature along a Road Network by Heat Balance Method, Journal of Civil Engineering El (Pavement Engineering), Vol. 69, No. 1, pp. 1-11 (2013)

[6] Akira Saida, Teruyuki Fukuhara, Akihiro Fujimoto, Masayuki Hirasawa, and Tateki Ishida, A calculation method for the shady area of road surfaces in wide areas using data from a digital housing map, Proceedings of the Cold Region Technology Conference, vol. 31, (2015)
# Roof snow slide-off experiments using membrane deformation

Hiroaki Terasaki<fnref n="1" />, a and Teruyuki Fukuhara<fnref n="1" />

**Abstract.** This paper describes the snow sliding performance of a membrane roof snow removal system (MRSRS), which was applied to three different types of pitched roofs. Slide-off experiments were conducted in Katsuyama city, Fukui Prefecture, Japan in 2012 and 2013. The experimental equipment consists of a snow slide membrane (SSM), an inflation/deflation blower. The SSM is made from PVC resin sheet, and is swelled or shrunk due to air flow induced by the blower. Video-cameras recorded the crack propagation of roof snow and subsequent sliding down of snow blocks from the roof due to the deformation of the SSM. It was found that the MRSRS showed a satisfactory snow sliding performance for most experimental cases. The time required for cleaning snow from a roof was about 15 minutes at the maximum for snow depths varying from 0.1 to 0.65m.

## 1 Introduction

Every year in Japan, many people have been killed or injured while removing snow from rooftops. Especially, 152 people were killed in roof snow related accidents in 2006 [1]. In 2012, 131 people were killed or injured due to a heavy snowfall and 76% of them were caused by roof snow removal related accidents. 67% of them were elderly persons over the age of 65 [2]. This statistical percentage has never been changed in recent years and may reflect a social background such as declining birth rate and aging population. Heating systems using a heat tape/cable or a boiler are an effective solution [3, 4], but are very expensive in its energy use (electric power or fuel oil). For example, about 300-800 US$ is fuel expense for roof snow removal over the winter period in a part of heavy snow regions in Japan, although it depends on the snowfall conditions. In 2014 many houses, carports and greenhouses were damaged by snow load on rooftops in Kanto area [5, 6], which is near the border between snowy and non-snowy regions.

Fig. 1 shows the collapse of a cooperative pack house for packing vegetables and fruits due to excessive roof snow load in Koufu city, Yamanashi prefecture. Fig. 2 shows the collapse of strawberry greenhouses due to excessive snow accumulation in the gutters in Komoro

city, Nagano prefecture. Renewing houses and equipment had a significant economic burden on farmers. Once heavy snowfall would occur in non-snowy regions, people removing roof snow would be exposed to more serious hazards associated with house or roof collapses due to snow loads falling down from a roof and an avalanche of snow falling off a roof.

In order to reduce the snow removal works and expense, we have been developing a new roof snow removal system with a membrane structure (membrane roof snow removal system; MRSRS) [7, 8]. The MRSRS can clear snow without going on a roof and does not require large-capacity electricity (thermal energy) such as consumed by a heat tape/cable system or a hydronic roof heating system. The snowfall from the roof by the MRSRS can be enhanced by the membrane deformation, i.e. swell or shrink of the soft membrane due to air flow by means of an air blower with an inflation/deflation feature (an inflation/ deflation blower). The MRSRS can terminate the roof snow removal within a reasonable amount of time after the start of the snow removal operation. Thus people below a roof can be protected from an unexpected sliding snow hazard.

This paper shows the snow removal performance of the MRSRS through field experiments conducted in Katsuyama city, Fukui prefecture, Japan from 2012 to 2014.

<figure><img src="image_595.png" /><figcaption>**Fig. 1** Collapse of packhouse and equipment for packing</figcaption></figure>

<figure><img src="image_596.png" /><figcaption>**Fig. 2** Collapse of greenhouse due to excess snow load</figcaption></figure>

<figure><img src="image_597.png" /></figure>

<footnote n="1">¹University of Fukui, faculty of engineering, 910-8507 Bunkyo 3-9-1, Fukui-city, Fukui prefecture, Japan.</footnote>

<footnote>a Corresponding author: terasaki@u-fukui.ac.jp</footnote>
<figure><img src="image_598.png" /><figcaption>Fig. 3 SSM for the first test</figcaption></figure>

<figure><img src="image_599.png" /><figcaption>Fig. 5 MRSRS for the third test</figcaption></figure>

<figure><img src="image_600.png" /><figcaption>Fig. 4 SSM on a dummy roof for the second test</figcaption></figure>

<figure><img src="image_601.png" /></figure>

## 2 Snow sliding experiments

The slide-off performance of roof snow using the MRSRS was evaluated with data from three demonstration tests in Katsuyama city, Fukui prefecture, Japan. The annual maximum depth of snow cover in Katsuyama city ranged 0.4 to 2.1m in the period of 2000-2010 [9]. The first, second and third tests were carried out from January 31 to February 18, 2012, from December 25, 2012 to February 18, 2013, and from December 25, 2012 to February 18, 2013, respectively. The experimental equipment consists of a PVC resin membrane (hereafter referred to as ‘snow slide membrane (SSM)’), an inflation/deflation blower (550W/100V) in the marketplace and a one-third pitched roof. The roof structure was changed for each demonstration test to design a wooden frame structure for mounting the SSM. The dynamic deformation of the SSM using the air blower can help improve sliding performance of the roof snow on the SSM.

In the first test (2012) one SSM (1.8m by 3.6 m) was mounted on a 3:10 pitched dummy wooden roof (1.8m by 3.6m) as shown in Fig. 3. The maximum height of the inflated SSM, ‘rise’ was 0.3m. The SSM was shortened approximately 0.1m in the horizontal (parallel to the ridge) and vertical (perpendicular to the ridge) directions, respectively to fix the SSM to the margin of the roof.

Therefore, the SSM can not be inflated at the edge of the roof.

In the second test (2013), two sets of the membrane (1.8m by 4.0m) were fixed onto the surface of a dummy roof with clay tiles as shown in Fig. 4. The second test was conducted to develop a more practical MRSRS by utilizing the results of the first test.

In the third test (2013) the latest MRSRS was applied to the roof of 2-story barn shown in Fig. 5. Five sets of the membrane (2.5m by 1.8m) were fixed onto the surface of a roof with clay tiles of a residential house. The SSM was mounted on the wooden frame combined with wooden roof boards under the roof tiles. The family members controlled the MRSRS according to their convenience. Actually they operated the inflation/deflation blower to supply air into or suck air from the SSM, observing the amount of snow remaining on the roof. The deformation of the SSM was generated due to the inflation-induced swelling at first and then turned to the deflation-induced shrinking. This inflation/deflation cycle was repeated until the snow removal was terminated.

Three video-cameras were used to measure an elapsed time to finish the snow removal as well as to observe the crack propagation of roof snow and subsequent sliding down of snow blocks from the roof. Other measurement items in the field tests were snow
<figure><img src="image_602.png" /><figcaption>Fig. 6 Snow slide-off motion in the first test (1/31)</figcaption></figure>

<figure><img src="image_603.png" /><figcaption>Fig. 7 Snow slide-off motion in the first test (2/18)</figcaption></figure>

<table><caption>Table 1 Overview of the first test result</caption><thead><tr><th>Date (2012)</th><th>Whether condition</th><th>Air temp. (°C)</th><th>Snow temp. (°C)</th><th>Water content (%)</th><th>Snow depth (mm)</th><th>Snow density (kg/m³)</th><th>Roof snow load (kg)</th><th>Sliding velocity (m/s)</th><th>Snow removal time (min)</th><th>Volume ratio of snow removal (%)</th></tr></thead><tbody><tr><td>1/31</td><td>Snow</td><td>+0.5</td><td>+0.1</td><td>10.88</td><td>332</td><td>59.8</td><td>129</td><td>0.4</td><td>2.6</td><td>72</td></tr><tr><td>2/4</td><td>Cloudy</td><td>-1.0</td><td>-0.3</td><td>5.28</td><td>476</td><td>80.9</td><td>250</td><td>1.3</td><td>14.8</td><td>74</td></tr><tr><td>2/9</td><td>Cloudy</td><td>-2.8</td><td>-1.8</td><td>5.57</td><td>467</td><td>130.5</td><td>395</td><td>1.4</td><td>15.4</td><td>79</td></tr><tr><td>2/18</td><td>Sunny</td><td>-2.8</td><td>+0.4</td><td>6.61</td><td>649</td><td>104.2</td><td>438</td><td>0.5</td><td>7.3</td><td>99</td></tr></tbody></table>

density, snow depth, volumetric water content, snow and atmospheric temperatures on the SSM.

## 3 Experimental results and discussions

Fig. 6 shows the crack propagation of roof snow and the sliding down off of the roof in the first test, which was conducted on January 31, 2012. The snow depth and the bulk snow density were 0.33m and 59.8kg/m³, respectively, and the snow weight per unit roof area was 19.8kg/m². The atmospheric temperature was 0.5°C during the experiment. The snow sliding off of the roof occurred 8 seconds later from the beginning of the inflation (swell of the SSM) operation and 73% of the snow volume fell down onto the ground surface below the roof 49 seconds later. Thus the inflation operation ended and turned to the deflation one (shrink of the SSM). 69 seconds later a snow block sled down from the central part of the roof, then the experiment was terminated. It was confirmed that about 72% of the roof snow fell down onto the ground by three set of the inflation/deflation operation.

Fig. 7 shows the crack propagation of roof snow and the sliding down off of the roof in the first test, which was conducted on February 18, 2012. The snow depth and the bulk snow density were 0.65m and 104.2kg/m³, respectively. The snow weight per unit roof area was 67.6kg/m² and was 3.6 times heavier than that of Fig. 6. The atmospheric temperature was -2.8°C during the experiment. About 15.4% of the snow sliding off of the roof started from the left eaves of the roof 15 seconds later from the beginning of the inflation operation. Subsequently the snow sliding lasted intermittently, but snow blocks kept staying on the middle upper and right edge of the roof when 84 seconds have passed. About 67.9% of the snow volume fell down onto the ground surface by the first inflation/deflation cycle. Finally, almost 100% of the snow removal was terminated 7.3 minutes later, which was in the 6th inflation/deflation cycle. Four experiments were carried out in the first test, and average snow weight per unit area was 47kg/m². The velocity of snow blocks sliding down from the roof was varied 0.4 to 1.4m/s. The roof snow removal was satisfactory for every experiment and the time required to terminate the snow removal was in the range of 2 to 15 minutes (See Table 1).
<figure><img src="image_604.png" /><figcaption>**Fig. 8** Crack propagation of roof snow in the second test</figcaption></figure>

Fig. 8 shows the crack propagation of roof snow and the sliding down off of the roof in the second test, which was conducted on January 18, 2013. The snow depth and the bulk snow density were 0.46m and 285.9kg/m³, respectively. The snow weight per unit roof area was 131.7kg/m² (Total snow weight on the SSM was 947kg), which was 6.7 times heavier than that of Fig. 6. The atmospheric temperature was 0.1°C during the experiment. The snow sliding off of the roof started from the right eaves of the roof 1.5 minutes later from the beginning of the inflation operation. A large crack appeared in a direction parallel to the ridge of the roof about 3.4 minutes later. Finally, when about 95% of the snow volume fell down onto the ground surface 8.2 minutes later, the snow removal operation was stopped. Six experiments were carried out in the second test without any trouble. The time required to terminate the snow removal ranged 0.5 to 8 minutes.

Fig. 9 shows the snow sliding down off of the roof in the third test, which was conducted on January 12, 2014. The maximum snow depth was 0.065m because of a light snow fall. The atmospheric temperature was 0.2°C during the experiment. The snow sliding off of the roof started suddenly about 20 seconds later from the beginning of the inflation operation. Finally, the snow removal was terminated within one minute. Unfortunately, only a few experiments in this winter were carried out in the third test because of a light snow fall.

## 4 Conclusions

In order to reduce roof-snow removal related accidents, we have been developing a new roof snow removal system with a membrane structure (membrane roof snow removal system; MRSRS). The slide-off performance of the MRSRS is demonstrated by the membrane deformation, i.e. swell or shrink of the soft membrane using an air blower, so that the snow removal can be carried out without going on a roof.

We conducted field snow removal tests using the MRSRS mounted on three kinds of sloped roofs for two winter seasons (from 2011 to 2014) and surveyed the

<figure><img src="image_605.png" /><figcaption>**Fig. 9** Snow sliding-off in the third test</figcaption></figure>

slide-off conditions for a range of snow depths, 0.2 to 0.65m and atmospheric temperatures, -3.0 to 0.2°C. It was found that the MRSRS showed a satisfactory snow slide-off performance, especially when snow is frozen hard. Conversely, the MRSRS did not go as smoothly as expected when roof snow was very fluffy. The time required for cleaning snow from a roof in 2013 and 2014 was about 15 minutes at the maximum.

Further field experiments will be conducted to improve the snow-removal performance of the MRSRS technically and economically.

## Acknowledgments

One part of this research was supported by Nohmura foundation for membrane structure's technology is acknowledged. We gratefully acknowledge the society for membrane roof snow removal system researches for kind cooperation. In particular, the technical support provided by Fukui Taiyo Co. Ltd. is also acknowledged.

## References

1. A. Sato, Journal of JSNDS, **25-1**, 71-81 (2006)

2. Cabinet Office, Government of Japan, (http://www.bousai.go.jp/setsugai/index.html), (2015/10/31 reference)

3. S. Kamimura, T. Umemura, Journal of JSSE, **12-3**, 212-21719 (1996)

4. T. Yamaguchi, Y. Habu, Journal of JSSE, **13-1**, 13-19 (1997)

5. D. Fukazawa, Journal of JSSE, **30-2**, 114-118 (2014)

6. T. Takahashi, Summaries of technical papers of Annual Meeting AIJ(B. Structures I), 95-96 (2014)

7. H. Terasaki, A. Fujimoto, T. Fukuhara, Summaries of JSSI & JSSE joint conference, 257 (2013)

8. H. Terasaki, A. Fujimoto, T. Fukuhara, Summaries of JSSI & JSSE joint conference, 270 (2014)

9. Katsuyama city office, (http://www.city.katsuyama.fukui.jp/docs/uploads/data/3658_data_lib_data_1103_28105242.pdf), (2015/10/31 reference)
# Accuracy of snow depth measurements on roofs measured with photogrammetry

Takahiro Chiba<fnref n="1" />,ª and Thomas K. Thiis<fnref n="2" />

**Abstract.** In this study, we conducted the photogrammetry using digital images for measuring snow depth on roofs. Two kinds of photo recording platform were considered in this study. Remotely Piloted Aircraft System (RPAS) and hand-held camera. To be able to validate the photogrammetry method, the snow depth distribution on the roofs were simultaneously measured with a snow sonde. The accuracy of the snow depth estimated by photogrammetry was examined by comparison with estimated value and measured value. As the results, the accuracy of estimated snow depth was affected by size of 3D mesh generated using digital images.

## 1 Introduction

The relationship between projective geometry and photogrammetry was first developed by Sturms and Hauck in Germany in 1883 [1]. Use of recently developed software to generate 3D mesh of objects using digital images is now relatively easy. 3D mesh for large areas can be obtained using images taken by aerial shot. Photogrammetry using digital images is being applied in research fields such as sediment disaster and glacier observation [1, 2] Sakurai et al (1998, 2000) measured the snow depth on roofs in discreet points using photogrammetry and helicopter and estimated the accuracy to be 30 - 40 mm [3, 4]. Yan et al (2008) has measured snow distribution on model building reproduced wind tunnel test based on the photogrammetry [5]. However, photogrammetry has not yet been used to measure the continuous snow distribution on full scale buildings

In this study, we tested photogrammetric measurements of snow distribution on four buildings with different roof shapes. The accuracy of the measurements is compared to snow sonde measurements and the accuracy of the photogrammetric measurements is estimated

## 2 Measuring methods

Table 1 shows a summary of the buildings for the photogrammetry in this study. The buildings all have different size, height, and roof shape. The roof shapes were three kinds of roof shape such as arched roof, frat roof, and pitched roof. The usefulness of No.1, No.2, No.3 and No.4 is sport arena, 4 story schoolhouse, garage and cabin respectively. In this study, to examine the accuracy of photogrammetric depth of roof snow, we measured the depth using snow sonde. The maximum depth dmax, No.1 was 0.30 m (3/2/2015), No.2 was 0.04 m (6/12/2014) and 0.09 m (11/1/2015), No.3 was 0.08 m (10/1/2015), and No.4 was 0.90 m (4/3/2015).

In this study, 3D mesh of surface of roof snow was generated using the software PhotoScan from Agisoft. The photogrammetric depth of roof snow was measured based on the 3D mesh. To obtain the suitable mesh, it is

<table><caption>Table 1. Buildings in the survey.</caption><thead><tr><th>Buildings</th><th>Summary</th></tr></thead><tbody><tr><td></td><td><strong>【No.1 Arched roof】</strong><ul><li>Site: Oslo, Norway</li><li>Size: 86 × 120m</li><li>Height: 28m (Radius: 62m)</li><li>Use: Football stadium</li><li>Date: 3/2/2015 (d<sub>max</sub> = 0.30m)</li></ul></td></tr><tr><td></td><td><strong>【No.2 Flat roof】</strong><ul><li>Site: Ås, Norway</li><li>Size: 11.7 × 31.5m</li><li>Height: 15m (Ph: 0.5m)</li><li>Use: School building</li><li>Date: 6/12/2014 (d<sub>max</sub> = 0.04m)<br>11/1/2015 (d<sub>max</sub> = 0.09m)</li></ul></td></tr><tr><td></td><td><strong>【No.3 Pitched roof I】</strong><ul><li>Site: Ås, Norway</li><li>Size: 6.8 × 22.3m</li><li>Height: 2.0m (Slope: 24.5°)</li><li>Use: Garage</li><li>Date: 10/1/2015 (d<sub>max</sub> = 0.08m)</li></ul></td></tr><tr><td></td><td><strong>【No.4 Pitched roof II】</strong><ul><li>Site: Gållå, Norway</li><li>Size: 6.0 × 9.0m</li><li>Height: 2.5m (Slope: 28.0°)</li><li>Use: Cabin</li><li>Date: 4/3/2015 (d<sub>max</sub> = 0.90m)</li></ul></td></tr></tbody></table>

<table><caption>Table 2. Photo recording methods used in each case</caption><thead><tr><th>No.</th><th>Shooting method</th><th>Camera</th><th>Number of images</th><th>Shooting distance (Mean value)</th></tr></thead><tbody><tr><td>1</td><td>RPAS</td><td>Canon IXUS (16M pixel)</td><td>250</td><td>45m</td></tr><tr><td>2</td><td>Hand-held</td><td>Pentax Q (12M pixel)</td><td>25</td><td>5m</td></tr><tr><td>3</td><td>Hand-held</td><td>Pentax Q (12M pixel)</td><td>60</td><td>7m<br>15m</td></tr><tr><td rowspan="2">4</td><td>RPAS</td><td>Canon IXUS (16M pixel)</td><td>245</td><td>15m</td></tr><tr><td>Hand-held</td><td>Pentax Q (12M pixel)</td><td>89</td><td>7.5m</td></tr></tbody></table>

necessary to use photographs which have more than 60% overlap in each other. Also size of the mesh become small

<figure><img src="image_606.png" /></figure>

<footnote n="1">¹Department of Architecture, Faculty of Engineering, Hokkaido University of Science, Sapporo, Japan</footnote>

<footnote n="2">²Department of Mathematical Science and Technology, Norwegian University of Life Science, Ås, Norway</footnote>

<footnote>ª Corresponding author: chiba@hus.ac.jp</footnote>
<figure><img src="image_607.png" /><figcaption>**Figure 1.** Photographing the arched roof (No.1).</figcaption></figure>

<figure><img src="image_608.png" /></figure>

<figure><img src="image_609.png" /><figcaption>**Figure 2.** 3D model and position of images used in No.1.</figcaption></figure>

with the pixel's number increases. Therefore, Accuracy of the 3D mesh is affected by photograph's number and the shooting distance. Table 2 shows photo methods, property of digital cameras, and shooting distance. Two kinds of photo recording platforms were used in this study. Remotely Piloted Aircraft System (RPAS) and hand-held camera. We used digital camera Canon IXUS (16M pixel) in RPAS and Pentax Q (12M pixel) in hand-held. Approximately 250 photographs were taken in RPAS. The shooting distance increased with building size increase. For hand-held camera, Number of photograph was less compared to RPAS, and also shooting distance was short.

# 3 Results

## 3.1 Conditions of generated 3D mesh

Figure 1 shows the use of the RPAS in case No.1 (Arched roof). The camera used with the RPAS was a standard Canon IXUS camera that was attached to the RPAS and programmed to take 20 pictures every minute. Figure 2 shows the shooting position of each picture and the 3D photogrammetrically surveyed model of the building. 250 images were taken in the investigation, and approximately 30% of the pictures were discarded due to bad quality. Figure 3 shows a detail of the 3D mesh. In the area which could be displayed as suitable texture, detailed mesh was sufficiently generated.

Figure 4 and Figure 5 shows quality of photographs and conditions of 3D mesh in case of No.2 (Flat roof). The

<figure><img src="image_610.png" /><figcaption>**Figure 3.** Summary of obtained mesh size</figcaption></figure>

<figure><img src="image_611.png" /></figure>

<figure><img src="image_612.png" /><figcaption>**Figure 4.** 3D model and position of images used in No.2 (6/12/2014).</figcaption></figure>

<figure><img src="image_613.png" /></figure>

<figure><img src="image_614.png" /><figcaption>**Figure 5.** 3D model and position of images used in No.2 (11/1/2015).</figcaption></figure>

conditions of 3D mesh were different in two kinds of weather such as sunny and cloudy. For sunny weather,
<figure><img src="image_615.png" /><figcaption>< Cloudy weather ></figcaption></figure>

<figure><img src="image_616.png" /><figcaption>< RPAS ></figcaption></figure>

<caption>**Figure 7.** 3D model and position of images used in No.4.</caption>

pattern of snow surface could be taken clearly. Also the detailed 3D mesh was sufficiently generated. However, for cloudy weather, it was difficult to recognize the pattern of snow surface from the photographs. The generated 3D mesh was the area which was sprinkled the powdered blue choke, and which was placed some foot stamps. Figure 6 shows conditions of generated 3D mesh in No.3 (Pitched roof I). The 3D mesh was similar to the conditions of No.2. According to these results, the quality of 3D mesh of snow surface was affected by the weather conditions of when were taken photographs. It is desirable that the shooting condition of snow surface is sunny, which is easy to recognize the pattern. Figure 7 shows conditions of generated 3D mesh in No.4 (Pitched roof II). For the sunny weather, the pattern of snow surface could be taken

<figure><img src="image_617.png" /><figcaption>< Sunny weather ></figcaption></figure>

<figure><img src="image_618.png" /><figcaption>< Hand-held camera ></figcaption></figure>

in both RPAS and hand-held camera. However, the quality of 3D mesh obtained from RPAS was not good compared to hand-held camera. This is that unfocussed photographs caused by flight shooting was included in the 3D mesh analysis.

## 3.2 Comparison with photogrammetric depth and sonde measurements

Figure 8 shows comparison with photogrammetric depth and sonde measurements in No.1 (Arched roof), and distribution of the error which was calculated by photogrammetric depth minus sonde measurements. In upper side of the roof, the photogrammetric depth was similar to the sonde measurements. For lower side of the
<figure><img src="image_619.png" /><figcaption>**Figure 8.** Comparison with photogrammetric depth and sonde measurements, and distribution of the error (No.1).</figcaption></figure>

roof, the error between the photogrammetric depth and sonde measurements was large. The distribution of the error in the upper side had normal distribution. However, the error of the lower side was more than 100 mm. The error of the lower side might be affected by some unfocussed photographs and long shooting distance. Figure 9 shows the error and the distribution in No2 (Flat roof). The mean error between the photogrammetric depth and sonde measurements was 1 to 3 mm. To be taken by hand-held camera, also to be short shooting distance, the error was very small. In addition, the error in case of sunny weather was small compared to cloudy weather. Figure 10 shows the error and the distribution in No3 (Pitched roof I). The error between photogrammetric depth and sonde measurements increased with shooting distance increase. Figure 11 shows the error and the distribution in No4 (Pitched roof II). The error was large compared to the case of stated above. Also the distribution was not normal distribution. The roofing of this building has been constructed in traditional method in Norway, which has some planting. The tip of the snow sonde using in this investigation was deeper than the roof surface.

## 3.3 Relationship between shooting distance and accuracy of photogrammetric depth

The size of 3D mesh depended on number of pixel in the digital photographs. Therefore, the photogrammetric depth might be affected by the shooting distance. Figure 12

<figure><img src="image_620.png" /><figcaption>**Figure 9.** Comparison with photogrammetric depth and sonde measurements, and distribution of the error (No.2).</figcaption></figure>

<figure><img src="image_621.png" /><figcaption>**Figure 10.** Comparison with photogrammetric depth and sonde measurements, and distribution of the error (No.3).</figcaption></figure>
<figure><img src="image_622.png" /></figure>

<figure><img src="image_623.png" /></figure>

<figure><img src="image_624.png" /></figure>

<figure><img src="image_625.png" /><figcaption>**Figure 11.** Comparison with photogrammetric depth and sonde measurements, and distribution of the error (No.4).</figcaption></figure>

shows relationship between shooting distance and mesh's mean spacing. The mean spacing increased with shooting distance increase in each shooting method. In this study, the accuracy of the photogrammetric depth was defined as $|μ| + σ$ (μ: mean error, σ: standard deviation of the error) [5]. Figure 13 shows relationship between shooting distance and $|μ| + σ$. The accuracy of the photogrammetric depth was similar to the mean spacing in except lower side roof of No.1 and No.4. Therefore, the accuracy of the photogrammetric depth can be estimated using mean spacing of the 3D mesh.

## 4. Conclusions

In this study, we conducted shooting of digital photographs by RPAS and hand-held camera, and then examined accuracy of photogrammetric snow depth on roofs. As the results, it was found that accuracy of the photogrammetric depth depended with mean spacing generated 3D mesh.

<figure><img src="image_626.png" /><figcaption>**Figure 12.** Relationship between shooting distance and mesh's mean spacing.</figcaption></figure>

<figure><img src="image_627.png" /><figcaption>**Figure 13.** Relationship between shooting distance and accuracy of photogrammetric depth.</figcaption></figure>

## References

1. Doyle, F.: The Historical Development of Analytical Photogrammetry, Photogrammetric Engineering, 30(2), pp.259-265 (1964)

2. Uchiyama, S., Inoue, H., Suzuki, H.: Approached for Reconstructing a Three-dimensional Model by SfM to Utilize and Apply this Model for Research on Natural Disaster, Research Report of Earth Science and Disaster Prevention, No.81, pp.37-60 (2014)

3. E. Bernard, J.M. Friedt, F. Tolle, et al.: Monitoring seasonal snow dynamics using ground based high resolution photography, ISPRS Journal of Photogrammetry and Remote Sensing, 75, pp.92-100 (2013)

4. Sakurai, S., Joh, O., Shibata, T.: Survey of Roof Snow Depth by Aerial Photogrammetry, Proceedings of the Second International Conference on Snow Engineering, pp.93-103 (1993)

5. Sakurai, S., Joh, O., Shibata, T.: Aerial photogrammetry of roof snow depths using three different aircraft, Proceedings of the Fourth International Conference on Snow Engineering, pp.81-87 (2000)

6. Yan, K. and Cheng, T.: Close Shot Photogrammetry for Measuring Wind-Drifted Snow Distribution on Stepped Flat Roofs, 2008 ISECS International Colloquium on Computing Communications, Control, and Management, pp.332-335 (2008)
# A new ring-shaped wind tunnel facility to study wind-packing of snow

Christian G. Sommer<fnref n="1" />,<fnref n="2" />,*, Michael Lehning<fnref n="1" />,<fnref n="2" /> and Charles Fierz<fnref n="1" />

**Abstract.** A new wind tunnel was designed and built at SLF. The facility is ring-shaped to simulate an infinite fetch. This is important for experiments where the observed processes have a slow time scale (minutes to hours). The wind tunnel was developed to study the formation of wind-packed snow. The facility is equipped with sensors to monitor environmental parameters such as wind speed, air temperature and air humidity. A SnowMicroPen and an industrial camera allow to measure properties of the snow surface. The facility is flexible and mobile having outer dimensions of 2.3x1.3x0.5 m. Airflow is created by a model aircraft propeller and the wind speed reaches values of up to 10 m/s. First experiments show that saltation is needed for wind crust formation.

## 1 Introduction

An open-circuit linear wind tunnel already exists at SLF and has, for example, been used to measure the saltation threshold of snow [1]. For slow processes like the formation of a wind slab/crust, the fetch of this wind tunnel is too short because drifting particles leave the facility in less than a second. A ring-shaped wind tunnel mimics an infinite fetch and is therefore better suited to study the formation of wind-packed snow. Wind-packing is the process through which a hard surface layer is formed due to wind action [2].

Ring-shaped wind tunnels have been built before. At the University of Heidelberg such facilities have been in operation since 1980 and are used to study air-sea gas transfer under different water surface conditions [3].

The primary goal of our new wind tunnel is to study the formation of wind slabs but care was taken to design a flexible and mobile facility. For example, it could also be used to study the evolution of saltating particles or for experiments in the field.

## 2 First prototype and experiments

To gain a basic understanding of the flow in a curved duct and how drifting snow behaves in such a situation, a prototype wind tunnel was built and used for preliminary experiments. These tests also provided valuable insight as to how such a facility is best operated.

### 2.1 Design

The prototype had an outer diameter of about 1.3 m. The channel was 18 cm wide and 50 cm high (Figure 1). A model-aircraft propeller created the airflow. The correct propeller was chosen based on the Cordier Diagram [4] after estimating the pressure drop and the volume flow in the tunnel. The propeller rotated at up to 12000 rpm and was driven by an electric motor. Wind speeds of up to 12 m/s could be reached. The covers of the wind tunnel were removable and a section was made of transparent Plexiglas. The prototype was equipped with a wind speed

sensor and an instrument to measure air temperature and humidity.

<figure><img src="image_628.png" /><figcaption>**Figure 1.** The prototype wind tunnel deployed in the field. The outer diameter is about 1.3 m. The channel width is 18 cm. The insert shows the propeller.</figcaption></figure>

### 2.2 Operation

The prototype wind tunnel was open at the bottom and could therefore simply be placed on the snow surface by two people. To collect fresh snow, the covers were removed and the wind tunnel was left open during a snowfall. Unfortunately, the resulting snow surface in the channel was usually not flat and appeared to have been influenced by wind. Placing the wind tunnel on the snow surface was also problematic as the rings tended to settle considerably, especially in sunny weather.

### 2.3 Results

Measurements of air temperature and humidity revealed considerable variations of these variables depending on whether the covers were closed or partly open.

During operation, the snow did not accumulate at the outer wall as might have been expected. However, surface features formed rapidly (Figure 2a).

<figure><img src="image_629.png" /></figure>

<footnote n="1">¹WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland</footnote>

<footnote n="2">²CRYOS, School of Architecture, Civil and Environmental Engineering, EPFL, Lausanne, Switzerland</footnote>

<footnote>a Corresponding author: sommer@slf.ch</footnote>
Large snow accumulations behind the propeller (Figure 2b) revealed the poor quality of the flow in the tunnel. Because of the centrifugal effects, a boundary layer with a logarithmic profile cannot be achieved but the flow quality should be improved nevertheless (see below).

<figure><img src="image_630.png" /><figcaption>**Figure 2.** (a): The snow surface in the channel showing surface features. (b): Snow accumulations on the inner wall downstream of the propeller.</figcaption></figure>

## 3 Redesign of the wind tunnel

To increase the flow quality a honeycomb and two one-metre long straight sections were added to the tunnel (Figure 3). The straight sections also provide additional space for measurements. The covers feature four circular holes, which can be left open or closed. This allows a basic control over air temperature and humidity. When closed, both variables tend to increase. Opening the holes leads to the entrainment and mixing with surrounding air, which is generally drier and colder.

<figure><img src="image_631.png" /><figcaption>**Figure 3.** The redesigned wind tunnel.</figcaption></figure>

The new wind tunnel features an automatic data acquisition system based on LabVIEW to measure parameters such as wind speed, air temperature and humidity at three locations as well as snow temperature and snow surface temperature. LabVIEW is also used to control an industrial camera. This camera will detect

drifting snow and allow to perform near-infrared (NIR) photography [5]. Additional measurements include the snow height (millimetre scale) and the snow hardness (using a SnowMicroPen [6]).

The wind tunnel now includes an aluminium structure that allows the tunnel to be lifted by a crane. The new facility is operated as follows: Fresh snow is collected on wooden trays outside the building, the snow-filled trays are then brought inside on a cart and the wind tunnel is lowered onto this snow surface. This ensures that the snow surface is flat and that the wind tunnel is in a stable position. The same procedure to collect snow is used in the straight wind tunnel facility [1].

## 4 Results

During the winter 2016, experiments were performed to test which processes are important for the formation of wind-packed snow. Based on literature, it appears that the air humidity has to be high and that the main process is fragmentation of snow particles in the saltation layer followed by sintering [2, 7]. Therefore, experiments with and without drifting snow were carried out. Thus far in our experiments, we never observed a relative humidity below about 80% even with the holes opened.

The experiments showed that no hardening occurs if there is no saltation. If there is drifting snow, the hardening is closely correlated with areas of deposited snow. Erosion without hardening and deposition appear to alternate in a random fashion in space and time. For the moment these processes can only be analysed qualitatively.

<figure><img src="image_632.png" /><figcaption>**Figure 4.** Relative velocity profile at the center of the channel in the main test section.</figcaption></figure>

The flow quality turned out to be improved by the addition of the straight sections. The flow is still chaotic behind the propeller but can now settle sufficiently until
it reaches the test section. The honeycomb only covered the top half of the channel to limit contact with flying snow particles. Unfortunately, many particles still reached the honeycomb, so that it had to be removed due to clogging. The flow in the test section could, however, be further improved by moving the propeller to the rightmost position in Figure 3. This made the saltation intensity more uniform across the width of the channel.

Figure 4 shows a velocity profile in the main test section. As mentioned before, there is no logarithmic profile at the surface. The wind speed is almost constant over much of the channel height. The reference wind speed $V_{ref}$ used to normalize the profile is the wind speed measured in the usual position of the MiniAir wind speed probe.

## 5 Outlook

For next winter we would like to introduce a system to better control the temperatures in the wind tunnel while the air humidity is now less a concern, because there is no hardening without saltation even if the humidity is high. At low air humidity, hardening would be even less likely. Moreover, with saltation, the air close to the surface is almost saturated in any case.

In addition, a system to measure quantitatively erosion and deposition appears necessary. A possibility would be to use a Microsoft Kinect, which is a low-cost 3D scanner. Otherwise, the wind tunnel and its operation will remain largely the same.

## References

1. A. Clifton, J. Rüedi, M. Lehning, J. Glaciol., **52**, 585-596 (2006)

2. G. Seligman, *Snow structure and ski fields*, (1936)

3. B. Jähne, *Zur Parametrisierung des Gas-austauschs mit Hilfe von Laborexperimenten* (1980)

4. O. Cordier, BWK Zeitschrift, **5**, 337-340 (1954)

5. M. Matzl, M. Schneebeli, J. Glaciol., **52**, 558-564 (2006)

6. M. Schneebeli, J.B. Johnson, Ann. Glaciol., 26, 107-111 (1998)

7. V. Kotlyakov, *The Snow Cover of the Antarctic and its Role in the Present Day Glaciation of the Continent* (1966)
# The use of sheet piles as measures against rapid mass flows

Árni Jónsson<fnref n="1" />ª, Guðmundur Heiðreksson<fnref n="2" />, Torfi B. Jóhannsson<fnref n="3" />, Magnús Steinarsson<fnref n="3" />

**Abstract.** Steel sheet piles have been used for mitigation against small snow avalanches and rock falls for over twenty years in Iceland in areas with limited space for other types of mitigation measures at road sides. Those approx. 3 m high structures have proved to be useful and have resulted in fewer road closures. Little is known about the forces that avalanche or rock falls exert to these structures and it hampers further development. For this reason, the Icelandic Road and Coastal Administration (IRCA) and the Norwegian Geotechnical Institute (NGI) decided to instrument one such wall in north Iceland.

## 1 Introduction

Narrow fjords with steep mountainsides are a challenge for road safety in Iceland, Norway and many other mountainous countries. Conventional mitigation measures in the run-out zone, like dams, are usually not applicable due to limited space. Supporting structures in the starting zone are in many cases too expensive in relation to the traffic volume of the road. Therefore space-saving structures are needed.

While steel sheet piles are well known as a wall material in piers and in excavations in loose and unstable soil, there are virtually no reports on their use in mitigation against rapid mass movements. However, for over twenty years steel sheet piles have been protecting road sections in Iceland against small snow avalanches and rock falls. These typically 3 m high structures have proved to be useful and have resulted in fewer road closures even though the snow cloud and part of the dense part can overtop the wall. Larger/higher structures to stop larger avalanches are feasible.

Little is known about the forces that avalanches or rock falls exert on the steel sheet piles and how the latter react to these loads. Yet good control over this is necessary for ensuring the functioning of the walls and optimizing their design also with respect to cost. For this reason, the Icelandic Road and Coastal Administration (IRCA) and the Norwegian Geotechnical Institute (NGI) decided to instrument one such wall in northern Iceland.

## 2 The test site

The first installations of steel sheet piles were alongside the road in Óshlíð just outside of Ísafjörður in Iceland. The experience from these steel sheet pile walls was positive and therefore protection of other road sections was considered. The road section between the villages Dalvik and Ólafsfjörður in northern Iceland is known for high avalanche activity, especially along the section just outside the abandoned farm at Sauðanes [1]. IRCA installed three steel sheet pile sections in three known avalanche paths, each of about 50 m in length. Avalanches usually fall several times per winter in these

paths. Even though they are rather small, they are nevertheless big enough to throw cars off the road.

<figure><img src="image_633.png" /><figcaption>**Figure 1.** Installation of the steel sheet piles in 2011. Photo: IRCA</figcaption></figure>

The steel sheet pile wall measures about 3 m above the ground and approximately 1.5 m in the ground see Figure 1. It is built of Z profiles, which gives approx. 40 cm depth of the form in flow direction. Due to the thin layer of loose material at the site, it was necessary to excavate a trench, fill it with compacted gravel, and drive the sheet piles into it.

In order to have sufficient storage capacity for snow avalanches and to dissipate part of the kinetic energy of both rocks and snow avalanches, the foot of the slope was removed to a distance of about 16 m from the wall. It is, however, necessary to clear this area from avalanche debris after each event because subsequent avalanches would otherwise easily overflow the wall.

## 3 Instrumentation

The instrumentation consists of five strain gauges that are located on the middle sheet of the wall at 231, 144, 67, -10 and -87 cm from the ground surface, Figure 2. Two further strain gauges are located on the fifth sheets to the north and the south from the central one, respectively, at a depth of -10 cm from the ground surface. The signals

<figure><img src="image_634.png" /></figure>

<footnote n="1">¹ Norwegian Geotechnical Institute (NGI), Sognsveien 72, 0806 Oslo, Norway</footnote>

<footnote n="2">² Icelandic Road and Coastal Administration (IRCA)Borgartúni 5-7, 105 Reykjavík, Iceland</footnote>

<footnote n="3">³ MogT Engineering, Akralind 1, 201 Kópavogur, Iceland</footnote>

<footnote>ª Corresponding author: arni.jonsson@ngi.no</footnote>
from these seven sensors are sampled at 270s-1 and
stored in Campbell CR 5000 data logger that is placed on
the outs side of the wall and can be accessed remotely.
The battery is sufficient for two months of continuous
unattended operation and 100W solar panel is also as a
reserve power. The data is sent through a 3G router to
the base in Kópavogur Iceland.

<figure><img src="image_635.png" /><figcaption>**Figure 2.** Installation of monitoring instruments in January 2015. Photo: MogT.</figcaption></figure>

The strain gauges were installed in January 2015. Due
to an unusual winter 2014/2015 no avalanche has hit the
wall (which is unusual for this location in a normal
winter). Therefore, no results can be presented yet, but
we expect to obtain measurements during the winter
2015/2016.

4 Conclusions

Sheet pile walls can provide adequate and cost-effective
protection against rock fall and small snow avalanches.
They are particularly valuable in locations close to the
foot of slopes where there is little space available. The
ongoing measurement campaign on a road in northern
Iceland will help to optimize their design and to put the
dimensioning of such structures on a secure footing.

References

1. ORION Consulting. (2007). ÓLAFSFJARÐAR-VEGUR (82), DALVÍK – ÓLAFSFJÖRÐUR. Greinargerð um snjóflóð, snjóflóðahættu og tillögur um varnaraðgerðir. (e: Report on snow avalanches, snow avalanche danger and proposed mitigation measures).
# In flight wet snow particles characterisation

Philippe Delpech<fnref n="1" />,ª, Guy Febvre<fnref n="2" />, Christophe Gourbeyre<fnref n="2" />, Dominique Lenoir<fnref n="1" /> and Fabrice De Oliveira<fnref n="1" />

**Abstract.** Wet snow is composed of water particles, in transient state between liquid and solid state. Snow characteristics as the Liquid Water Ratio (LWR) of in-flight snow particles is valuable information along ambient temperature, wind velocity and mass flux to ensure the reproducibility of the snow tests undertaken in climatic wind tunnel, as well as the analysis of the phenomena of snow accumulations and accretions to test structures. The paper discusses the potentiality of optical measurement systems to assess the snow LWR. The design of a thermal measurement system based on the hot wire probe concept is presented. The mechanical and thermal parts are described. The analyses of the early experimental results are tackled, as the prospects of optimization.

## 1 Introduction

Ice accretions due to driving wet snow events are common atmospheric icing phenomena and concern several fields of engineering, i.e. civil engineering, transport, energy production, etc.... Precipitation particles which generate wet snow accretion are characterized by a mixed phase. The water/solid ratio of water particles can be evaluated according the liquid water ratio: $LWR$. This dimensionless parameter represents the ratio of the liquid mass of the particle to the total mass of the particle: $LWR = \frac{m_l}{m_p}$.

Climatic wind tunnel testing with artificial snow making capacity belongs to the usual methods of evaluation of constraints applied to structures due to regular and wet snow events.

<figure><img src="image_636.png" /><figcaption>**Figure 1.** Snow test in a climatic wind tunnel</figcaption></figure>

Moreover, wind tunnel experiments support the development of numerical models to be used to assess the risks of large scale snow and ice accretion on building or vehicle elements. This requires that experimental conditions leading to a specific snow accumulation are accurately identified including measurement and control of freezing precipitations that are produced in the climatic chamber.

Previous works have shown the primary effect of the LWR of snow on the snow accretion mass and volume [1]. The experimental approach was based on the assessment of wet snow accretion formation on simple

geometric shapes. Cylinders were placed in the snow particle flow produced in the climatic wind tunnel. If all other parameters are kept constant, the ambient temperature setting (from -10°C to -2°C) allows to modify the thermodynamic state of the snow particle at time of impact. It is then possible to assess the effect of the liquid water ratio on the accretions and perform a parametric study.

A numerical model for two-phase flows simulation was developed in parallel. The study has been setup mainly to identify the most important parameters that drive the accretion phenomenon. In the particular wind tunnel conditions, the results obtained with -10°C and -2°C experimental tests provided the limiting cases as being the conditions were the accretion was either very thin and could not be weighted or too humid and could no longer be considered as actual snow.

With the three intermediate ambient temperatures, 6°C, -5°C, -4°C, one could observe the evolution of the accretion sizes to the structures (Figure 2).

<figure><img src="image_637.png" /><figcaption>**Figure 2:** Examples of wet-snow accretion (ambient temperature -6°C top and -4°C bottom)</figcaption></figure>

Qualitatively, one could observe how the augmentation of temperature induces accretions more humid and dense on the cylinders.

Evaluation of the parameters, which govern wet snow accretion, leads to the possibility to undertake a

<figure><img src="image_638.png" /></figure>

<footnote n="1">¹Centre Scientifique et Technique du Bâtiment (CSTB), CAPE Department, 11 rue Henri-Picherit 44300 Nantes, France</footnote>

<footnote n="2">²Laboratoire de Météorologie physique, UMR 6016, université Blaise Pascal, CNRS, 63178 Aubière, France</footnote>

<footnote>ª Corresponding author: philippe.delpech@cstb.fr</footnote>
numerical study to characterize the different accretions by using a so called “stick-function” for wet snow particles. Such a modelling requires to assess experimentally the sticking capacity of snow and the associated LWR at the impact time.

There are several techniques available to measure liquid mass fraction of snow deposited on the ground. They are based on electric permittivity measurements or melting calorimetry [2]. Measurement pieces of equipment are readily available and commonly operated in the field in avalanche engineering to assess stability of snow cover.

On the other hand, there are few means of measuring in real time the LWR of inflight snow particles. The objective of this article is to present the methods tested in the climatic chamber of CSTB either based on optical and thermal measurement systems.

## 2 Experimental Setup and test conditions

The experimental test conditions used for the snow particle measurements are inspired from a configuration commonly implemented for snow icing experiments in the CSTB climatic wind tunnel.

The snow is produced by one snow cannon placed on the central axis of the test section at 7.30m from the wind tunnel nozzle. The measurements area is located 10m downstream of the snow canon (Figure 3). The snow cannon has been setup in a counter-current configuration to enhance the spatial uniformity of particle concentration in the air flow. This configuration also ensures that particles are carried out to the test structure in equilibrium with the air flow.

<figure><img src="image_639.png" /><figcaption>**Figure 3.** Experimental setup for the wet snow icing tests</figcaption></figure>

The snow used during the tests is produced by one high-pressure snow cannon (model Y10 York). This cannon produces snow by mixing water and air at high pressure (from 6 to 10bar), after the mixing the flow is expulsed by an orifice at high speed (80 to 100m/s). The snow cannon injects in the air flow particles of water which temperature is close to 0°C. The particles begin to freeze as soon as they enter in contact with the cold air stream.

<figure><img src="image_640.png" /><figcaption>**Figure 4.** Positioning of snow cannon against the flow in the wind tunnel</figcaption></figure>

The distribution of water droplets produced by the snow cannon has been characterized in several previous studies with the help of different instruments (Malvern Spraytec, Aerometrics PDPA). The measurements have revealed a medium particle size close to 250µm as shown in (Figure 5).

<figure><img src="image_641.png" /><figcaption>**Figure 5.** Particles diameter distribution (Malvern Spraytec)</figcaption></figure>

The measurements were made for ambient temperatures between -10 °C and + 5 °C. The wind speed was varied between 10m/s and 20m/s. The settings of the snow cannon have been also adjusted to test several air / water ratios.

## 3 Optical measurement systems

The in situ means traditionally used to characterize cloud particles are of two types, the imagers (2DC, 2DS, CPI ...) or laser particle size analyzers based on the principles of light scattering by a particle (FSSP, CDP, ...).

The imager type probes are well suited to the discrimination of solid and liquid phases of natural icing particles since the morphology parameter identifies the type of particles without doubts especially for larger ones.

### 3.1 2DS probe measurements

The 2DS is an imager whose operating principle is based on the recording signal from an array of photodiodes illuminated by a collimated laser. The path of a particle in the laser beam disturbs the lighting of the photodiodes. The sampling rate of the photodiode array being controlled by the velocity of the particle, that is to say the speed of the air flow passing through the sampling volume, the two-dimensional image of the particle is reconstituted with pixel resolution of 10 microns [3].
Discrimination of water and ice is essentially based on the shape of particles, assuming a spherical shape corresponds to the liquid phase [4]. Indeed vapor diffusion and / or coalescence crystal growth processes usually lead to non-spherical geometries, although some cases of spherical crystals or deformed water drops situations have been reported which animates the specialized scientific community. Hence, according the analysis of the images, discrimination water/ice can be made, based on the assumption that the phase ice leads to an aspect ratio of the particles different than 1.

<figure><img src="image_642.png" /><figcaption>**Figure 6.** Particle imaging probes 2DS (left) and FSSP (right)</figcaption></figure>

Initial measurements were made at positive temperature with the 2DS probe in order to get a reference data sample of liquid droplets. Measurements in freezing conditions were then in varying ambient temperature, wind velocity and location in the wind tunnel test section.

<figure><img src="image_643.png" /><figcaption>**Figure 7.** Snow test with the particle imaging probes 2DS</figcaption></figure>

Computerized post-treatment enables processing of the images captured by the 2DS one by one with artifacts elimination algorithm. A filtering function from a standard aspect ratio is used as a mean to discriminate water from ice. Characteristic parameters are extracted from the particle morphology.

<figure><img src="image_644.png" /><figcaption>**Figure 8.** 2DS sample image and definition of characteristic length in terms of number of shaded pixels.</figcaption></figure>

The aspect ratio parameter $\alpha$ is defined as the X/Y ratio. Filtering is based on a user defined value of this ratio from 1 to infinity. It is commonly accepted by the operators of 2DS that the water / ice discrimination corresponds to the limiting value $\alpha = 2$.

In the experimental conditions of the wind tunnel, the assumption is that the ice phase is due to the freezing of droplets. The vapor diffusion growth process (Wegener-Bergeron-Findeisen) leading to dendritic shapes require longer periods than the wind tunnel flight time that it is the order of the second. The deformation of the droplets, if any, during freezing will be minimal.

Hence, the differentiation criterion suggested by the 2DS manufacturer should be revalued. For this it is necessary to assess the parameter $\alpha$ as a filtering parameter. This was done by counting the number of drops detected by the 2DS according the value of $\alpha$.

Measurements made at positive temperature, for which water droplets produced by the snow cannons remain liquid during their trajectory, allow assessing the sensitivity of the parameter $\alpha$ to image artifacts or to deformation of the drops during flight.

After eliminating image artifacts, 55000 different particle images were processed. For each image the X/Y ratio was calculated. It was then possible to count the number of particles with respect to the parameter $\alpha$. This count is normalized by the total amount of particles.

For the icing experiments the same approach was followed regarding the sensitivity analysis of the $\alpha$ parameter at different stages of freezing along their trajectory. The normalized counting of the number of particles as a function of aspect ratio was plotted for freezing and non-freezing conditions.

<figure><img src="image_645.png" /><figcaption>**Figure 9:** Evolution of the number of freezing droplets with respect to the aspect ratio during 3 experiments at positive (Run 5) and negative temperature (Run 9 and 11) according the 2DS probe measurements.</figcaption></figure>
Filtering based on the value of $\alpha$ does not highlight significant differences between the run. It is therefore not possible with this criterion to identify possible morphological evolution of the particles depending on the icing conditions. We can conclude that the 2DS probe cannot identify the morphological differences between a drop of water and particles sampled at a lower temperature. According the 2DS probe, the spherical particle geometry seems maintained regardless of temperature.

Nevertheless, careful examination of the images provided by the 2D-S could indicate some dependence of the surface condition of the particles depending on the temperature. The development of a specific analysis tool of the roughness of the contour of the particle images, could, if appropriate, quantify this observation.

It seems that the 2D-S instrumentation will not distinguish any phase difference within a snow particle.

## 3.2 CPI probe measurements

The CPI (Cloud Particle Imager) probe is an optical instrument that allows high-resolution imaging of cloud particles [8]. It allows the observation and digital recording (CCD camera, 1M pixels) image of the particles (from 20 to 2300 microns) with remarkable precision (pixel resolution of 2.3 microns). It uses an electro-optic system that allows real-time sampling of a maximum volume of 1L/s at 200m/s at a rate of 40 frames per second.

The CPI probe produces images by freezing the motion of the particles using a 25ns pulsed, high power laser diode. A particle detection system (PDS), made of two laser beams, defines the focal plane, identifies candidate cloud particles and triggers the imaging system (Figure 10).

<figure><img src="image_646.png" /><figcaption>**Figure 10.** Schematic drawing of the internal electro-optical configuration of the CPI (from SPEC, Inc).</figcaption></figure>

What makes the CPI probe particularly interesting for the observation of natural could particles is that, in addition to discrimination of the thermodynamic phase of the particles, the information delivered allows for the shape recognition of particles as well as the quantitative observation of their surface state (degree of icing for example).

<figure><img src="image_647.png" /><figcaption>**Figure 11.** The CPI Particle imaging probe (side and front view)</figcaption></figure>

As in the case of measurements with the 2DS probe, several ambient condition configurations were tested. The reference case was provided by measurements in positive temperature conditions. In this case, the particles produced by the snow gun remained liquid. Further measurements in freezing and intermediate thermal conditions were performed.

<figure><img src="image_648.png" /><figcaption>**Figure 12.** Setting of the CPI Particle imaging probe</figcaption></figure>

The images produced by the CPI probe at positive temperature (+10°C) are characteristic of liquid droplets. They show spherical shapes including a bright spot at their center due to light diffraction. Let us precise that for all the CPI images, the dark and bright areas have been inverted to enhance the visual contrast detection.

<figure><img src="image_649.png" /><figcaption>**Figure 13.** Sample of snow particle images obtained by the CPI probe for ambient temperature of + 10°C.</figcaption></figure>

Conversely, the images of particles obtained at low temperature (-15°C) still show the Fresnel spot in the particle center but with heterogeneous shapes which are characteristics of ice crystals.
<figure><img src="image_650.png" /><figcaption>**Figure 14.** Sample of snow particle images obtained by the CPI probe for ambient temperature of -15°C.</figcaption></figure>

Images obtained for the intermediate temperatures of -3°C and -5°C have mixed populations of particles which generally exhibit less deformed contours compared to observed shapes at -15°C.

<figure><img src="image_651.png" /><figcaption>**Figure 15.** Sample of snow particle images obtained by the CPI probe for ambient temperature of -5°C.</figcaption></figure>

Using the CPI images, a phase criterion based on a geometric aspect ratio seems being usable to discriminate the particle phase. Hence, defining a coefficient of sphericity as the aspect ratio of particles (i.e. coefficient ratio close to 1 meaning a round particle), one can sort the number of particles according to the coefficient of sphericity for different ambient temperature. One can observe that the number of round particles decrease with the temperature. At +10 °C more than 75% of particles are spherical while at -15°C, about 25% of particles can be considered spherical.

<figure><img src="image_652.png" /><figcaption>**Figure 16.** Coefficient of sphericity of particles at different ambient temperature (Run 0: +10°C, Run 9: -3°C, Run 8: -5°C, Run 6: -15°C).</figcaption></figure>

# 4 The hot wire snow probe

The hot wire snow probe is derived from an airborne in-cloud icing probes, embarked on meteorological aircraft, and known as the Nevzorov sensor [5, 6, 7]. It consists of two separate sensor elements, with convex and concave windward face, placed in an airflow carrying freezing particles. The convex sensor mainly collects the liquid particles, while the concave sensor collects all of the particles (solid and liquid).

## 4.1 Working principle of the snow probe

The working principle of the probe is similar to aforementioned airborne cloud particle measurement probe.

It is made of two heated elements with a convex (or circular) and a concave element facing the wind. The geometry of these sensors is such that the solid particles, carried by the air flow, break or bounce in contact with the convex surface. Hence the circular probe only collects liquid particles. The semi-circular probe has a concave geometry that allows collecting all of incoming particles.

<figure><img src="image_653.png" /><figcaption>**Figure 17.** Working principle of the Liquid and Total Water sensors of the hot wire snow probe</figcaption></figure>

Both elements are heated at elevated temperature (150 °C) to allow the melting and evaporation of the collected snow particles. The power needed to maintain the temperature of each element to a stabilized value is measured. From the coupled heat balance of each probe element one can deduce the liquid and solid water content present in the airflow.

## 4.2 The Probe Design

Prototype version of the sensors are in the form of a copper wire coil surrounding a cylindrical hollow support made of refractory material, with a length of about 60mm and 10mm in diameter. The wire diameter is chosen to be sufficiently fine so as to obtain uniform heat dissipation throughout the winding. The support is suspended by fine wires in a circular frame. This arrangement aims to reduce the probe contact surface with its support.
<figure><img src="image_654.png" /><figcaption>Figure 18. Prototype of the hot wire snow probe.</figcaption></figure>

Given the amplitude of variation of the operating conditions of the hot-wire probe, a robust control system CRONE (Non Integer Order Robust Control) was implemented to ensure the stability of the regulation regarding the uncertainties of the process [9].

## 4.3 Thermal balance

Let us assume C (kg/m³) is the water concentration in the air flow and x.C (kg/m³) concentration of solid water phase, x being the solid fraction of water.

The power required to maintain both the O (liquid water sensor) and U (total water sensor) probes at the set temperature Tp can be divided into four contributions:

Pdry, power dissipated by convection: This is actually the power dissipated to the air flow,

Pmelt, latent heat of melting ice,

Pwater, sensible heat to raise the temperature of the water to the vaporization temperature,

Pvap, latent heat of vaporization of water,

Let Po be the power required to maintain the O probe at constant temperature:

$$Po=Pdry+Pwater+Pvap \quad (1)$$

Let Pu be the power needed to maintain the U probe at constant temperature:

$$Pu=Pdry+Pmelt+Pwater+Pvap \quad (2)$$

Detailing each equation one obtains a system of two equations with two unknowns, C(kg/m³) the water particle concentration and x.C (kg/m³) the concentration of solid water, x being the solid fraction of water.

The resolution of the equation system leads to:

$$x.C = \frac{\frac{P_u-P_u_{dry}}{v*Au} - \frac{P_o-P_o_{dry}}{v*Ao}}{Lf+Lv+Cpwater*100} \quad (3)$$

$$C = \frac{\frac{P_u-P_u_{dry}}{v*Au} - Lf \times x.C}{Lv+Cpwater*100} \quad (4)$$

One obtains the values of total and solid fraction concentration of water in the air flow from the measured power dissipated by the U and O probes.

## 4.4 Preliminary results

Measurements made with a preliminary design of the probe have shown promising results. Several experiments were made at -10°C. Examples of measured dissipated power are:

$$\begin{aligned} Po_{dry} &= 27,4\text{W}, & Pu_{dry} &= 40,7\text{W}, \\ Po &= 40,6\text{W}, & Pu &= 101,8\text{W} \end{aligned}$$

The powers dissipated by the TW and LW sensors are used to calculate the snow particle concentration C= 4.2g/m³, and the fraction of solid water x=50%.

In parallel, a mesh collector was used to measure the snow particle concentration of 4.9 g/m³

The assessed total snow concentration and LWR are realistic.

<figure><img src="image_655.png" /><figcaption>Figure 19. Early version of the LW hot wire snow probe.</figcaption></figure>

## 5 Comments and perspectives

Measurements made with the 2DS probe to analyze the icing particles from snow cannons show that there is no morphological difference between liquid and solid phase particles produced in the climatic wind tunnel. The spherical particle geometry seems preserved whatever the temperature and the state of solidification.

In the analysis there is nothing to disambiguate the phase of negative temperature particles, that is to say, the fact of being in the presence of supercooled drops or frozen drops.

The measurements made with the CPI probe were more instructive. In particular, they confirmed the deformation of frozen particles with respect to liquid ones. The comparison of different situations in positive and negative temperature show that a criterion based on the sphericity coefficient can be used to post- process the images provided by the CPI. However, the method is far from being fully operational, since a truly quantitative information on the solid fraction of a complete population of particles requires statistical identification of the number of particle and as well as their volume associated with the sphericity coefficient. Such development has not been undertaken to date.

In parallel, the development of the hot wire probe should continue to provide a robust measurement tool that would monitor in real time the snow flow conditions produced in the wind tunnel. Measurements made with a preliminary design of the probe have shown promising results. The powers dissipated by the TW and LW sensors were used to calculate the snow particle
concentration which was close to that measured with a
mesh collector.

Further experiments are planned with the improved
probe design to confirm the relevance of this approach
and establish the correspondence with actual snow mass
accumulated on simple shapes.

Adaptation of the probe for measurements onboard of
road or rail vehicle could be further developed.

References

1. Vigano A. Experimental and Numerical modelling of wet snow accretion on structures. PhD thesis, France, (2012)

2. Boyne, H.S., Fisk, D.J., A laboratory comparison of field technique for measurement of the liquid fraction of snow. CRREL Spec. Rep 90.3 (1990)

3. Lawson, R. Paul, Darren O’Connor, Patrick Zmarzly, Kim Weaver, Brad Baker, Qixu Mo, et Haflidi Jonsson, The 2D-S (Stereo) Probe: Design and Preliminary Tests of a New Airborne, High-Speed, High-Resolution Particle Imaging Probe. *Journal of Atmospheric and Oceanic Technology*, 23, no 11 (novembre 2006): 1462-1477, (2006)

4. Baumgardner, D., J.L. Brenguier, A. Bucholtz, H. Coe, P. DeMott, T.J. Garrett, J.F. Gayet, Airborne instruments to measure atmospheric aerosol particles, clouds and radiation: A cook's tour of mature and emerging technology. *Atmospheric Research*, *102*, no 1-2 (octobre 2011): 10-29, (2011)

5. Merceret F.J., Schricker T.L., A New Hot-Wire Liquid Cloud Water Meter, *J. Appl. Met.*, 14, 319-326 (1975)

6. King W.D., Parkin D.A., and Handsworth R.J., A hot-wire liquid water device having fully calculable response characteristics, *J. Appl. Met.*, 17, 1809-1813 (1978)

7. Korolev, A.V., Strapp J.W., Isaac G.A., Nevzorov A.N., The Nevzorov Airborne Hot-Wire LWC–TWC Probe Principle of Operation and Performance Characteristics, *J. Atm. Oce. Met.*, 15, 1495-1510. (1998)

8. Lawson R. P., Baker B.A., Schmitt C.G., and Jensen T.L., An overview of microphysical properties of Artic clouds observed in May and July 1998 during FIRE. ACE. *J. Geophys. Res.*, 106, 14989-15014, (2001)

9. Oustaloup A. (1991), « La commande CRONE », Editions Hermès, Paris
# CR 1-1-3/2012 - the snow loads code in Romania

Alexandru Aldea¹,ª, Sorin Demetriu¹, Dan Lungu¹, Cristian Neagu¹, Radu Vacareanu¹ and Cristian Arion¹

¹Technical University of Civil Engineering Bucharest, Bd. Lacul Tei nr.122-124, Bucharest 020396 Romania

**Abstract.** The paper presents the most recent Romanian code for snow loads, CR 1-1-3/2012, enforced since October 2013. The code is harmonised with the Eurocode EN 1991-1-3 in what concerns the general approach and the snow loads on roofs. The paper focuses on the zonation of the snow load on the ground, using data recorded during the time interval 1930-2005 at 122 meteorological stations. The Gumbel probability distribution for maxima was used for computing characteristic values of snow load on the ground with an annual probability of exceedance of 0.02 (i.e., mean return period of 50 years). The zonation map is developed at ground level and is valid up to an altitude of 1000 m. The code provides relationships for establishing snow loads on the ground at altitudes between 1000 m and 1500 m. CR 1-1-3/2012 does not consider zones with exceptional snow loads on the ground. However, the paper includes considerations on several cases where the criteria for exceptional snow loads are fulfilled.

## 1 Introduction

### 1.1 Romania's winters

Located in Eastern Europe (between 43.55° and 48.28° North latitude and 20.25° and 29.83° East longitude), Romania is a country with a transition temperate-continental climate [1].

The exiled Roman poet Ovid (Publius Ovidius Naso, 43 BC – AD 17/18) left probably the oldest (AD 8-12) mentions on the hard winters on the Romanian Black Sea Coast in his work Tristia (i.e. “Sorrows”) and Epistulae ex Ponto (i.e. "Letters from the Black Sea") [2]:

> "And when dark winter shows its icy face,
> and the earth is white with marbled frost, [...]  
> Snow falls, and, once fallen, no rain or sunlight melts it,
> since the north wind, freezing, makes it permanent.

> So another fall comes before the first has melted,
> and in many parts it lingers there two years. [...]

> Shall I speak of solid rivers, frozen by cold,
> and water dug out brittle from the pools?

> The Danube itself, no narrower than lotus-bearing Nile,
> mingling with deep water through many mouths,
> congeals, the winds hardening its dark flow,
> and winds its way to the sea below the ice:

> Feet cross now, where boats went before, [...]

> I've seen the vast waters frozen with ice,
> a slippery shell gripping the unmoving deep.

> Seeing was not enough: I walked the frozen sea, [...]

> The ships stand locked in frozen marble,
> and no oar can cut the solid wave."

> "I'm here, abandoned, on the furthest shores of the
> world,
> where the buried earth carries perpetual snowfall. [...]

> here winter makes the sea a pathway for walkers, [...] [2].

If in mountain region first snows appear even in August and September, in general the snowy winter comes for most of the territory in November and last until March-April. Based on data from the time interval 1961-2000, the average annual number of days with snow falls varies between ~20 (lowlands and plains), ~30 days (hills and plateau) to ~100 days (top of mountains) [3]. The

average annual number of days with snow layer on the ground varies between less than 20 days on the Black Sea shore and over 200 days on high mountain tops. As an example, in Tables 1 and 2 are presented data [3] [4] from several meteorological stations in Romania, whose locations are shown in Figure 1 (design snow load data for the same stations are presented in Chapter 2).

<table><caption>**Table 1.** Examples of snow data [3] [4] at meteorological stations in Romania: (i) station altitude, (ii) average annual number of days with snow layer (1926-1955) (iii) average annual number of days with snow layer (1961-2000), (iv) maximum annual number of days with snow layer (1961-2000)</caption><thead><tr><th>Station</th><th>(i)<br>[m]</th><th>(ii)<br>1926-1955</th><th>(iii)<br>1961-2000</th><th>(iv)</th></tr></thead><tbody><tr><td>Constanța</td><td>13</td><td>24</td><td>15</td><td>44</td></tr><tr><td>Bucharest</td><td>90</td><td>53</td><td>48</td><td>93</td></tr><tr><td>Vârful Omu</td><td>2504</td><td>219*</td><td>220</td><td>280</td></tr><tr><td>Târgu Mureș</td><td>308</td><td>57</td><td>62</td><td>92</td></tr><tr><td>Brașov</td><td>534</td><td>71</td><td>73</td><td>102</td></tr><tr><td>Sibiu</td><td>443</td><td>54</td><td>58</td><td>102</td></tr><tr><td>Iași</td><td>102</td><td>57</td><td>65</td><td>115</td></tr><tr><td>Bacău</td><td>184</td><td></td><td>64</td><td>115</td></tr><tr><td>Baia Mare</td><td>216</td><td></td><td>63</td><td>98</td></tr><tr><td>Timișoara</td><td>86</td><td>30</td><td>29</td><td>63</td></tr></tbody></table>

<figure><img src="image_656.png" /><figcaption>**Figure 1.** Location in Romania of the meteorological stations from Tables 1÷4</figcaption></figure>

<footnote>ª Corresponding author: aldea@utcb.ro</footnote>

<footnote>* data from 1941-1955</footnote>
In Figure 2 are exemplified histograms of the monthly average number of days with snow layer (1926-1955) for several meteorological stations from those indicated in Table 1 (data from [4]).

<figure><img src="image_657.png" /><figcaption>**Figure 2.** Examples of histograms of the monthly average number of days with snow layer (1926-1955) for meteorological stations in Romania</figcaption></figure>

In Table 2 are indicated values of the maximum annual snow depths [3] [4] at several meteorological stations in Romania.

<table><caption>**Table 2.** Examples of snow data [3] [4] at meteorological stations in Romania: station altitude A, maximum annual snow depth $h_{max}$ for 1926-1955 and for 1961-2000</caption><thead><tr><th rowspan="2">Station</th><th>Alt.</th><th><i>h</i><sub>max</sub></th><th><i>h</i><sub>max</sub></th></tr><tr><th><i>A</i></th><th>1926-1955</th><th>1961-2000</th></tr><tr><th></th><th>[m]</th><th>[m]</th><th>[m]</th></tr></thead><tbody><tr><td>Constanța</td><td>13</td><td>0.54</td><td>0.46</td></tr><tr><td>Bucharest</td><td>90</td><td>1.06</td><td>0.80</td></tr><tr><td>Vârful Omu*</td><td>2504</td><td>3.70</td><td>2.92</td></tr><tr><td>Târgu Mureş</td><td>308</td><td>0.75</td><td>0.48</td></tr><tr><td>Braşov</td><td>534</td><td>0.66</td><td>0.44</td></tr><tr><td>Sibiu</td><td>443</td><td>0.65</td><td>0.60</td></tr><tr><td>Iaşi</td><td>102</td><td>0.64</td><td>0.66</td></tr><tr><td>Bacău</td><td>184</td><td></td><td>0.65</td></tr><tr><td>Baia Mare</td><td>216</td><td></td><td>0.82</td></tr><tr><td>Timișoara</td><td>86</td><td>0.6</td><td>0.43</td></tr></tbody></table>

* data from 1941-1955

An exceptionally hard winter with heavy snow falls and blizzards was experienced in 1953-1954, when in the southern and eastern Romania the snow layer depth over passed 1 m at 20 meteorological stations (a maximum of 1.73 m was observed), and the snowdrifts reached 4÷6 m height due to strong winds reaching 125 km/h [4]. In Figure 3 is presented an image from Bucharest [5] during the 1954 winter. Almost every winter significant snowdrifts occur in south-eastern Romania (Figure 4).

<figure><img src="image_658.png" /><figcaption>**Figure 3.** Tramway in Bucharest during 1954 winter [5]</figcaption></figure>

<figure><img src="image_659.png" /><figcaption>**Figure 4.** Snow drift in south-eastern Romania (January 2014 [6])</figcaption></figure>
## 1.2 Meteorological observations

The first meteorological observations were made on Romanian territory starting with 19th century (in 14 major cities), and the National Meteorological Institute of Romania was established in 1884, Romania being one of the founding countries of the International Meteorological Organization [1]. The meteorological network quickly developed: 1887 - 30 stations, 1899 - 50 stations, 1906 - 66 stations [3], 2013 – 258 stations [1].

Nowadays the meteorological observations are performed by the National Meteorological Administration [1], with 71% of stations in lowlands, 12% in hilly areas, 4% on the sea shore and 13% in mountains. Some stations are located on mountain's top, like Cehălău Toaca – 1897 m and Călimani – 2021 m, the highest station being Vârful Omu, located at 2504 m.

The Romanian meteorological network is integrated in the permanent world survey within the Region VI – Europe of the World Meteorological Organization.

## 1.3 Snow load codes

In Romania snow loads were considered in design since 1950, the code being revised in 1956, 1974, 1978 and 1992 [7].

The 1992 code consisted of 12 pages: 4 pages indicate the snow load on the ground (map and table with main localities), 5 pages the snow load on the roof, 1 page the partial safety factors and 2 pages the snow loads principles. The characteristic snow load on the ground was defined with 10 years mean return period. The territory was divided in 4 areas A÷D plus the mountain area E for which a table for snow load on the ground was recommended (with altitude dependent values from 700m to 2500m). In Figure 5 is presented the zonation map of the snow load on the ground (in kN/m²) from the 1992 snow load code. The E zones contours are not shown in Figure 5, they were highly irregular, identifying the borders of the regions with altitudes higher than 700 m.

<figure><img src="image_660.png" /><figcaption>**Figure 5.** Zonation of snow load on the ground in the 1992 code</figcaption></figure>

As Romania became a candidate state for joining European Union, in 2005 was issued the CR 1-1-3/2005 snow loads code, enforced from 2006. The provisions were following the Eurocode EN 1991-1-3

recommendations. A major change was the definition of the characteristic snow load on the ground with 50 years means return period. The lognormal probability distribution was used for computing the characteristic values of snow load on the ground [8] [9]. In Figure 6 is presented the zonation map of the snow load on the ground (in kN/m²) from the 2005 code.

<figure><img src="image_661.png" /><figcaption>**Figure 6.** Zonation of snow load on the ground in the 2005 code</figcaption></figure>

An updated edition of the Romanian snow loads code, CR 1-1-3/2012 [10] was enforced in 2013. This code is harmonised with the Eurocode EN 1991-1-3 [11] in what concerns the general approach and the snow loads on roofs.

# 2 The 2012 snow loads code for design

## 2.1 Snow load on the ground

The setting of the snow load on the ground in the recent Romanian code CR 1-1-3/2012 [10] was done using data from 122 meteorological stations [12].

The snow data (annual maxima) was available from the period 1930-2005, with different time intervals for different stations. In case of three recently installed meteorological stations the number of available annual maxima was 10÷13 (they were included in the data set in order to ensure a reasonable geographical coverage of stations); the largest number of data at a station was from 74 years with snow, and the average number of data was 48, a number that can be considered as reasonable for establishing values with a mean return period of 50 years.

The coefficient of variation of the maximum annual ground snow load in Romania varies between 0.35 and 1.38, with an average value of 0.59). The frequency histogram of the coefficient of variation is shown in Figure 7. In Figure 8 is presented the coefficient of variation as function of the altitude. The range of coefficients of variation and the tendency to decrease with altitude are similar to those from European countries [13], and one may notice that this tendency is slightly slower than in the case of Germany for example.

The skewness of the maximum annual ground snow load was found to vary in between 0.22 and 4.14, with an average value of 1.38. The skewness frequency histogram is shown in Figure 9.
<figure><img src="image_662.png" /><figcaption>**Figure 7.** Histogram of the coefficient of variation of observed annual maximum snow loads on the ground at 122 meteorological stations in Romania</figcaption></figure>

<figure><img src="image_663.png" /><figcaption>**Figure 8.** Coefficient of variation of observed annual maximum snow loads on the ground at 122 meteorological stations versus altitude in Romania</figcaption></figure>

The largest values of the coefficient of variation were observed at low altitudes, but some large values also came out at altitudes higher than 1700 m.

<figure><img src="image_664.png" /><figcaption>**Figure 9.** Histogram of the skewness of observed annual maximum snow loads on the ground at 122 meteorological stations in Romania</figcaption></figure>

In Figure 10 is presented the variation of the mean value of the annual maximum snow load on the ground with altitude. In Figures 11 and 12 are shown the standard deviation and the coefficient of variation versus the mean value of the annual maximum snow load on the ground. Again the tendencies are similar to those from other European countries [13].

<figure><img src="image_665.png" /><figcaption>**Figure 10.** Standard deviation versus mean value of observed annual maximum snow loads on the ground at 122 meteorological stations in Romania</figcaption></figure>

<figure><img src="image_666.png" /><figcaption>**Figure 11.** Coefficient of variation versus mean value of observed annual maximum snow loads on the ground at 122 meteorological stations in Romania</figcaption></figure>

In Table 3 are exemplified annual maximum snow load on the ground data and statistics at the meteorological stations from Table 1 and Figure 1.

<table><caption>**Table 3.** Examples of data and statistics of annual maximum snow load on the ground meteorological stations in Romania: station altitude, number of years with snow data, coefficient of variation (COV), and skewness</caption><thead><tr><th>Station</th><th>Alt. [m]</th><th>No. yrs.</th><th>COV</th><th>Skew.</th></tr></thead><tbody><tr><td>Constanţa</td><td>13</td><td>45</td><td>0.79</td><td>1.71</td></tr><tr><td>Bucharest</td><td>90</td><td>69</td><td>0.54</td><td>1.40</td></tr><tr><td>Vârful Omu</td><td>2504</td><td>65</td><td>0.69</td><td>1.68</td></tr><tr><td>Târgu Mureş</td><td>308</td><td>60</td><td>0.49</td><td>1.19</td></tr><tr><td>Braşov</td><td>534</td><td>67</td><td>0.44</td><td>0.85</td></tr><tr><td>Sibiu</td><td>443</td><td>64</td><td>0.45</td><td>0.91</td></tr><tr><td>Iaşi</td><td>102</td><td>61</td><td>0.69</td><td>1.94</td></tr><tr><td>Bacău</td><td>184</td><td>58</td><td>0.57</td><td>0.70</td></tr><tr><td>Baia Mare</td><td>216</td><td>60</td><td>0.54</td><td>0.95</td></tr><tr><td>Timișoara</td><td>86</td><td>48</td><td>0.68</td><td>1.37</td></tr></tbody></table>

The Gumbel probability distribution for maxima was used for computing characteristic values of snow load on the ground with an annual probability of exceedance of 2% (i.e., mean return period of 50 years). Whenever conversions from snow depth to snow load were done, the snow weight density was considered to be 2 kN/m³.
Gumbel distribution is recommended by the Eurocode [11] and was found appropriate for modelling snow loads on the ground in several countries around the world [13, 14, 15, 16, 17]. In Figure 12 is presented the skewness versus the coefficient of variation for the annual maximum snow load on the ground in Romania. The plot suggests that in future detailed analysis of data at each station are necessary, and that probably a mixed solution like the one in case of Germany [13] may apply. Moreover, "For future research it is recommended that to solve this problem it will be necessary to work together with meteorological people taking into account local climatic conditions" [13, Annex 3].

<figure><img src="image_667.png" /><figcaption>**Figure 12.** Skewness versus coefficient of variation of observed annual maximum snow loads on the ground at 122 meteorological stations in Romania</figcaption></figure>

In Table 4 are exemplified annual maximum snow load on the ground data and statistics together with the characteristic values of snow load on the ground (computed with 2% annual probability of exceedance in Gumbel distribution for maxima).

The Romania zonation map of snow load on the ground has areas of constant values according to the set of values recommended by ISO 4355 [18]: 1.5, 2.0 and 2.5 kN/m². The corresponding code values of the snow load on the ground for the selected stations in Table 1 and Figure 1 are also given in Table 4.

<table><caption>**Table 4.** Examples of data and statistics of annual maximum snow load on the ground meteorological stations in Romania: maximum snow load, mean annual maximum snow load, characteristic value, and code snow load $s_k$</caption><thead><tr><th>Station</th><th>Max.<br>load<br>[kN/m²]</th><th>Mean<br>load<br>[kN/m²]</th><th>Charact.<br>load<br>[kN/m²]</th><th>$s_k$<br>[kN/m²]</th></tr></thead><tbody><tr><td>Constanţa</td><td>1.7</td><td>0.5</td><td>1.4</td><td>1.5</td></tr><tr><td>Bucharest</td><td>2.0</td><td>0.7</td><td>1.6</td><td>2.0</td></tr><tr><td>Vârful Omu</td><td>14.9</td><td>4.3</td><td>12.1</td><td>-</td></tr><tr><td>Târgu Mureş</td><td>1.1</td><td>0.4</td><td>1.0</td><td>1.5</td></tr><tr><td>Braşov</td><td>1.4</td><td>0.6</td><td>1.3</td><td>2.0</td></tr><tr><td>Sibiu</td><td>1.1</td><td>0.5</td><td>1.0</td><td>1.5</td></tr><tr><td>Iaşi</td><td>2.5</td><td>0.6</td><td>1.8</td><td>2.5</td></tr><tr><td>Bacău</td><td>1.7</td><td>0.7</td><td>1.8</td><td>2.5</td></tr><tr><td>Baia Mare</td><td>1.7</td><td>0.6</td><td>1.5</td><td>2.0</td></tr><tr><td>Timișoara</td><td>1.2</td><td>0.4</td><td>1.0</td><td>1.5</td></tr></tbody></table>

The Romania's zonation map is for snow load on the ground (and not at sea level) and is valid for altitudes lower or equal to 1000 m, Figure 13.

<figure><img src="image_668.png" /><figcaption>**Figure 13.** Zonation of the snow load on the ground in Romania, for altitudes $\le 1000$ m [10]</figcaption></figure>

The central and western part of Romania (somehow protected by Carpathian Mountains) and the south-eastern corner on Black Sea coast shows the lowest snow load, while the north-east and south-west parts, exposed to strong winter winds have the highest snow loads.

For altitudes $1000 m < A \le 1500 m$, the code snow load on the ground is given by following relations, equations (1) and (2).

For areas with $s_k (A \le 1000 m) = 2.0$ kN/m²:

$$s_k (1000 \text{ m} < A \le 1500 \text{ m}) = 2.0 + 0.00691 (A - 1000) \quad (1)$$

for areas with $s_k (A \le 1000 m) = 1.5$ kN/m²:

$$s_k (1000 \text{ m} < A \le 1500 \text{ m}) = 1.5 + 0.00752 (A - 1000) \quad (2)$$

where $s_k (A \le 1000 m)$ values are those from Figure 13. In Table 5 are given examples of snow loads on the ground at different altitudes, from the application of equations (1) and (2).

<table><caption>**Table 5.** Examples of snow loads on the ground at different altitudes between 1000 m and 1500 m</caption><thead><tr><th rowspan="3">Altitude A<br>[m]</th><th colspan="2">s<sub>k</sub> (1000 m &lt; A &le; 1500 m), kN/m<sup>2</sup></th></tr><tr><th colspan="2">Zone where</th></tr><tr><th>s<sub>k</sub> (A&le;1000 m)=<br>1.5 kN/m<sup>2</sup></th><th>s<sub>k</sub> (A&le;1000 m)=<br>2.0 kN/m<sup>2</sup></th></tr></thead><tbody><tr><td>1000</td><td>1.5</td><td>2.0</td></tr><tr><td>1100</td><td>2.3</td><td>2.7</td></tr><tr><td>1200</td><td>3.0</td><td>3.4</td></tr><tr><td>1300</td><td>3.8</td><td>4.1</td></tr><tr><td>1400</td><td>4.5</td><td>4.8</td></tr><tr><td>1500</td><td>5.3</td><td>5.5</td></tr></tbody></table>

The exceptional snow load on the ground, as indicated in [13], can be identified through the ratio of the maximum observed load to the characteristic snow load determined without that value. If the ratio is greater than 1.5, the conditions of exceptional snow load are fulfilled. In Romania such case appeared at several stations. For example, at Sulina, a city on the extreme eastern Black
Sea border, at an altitude of 3 m, the ratio was 1.54; at Giurgiu, in southern Romania on Danube river, at an altitude of 24 m, the ratio was 1.82. Also in mountain area, at Fundata, at an altitude of 1384 m, the ratio was 1.61. As mentioned in [14], it is difficult to draw exceptional loads maps, and in Romania also, future studies are necessary, involving up-to-date data and the cooperation of meteorology specialists. In CR 1-1-3/2012 there are no areas with exceptional snow loads.

## 2.2 Snow load on the roof

The snow load on the roof is established in the Romanian code CR 1-1-3/2012 in the same way as in the Eurocode, with the same loading patterns and shape coefficients.

However, a supplementary factor is considered in the Romanian code: the importance-exposure factor for snow loads $\gamma_{Is}$.

The importance-exposure building categories are defined in the Romanian code CR-0/2012 „Basis of constructions design” [19] based on the human and economic consequences that may be induced by a major natural and/or anthropic hazard and on the role and importance in post-disaster activities.

There are four importance-exposure categories with the following simplified description:

- category I – essential/vital for society and for post-disaster intervention (for example: emergency hospitals, medical emergency facilities, police stations, firefighter stations, communication centers, essential buildings for public administration, water storage constructions, constructions containing hazardous materials, etc.);

- category II – with high danger for humans in case of damage (for example: hospitals with over 100 beds, education facilities with over 250 persons capacity, residential, commercial, offices with over 300 persons capacity, museums and cultural heritage buildings, stadiums, etc.);

- category III – current buildings and constructions (all except those from categories I, II and IV), and

- category IV – of less importance, with low danger for humans in case of damage (for example: temporary constructions, agriculture facilities, storage facilities, etc.

For the categories III and IV the importance-exposure factor for snow loads $\gamma_{Is}=1$, for the category II $\gamma_{Is}=1,1$, and for the category I $\gamma_{Is}=1,15$. The values of the importance-exposure factor roughly correspond to an increase of the mean return period of snow load on the ground from 50 years to 100 years (considering the Gumbel distribution for maxima).

Other codes also have a similar factor. For example, in the International Building Code [20], ASCE-7 [21], New York City Building code [22], etc. are defined structural occupancy categories (category order is reversed compared to Romania) that have an associated importance snow factor $Is$ with values: for category I – $Is=0.8$, II – $Is=1$, III – $Is=1.1$ and IV – $Is=1.2$.

The 2005 Canadian National Building Code [23] defines importance categories with associated importance

snow factors: importance category Low – $Is=0.8$, Normal – $Is=1$, High – $Is=1.15$ and Post disaster – $Is=1.25$. The code CR 1-1-3/2012 was accompanied by comments and examples, published as an informative annex.

Following the French example [24], a snow load application/guide volume was published by the Technical University of Civil Engineering Bucharest [25].

## 3 Final considerations

Proper consideration of snow loads in the design of new buildings and in the evaluation of existing buildings will reduce the chances of accidents that, unfortunately, continue to appear from time to time.

For example, in Romania, due to snow load, in 2012 in Cluj [26] and Iasi [27] the metallic roof structure at entrance of shopping areas collapsed, Figures 14 and 15, and in Suceava [28], Cavnic [29], Podgoria [30] and Focsani [31] wooden roofs collapsed, Figures 16, 17, 18 and 19.

<figure><img src="image_669.png" /><figcaption>Figure 14. Collapse of a new metallic roof structure in Cluj [26]</figcaption></figure>

<figure><img src="image_670.png" /><figcaption>Figure 15. Collapse of a new metallic roof structure in Iasi [27]</figcaption></figure>

<figure><img src="image_671.png" /><figcaption>Figure 16. Collapse of an old wooden roof in Suceava [28]</figcaption></figure>
<figure><img src="image_672.png" /><figcaption>Figure 17. Collapse of a wooden roof structure in Cavnic [29]</figcaption></figure>

<figure><img src="image_673.png" /><figcaption>Figure 18. Collapse of a wooden roof structure in Podgoria [30]</figcaption></figure>

<figure><img src="image_674.png" /><figcaption>Figure 19. Collapse of a wooden roof structure in Focsani [31]</figcaption></figure>

The recent snow load code of Romania (2012) is harmonised with the Eurocode EN 1991-1-3. It adopted the same 2% annual probability of exceedance, and the characteristic snow load (obtained from Gumbel distribution) on the ground is defined at the ground level, and not at the Sea level.

The strong winter winds from south-west and north-east are correlated with the areas of highest characteristic snow load on the ground (2.5 kN/m²), while inside the Carpathian arch and on the south-eastern Black Sea shore the load is lower (1.5 kN/m²).

At present, an update of the zonation map is expected, for considering the observed snow data from the last 10 years, for performing a detailed analysis on the type of probability distribution to be considered and on the exceptional snow loads. Also, there is a need for details of snow loading for solar panels (on ground and on roofs) and other special cases.

## References

1. National Meteorological Agency (in Romanian) http://www.meteoromania.ro

2. Ovid, *Tristia* and *Epistulae ex Ponto* (AD 8-12) Book TIII.X:1-40 Winter in Tomis, and Book TIII.X:41-78 Barbarian Incursions, http://www-poetryintranslation.com/PITBR/Latin/ translation by Kline, A.S., accessed – April 2016

3. *Romania's climate*, by National Meteorological Administration, Romanian Academy Publishing house, 365p., in Romanian (2008)

4. O. Bogdan, A.F. Marinica, I. Marinica. Comparative climatic characteristics between the winter of 2011–2012 and the winter of 1953–1954 in the south of Romania, Rev. Roum. Géogr./Romanian Journal of Geography, 57, (1), p. 9–24 (2013)

5. http://www.otopeni.net/?p=916

6. http://adevarul.ro/locale/buzau/

7. STAS 10101/21-78 and 92. *Actions in construction. Snow loads* (in Romanian), National Institute of Standardization (1978 and 1992)

8. D. Lungu, S. Demetriu, A. Aldea. Basic Code parameters for Environmental Actions in Romania harmonised with EC1, Proceedings 7th International Conference on Applications of Statistics and Probability in Civil Engineering, Reliability and Risk Analysis, ICASP-7, Paris, Vol. 2, p. 881-887, A.A. Balkema, Rotterdam (1995)

9. D. Lungu, A. Aldea, S. Demetriu. Probabilistic wind and snow hazards assessment for Romania, Proceedings of the 1st International Scientific-Technical Conference – Technical Meteorology of the Carpathians, Ukraine, p.35-43 (1998)

10. CR 1-1-3/2012 – *Design code. Evaluation of snow loads on constructions*, Ministry of Regional Development and Tourism, Romania, 36p. (2013)

11. European Standard EN 1991-1-3, Eurocode 1, 2002, 2006. Basis of design and actions on structures, Part 1-3: Snow loads. CEN/TC250

12. D. Lungu, S. Demetriu, A. Aldea, C. Arion, R. Vacareanu. Statistics of the Maximum Annual Snow Load in Romania. Proceedings 6th International Symposium on Environmental Effects on Buildings and People: Actions, Influences, Interactions, Discomfort, EEBP VI, Book of keynote lectures and extended abstracts / eds. A. Flaga, T. Lipecki. - Cracow: Polish Association for Wind Engineering, CD-ROM, 8p. (2010)

13. L. Sanpaolesi. Scientific Support Activity In The Field Of Structural Stability Of Civil Engineering Works - Snow Loads, Final Report, Commission Of The European Communities, DGIII - D3, Contract n° 500269/1996, 55p. + Annexes 1-5, 75p. (1998)

14. L. Sanpaolesi. Snow loads on roofs in Europe: research and standardization. *Proceedings of Snow Engineering International Conference*, Hjorth-Hansen, Holand, Loset and Norem (eds.), Balkema, p.3-10 (2000)

15. S. Sakurai, O. Joh. Statistical analysis of annual extreme ground snow depths for structural design, J. of Struct. Constr. Engngr., AIJ, nr.436, 11p. (1992)
16. S. Sakurai, O. Joh, T. Shibata. Statistical analysis of annual extreme ground snow loads for structural design, J. of Struct. Constr. Engngr., AIJ, nr.437, 10p. (1992)

17. V. Otstavnov. Elaboration of draft map for snow loads in Russia, Research Report 16-13-135/96, CNIISK, Moscow (1996)

18. ISO DIS 4355. Bases for design of structures. Determination of snow loads on roofs (1992-2013)

19. CR-0/2012. Basis of constructions design. Ministry of Regional Development and Tourism, Romania, 32p. (2012)

20. International Building Code, International Building Council, USA, 684p. (2003)

21. ASCE/SEI 7-10. Minimum design loads for buildings and other structures. American Society of Civil Engineers, USA, 658p. (2010)

22. New York City Building Code 2008, with 2011 Supplement, http://publicecodes.cyberregs.com/st/ny/ (2008)

23. R. Riffel. 2005 National Building Code. Wind and Snow Importance Factors, Canadian Society for Civil Engineering Annual Conference, http://www.ucalgary.ca/en/civil/csce_calgary/2004/ri ffellcodecommittee (2004)

24. Actions de la neige sur les bâtiments. D'après l'Eurocode 1, Calcul des charges de neige sur les toitures, 71p, CSTB (2010)

25. A. Aldea, C. Neagu, C. Arion. Guide for snow loads according to CR 1-1-3/2012, Ed. Conspress of Technical University of Civil Engineering Bucharest, 77p., (2013)

26. http://www.stiridecluj.ro/

27. http://adevarul.ro/

28. http://www.romaniatv.net/

29. http://maramedia.ro

30. http://www.jurnaluldebuzau.ro/

31. http://www.monitorulvn.ro/
Authors index

<table><tr><td>AGUINAGA Sylvain</td><td>276</td></tr><tr><td>ALDEA Alexandru</td><td>351</td></tr><tr><td>ARION Cristian</td><td>351</td></tr><tr><td>BAKLANOV Jurij</td><td>320</td></tr><tr><td>BLOMQVIST Göran</td><td>282</td></tr><tr><td>BOND Jill</td><td>198, 246</td></tr><tr><td>BOUCHET Jean-Paul</td><td>276</td></tr><tr><td>BOUTANIOS Ziad</td><td>20</td></tr><tr><td>BROOKS Albert</td><td>198, 246</td></tr><tr><td>CHIBA Takahiro</td><td>121, 173, 334</td></tr><tr><td>CHURIN Pavel</td><td>184</td></tr><tr><td>COCCA John</td><td>146</td></tr><tr><td>CROCE Pietro</td><td>73</td></tr><tr><td>CZWIKLA Benjamin</td><td>93, 152</td></tr><tr><td>DALE Jan</td><td>198, 246</td></tr><tr><td>DE OLIVEIRA Fabrice</td><td>344</td></tr><tr><td>DELPECH Philippe</td><td>276, 344</td></tr><tr><td>DEMETRIU Sorin</td><td>351</td></tr><tr><td>FAN Feng</td><td>30, 87, 137, 256</td></tr><tr><td>FEBVRE Guy</td><td>344</td></tr><tr><td>FIEBIG Jennifer</td><td>40</td></tr><tr><td>FIERZ Charles</td><td>339</td></tr><tr><td>FLAGA Andrzej</td><td>238</td></tr><tr><td>FLAGA Łukasz</td><td>238</td></tr><tr><td>FORMICHI Paolo</td><td>73</td></tr><tr><td>FUJIMOTO Akihiro</td><td>289</td></tr><tr><td>FUKUHARA Teruyuki</td><td>330</td></tr><tr><td>GAMBLE Scott</td><td>198, 246</td></tr><tr><td>GLADYSHEVA Olga</td><td>320</td></tr><tr><td>GOURBEYRE Christophe</td><td>344</td></tr><tr><td>GU Ming</td><td>101, 141, 179</td></tr><tr><td>HAGENMULLER Pascal</td><td>135</td></tr><tr><td>HARADA Yusuke</td><td>121</td></tr><tr><td>HASLER Michael</td><td>130, 132</td></tr><tr><td>HEIDREKSSON Guðmundur</td><td>342</td></tr><tr><td>HIRASAWA Masayuki</td><td>325</td></tr><tr><td>HITOMITSU Kikitsu</td><td>166</td></tr><tr><td>HØYLAND Knut Vilhelm</td><td>269</td></tr><tr><td>HUANG Peng</td><td>179</td></tr><tr><td>IRWIN Peter A.</td><td>206</td></tr></table>

<table><tr><td>ISHIDA Tateki</td><td>289, 325</td></tr><tr><td>ITO Yoshiomi</td><td>260</td></tr><tr><td>JAMIESON Bruce</td><td>118</td></tr><tr><td>JÄRLSKO Ida</td><td>282</td></tr><tr><td>JASAK Hrvoje</td><td>20</td></tr><tr><td>JOHANNSSON Torfi B.</td><td>342</td></tr><tr><td>JONES Alan S.T.</td><td>118</td></tr><tr><td>JONSSON Árni</td><td>342</td></tr><tr><td>KAMIMURA Seiji</td><td>260</td></tr><tr><td>KANG Luyang</td><td>141</td></tr><tr><td>KARLSSON Emelie</td><td>282</td></tr><tr><td>KASBERGEN Cor</td><td>269</td></tr><tr><td>KASPERSKI Michael</td><td>53, 93, 152</td></tr><tr><td>KATO Saeka</td><td>26</td></tr><tr><td>KIMBAR Grzegorz</td><td>83</td></tr><tr><td>KLEIN-PASTE Alex</td><td>297</td></tr><tr><td>KNOFLACH Christoph</td><td>130, 132</td></tr><tr><td>KOSS Hans Holger Hundborg</td><td>40</td></tr><tr><td>LANDI Filippo</td><td>73</td></tr><tr><td>LEHNING Michael</td><td>339</td></tr><tr><td>LENOIR Dominique</td><td>344</td></tr><tr><td>LI Jialiang</td><td>179</td></tr><tr><td>LINDSTRÖM Bengt</td><td>282</td></tr><tr><td>LIU Mengmeng</td><td>30, 87</td></tr><tr><td>LUNGU Dan</td><td>351</td></tr><tr><td>MARGRETH Stefan</td><td>228</td></tr><tr><td>MARSILI Francesca</td><td>73</td></tr><tr><td>MATSUSHITA Hiroki</td><td>121</td></tr><tr><td>MATSUZAWA Masaru</td><td>121</td></tr><tr><td>MCCALLUM Adrian</td><td>302</td></tr><tr><td>MO Huamei</td><td>87</td></tr><tr><td>MOCHIDA Akashi</td><td>26, 214</td></tr><tr><td>NAAİM Florence</td><td>107</td></tr><tr><td>NACHBAUER Werner</td><td>130, 132</td></tr><tr><td>NAKAMURA Kazuki</td><td>173</td></tr><tr><td>NEAGU Cristian</td><td>351</td></tr><tr><td>NISKA Anna</td><td>282</td></tr><tr><td>NUIJTEN Anne</td><td>269</td></tr><tr><td>O'ROURKE Michael</td><td>146, 221, 234</td></tr><tr><td>OKAZE Tsubasa</td><td>26, 214</td></tr></table>
<table>
  <tr>
    <td>OMIYA Satoshi</td>
    <td>121</td>
  </tr>
  <tr>
    <td>OTSUKI Masaya</td>
    <td>166</td>
  </tr>
  <tr>
    <td>PALIER Pierre</td>
    <td>276</td>
  </tr>
  <tr>
    <td>PANFEROV Konstantin</td>
    <td>320</td>
  </tr>
  <tr>
    <td>PILLOIX Thibault</td>
    <td>135</td>
  </tr>
  <tr>
    <td>PODDAEVA Olga</td>
    <td>184</td>
  </tr>
  <tr>
    <td>POTAC Jan</td>
    <td>221, 234</td>
  </tr>
  <tr>
    <td>PUTTEN Joost van</td>
    <td>130, 132</td>
  </tr>
  <tr>
    <td>QIANG Shengguan</td>
    <td>101</td>
  </tr>
  <tr>
    <td>RIJIN He</td>
    <td>34</td>
  </tr>
  <tr>
    <td>ROHM Sebastian</td>
    <td>130, 132</td>
  </tr>
  <tr>
    <td>SAIDA Akira</td>
    <td>325</td>
  </tr>
  <tr>
    <td>SAITO Yoshihiko</td>
    <td>166</td>
  </tr>
  <tr>
    <td>SAMODUROVAA Tatiana</td>
    <td>320</td>
  </tr>
  <tr>
    <td>SATO Kenji</td>
    <td>289, 312</td>
  </tr>
  <tr>
    <td>SCARPAS Tom</td>
    <td>269</td>
  </tr>
  <tr>
    <td>SCHINK Damian</td>
    <td>284</td>
  </tr>
  <tr>
    <td>SOMMER Christian G.</td>
    <td>339</td>
  </tr>
  <tr>
    <td>STAUDACHER Lars</td>
    <td>284</td>
  </tr>
  <tr>
    <td>STEGER Hagen</td>
    <td>284</td>
  </tr>
  <tr>
    <td>STEINARSSON Magnús</td>
    <td>342</td>
  </tr>
  <tr>
    <td>SUN Lulu</td>
    <td>179</td>
  </tr>
  <tr>
    <td>SZILDER Krzysztof</td>
    <td>188</td>
  </tr>
  <tr>
    <td>TAKAHASHI Kazuya</td>
    <td>160</td>
  </tr>
  <tr>
    <td>TAKAHASHI Naoto</td>
    <td>289, 312, 325</td>
  </tr>
  <tr>
    <td>TAKAHASHI Toru</td>
    <td>166, 173</td>
  </tr>
  <tr>
    <td>TAKAHASHI Wataru</td>
    <td>121</td>
  </tr>
  <tr>
    <td>TAKEICHI Kiyoshi</td>
    <td>289</td>
  </tr>
  <tr>
    <td>TANAKA Shunsuke</td>
    <td>289</td>
  </tr>
  <tr>
    <td>TERASAKI Hiroaki</td>
    <td>330</td>
  </tr>
  <tr>
    <td>THIIS Thomas K.</td>
    <td>47, 221, 234, 334</td>
  </tr>
  <tr>
    <td>TOKUNAGA Roberto</td>
    <td>289, 312</td>
  </tr>
  <tr>
    <td>TOMINAGA Yoshihide</td>
    <td>10, 26, 214</td>
  </tr>
  <tr>
    <td>TSUTSUMI Takuya</td>
    <td>166</td>
  </tr>
  <tr>
    <td>UEMATSU Yasushi</td>
    <td>160</td>
  </tr>
  <tr>
    <td>VACAREANU Radu</td>
    <td>351</td>
  </tr>
  <tr>
    <td>WHITE Greg</td>
    <td>302</td>
  </tr>
  <tr>
    <td>XIAOYING Sun</td>
    <td>34</td>
  </tr>
  <tr>
    <td>YUE Wu</td>
    <td>34</td>
  </tr>
  <tr>
    <td>ZEN Junki</td>
    <td>260</td>
  </tr>
  <tr>
    <td>ZHANG Guolong</td>
    <td>87, 137, 256</td>
  </tr>
  <tr>
    <td>ZHANG Qingwen</td>
    <td>30, 87, 137</td>
  </tr>
</table>

<table>
  <tr>
    <td>ZHANG Yu</td>
    <td>256</td>
  </tr>
  <tr>
    <td>ZHOU Xuanyi</td>
    <td>101, 141, 179</td>
  </tr>
  <tr>
    <td>ZORN Roman</td>
    <td>284</td>
  </tr>
  <tr>
    <td>ŻURANSKI Jerzy Antoni</td>
    <td>83</td>
  </tr>
</table>
CSTB

le futur en construction

Centre scientifique et technique du bâtiment
11, rue Henri-Picherit - BP 82341
44323 Nantes Cedex 3
France

<figure><img src="image_675.png" /></figure>

Norwegian University
of Life Sciences

Norwegian University of Life Sciences
P.O. Box 5003
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