**2. Methodology**

As mentioned before, the aim of this chapter is not to execute an excessive assessment of the ice melting impact on the design wave heights, but rather stress and highlight the challenge that might occur in a worst-case scenario when there is no ice in the Arctic. In this way, one can have a better understanding of the magnitude of change that could be expected. These effects are also present, possibly in a less extend and locally, when there is a partial reduction of the ice surface and not total disappearance.

The methodology chosen is based on the assumption that the Arctic Ocean in a free-ice period can be considered as a gigantic ocean, surrounded by the northern coasts of the neighboring countries. When one aims to estimate the characteristic wave height, two factors are the main contributors that need to be taken into consideration. One is the fetch length, the length of water over which a given wind can blow, and this is also the main factor that creates storm surge which also leads to coastal erosion and flooding. The other factor is the wind characteristics, such as duration and velocity. Thus, focus initially was given on areas that have the longest potential fetch distance, assuming that the wind conditions (duration and speed) are similar from all directions.

Taking all the aforementioned factors into consideration and also the available data and their quality, the northern part of Svalbard Island is chosen to be examined. As per now, this part of the Arctic region is covered by ice during most of the year, but in a free ice future scenario, long fetches are revealed that can potentially generate high waves. Moreover, statistical studies have showed that the percentage of north easterly winds occurring annually at the examined area is significant which testifies the relevance of the choice of location and direction for the study. Five different meteorological stations at the north and northeast area of Svalbard are selected to acquire the desired wind data. These data are analyzed to extract information regarding the most extreme wind incidents and storms from 2000 to 2014. The collected data refer to the early fall period of the year (September and October), as this is the period when the Arctic is expected to have the lowest ice percentage.

The stations are as follows [4]:


**29**

**Figure 3.**

*Coastal Erosion Due to Decreased Ice Coverage, Associated Increased Wave Action…*

the directions that are chosen are all between 320 and 55o

Since the main focus of this study is to examine the difference in wave height estimates due to the shrinkage of ice coverage, the directions that are examined are those that showed the most dramatic change in length. Thus, for the examined area,

in the case of ice coverage disappearance, the increase of the fetch length in some directions is up to three times longer than the one today (from presently 500 to 2000 km to the northern coast of Russia and from 200–250 to 1500–3000 km to the

The calculation of the maximum characteristic wave height is made by using the Jonswap method. This method is chosen as it is judged appropriate for open sea waves and considers the influence of the fetch length. According to this method, a wind generated wave can be either fetch limited (limited by the available distance over which it has been generated) or duration limited (limited by the period of time

In order to find the largest wave height that can occur due to the wind phenomena in the region, all the characteristic significant waves, Hs, for the directions of interest were assessed. In Svalbard, the examined directions were NNW, N, and NNE (North-Northwest 340°, North 0°, and North-Northeast 32.5°). Those directions were chosen because we wanted to cover as much as we could of the examined area for three different directions. For that reason, straight lines were drawn for each 2.5° with the use of maps from Google Earth (see **Figure 3**) until the opposite

For each and every one of the three wind directions that were examined (NNW, N, and NNE), wind was assumed from an angle of 45°, that is, from −22.5 to +22.5o for each direction (usually the spreading used is 90°, but here, because of the limited examined area, we had to choose a smaller and more narrow area, the half). The fetch length, F, was drawn for every αi = 2.5° angle around each direction, and

> \_\_\_\_\_\_\_\_\_\_\_\_*ai* ∑*i*=−*<sup>N</sup> <sup>N</sup> Fi* cos<sup>2</sup>*ai*

where N is the number of each fetch line drawn between −22.5 and + 22.5° for

The examined directions were chosen based on the morphology of the area; the islands and coasts of Greenland at the northwest part, for example, do not allow the

*Present maximum and minimum available fetch lengths north of Svalbard during early autumn periods (left).* 

*Future fetch lengths available in a free ice Arctic Ocean, between 320 and 55° in steps of 2.5°.*

. As shown in **Figure 3**,

(1)

*DOI: http://dx.doi.org/10.5772/intechopen.80604*

coasts of Canada and Alaska).

that the wind is blowing).

coasts were reached.

they are calculated by the following quation [5]:

*<sup>F</sup>* <sup>=</sup> <sup>∑</sup>*i*=−*<sup>N</sup> <sup>N</sup> Fi* cos<sup>2</sup>

each of the three directions (NNW, N, and NNE).

development of long enough fetches to be considered.


*Coastal Erosion Due to Decreased Ice Coverage, Associated Increased Wave Action… DOI: http://dx.doi.org/10.5772/intechopen.80604*

Since the main focus of this study is to examine the difference in wave height estimates due to the shrinkage of ice coverage, the directions that are examined are those that showed the most dramatic change in length. Thus, for the examined area, the directions that are chosen are all between 320 and 55o . As shown in **Figure 3**, in the case of ice coverage disappearance, the increase of the fetch length in some directions is up to three times longer than the one today (from presently 500 to 2000 km to the northern coast of Russia and from 200–250 to 1500–3000 km to the coasts of Canada and Alaska).

The calculation of the maximum characteristic wave height is made by using the Jonswap method. This method is chosen as it is judged appropriate for open sea waves and considers the influence of the fetch length. According to this method, a wind generated wave can be either fetch limited (limited by the available distance over which it has been generated) or duration limited (limited by the period of time that the wind is blowing).

In order to find the largest wave height that can occur due to the wind phenomena in the region, all the characteristic significant waves, Hs, for the directions of interest were assessed. In Svalbard, the examined directions were NNW, N, and NNE (North-Northwest 340°, North 0°, and North-Northeast 32.5°). Those directions were chosen because we wanted to cover as much as we could of the examined area for three different directions. For that reason, straight lines were drawn for each 2.5° with the use of maps from Google Earth (see **Figure 3**) until the opposite coasts were reached.

For each and every one of the three wind directions that were examined (NNW, N, and NNE), wind was assumed from an angle of 45°, that is, from −22.5 to +22.5o for each direction (usually the spreading used is 90°, but here, because of the limited examined area, we had to choose a smaller and more narrow area, the half). The fetch length, F, was drawn for every αi = 2.5° angle around each direction, and they are calculated by the following quation [5]:

$$F\_{\perp} = \frac{\sum\_{l=-N}^{N} F\_l \cos^2 a\_l}{\sum\_{l=-N}^{N} F\_l \cos^2 a\_l} \tag{1}$$

where N is the number of each fetch line drawn between −22.5 and + 22.5° for each of the three directions (NNW, N, and NNE).

The examined directions were chosen based on the morphology of the area; the islands and coasts of Greenland at the northwest part, for example, do not allow the development of long enough fetches to be considered.

#### **Figure 3.**

*Present maximum and minimum available fetch lengths north of Svalbard during early autumn periods (left). Future fetch lengths available in a free ice Arctic Ocean, between 320 and 55° in steps of 2.5°.*

*Arctic Studies - A Proxy for Climate Change*

summer and early fall [3] (**Figure 2**).

are similar from all directions.

The stations are as follows [4]:

• KARL XII (99935): Latitude: 80.653, Longitude: 25.008

• KVITØYA (99938): Latitude: 80.07, Longitude: 31.5

• HOPEN (99720): Latitude: 76.5097, Longitude: 25.0133

• KONGSØYA (99740): Latitude: 78.9277, Longitude: 28.892

• VERLEGENHUKEN (99927): Latitude: 80.059, Longitude: 16.25

**2. Methodology**

can be challenged due to higher waves generated by rapid storms and changing seafloor conditions. In the future Arctic Ocean, wave conditions like those will be

Moreover, the existence of ice on the sea surface makes the phenomenon of wave and ice interaction complex. Ice masses suppress waves, diminishing them, but also waves alter and influence the thickness and the growth of the ice. Waves start penetrates more and more into the weakened sea-ice reaching the marginal ice zone, the part of the ice cover that interacts with the open ice-free ocean. This loop produces a positive feedback that could accelerate the loss of ice especially during

As mentioned before, the aim of this chapter is not to execute an excessive assessment of the ice melting impact on the design wave heights, but rather stress and highlight the challenge that might occur in a worst-case scenario when there is no ice in the Arctic. In this way, one can have a better understanding of the magnitude of change that could be expected. These effects are also present, possibly in a less extend and locally, when there is a partial reduction of the ice surface and not total disappearance. The methodology chosen is based on the assumption that the Arctic Ocean in a free-ice period can be considered as a gigantic ocean, surrounded by the northern coasts of the neighboring countries. When one aims to estimate the characteristic wave height, two factors are the main contributors that need to be taken into consideration. One is the fetch length, the length of water over which a given wind can blow, and this is also the main factor that creates storm surge which also leads to coastal erosion and flooding. The other factor is the wind characteristics, such as duration and velocity. Thus, focus initially was given on areas that have the longest potential fetch distance, assuming that the wind conditions (duration and speed)

Taking all the aforementioned factors into consideration and also the available data and their quality, the northern part of Svalbard Island is chosen to be examined. As per now, this part of the Arctic region is covered by ice during most of the year, but in a free ice future scenario, long fetches are revealed that can potentially generate high waves. Moreover, statistical studies have showed that the percentage of north easterly winds occurring annually at the examined area is significant which testifies the relevance of the choice of location and direction for the study. Five different meteorological stations at the north and northeast area of Svalbard are selected to acquire the desired wind data. These data are analyzed to extract information regarding the most extreme wind incidents and storms from 2000 to 2014. The collected data refer to the early fall period of the year (September and October), as this is the period when the Arctic is expected to have the lowest ice percentage.

changing the known environment for nature and humans.

**28**

As long as the wind duration is considered, it is important to mention, here, that it would have been reasonable to have data with annual percentage of occurrence for each wind velocity in each direction. However, such data were not available; therefore, all the calculations are performed for specific events collected by the five stations over the past 15 years. So, for every fetch direction, one average wind speed is calculated. This means that every storm observed in the data is related to the three main directions (NNW, N, and NNE), and a mean wind velocity is calculated which is used to describe the wind at 10 m altitude.

Steps of the Jonswap method [5]:

*Step 1.* Calculation of the frictional wind velocity

Steps of the Jonesup method [5]:

Step 2. Calculation of the frictional wind velocity

$$u\_\* = W\sqrt{0.001(1.1 + 0.035W)}\tag{2}$$

where W = mean velocity at 10 m height.

*Step 2.* Calculation of the equivalent fetch, Feq, depending on the duration of the wind:

$$\frac{\text{g}\,F\_{aq}}{\text{u}\_{\ast}} = \,\,\,\,\,\,0.00523 \left(\frac{\text{g}\,t\_d}{\text{u}\_{\ast}}\right)^{1.5} \tag{3}$$

where g = gravity acceleration, 9.81 m/s2 ; td = the duration of the wind blowing; Feq = the equivalent fetch length.

*Step 3.* Checking whether the wave is duration or fetch limited:


*Step 4.* Calculation of the characteristic wave height

$$\frac{\text{g}H\_{\text{s}}}{\text{u}\_{\text{s}}^{2}} = \text{ } \text{ } \text{0.0413} \left(\frac{\text{g}F}{\text{u}\_{\text{s}}^{2}}\right)^{0.5} \text{ } \tag{4}$$

$$\frac{\text{g}\,H\_{\ast}}{\text{u}\_{\ast}^{2}} = \text{ } \text{ } \text{O.0413} \left(\frac{\text{g}\,F\_{aq}}{\text{u}\_{\ast}^{2}}\right)^{0.5} \text{ } \tag{5}$$

Hs = characteristic wave height.

*Step 5.* Calculation of the characteristic period of the wave

$$\frac{\text{g }T\_i}{u\_\*} = \text{ } \textbf{0.71345} \left( \frac{\text{g } F}{u\_\*} \right)^{0.33} \text{ } \tag{6}$$

**31**

**4. Discussion**

*Coastal Erosion Due to Decreased Ice Coverage, Associated Increased Wave Action…*

**Direction Fetch F (km)** North-Northeast 2661 North 3130 North-Northwest 2494

*Final fetch lengths for each examined direction in a future ice-free Arctic.*

*Final wave significant heights and characteristic periods in a future ice free Arctic.*

**Significant wave height and characteristic period**

**Significant wave height and characteristic period**

**W (m/s) td (hours) Fetch** 

*Final wave significant heights and characteristic periods in today's conditions.*

Eq. (1). This fetch is as expected in the case of an ice-free Arctic Ocean. Based on the aforementioned available fetch, the significant height of the waves together with the characteristic wave period was calculated and shown in **Table 2**.

**(km)**

NNW 16.60 90 160 630.51 Fetch limited 3.59 11.12 N 11.38 102 150 2418.72 Fetch limited 2.25 14.94 NNE 14.55 36 350 2307.72 Fetch limited 4.52 16.20

**W (m/s) td (hours) u\* Feq (km) Comment Hs (m) Ts (s)**

**Feq (km) Comment Hs (m) Ts (s)**

NNW 16.60 90 0.68 630.51 Duration limited 7.13 11.12 N 11.38 102 0.44 2418.72 Duration limited 9.03 14.94 NNE 14.55 36 0.58 2307.72 Duration limited 11.70 16.20

Since the aim of the chapter is to compare the waves of the future ice-free scenario with those of today, wave characteristic heights based on current conditions

All in all, the results show a significant increase of the height in the case of an ice-free Arctic Ocean. Actually, since the waves were duration limited, it is possible that such waves can be generated even with some permanent ice coverage. In detail, in the NNW direction, the wave height was almost doubled, from 3.59 to 7.13 m. In the North direction, the most significant change is observed with more than three times magnification of the characteristic height, from 2.25 to 9.03 m. Last, in the

The examined scenario of ice retraction should not be considered as topical only in the Svalbard area. Many measurements and experimental campaigns have

NNE direction, the prediction shows an increase from 4.52 to 11.70 m.

are calculated and shown in **Table 3**.

*DOI: http://dx.doi.org/10.5772/intechopen.80604*

**Final fetches for each direction**

**Table 1.**

**Wind direction**

**Table 2.**

**Wind direction**

**Table 3.**

Ts = characteristic wave period.

## **3. Results**

Based on the previous methodology, the results of the calculation are as shown below. **Table 1** is showing the maximum possible fetch distances, as calculated using *Coastal Erosion Due to Decreased Ice Coverage, Associated Increased Wave Action… DOI: http://dx.doi.org/10.5772/intechopen.80604*


**Table 1.**

*Arctic Studies - A Proxy for Climate Change*

is used to describe the wind at 10 m altitude. Steps of the Jonswap method [5]:

*u*<sup>∗</sup> = *W*√

*gFeq* \_\_\_\_

Feq = the equivalent fetch length.

height calculation.

*gHs* \_\_\_\_

*gHs* \_\_\_\_

Hs = characteristic wave height.

\_\_\_

Ts = characteristic wave period.

wind:

where W = mean velocity at 10 m height.

where g = gravity acceleration, 9.81 m/s2

*Step 1.* Calculation of the frictional wind velocity

As long as the wind duration is considered, it is important to mention, here, that it would have been reasonable to have data with annual percentage of occurrence for each wind velocity in each direction. However, such data were not available; therefore, all the calculations are performed for specific events collected by the five stations over the past 15 years. So, for every fetch direction, one average wind speed is calculated. This means that every storm observed in the data is related to the three main directions (NNW, N, and NNE), and a mean wind velocity is calculated which

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

*g td* \_\_\_\_ *u*∗ 2) 1.5

*Step 2.* Calculation of the equivalent fetch, Feq, depending on the duration of the

• If Feq > F, then the wave is fetch limited, and the fetch, F, of the specific direction (Eq. (1)), needs to be used for the calculation of the characteristic height, Hs.

• If Feq < F, then the wave is duration limited, and the Feq should be used for the

*gF*\_\_\_\_ *u*∗ 2) 0.5

*gFeq* \_\_\_\_ *u*∗ <sup>2</sup> ) 0.5

*gF*\_\_\_\_ *u*∗ 2) 0.33

<sup>2</sup> <sup>=</sup> 0.0413(

<sup>2</sup> <sup>=</sup> 0.0413(

*<sup>u</sup>*<sup>∗</sup> <sup>=</sup> 0.71345(

Based on the previous methodology, the results of the calculation are as shown below. **Table 1** is showing the maximum possible fetch distances, as calculated using

*<sup>u</sup>*<sup>∗</sup> <sup>=</sup> 0.00523(

*Step 3.* Checking whether the wave is duration or fetch limited:

*Step 4.* Calculation of the characteristic wave height

*u*∗

*u*∗

*Step 5.* Calculation of the characteristic period of the wave

*gTs*

0.001(1.1 <sup>+</sup> 0.035*W*) (2)

; td = the duration of the wind blowing;

(3)

(4)

(5)

(6)

**30**

**3. Results**

*Final fetch lengths for each examined direction in a future ice-free Arctic.*


**Table 2.**

*Final wave significant heights and characteristic periods in a future ice free Arctic.*


**Table 3.**

*Final wave significant heights and characteristic periods in today's conditions.*

Eq. (1). This fetch is as expected in the case of an ice-free Arctic Ocean. Based on the aforementioned available fetch, the significant height of the waves together with the characteristic wave period was calculated and shown in **Table 2**.

Since the aim of the chapter is to compare the waves of the future ice-free scenario with those of today, wave characteristic heights based on current conditions are calculated and shown in **Table 3**.

All in all, the results show a significant increase of the height in the case of an ice-free Arctic Ocean. Actually, since the waves were duration limited, it is possible that such waves can be generated even with some permanent ice coverage. In detail, in the NNW direction, the wave height was almost doubled, from 3.59 to 7.13 m. In the North direction, the most significant change is observed with more than three times magnification of the characteristic height, from 2.25 to 9.03 m. Last, in the NNE direction, the prediction shows an increase from 4.52 to 11.70 m.
