LATLAS

Documentation

11.09.2018

1. Project's presentation

The LATLAS project aims at supplying an interactive Internet platform with an atlas of waves for the main Swiss lakes. The characteristics of waves (significant height, period, wavelength, direction) generated for every prevailing wind are provided for various return periods. This database provides a common basis for the choice of the dimensioning waves. This tool is meant to be used by administrations as well as societies of civil and environmental engineering working in the lakeside domain. It is also intended for the various lakes-users interested in this theme.

2. Definitions

The fetch in a point is the distance over water travelled by the wind from the shore up to this point. In general, a larger fetch generates bigger waves as the wind rubs longer on the water and thus allows the development of larger waves.

The significant height is used to describe the height of waves. It corresponds to the average height of the third of the strongest waves classified in decreasing order. The height is measured between a crest and a troughs (total amplitude). During a wave episode, the crest to trough distance of the largest wave is approximately twice de significant height (see Equation 3 for exact formula).

The return period measures the probability of occurrence of a wave. It corresponds to the average frequency of an event. So each year, a wave with a return period of 20 years has a 1/20 probability to be observed.

The refraction is due to the decrease of the waves' speed at the approach of the shore (lower depth). It involves that the waves, which arrive with certain angle, "turn" until being perpendicular to the coast (more exactly, perpendicular to isobaths or lines of equal depth).

3. Methodology

Within the framework of the project LATLAS, only waves generated by the friction of the wind on the water surface are studied. These waves depend on four variables: the intensity of the wind, the duration of the wind, the fetch and the bathymetry.

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Winds As first step, the scenarios of wind used for the waves' calculation are chosen. An analysis of the historical measurements of the surrounding meteorological stations provides the prevailing winds. For each wind, the average wind speeds are computed, for several events durations and several probabilities of occurrence (e.g. mean wind speed for a three-hour storm occurring once in a century). This information is summarized in the Intensity-Duration-Frequency curve (IDF curve). As expected, the more likely and long-lasting a wind is, the lower its speed is. These IDF curves, associated with the COSMO2 model from MeteoSwiss (WINDSIM model from Meteotest for the Lake Lucerne and Lake Zürich), allow to define the wind fields over the whole surface of the lake. The analysis of 108 measurement stations of the network SMN (SwissMetNet) provides a formula to compute the speed at a point (x, y) of the lake for a given return period: 0.65 푣푟푒푓(푥, 푦) 푣푇푅(푥, 푦) = 푣푇푅(푠푡푎푡푖표푛) ( ) Equation 1 푣푟푒푓(푠푡푎푡푖표푛)

In this formula, vRP(x, y) is the wind speed over the lake for a given return period. vRP(station) is the wind speed at the station for this return period, determined thanks to IDF curves. vref(x, y) and vref(station) are the wind speeds over the lake and at the station for the reference wind field (simulation COSMO2 or WINDSIM).

Presently, this formula is only used for the Lakes Lucerne and Zürich. For the other lakes, a linear scaling is used (value of the exponent equal to 1 instead of 0.65).

These fields serve directly as input in the waves' model.

Waves The waves are computed with the numerical model SWAN (Simulating WAves Nearshore) which requires the lake's bathymetry and a wind field as initial conditions.

For every return period and every wind direction, simulations are made for several wind durations. For a small fetch, the biggest waves will result from an intense but short-term wind, while for more important fetches, a less powerful but longer-lasting wind will give the most important waves. For Lakes Geneva, Neuchâtel, Morat and Biel, ten durations of wind are considered (10, 20, 30, 40 and 50 minutes, 1, 2, 3, 4 and 5 hours). As the shortest and longest durations rarely creates the largest waves, seven durations of wind are considered for Lakes Lucerne and Zurich (¼ h, ½ h, ¾ h, 1 h, 1h½, 2 h and 3 h). Considering all simulations together allows the determination of the waves' significant heights for every point of the lake. The period, the wavelength, the direction of waves and the duration of wind which are linked to this significant height are recorded.

These computations are made for every wind and every probability. For the eight cardinal directions, a waves' rose is created. The obtained values take into account the direction of the wave and its significant height. A wave not moving in a parallel to the selected direction is reduced by the cosine of the angle between the selected direction and the direction of the wave. For every return period and every propagating direction, the largest wave is extracted from all the results obtained for the various scenarios of wind. The following return periods are used for Lake Geneva, Lake Neuchâtel, Lake Morat and Lake Biel: 2, 20 and 50 years. For the

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Lake Zürich and the Lake Lucerne, the periods of return are 2.33, 30, 100, 300 years. A more detailed presentation of this modelling method can be found in the article "Scaling wind fields to estimate extreme wave heights in mountainous lakes" (Marc Diebold & Philippe Heller (2017), Journal of Applied Water Engineering and Research, DOI: 10.1080/23249676.2017.1317294)

4. Website user guide

The Swisslakes platform comprises 3 levels to reach the various information. These levels are detailed hereafter.

"Swiss" level  Main Menu The main menu represents by blue squares the various lakes studied as presented in Fig. 1. The wheel of the mouse allows to zoom, pressing the left button allows to move. To access a lake, left-click on it.

Fig. 1: "Swiss" level: Website main menu

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"Lake" level The window is then centred on the lake of interest as presented in Fig. 2. The name of the lake as well as technical information on its modelling (source data, prevailing winds, IDF curves,…) are available in the upper left part of the window. The button << Back to all lakes allows to return to the main menu.

Fig. 2: "Lake" level: Lake's name, back to "Swiss" level, lake's information

The left part of the window allows then to choose the variable shown as well as the wind direction and the return period (Fig. 3).

Fig. 3: "Lake" level: choices of presented variable, prevailing wind and return period

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On the left side are the link towards this User Guide, the possibility to send a comment and a link towards the technical presentations given during the inauguration day (Fig. 4).

Fig. 4: "Lake" level: User Guide, send a comment, presentations of the inauguration day

Finally, the scale of the map as well as that of the presented variable are visible in the bottom right corner of the map (Fig. 5). The numbers given in the scale of the variable give the lower value for each colour.

Fig. 5: "Lake" level: Scale of the map and of the presented variable

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Variables definitions

 Bathymetry / Lake Depth Units : meters Depth of lake, given with regard to the level of the lake used for the simulations. This level is given in the data sheet associated with the lake.

 Significant Wave Height (Hauteur significative des vagues) Units : meters Maximal significant height reached during the simulations for the various return periods. The significant wave height corresponds to the average height of the third of the strongest waves classified in decreasing order. The height is measured between a crest and a troughs (total amplitude).

 Wave period (Période des vagues) Units : seconds  The peak wave period is the wave period with the highest energy. The peak period is the commonly used value for wave's formulae. This value differs from the mean period of the spectrum of waves, which comprises several periods and wavelengths In deep water, the peak period to mean period ratio is usually between 1.2 and 1.5.

 Wavelength (Longueur d'onde des vagues) Units : meters The peak wavelength is the wavelength related to the peak period (see above).

 Wave direction (Direction des vagues) Units : degrees in nautical convention (0° = North) Direction of the wave (wave's origin).

 Directional Significant Wave Height (Hauteur significative des vagues en fonction de leur direction) Units : meters Maximal significant wave height relative to the maximal significant wave height reached among the different scenarios and lowered in function to their direction relatively to the selected direction. For example, in the case where only two winds are prevailing (Bise and Foehn), the value given for East (90°) is :

퐻푠𝑖푔푀푎푥,퐵𝑖푠푒 ∙ 푐표푠(퐷푖푟푊푎푣푒푠퐵𝑖푠푒 − 90°); 퐻푠𝑖푔,퐷𝑖푟90 = max [ ] Equation 2 퐻푠𝑖푔푀푎푥,퐹표푒ℎ푛 ∙ 푐표푠(퐷푖푟푊푎푣푒푠퐹표푒ℎ푛 − 90°)

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Above, HsigMax,Bise et HsigMax,Foehn are the significant wave heights obtained among the

Bise and Foehn conditions. DirWavesBise and DirWavesFoehn are the directions of the Bise waves (respectively Foehn waves). A result is presented on Fig. 6.

Fig. 6: "Lake" level: Significant wave height according to wave's direction

Note on maximal wave height

The maximal height reached by a wave can be determined according to its significant height.

Because of the statistical nature of significant height, the number of vague Nvagues (and thus the event's duration) considered for its calculation impacts on the factor allowing to pass from significant height to maximal height Hmax:

퐻푚푎푥 = 퐻푠𝑖푔 ∙ 0.706 ∙ √푙푛(푁푤푎푣푒푠) Equation 3

For durations considered (15 minutes to 5 hours), an estimation of the maximal height is given by:

1.6 ∙ 퐻푠𝑖푔 < 퐻푚푎푥 < 2.2 ∙ 퐻푠𝑖푔 Equation 4

As an example, for the 50-year return period Bise over Geneva Lake, the largest significant wave height from the simulations is 1.82 m, offshore from Corsier (GE). For that scenario, the maximal wave height reaches 3.6 m. Over the lake, for all points with a significant height over

1 m, the Hmax/Hsig ratio is always comprised between 1.86 and 2.12.

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"Point" level By clicking a point on the lake, the coordinates of the point as well as all the calculated values for the chosen wind scenario are shown on the left (Fig. 7). As the polygons representing the lake have been smoothed, the "point" values can slightly differ from the colour display at that specific location.

Fig. 7: "Point" level: Values for a given point a data download as CSV

A tab also appears at this level of zoom and allows an automatic extraction of the significant waves' values of the selected point ("Download Point Data have CSV"). The obtained file CSV contains all the available information for the selected point:

 X,Y coordinates in the CH1903+ / LV95 coordinates system (in the file's title)  Depth  Significant wave height, for every prevailing wind and every return period  Wavelength for every prevailing wind and every return period  Wave periods for every prevailing wind and every return period  Significant wave height as a function of wave's direction, for the 8 main wind directions and every return period

The display on the lake depends on the selected variable:

 If the lake depth is selected, then the depth at that point is displayed (Fig. 7).  If the wave direction is selected, the wave direction at that point and for the selected scenario (wind direction and return period) is displayed.  If the significant height, the period or the wavelength is selected, a waves' rose appears at that point. This rose presents the significant heights (Fig. 8), periods or wavelengths for the various prevailing wind and return periods.

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Fig. 8: "Point" level: Waves' rose for a given point

Finally, for the significant wave height as a function of their direction, a wave rose with 8 quadrants is computed (wave height reduced by the cosine) (Fig. 9).

Fig. 9: "Point" level: Waves' rose for a given point according to waves' direction

Note: If a value do not appear, it is because that value is strictly equal to the one of the next return period.

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5. Application example

When modelling the waves nearby Geneva, the Swisslakes platform was used to provide boundary conditions to the Mike21 model for Geneva Lake (Lac Léman). Mike21 is a software developed by DHI which allow the modelling of waves as well as the currents induced by these waves. In the Geneva case, Mike21 used a fine mesh which was covering only the South part of the lake over 2 km. For the North open boundary, Mike 21 required the significant wave height, the wave period and the wave direction. These would now been easily provided by Swisslakes as can be shown on Fig. 10, and getting several values for a finer resolution on the boundary would be done in a couple of minutes.

Mesh for Mike21

Fig. 10: Use of Swisslakes to get boundary conditions North of Geneva

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6. Uncertainties

The accurate modelling of waves depends on the wind fields' precision. The meteorological stations used have 30 to 40 years of wind measurements. The confidence interval for IDF curves can be statistically estimated and errors on wind intensity are displayed on Tab. 1.

Tab. 1: Uncertainties on wind speed predictions

Return period (years) 2.33 30 100

Possible error on wind intensity (%) 2 5 10

As the relation between wind speed, fetch and significant wave height is not linear, this lead, for Lakes Lucerne, Geneva and Zurich, to the uncertainties displayed on Tab. 2. Similar values are expected for the other lakes.

Tab. 2: Uncertainties on wave height predictions

Return period (years) 2.33 30 100

Error on wave height, Lake Lucerne 3.0 7.6 15.4 (%)

Error on wave height, Lake Geneva 1.8 5.3 10.0 (%)

Error on wave height, Lake Zurich (%) 1.8 5.0 9.8

The wind direction impacts the results as it can modify and increase the fetch. The associated error can at most reach 15%.

Uncertainties result as well form the physical model SWAN. It has been successfully tested against real cases and various studies agree to give a margin of error inferior to 15%.

Finally, a sensitivity analysis showed that the size of the mesh can change the results by around 5%.

Aggregating the errors given above leads to an estimate of the error. That error can reach 40% for the 2 years return period and 60% for the 100 years return period.