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Wave Life Cycle I: Generation

1. Introduction
1.1 Wave Life Cycle
1.2 Wave Growth
2. Wind Speed

2.1 Wind-Wave Creation
2.2 Wind Speed Limitations

2.2.1 Wind Speed Limitations (1 of 4): Wind Speed, Wave Speed and Wave Growth
2.2.2 Wind Speed Limitations (2 of 4): Simplified Deep Water Wave Speed Equation
2.2.3 Wind Speed Limitations (3 of 4): Duration and Wind Speed
2.2.4 Wind Speed Limitations (4 of 4): Question

2.3 Wind Speed Variability
2.3.1 Wind Speed Variability (1 of 2): Changes in Wind Speed
2.3.2 Wind Speed Variability (2 of 2): Question
3. Fetch

3.1 Definition
3.2 Fetch Boundaries
3.3 Fetch Limitations
3.4 Fetch Width

3.4.1 Fetch width (1 of 3): Impact of Fetch Dimension
3.4.2 Fetch Width (2 of 3): Wave-Wave Energy Transfer
3.4.3 Fetch Width (3 of 3): Large vs. Small Fetch Width

3.5 Fetch Length

3.5.1 Fetch Length (1 of 3): Changes in Fetch Length
3.5.2 Fetch Length (2 of 3): Question
3.5.3 Fetch Length (3 of 3): Question

3.6 Dynamic Fetch

3.6.1 Dynamic Fetch (1 of 8): Description
3.6.2 Dynamic Fetch (2 of 8): Dynamic Fetch Graph from MSC
3.6.3 Dynamic Fetch (3 of 8): Wave Speed vs. Fast Storm Speed
3.6.4 Dynamic Fetch (4 of 8): Wave Speed vs. Slow Storm Speed
3.6.5 Dynamic Fetch (5 of 8): Maximum Wave Growth
3.6.6 Dynamic Fetch (6 of 8): Wave Speed vs. Optimal Storm Speed
3.6.7 Dynamic Fetch (7 of 8): Dynamic Fetch Conceptual Animation
3.6.8 Dynamic Fetch (8 of 8): Model Forecasting

3.7 Dynamic Fetch Question

4. Wind Duration

4.1 Definition
4.2 Wind Duration Limitations
4.3 Wind Gusts
4.4 Factor Notes

5. Fully Developed Seas
5.1 Definition
5.2 Fully Developed Sea Limitations
6. Special Wind Events
6.1 Coastal Jet
6.2 Gap Winds
6.2.1 Definition
6.2.2 Gap Wind Example

6.3 Katabatic Winds
6.4 Instability Mixing
6.5 Ocean Current

7. Observations
7.1 Satellite Scatterometry
7.1.1 Scatterometry Operations
7.1.2 Scatterometry Theory
7.1.3 Radar Viewing Geometry
7.1.4Caveats
7.1.5 Limitations
7.1.6 QuikSCAT vs. Buoy
7.1.7 Where to Find Scatterometry Data

7.2. Buoys and C-MAN

7.2.1 Buoy Operations
7.2.2 Question

7.3. Ship Observations

7.3.1 VOS Program
7.3.2 VOS Data

8. Case Study

9. Module Summary

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1. Introduction

1.1. Wave Life Cycle

The life cycle of a wave starts when the wind interacts with the water surface and begins to create a disturbance. Here the wave is born and begins to develop. The wave grows and begins to move as the wind continues its forcing. Eventually the wave moves outside of the area of initial wind forcing and propagates across the water until breaking on a distant shore.

Except for tides and tsunamis, nearly all waves are born from wind blowing over and interacting with the water surface. This module will discuss the process of wind-wave generation and the factors that limit wave growth. Wave propagation and dispersion will be covered in the third module of this series.

As discussed in the first module of the Wind and Waves series titled Wave Types and Characteristics, the main parts of a wave are its height, length, and period. The height is the distance between the wave's trough and crest. The length is the distance between two troughs or crests. The period is the time it takes for the wave length to pass by a point.

Parts of a Wave

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1.2. Wave Growth

There are three basic components to wave growth:

Fetch is the distance over which the wind blows from a constant direction and at a constant speed. Duration is how long the wind affects that distance. This module will discuss how fetch and duration relate to wave growth in deep water. Shallow water wave processes will be discussed in a separate module.

The Wave Analysis and Forecasting Nomogram quantitatively illustrates the relationship between wind speed, wind duration, fetch length, and wave growth. Wind speed is charted on the y-axis and fetch length on the x-axis. Contour lines represent wind duration, wave height and wave period. The nomogram will be used throughout this module to help easily visualize these types of relationships.

Wave Analysis and Forecasting Nomogram

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2. Wind Speed

2.1 Wind-Wave Creation

A capillary wave has a wavelength of less than approximately 1.7 centimeters. The exact process of how wind initially creates capillary waves on a smooth water surface is not precisely known, but there are two widely recognized mechanisms that force growth once a wave is larger than capillary size. One is form drag and the other is frictional drag. Once the wave has been created, the wind flowing over the wave can continue to help it grow. Notice the eddy on the leeward side of the wave in the graphic. Form drag occurs when the eddy creates a localized low pressure on the leeward side of the wave, thus allowing the leading edge of the wave crest to increase in height. On the windward side of the leading wave, frictional drag occurs as localized high pressure is created. In essence, the leading edge of the wave crest is lifted up while the leading edge of the wave trough is pushed down and overall wave height is increased.

Wave Sheltering Effect

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2.2 Wind Speed Limitations

2.2.1 Wind Speed Limitations (1 of 4): Wind Speed, Wave Speed and Wave Growth

As soon as the wind speed and wave speed are equal, the downward force on the windward side of the crest and the upward force on the leeward side of the crest will no longer exist. Essentially wave growth will not occur when the wind speed is less than or equal to the wave speed.

2.2.2 Wind Speed Limitations (2 of 4): Simplified Deep Water Wave Speed Equation

Remember that wave speed in deep water can be simplified in terms of wavelength (L). Since wavelength is not easily measured by buoys we use the general wave speed equation to substitute for wavelength in terms of wave period, which is regularly measured and reported.

From here further simplification of the equation reveals that wave speed in deep water is equal to 1.56 meters per second squared times the period. A conversion of the constant to knots is performed so that the wave speed will be in the same units as the wind speed. The result is that the wave speed is approximately equal to three times the wave period.

Wave Speed Equation

2.2.3 Wind Speed Limitations (3 of 4): Duration and Wind Speed

Here are some examples of individual wave speeds for various wave periods at a constant wind speed. Notice that for higher wind speeds a longer duration is needed for the wave speed to equal the wind speed.

Table of wind durations for various wave speeds and periods

2.2.4 Wind Speed Limitations (4 of 4): Question

Using the simplified deep-water wave speed equation C=3T, identify the model times when wave growth will occur for wind and waves moving in the same direction.

Forecast
Hour

Day/Hour
(UTC)
Wave
Period (s)
Wind
Speed (kt)
C~3T
00
22/09
8
8
 
03
22/12
8
5
 
06
22/15
4
13
 
09
22/18
5
16
 
12
22/21
6
20
 
15
23/00
8
16
 
18
23/03
7
13
 
21
23/06
7
10
 
24
23/09
7
10
 


Answers:

Notice that as the wind speed increases during the middle of the forecast, the wave period also increases. Comparison of the wind speed and the calculated wave speed shows that the wind speed is greater than the wave speed during these three forecast periods, indicating wave growth. For the first six hours and the last nine hours of the forecast, however, the wind speed is less than the calculated wave speed, indicating that the primary waves forecast in those times are not being generated by the wind, but instead are passing swell.

Forecast
Hour

Day/Hour
(UTC)
Wave
Period (s)
Wind
Speed (kt)
C~3T
00
22/09
8
8
24
03
22/12
8
5
24
06
22/15
4
13
12
09
22/18
5
16
15
12
22/21
6
20
18
15
23/00
8
16
24
18
23/03
7
13
21
21
23/06
7
10
21
24
23/09
7
10
21
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2.3 Wind Speed Variability

2.3.1 Wind Speed Variability (1 of 2): Changes in Wind Speed

Waves are constantly entering and leaving wave generation areas. If a wave moves into an area where the wind speed is slower than the wave speed, the wind will have no effect on the wave. But if the wave moves into an area where the wind speed is greater than the wave speed, the wave will grow.

Observe what happens when the wind over a fetch blows for 24 hours at 15 knots. The intersection of the 24 hour duration line and the 15 knot wind speed occurs at a wave height of 4.5 feet and wave period of 5 seconds. Using the simplified deep water wave speed equation of C=3T, a period of 5 seconds gives approximately 15 knots for the wave speed, which is equal to the wind speed. To see what happens if this wave moves into an area with a wind speed of 25 knots for another 24 hours, follow the wave height line until it reaches the 25 knot wind speed line. Next, follow the 25 knot wind speed line for 24 hours. In this case, the start point is around the 3.5 hour duration line. Adding 24 hours to that duration gives a final duration of approximately 28 hours. The nomogram demonstrates that increasing the wind speed to 25 knots for an additional 24 hours causes the wave height to increase to approximately 11 feet. Remember that decreasing the wind speed has no effect on the waves created in the original generation region. If these waves move into an area where the wind speed is less than 15 kt, they continue to have a wave height of 4.5 feet, but are considered swell since they have moved outside of the original generation area.

ve Nomogram showig wind speed change

Click here to see the nomogram animation.

2.3.2 Wind Speed Variability (2 of 2): Question

Using the wave nomogram, answer the following question:

If a wind blows over an 80 nautical mile fetch at 13 knots, generating a wave that then moves into an area with 18 knot winds for another 16 hours, what would the resulting wave height be?

a) 4 ft
b) 6 ft
c) 8 ft
d) 10 ft

The correct answer is b). The intersection of the 80 nautical mile fetch line and the 13 knot wind speed line gives a wave height of approximately 3.5 feet. To obtain the new height of the wave when it moves into an area with 18 knot winds for 16 hours, we must follow the 3.5 wave height line up to the 18 knot wind speed line and then add 16 hours to the duration from that point. The new wave height under these conditions would be 6 feet.

Wave Analysis and Forecasting Nomogram

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3. Fetch

3.1. Definition

Fetch is the distance over which the wind blows from a constant direction and at a constant speed. Winds that abruptly speed up, slow down, or change direction significantly would constitute the need for a new fetch to be determined. It is important to realize that waves of some type will already exist in the new fetch region. Using the wave nomogram or some other application may tell you the maximum height that the waves in the new fetch region will reach, but the timing of that maximum will depend on the height of the waves entering the new fetch.

Understanding how the fetch region is changing or how many different fetch regions exist can help the forecaster confirm that the numerical wave models are correct in their analysis and forecasts.

Fetch with change in direction and change in speed

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3.2. Fetch Boundaries

In this example of surface winds over the Gulf of Alaska, several fetches can be seen. The ovals denote just a few of the possible fetches. When evaluating fetch, a forecaster only needs to be concerned with the fetches that will propagate waves into the forecast area. There are no set guidelines to determine the fetch boundary since changes in wind speed and direction can be fairly subtle over open water. Just remember that once the wind speed decreases or wind direction begins to change, the wave will no longer grow.

Surface winds in the Gulf of Alaska

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3.3. Fetch Limitations

While wind speed is the ultimate limiting factor of wave growth, growth is also limited by the size of the fetch region. Fetch size can be constrained primarily by land mass blocking and wind area.

An example of land mass blocking occurs in the Great Lakes. Here the water surface area is limited so the fetch can be no larger than the long axis of the lake itself.

Map of Lake Michigan

Another example is a west wind along the Atlantic Coast of the United States. In this case the nearshore waters have a small fetch which severely limits wave growth.

QUIKSCAT winds over the Gulf of Mexico and Eastern Seaboard

The extent of the wind area is another way to limit fetch. If the wind is generated by a mesoscale event such as an outflow boundary from a thunderstorm, the fetch will be of a small size.

Outflow boundary over the Gulf of Mexico
Click here to see the outflow boundary animation.

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3.4. Fetch Width

3.4.1. Fetch Width (1 of 3): Impact of Fetch Dimension

A fetch is like a snowflake in that no two are alike. Some fetches are long and narrow while others are short and wide. The dimensions of the fetch have an impact on wave growth by determining the amount of wave energy that stays within the wave generation area. Within the fetch a general wind direction can be determined, but many small variations will occur. This means that there are smaller waves created that propagate out of the sides of the fetch region while the predominant wind direction generates larger waves that exit from the downwind end of the fetch.

Note that the winds exiting the side of the fetch would have a greater distance within which to grow if the fetch width increased.

Wave growth within a fetch

Click here to see the fetch wave growth animation.

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3.4.2. Fetch Width (2 of 3): Wave-Wave Energy Transfer

Within the fetch there is a wave-to-wave energy transfer. This is what helps build the larger waves. Wave energy also bleeds out the sides of the fetch due to wave spreading. Compare fetches of different widths. Fetch B covers three times the area of Fetch A. While the same amount of energy is dissipated from the sides of both fetches, the amount lost as a percentage of the fetch's total energy is larger in fetch A. Therefore a narrower fetch will result in smaller waves.

Energy Loss in small versus large fetch areas

Click here to see the fetch energy animation.

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3.4.3. Fetch Width (2 of 3): Large vs. Small Fetch Width

It is important to analyze the width of the fetch area. Imagine a narrow fetch and winds within that area. If the winds turn slightly, one might define a new fetch because the uniformity of the winds has been broken. However, with a wide fetch the slight turning of the winds is much less significant to the overall uniformity of the area and a single fetch could still be defined.

Comparison of Large and small fetch areas

Click here to see the fetch dimensions animation.

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3.5. Length

3.5.1 Fetch Length (1 of 3): Changes in Fetch Length

When a fetch changes because the wind speed or direction changes, the waves within the fetch stop growing. A new set of waves begins to grow based on the characteristics of the new fetch. The original waves begin to propagate out of their fetch generation region. But what happens when the wind speed and direction remain the same, but the fetch length increases?

Looking at the wave nomogram shows that a 5 ft wave can be created by a 25 kt wind after just 20 n mi. If conditions change and this fetch length is increased by 60 n mi, then the wave can reach a height of 8 ft. Notice that the change in fetch length has its greatest effect on wave height for small fetches. When a given wind speed has persisted over a long distance, wave height changes due to increases in fetch length are fairly small.

Wind Wave Nomogram and changes in fetch length

3.5.2 Fetch Length (2 of 3): Question

Using the wave nomogram, answer the following question:

If a wind blows over a 10 nautical mile fetch at 21 knots, what would the resulting wave height be?

a) 2 ft
b) 3 ft
c) 6 ft
d) 8 ft

Answers: b), 3 ft. Locate the intersection of the 10 nautical mile fetch on the x-axis and the 21 knot wind speed line on the y-axis. This gives a wave height of approximately 3 feet.

3.5.3 Fetch Length (3 of 3): Question

Using the wave nomogram, answer the following question:

What would cause the larger increase in wave height for this situation: increasing the wind speed by 60 knots or increasing the fetch length by 60 nautical miles?

a) Increasing the wind speed by 60 kt
b) Increasing the fetch length by 60 n mi

Answer. The correct answer is a). Increasing the wind speed by 60 kt would increase the wave height to approximately 15 feet. Increasing the fetch length by 60 n mi would increase the wave height to approximately 6 feet. Therefore, increasing the wind speed would cause a larger increase in wave height.

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3.6. Dynamic Fetch

3.6.1. Description

When storm systems move, waves in the right quadrant, or right of track, may grow larger than expected because the waves are moving in the same direction as the advancing fetch. The graphic demonstrates a tropical cyclone with a straight storm path and a fetch in the right of track outlined with a dotted white line. The waves in this outlined fetch area are affected by the fetch winds longer, which leads to continued growth. The distance over which the waves actually grow is called the effective or dynamic fetch, shown in the graphic by a purple rectangle.

Dynamic Fetch

Click here to see the dynamic fetch introduction animation.

The dynamic fetch length may be different than the stationary fetch length measured within an identical stationary storm system. In addition to the stationary storm factors of wind speed, duration, and fetch, the assessment of dynamic fetch requires knowledge of an additional factor: the translation speed, or storm speed, of the wave-generating cyclone. There is a non-linear relationship between all of these factors, which makes the forecasting of wave heights in dynamic fetch situations a complex problem.

First, let's look at a tool that allows forecasters to estimate the degree of dynamic fetch that will occur for a given set of storm parameters. Then, using this tool, one can determine if dynamic fetch will lead to wave heights that are different than expected.

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3.6.2 Dynamic Fetch Graph from MSC

The Meteorological Service of Canada Atlantic Storm Prediction Centre in Dartmouth, Nova Scotia, has developed a tool that allows forecasters to see the potential effects of dynamic fetch in a storm system. The following is a description of the graphical output of this tool.

The user inputs the fetch area wind speed, the wave generation fetch length, and the storm speed. For this chart the user has input 70 knots for the wind speed, 50 nautical miles for the fetch length, and 15 knots for the storm speed, referred to on the chart as "motion." These parameters are similar to what would be found just outside the center of a category 1 hurricane. Notice that the graph is similar to a histogram in that time is on the y-axis while distance is on the x-axis. Unlike the traditional histogram, the time moves forward going up the y-axis. The red box represents the fetch length entered by the user, which stays constant as time increases. The height of the red box has no relevance. The leading edge of the fetch box is on the right and the trailing edge is on the left. One can imagine the wind blowing from left to right across the fetch in the graph, with the distance on the x-axis representing the movement of the fetch area over the time period on the y-axis. Inside the fetch box, the positions of each wave are represented by a star and are placed at intervals of 10 nautical miles.

A line is drawn through the position points of a given wave as it moves in time. This helps the user see how many of the waves remain growing within the fetch region and how their relative position within the fetch is changing over time. The wave position number is shown when the wave falls outside of the fetch region. From 0 to 1 hour, the fetch box has moved 15 nautical miles, corresponding to the input storm speed of 15 knots. The wind speed is used to determine the change in wave height and period, and hence the corresponding wave speed, as well as distance traveled in this one hour span. Notice that both the fetch box and the waves have moved to the right, but the position of the waves within the fetch box has also changed. At one hour the wave in position 6 has moved outside of the fetch region and is no longer growing. The remaining five waves are still in the fetch area but their positions have moved toward the trailing edge of the fetch. In essence, the fetch is moving faster than the waves it is generating. As time increases the wave positions continue to change until they all are either outrun by the fetch or move ahead of the fetch. In this case, the waves that initially started at positions 5 and 6 have been outrun by the fetch region, while those that started in positions 1 through 4 have sped up and moved out ahead of the fetch area. Remember that we are looking at only one set of waves that have started at time zero, while in the real world waves are constantly being generated throughout the entire time period.

3.6.3 Wave Speed vs. Fast Storm Speed

In order to assess wave growth in a dynamic fetch event, the forecaster must determine how long the waves will remain in the fetch area that is moving parallel to the track of the cyclone. In some instances the storm speed will be faster than the wave speed, and the waves will not remain in the fetch area for a long period of time. Such fast-moving systems may quickly outrun the waves they generate even if the dynamic fetch length is less than the stationary fetch length. Examine this graph where the cyclone is moving at 25 knots and has a 65 knot wind speed over a 60 nautical mile fetch. After just 5 hours, all of the waves have fallen behind the quickly moving cyclone. Examining the distance that the waves traveled before being outrun by the system reveals that the wave in position 1 is the only wave to have stayed in the fetch area for the entire 60 nautical miles. Because waves in positions 2 through 7 are effectively influenced by a shorter fetch length, their resulting wave heights are less than if the storm system were stationary. In other words, their resulting wave heights are less than what the Bretschneider wave nomogram would predict.

Dynamic fetch: distance vs. elapsed time. Winds 65 knots, fetch 60 nautical miles, storm speed 25 knots

3.6.4 Wave Speed vs. Slow Storm Speed

Similarly, a slow-moving system may be outstripped by the waves it creates. The graph shows the same cyclone with a much slower storm speed of 5 knots. In this case waves starting in positions 5 through 7 remain in the fetch area for a longer time compared to a stationary storm system with the same fetch length and wind speed. Therefore, the cyclone and these generated waves are said to be "resonant" to some degree. This resonance between storm speed and wave speed leads to wave heights that are greater than the Bretschneider wave nomogram would predict. However, waves starting in positions 1 through 4 will have wave heights that are equal to or less than that determined from the wave nomogram. These waves move ahead of the cyclone fairly quickly and propagate away as swell before the entire 60 nautical mile fetch can act on them.

Dynamic fetch: distance vs. elapsed time. Winds 65 knots, fetch 60 nautical miles, storm speed 5 knots

When there is less wave growth than for a comparable stationary fetch, the cyclone and the generated waves are said to be "dissonant." If the forecaster can assess how long the waves will remain in harmony with the moving storm system, a traditional wave growth calculation can be performed using the dynamic fetch length and duration.

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3.6.5 Maximum Wave Growth

When the cyclone and waves move at speeds that are resonant, the dynamic fetch can be considerably larger than its stationary counterpart. Many forecasters make the mistake of assuming that wave speed and storm speed must increase at the same rate in order for dynamic fetch to occur. In reality, only small subsets of storms move this way. In the case of tropical cyclones, studies have shown that the dynamic fetch waves at the leading edge of hurricanes travel 30 to 150% faster than the storm itself. Examine the animation below to see why this is true. Optimal dynamic fetch situations result from waves originating at the leading edge of the storm, then losing ground to the more quickly advancing system, then speeding up before the trailing edge of the fetch passes them by, and finally accelerating back through the fetch to the leading edge once again. The dynamic fetch length of the leading edge wave is again represented by the purple rectangle. If the storm motion remains constant, then this scenario reaches a steady state of high fast-moving waves at the storm's leading edge. Notice that the wave at the leading edge has the largest height and is outrunning the stationary fetch area shown by the dotted white rectangle.

Optimal Dynamic Fetch

Click here to see the dynamic fetch animation.

3.6.6 Wave Speed vs. Optimal Storm Speed

Dynamic fetch wave growth can be illustrated by taking the cyclone from the previous example and setting the storm speed to 20 knots. Notice that all of the waves are outrun by the cyclone except for the wave starting closest to the leading edge of the fetch. This wave grows as its position in the fetch lags toward the trailing edge. As the wind continues to influence this wave, its height and period increase. Remember that in deep water the wave speed is dependent on the wave length, and hence the period. Therefore, as the period increases, the wave speed increases as well. At some point between 11 and 13 hours the wave and fetch have nearly the same speed and continued growth causes the wave to accelerate forward through the fetch area and out the leading edge.

Dynamic fetch: distance vs. elapsed time. Winds 65 knots, fetch 60 nautical miles, storm speed 20 knots

To best illustrate how optimal dynamic fetch occurs, it's helpful to look at the conceptual animation and the graph side by side. Each image shows the same seven waves that start in the fetch area. The fetch box on the graph is highlighted to show the corresponding time within the animation. Notice how quickly waves 3 through 7 are outrun by the storm system. Wave 2 experiences a small degree of dynamic fetch, but it is wave 1 that eventually equals the speed of the system by the time it reaches the trailing edge of the fetch. It then continues to grow as it accelerates back through the fetch and out the front edge.

Dynamic Fetch - Optimal Storm Speed

Click here to see the optimal storm speed animation.

If a forecaster's criteria for the occurrence of optimal dynamic fetch is that storm speed and wave speed be equal, they will actually be focusing on storms that move too quickly. In fact, the storm and waves are often dissonant in such cases, resulting in wave heights being smaller than anticipated.

3.6.7 Dynamic Fetch Conceptual Animation

Dynamic fetch frequently affects the offshore waters of Canada when a tropical storm curves to the northeast and moves along the U.S. Atlantic seaboard. Examine the image presented here. The fetch to the right of the storm path is highlighted.

Initially, as the storm curves, groups of wind waves are shown developing in this fetch. These waves have varying paths due to the curving motion of the storm and will impact different parts of the U.S. East Coast.

As the storm path straightens, wave growth from dynamic fetch begins to occur. For this illustration there are four groups of waves inserted consecutively just after the tropical cyclone begins moving in a straight path. Remember that waves are constantly being generated in all areas of a real tropical storm as it moves, but for illustration purposes most are not shown here. As the storm moves most of the waves lag behind the quickly moving system. Eventually, the waves from each of the four initial groups can be seen moving back through the fetch area and then ahead of the system.

Keep in mind that dynamic fetch waves are moving faster than the other waves generated by the storm and are preceded by comparatively smaller waves, giving little warning of impending arrival of the larger dynamic fetch waves. This is shown by the sharp gradient in wave height that occurs ahead of the system and the rather weak gradient in the wake of the system.

To see if dynamic fetch could occur with various combinations of wind speeds, fetch lengths, and storm speeds, use the Dynamic Fetch link below.

Wave Growth Within Dynamic Fetch

Click here to see the dynamic fetch animation.

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3.6.8 Model Forecasting

Assessing the sensitive thresholds for these parameters within tropical cyclones can be complex. In addition to the manual dynamic fetch tool just discussed, the Canadian Hurricane Centre has developed a dynamic, or trapped, fetch wave model which uses data from a parametric hurricane wind model. The trapped-fetch model runs quickly because it works on the assumption that only one spectral mode exists in dynamic fetch situations and simple wave growth formulations are sufficient. Changes in forecast track and intensity can be re-input to the trapped-fetch wave model with new output available in a matter of seconds.

Dynamic fetch model output

Forecasters need to be able to identify when a fetch is moving with the wind and parent storm system. When fetch movement, wind direction, and storm movement are in line, greater than expected wave growth will result.

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3.7 Dynamic Fetch Question

Using the plot of various mid latitude and tropical storms, identify which paths are most likely to develop dynamic fetch generated waves.

Map of continental US showing 6 different storms

Click here to see the storm animation.

A - Pacific Tropical Storm
B - Gulf Coast Tropical Storm
C - Atlantic Tropical Storm
D - Aleutian Low
E - Polar Low
F - Nor'easter

The correct answers are B, C, D, and F. However, this graphic does not depict the wind strength and storm speed associated with each choice. These two factors as well as the fetch length all need to be in harmony to some degree for dynamic fetch to occur. Even the acceleration of the storm is important, but the goal of this question is to review situations where dynamic fetch is more likely. An explanation for each choice follows.

Pacific tropical storms (A) that recurve and hit the west coast of North America typically do not travel in a straight path long enough for dynamic fetch to occur. While less likely, there is potential for some enhancement to wave growth from a dynamic fetch prior to the storm's recurving. These waves would move to the left of the path and out to sea as decaying swell, affecting mariners outside of the coastal and offshore zones. They could pose a threat since they are not "announced" by leading swell that gradually increases in height.

A Gulf Coast tropical storm (B) that passes between the Yucatan Peninsula and Cuba could move along a path conducive to dynamic fetch even though the distance before landfall is relatively short. Hurricane Ivan in 2004 had such a path and a record-setting measurement for significant wave height (52 ft) was recorded by NDBC buoy 42040, located about 75 miles southwest of Dauphin Island, Alabama. However, the buoy only recorded maximum sustained winds of 63 mph. The wave nomogram suggests that a fetch of approximately 500 n mi would be needed at that wind speed to reach a 52 ft wave height. Given the smaller fetches associated with tropical storms, dynamic fetch may have played a role in developing of that wave as well as the non-measured waves which surely exceeded the 52 ft averaged wave height. Output from the Canadian Trapped Fetch Model confirms that dynamic fetch generated waves of 17 meters, or about 55 feet, were predicted to occur.

Canadian trapped fetch model output

Atlantic tropical storms (C) that recurve before making landfall often develop a dynamic fetch as they travel toward the Canadian Maritime Provinces. Prior to this, the path can be sufficiently curved as the tropical storm turns from a westward to a northeastward direction, limiting the wave growth due to dynamic fetch. However, there are cases, such as Hurricane Bonnie in 1998, where dynamic fetch occurred while the storm moved westward, before recurving to the northwest. Again, the storm speed, path, and strength were key factors. Dynamic fetch waves in this case would have traveled toward the Bahamas while the storm moved toward the U.S. East Coast. These waves might have led to high surf and rip current conditions in the Bahamas. These hazardous conditions can catch beachgoers off guard since the storm has moved away and fair weather conditions exist at the time that the swell arrives at the beach.

Canadian Trapped Fetch Model Ooutput for Hurricane Bonnie 1998

The Aleutian low (D) shown here is fairly straight and could produce dynamic fetch. Aleutian lows continually impact the west coast of North America and their potential for creating dynamic fetch varies depending on the path of the storm, the storm speed, and wind speed.

(E) The winds associated with this polar low affect the Great Lakes. In this example, notice that the winds to the right of the path would flow parallel to the long axis of Lake Erie and Lake Ontario, The long axis of Lake Erie is around 195 n mi (~ 225 mi) while Lake Ontario's long axis is approximately 150 n mi (~ 175 mi) Therefore, dynamic fetch is not a large concern. For either of these lakes to experience dynamic fetch, storm size is an important factor. Let's look at a storm with 40 kt winds and a storm speed of 10 kt and then vary the fetch length from 10 to 20 n mi.

Dyanmic fetch, distance vs. time, winds 40 knots, fetch 10 nautical miles, storm speed 10 knotsDyanmic fetch, distance vs. time, winds 40 knots, fetch 10 nautical miles, storm speed 10 knots

For the 10 n mi fetch case, a maximum wave height of 4.7 m occurs after 9 hours and an effective distance of 92.1 n mi. In contrast, the 20 n mi fetch case for the same storm speed and wind speed results in a maximum wave height of 5.4 m after 12 hours and 132.9 n mi. This is a 33% increase in time and a 43% increase in distance before waves exit the front of the fetch and cease growing. This is a relatively large increase in time and effective distance necessary to generate maximum wave height given the fetch limitations of the Great Lakes. In addition the wind direction for the 20 n mi case would need to be nearly parallel to the long axis of Lake Ontario for the entire 12 hour period. If a polar low were to occur with a relatively smaller fetch length, it would allow a greater range of wind directions and fetch positions over the Great Lakes that could produce dynamic fetch. Notice that the optimal storm speeds for the 10 and 20 n mi fetch cases are 10.5 and 12 kt respectively. Also note the differences in optimal duration and effective fetch for these two cases.

Storm Speeds for 40 kt Wind (10 and 20 n mi) Fetch

Interestingly, the optimal effective fetch length for the 20 n mi case is greater than the long axis of either Lake Erie or Lake Ontario. Given that the Great Lakes are very fetch limited, it is unlikely that a storm of proper size, path, speed, and strength will develop that produces dynamic fetch.

(F) The nor'easter path is entirely over North America until reaching the North Atlantic. However, a nor'easter can occur close enough to the coast to have its winds affect the offshore waters. If the storm is large enough to maintain a consistent path, dynamic fetch could occur to some degree.

To see the potential of dynamic fetch for a range of different conditions, view the Dynamic Fetch Charts. These charts provide graphs of fetch and wave group movements previously shown in this section of the module. It includes the dynamic fetch wave height expected as well as the ratio of dynamic fetch wave height to relatively stationary fetch wave height.

Click here to see the Dynamic Fetch Charts.

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4. Wind Duration

4.1. Definition

We have seen how wind speed and fetch affect wave growth. Now we will investigate the third wave growth factor-wind duration. Duration is the length of time a wind in a given fetch affects wave growth. Given a high wind speed and long fetch length, the longer the wind blows, the larger the waves will grow.

Wave height for constant wind speed and fetch

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4.2. Wind Duration Limitations

Even with sufficient wind speed and fetch length the duration can be the limiting factor in wave growth. This can occur with fast-moving storms where the area of strong prefrontal winds is aligned with the angle to the general storm direction. In this case the fetch is constantly affecting a different part of the water surface for a short period of time.

duration limitation to wave generation

Click here to see the limits of wind duration on wave generation animation.

Mesoscale events are usually of short duration. These can include thunderstorm outflow boundaries, sea breezes, and land breezes. Strong, long-lived wind events can have a fetch persist for days, but if the fetch is moving perpendicular to the storm direction, the duration over any given area of water will be short. This can occur on the leading and trailing sides of hurricanes or around deep synoptic-scale lows.

Events with duration limitations

Click here to see the mesoscale event animation.

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4.3. Wind Gusts

A wind gust by itself is generally of insufficient duration to significantly contribute to wave growth. However, wind gusts can be a factor in wave growth if they occur frequently. The contribution of wind gusts is difficult to quantify but the overall effect is the generation of larger waves than expected. Some models, such as the NOAA WaveWatch III, do take gusty winds into account qualitatively, and forecasters should expect to see significant wave heights that are slightly larger than normal when gusty conditions exist.

AWIPS buoy and Ship obs, 1200 UTC 8 Oct 2003

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4.4 Factor Notes

At this point we have discussed each of the three wave growth factors and their limitations. While each is important to consider, their relationships to wave height are not equal. The effect on wave height is most sensitive to changes in wind speed, even for fetch limited or duration limited cases. Note that fetch width is a distant fourth in importance compared to these other factors. Therefore, when looking for areas of significant wave generation, wind speed should be the first factor to consider, followed by the fetch length and wind duration. Another way to look at it, is that increases in wind speed can more easily overcome the wave growth limitations of duration and fetch length. This highlights an important part of marine meteorology and numerical modeling: An accurate wind forecast is essential to an accurate wave forecast.

5. Fully Developed Seas

5.1. Definition

A fully developed or fully arisen sea describes a sea state in which the wave's characteristics are not changing. Provided the wave growth is not limited by fetch length or duration, wave growth eventually reaches equilibrium where the energy given to the waves by the wind equals the energy dissipated by the waves through dispersion and breaking.

High seas as seen through a porthole

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5.2. Fully Developed Sea Limitations

Ultimately wave growth is determined by the wind speed. The wave height is generally limited by the fetch length and wind duration for strong wind speeds. It is difficult for a fully developed sea to occur with wind speeds of 40 kt or greater because the fetch length and duration needed to create unchanging waves is relatively large. Even winds at 25 kt will need a moderate amount of time to become fully developed. It is much more likely for winds of 15 kt or less to produce fully developed seas since a much shorter fetch length and duration are needed. The stronger winds that affect many of the oceans and large lakes will not be able to reach their potential in terms of wave height generation due to changing or limiting fetch length and duration.

Point of fully developed seas for 12, 25 and 40 knot winds

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6. Special Wind Events

6.1. Coastal Jets

Low-level coastal jets occur along some coastlines due to the presence of low-level baroclinic structures. These winds may exceed 35 kt, leading to high waves and a potentially significant impact to marine interests along the coast and just offshore. Coastal jets also lead to significant low-level vertical wind shear, thus presenting a hazard to aviation in the coastal zone. Wind speeds are generally higher offshore than over land, and this difference persists throughout the day. On this particular day, land stations show 5 to 10 kt winds while coastal buoys have winds of 15 to 25 kt depending upon where along the California coast we look. There is little diurnal variation in offshore winds.

MSLP winds and isotachs over 20 knots for EAT 12 hr forecast valid 0000 UTC 22 August 1999

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6.2. Gap Winds

6.2.1. Definition

Gap winds are low-level winds that are associated with gaps or low areas in terrain. Gap winds can range in width from hundreds of feet to over one hundred miles. In unusual circumstances they can be associated with winds exceeding 50 kt. These winds are normally quite shallow, extending hundreds of feet to a few thousand feet above the surface. Large changes of wind, or wind shear, are found at their upper and lateral boundaries.

Synthetic aperture radar image showing gap winds over the Straight of Juan de Fuca

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6.2.2. Gap Wind Example

One example of the effect of gap winds on wave growth occurs in the Gulf of Tehuantepec. Chivela Pass, a gap that has both important atmospheric and oceanographic effects, cuts through the Sierra Madre of Mexico. The gap is approximately 120 n mi long, 20 n mi wide, and has a maximum elevation of only 820 ft. It provides a path for air to flow from the Bay of Campeche in the southern Gulf of Mexico to the Gulf of Tehuantepec in the Pacific Ocean.

Map of Chivela Pass and the Gulf of Tehuantepec

During the winter when cold, high pressure systems move southward along the eastern slopes of the Rockies and the Sierra Madre Mountains, a large pressure gradient can build across the gap. This results in strong northerly winds, known as Tehuantepecers, immediately downstream of the Pass. Tehuantepecers can reach 20 to 40 kt, with gusts exceeding 100 kt in extreme cases.The strong, persistent winds from Tehuantepecers can create waves that may propagate as swell as far south as the Galapagos Islands, nearly 1000 miles away.

QuikSCAT winds through Chivela Pass and on the Gulf of Tehuantepec

This and other strong, persistent atmospheric gap flows can have a significant influence on the nearby coastal waters. The strong winds that blow through the Chivela Pass result in substantial upper ocean mixing causing sea surface cooling of 10 to 13 degrees Celsius (8 to 14 degrees Fahrenheit).

SST and scatterometer winds over Central America

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6.3. Katabatic Winds

Katabatic winds are caused by gravitational flow of cooler air from higher surrounding terrain. Their effect on wave growth occurs more often in northern latitude coastal areas where high terrain is near the coast. They are similar to gap winds in that winds flowing offshore will be mesoscale in nature. Katabatic winds are very fetch- and duration-limited. Therefore, even strong winds from a katabatic event may have only a small effect on wave growth. Down slope winds will be strongest in a dry climate with high terrain when night skies are clear and winds aloft are weak.

Illustration of katabatic winds

Click here to see the katabatic wind animation.

Regional Note: Glacier Winds

Glacier emptying into sea

A type of katabatic wind that occurs in high latitude regions is referred to as a "glacier wind". These winds develop over glacier or snow fields located on high terrain. Unlike the katabatic wind just described, cold air is continually generated over these areas, and therefore affects winds both day and night. The wind strength is determined by the temperature contrast between the glacially cooled air and the surrounding environment as well as the distance that air travels over the glacier. For mariners in Alaska or northern Canada, these winds may cause choppy seas near locations where glaciers are in close proximity to the coast.

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6.4. Instability Mixing

Significant differences between water and air temperature can cause instability in the marine boundary layer and hence contribute to the development of stronger winds at the surface.

In the Great Lakes and other inland bodies of water, instability effects can be more important than pressure gradient forces in determining wind speed since water temperature variations can exceed those found over oceans. However, there are also many areas along the coast that experience instability in the marine boundary layer. If the air is cooler than the water, heat and moisture fluxes from water to air will destabilize the layer of air just above the water surface. The larger the difference in air and water temperature, the deeper the unstable layer becomes. The instability lends itself to convective motions and hence mixing between adjacent layers. This causes a direct transfer of higher wind speeds from the marine boundary layer to the surface of the water. These stronger, mixed winds will be more uniform in direction and speed and will increase the stress on the water surface.

These instability effects are most prevalent in the fall when water temperatures are still warm from summer heating but air temperatures have decreased. As shown in this plot of surface observations in the Great Lakes region, there is an air-water temperature difference of at least 10°F over the lakes. Notice that winds over land diminish to light or calm conditions as night progresses, but the winds over the water continue to persist with speeds of 10 to 20 kt due to the turbulent mixing of faster winds to the surface.

METAR buoy and ship obs 0500 UTC 5 October 2004

Click here to see the instability mixing animation.
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6.5 Ocean Current

An ocean or lake current can have an effect on wind wave growth. This is not to be confused with the effect on swell from a current. For wind waves moving with the current, the waves will be less steep and slightly lower in height. This occurs because the current moves the water with the wave motion, increasing wave speed. A water particle will not complete a circular motion but will be displaced in the direction of the current, effectively lengthening the wave.

Effect of ocean currents on wind waves-opposing current Effect of ocean currents on wind waves-matching current

For wind waves running against the current the opposite is true. These waves are steeper with slightly increased heights and travel more slowly. This effectively lengthens the duration and fetch. Note that heights for long period swell can increase dramatically if they oppose a current. While these concepts should be understood, they are difficult to incorporate into forecasts for two reasons: the exact location and speed of currents are not always known, and the angle of incidence between the wind and current is in constant flux.

Click here to see the effect of ocean current animation.
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7. Observations

7.1. Satellite Scatterometry

7.1.1. Scatterometry Operations

Scatterometry uses microwave remote sensing of the ocean surface to determine the wind speed and direction. The microwave portion of the electromagnetic spectrum is used for scatterometry because much of the global ocean is frequently covered by clouds and these clouds are transparent in the microwave spectrum. Small-scale roughness elements, such as capillary waves on the ocean surface, have about the same wavelength as microwave radiation. The fundamental assumption of scatterometry is that the amplitude and direction of small-scale roughness elements are an indicator of the local sea surface wind speed and direction.

Electromagnetic spectrum

7.1.2. Scatterometry Theory

The fraction of energy returned to the satellite is known as backscatter. A model function that relates backscatter, surface wind speed and direction, and radar-viewing geometry has been created from a mass of empirical data. Although there are observed aspects of scatterometry such as rain interference that have not been accounted for in this model, the wind speed can generally be determined from the strength of the backscatter signal.

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7.1.3 Radar Viewing Geometry

For a fixed-viewing geometry, backscatter increases with increasing wind speed and decreases with decreasing wind speed. Multiple measurements of backscatter are made at nearly the same place on the ocean's surface at nearly the same time with different viewing geometries. These data are plugged into the model function that derives wind speed and direction.

Mathematica formula for Backscatter  cross section

7.1.4 Caveats

Warning!

Theoretically, wind speed and direction can be measured with the scatterometry technique. However there are observed aspects of scatterometry that are not well understood. These are:

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7.1.5 Limitations

There are two kinds of instruments used in scatterometry. While we will not discuss them in detail here, it is important to point out that each has limitations.

A fan beam antenna is used on European satellites and NASA's NSCAT scatterometer. The fan beam approach can not measure wind speed and direction directly below the satellite. This blank area underneath the fan beam antenna is known as the nadir gap.

NSCAT imagery

The newer American satellite known as QuikSCAT uses a rotating antenna to take conical measurements. While this eliminates the problem of the nadir gap, the measurements within the nadir gap are not as accurate as those to the side of the satellite track. In addition, the measurements of backscatter near the very edge of the measuring swath are only sampled twice. At least four "looks" are needed to ensure an accurate interpretation of conical scatterometry output. Therefore, the winds measured at the edge of the swath of a rotating antenna are unreliable.

Satellite viewing geometry

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7.1.6 QuikSCAT vs. Buoy

Rain contaminates the backscatter signal and causes QuikSCAT wind speeds to be higher than in situ measurements up to about 30 kt. For wind speeds above 30 kt, the rain-caused error is less important and the QuikSCAT wind speed and direction products may be used operationally even if they are rain-flagged.

Satellite signal attenuation through clouds

7.1.7 Where to Find Scatterometry Data

Several Websites containing scatterometry data exist. A few of the more commonly referenced sites are listed here:

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7.2 Buoys and C-MAN

7.2.1 Buoy Operations

The National Data Buoy Center (NDBC) provides hourly observations from a network of about 70 buoys and 60 Coastal-Marine Automated Network (C-MAN) stations. All stations measure wind speed, direction, gusts, barometric pressure, and air temperature. In addition, all buoy stations and some C-MAN stations measure sea surface temperature, significant wave heights, and dominant wave periods.

Six meter buoy3 meter buoyCMAN station

Wind speed and direction are averaged over an eight minute period for buoys and over a two minute period for C-MAN stations. Wind gusts are an average of the five or eight second speeds taken during the respective measurement period.

Sensors on board the buoys measure the heave acceleration or the vertical displacement of the buoy hull for approximately 20 minutes prior to the scheduled observation time. Wave energies, frequencies, significant heights, and dominant periods are mathematically derived from these data.

7.2.2 Question

An NDBC buoy is reporting a 25 knot wind, a wave height of 8 feet, and a wave period of 9 s. Will the wave height associated with the 9 second wave period continue to grow?

Answer: The wave speed can be found by multiplying the period by 3 (9 x 3 = 27 knot wave speed). Since the wave speed is greater than the wind speed of 25 knots the wave height will not grow.

Therefore, looking at the buoy observations, one can tell if the waves are growing, or if they have reached their maximum height, and are just propagating through the area.

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7.3 Ship Observations

7.3.1 VOS Program

Volunteer Observing Ship program logo

The Voluntary Observing Ship or VOS Program obtains weather and oceanographic observations from moving ships. An international program under World Meteorological Organization auspices, the VOS has 49 participating countries. The United States program is the largest in the world, with over 1600 vessels. Port Meteorological Officers (PMOs) support the VOS Program by recruiting vessels to participate. Observations are taken by deck officers, coded in a special format known as ship's synoptic code, and transmitted into the NOAA data stream every six hours. It is important to note that instrumentation aboard VOS ships sits higher than instrumentation on buoys; therefore, a ship may report a higher wind speed than a buoy in the same area.

7.3.2 VOS Data

Data collected from ships participating in the VOS program usually include:

Because VOS observations are made subjectively without instruments, caution should be taken when using them. The date and time of the observation should be noted since the frequency of VOS reports is much less than land-based observations.

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8. Case Study

On 8 October 2003 at 1200 UTC a long-wave trough with several embedded disturbances was over the northeast Pacific ocean. At the same time to the south a subtropical high was centered around 30°N, 140°W.

AVN 500 hecto pascal 00 hour forecast valid 1200 UTC 08 October 2003

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A strong polar jet had moved into the long wave with the left exit region in a favorable position to enhance cyclogenesis in the southern embedded disturbance. The surface low that formed with this disturbance was located about 400 miles west of Vancouver Island at 1200 UTC and was moving toward the coast of west central British Columbia. The extratropical system would eventually reach an observed minimum pressure of 968 hPa before making landfall.

AVN 300 hecto pascal winds and wind speeds, MSLP 00 hour forecast valid 1200 UTC 08 October 2003

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Water vapor imagery depicted an expanding dry slot (subsidence region) indicative of strong cyclogenesis. At this time NDBC buoy 46005, which is just south of the cyclone, was experiencing 40 kt sustained winds gusting to 70 kt and 30 ft seas while some of the Canadian buoys closer to the storm had even larger values.

Satellite water vapor image, 1200 UTC 08 October 2003

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While strong winds and precipitation affected the coastal areas during landfall, cold air advection continued well upstream, as evidenced by the large area of stratocumulus clouds shown in the infrared satellite imagery and by the magnitude of baroclinicity shown in the 850 hPa model wind and temperature fields. This helped maintain a broad area of 25-35 kt winds that extended back to the Aleutian Island chain.

AVN 850 hecto pascal winds, temperature and infrared satellite, 00 hour forecast valid 1200 UTC 08 October 2003

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Question 1

Identify all of the fetch areas on the MSLP image.

AVN MSLP, winds and wind speed, 00 hour forecast valid 1200 UTC 08 October 2003

a) A
b) A & C
c) C
d) B & C
e) A & B

Answer:

The correct answer is e). Areas A and B indicate fetch due to the homogeneous characteristics of wind direction and speed within the area. Area C does not indicate homogeneous wind features. Direction and speed are both changing within this region.

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Question 2

Given forecasted wind speed and a fetch length of approximately 1000 n mi, what approximate wave height is possible in fetch area A?

AVN MSLP, winds, 12 hour forecast valid 000 UTC 9 October 2003

AVN wind speed, 12 hour forecast valid 0600 UTC 9 October 2003

Surface obs on moving buoys, ships and fixed buoys, 12 hour forecast valid 2300 UTC 8 October 2003

Wave analysis and forecasting nomogram

a) 15 ft
b) 25 ft
c) 30 ft

Answer:

The correct answer is a). An analysis of wind barbs shows that the lowest wind speed is 20 kt. However, the average wind speed over much of the fetch area is approximately 25 kt. Using the wave nomogram, and following across the 25 kt wind speed line to the vertical fetch length line of 1000 n mi shows that approximately a 15 ft wave is possible.

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Question 3

Do you expect the model wave heights calculated in Question 2 to be under or overestimated in fetch area A compared to satellite wind estimates?

SSMI wind speeds 000 UTC 08 october 2003

a) The model wave heights will be overestimated.
b) The model wave heights were accurate.
c) The model wave heights will be underestimated.

Answer:

The correct answer is c). From the SSMI/QuikSCAT data, wind speeds in fetch area A are estimated to be between 25 and 35 kt. Thus, corresponding wave heights are 15 to 25 ft, indicating that the model wave heights will be underestimated.

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Question 4

Given the wind speed of 25 kt calculated in Question 2 and a fetch length of 1000 n mi, calculate the wave height based on duration of generation shown by model forecasts for area A.

Click here to see the 1200 UTC 8 Oct-0000 UTC 10 Oct AVN MSLP and Winds animation.

Click here to see the 1200 UTC 8 Oct-0000 UTC 10 Oct AVN Wind Speed animation.

Wave analysis and forecasting nomogram

a) 10 ft
b) 13 ft
c) 15 ft

Answer:

The correct answer is a). Looking at the plots of MSLP, wind barbs, and wind speed it can be seen that the wind direction and speed are relatively consistent throughout the first 18 hours from 12 UTC on 08 October to 06 UTC on 09 October. The next time period of 12 UTC on 09 October shows that the winds have shifted counter clockwise and the wind speed has decreased due to a decreasing pressure gradient. This change in the wind field indicates that a separate set of waves will develop based on the new wind characteristics and hence a different fetch region. The waves from fetch area A will no longer grow at this point, and will propagate away from their source region. Following the 25 kt line horizontally until it intersects the blue dashed line of 18 hours reveals that wave growth of 10 feet will occur. Note that this value of wave height is less than that found in question 2 when only wind speed and fetch were considered.

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Question 5

Given the duration of 18 hours, wind speed of 25 knots, and fetch length of 1000 nautical miles determined in the previous questions, what is the limiting factor for wave growth in area A?

Wave analysis and forecasting nomogram

a) Wind speed
b) Fetch length
c) Duration

Answer:

The correct answer is c). Using the wave nomogram and 25 kt wind speed, notice that wave height will continue to grow for 48 hours then minimally after that. In this case, fetch length does not restrict wave growth because fetch area A is longer than the minimum required fetch length of 150 n mi for a duration of 18 hours. As seen in the previous question, the wave height for a 25 kt wind changes from 15 ft to 10 ft when the duration is considered. If duration is not taken into consideration, the forecast of wave height will be too large. In this case, there is ample fetch length and wind speed, but the amount of time needed to generate the maximum wave height is not sufficient. Therefore, our maximum wave height will be limited by duration.

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Question 6

Given the plot of wind speeds and a fetch length of 450 n mi, what approximate wave height is possible in fetch area B?

AVN MSLP winds, 12 hour forecast valid 0000 UTC 9 October 2003

AVN wind speed, 12 hour forecast valid 0000 UTC 9 October 2003

Surface obs for moving buoys, ships and fixed buoys, 12 hour forecast valid 2300 UTC 9 october 2003

Wave analysis and forecasting nomogram

a) 2 ft
b) 6 ft
c) 10 ft

Answer:

The correct answer is b). Analysis of the wind barbs shows that the average wind is approximately 15 kt throughout the fetch area. Carefully follow the 15 kt wind line on the Wave Nomogram over to 450 n mi to find that an approximate wave height of 6 ft will occur in fetch area B.

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Question 7

Given the 15 kt wind speed calculated in the previous question and a fetch length of 450 n mi, calculate the wave height based on duration of generation shown by the model forecast for area B.

Click here to see the 1200 UTC 8 Oct-0000 UTC 10 Oct AVN MSLP and Winds animation.

Click here to see the 1200 UTC 8 Oct-0000 UTC 10 Oct AVN Wind Speed animation.

Wave Analysis and Forecasting Nomogram

Answer:

For fetch B the entire period has consistent 15 knot winds. Therefore we use a duration period of 36 hours to calculate a significant wave height of approximately 5 feet.

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Question 8

Do you expect the model wave heights calculated in Question 6 to be under or over estimated in fetch area B compared to satellite wind estimates?

SSMI Wind Speeds 0000 UTC 09 Oct 2003

Answer:

The SSMI/QuikSCAT data estimates wind speeds in fetch area B to be 20 kt. Thus, corresponding significant wave heights would be about 9 feet indicating that the model wave heights will be underestimated.

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Question 9

What is the limiting factor for wave growth in fetch B?

Wave Analysis and Forecasting Nomogram

In this case the wind speeds are relatively low. When the speeds are low and the fetch length is relatively long, an increase in either duration or fetch length will not appreciably affect wave height. Increasing the duration or the fetch length for fetch area B would only increase the significant wave height by 1 foot. Wind speed is the limiting factor in wave growth for fetch area B because only an increase in the wind speed will cause a significant change in wave height.

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Module Summary

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