Validation of the WAM-model over the Baltic Sea

Examensarbete vid Institutionen för geovetenskaper

ISSN 1650-6553 Nr 156

Validation of the WAM model

over the Baltic Sea

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Abstract

In order to understand how waves influence the exchange of momentum, latent heat and other parameters, between the ocean surface and the atmosphere, one can use models. A coupling between a wave model and an atmospheric regional climate model, for the Baltic Sea, will be performed at the Meteorology Institute in Uppsala University. The wave model is a state of the art, third generation wave model called WAM.

The new version of the WAM model (cycle 4) needs to be validated. The aim of this thesis is to perform this validation and also to investigate what meteorological forcing one should use to achieve best results. Two different types of forcing are analyzed, ERA40 reanalysis and the RCA climate model. In order to do this, observations from six different buoys in the Baltic Sea will be compared with the model output from WAM. The parameters that will be compared in this study are significant wave height, direction and peak period.

A consistent phenomenon for all the buoys is a slightly underestimation by the model of what the rate of this increases with increasing wave height. If one compares the model output when WAM are forced with the RCA climate model and when it is forced with ERA40 reanalysis, the differences between them are notable but not large. ERA40 is slightly better.

Significant wave height is quite good and gives a reasonably result. Some buoys and periods are better and some are worse. There are some differences for the significant wave height between the east coast and the west coast of Sweden, when forcing the model with RCA. It is slightly better on the west coast. On the contrary, the results from ERA40 are very coherent. The quality of the hindcast for the direction and the peak period, in contrast to the significant wave height, is not that good. The results are not bad, but it only gives a rough picture of the sea state.

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Sammanfattning

I syfte att förstå hur vågor påverkar utbytet mellan havsytan och atmosfären av olika parametrar, till exempel impuls och latent värme, kan man använda sig av modeller. En sammankoppling mellan en vågmodell och en atmosfärisk klimatmodell, över Östersjön, ska utföras på Meteorologiska Instutitionen på Uppsala Universitet. Vågmodellen är en så kallad tredje generationens vågmodell och kallas WAM modellen.

Syftet med detta arbete är att granska den nya versionen av modellen samt att utreda vilken vind som är bäst att driva modellen med för att få bäst resultat. Två olika drivningsmedel användes, ERA40 och klimatmodellen RCA. För att kunna utföra denna granskning jämfördes observationer från sex olika bojar i Östersjön med utdata från WAM modellen.

Ett mönster som upptäcktes för alla bojar var att modellen underskattar våghöjden och att denna underskattning ökar när våghöjden ökar. Om man jämför modellens resultat när WAM är driven av klimatmodellen RCA och när den är driven av ERA40, är skillnaderna mellan dem noterbara men inte stora. ERA40 ger något bättre resultat. Resultatet för den signifikanta våghöjden visade sig vara ganska bra och gav hyfsat rimliga resultat. Vissa bojar och perioder var dock bättre och andra var sämre. När WAM drivs av RCA modellen ser man en antydan till att resultatet är något bättre på västkusten av Sverige än vad de är på östkusten. Kvalitén på återanalysen för

riktningen och ”peak period” (perioden där vågspektra har sitt maximum) är inte lika bra, i jämförelse med den signifikanta våghöjden. Resultatet är inte dåligt, det ger bara en grov bild av havsytan.

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Contents

1.Introduction ... 1

2. Theory ... 2

2.1 Wave theory ... 2

2.2 The WAM model ... 5

2.2.1 Deep water ... 5

2.2.2 Shallow water ... 7

2.2.3 Numerical aspects ... 7

2.3 Statistics ... 8

3.Model setup and data analysis ... 9

3.1 Model implementation of the Baltic Sea ... 9

3.2 Buoy data ... 10 3.3 Meteorological forcing ... 11 3.3.1 ERA-40 ... 11 3.3.2 RCA ... 11 3.4 Hindcast periods ... 11 4.Results ... 13 4.1 Period 1 ... 13 4.2 Period 2 ... 14 4.3 Period 3 ... 15 4.4 Period 4 ... 16 4.5 Period 5 ... 19 4.6 Period 6 ... 20 5.Model skills ... 22 5.1 ERA40 ... 22 5.2 RCA ... 23 6. Discussion ... 26

6.1 Significant wave height ... 26

6.2 Direction and peak period ... 27

6.3ERA40 vs. RCA ... 27

7.Conclusions ... 28

Acknowledgement ... 29

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1. Introduction

Forces acting on the water surface result in waves (Palménin, 2003). The growth of a wave is mainly controlled by the wind speed, wind duration and the fetch, where fetch is the transport distance of the wind over the water body. The greater the fetch is, the larger the waves become. The waves that are treated in this thesis are the so called ocean gravity waves. They are generated by the wind and can move great distances. In fact, ocean gravity waves can be found thousands of kilometers away from the places they were generated (WMO, 1998).

Waves can be described by models. The main purpose of a wave model is to make hindcasts and forecasts of the sea state. This can be used for many applications, such as ship routing, offshore industries and fishing. A frequently used wave model is the WAM (WAve Model) model, developed by the WAMDI (The Wave Model Development and Implementation) group during the 1980’s. The WAM model is a spectral wave prediction model that solves and describes the evolution of the energy balance equation for the two-dimensional wave spectrum (Komen et al., 1994). It is a global model, but can also be used as a regional model. The WAM model has been fully operational since June 1992 and today it is used by more than 100 institutes all over the world.

The WAM model has recently being introduced at the meteorological department in Uppsala, Meteorology Institute Uppsala University (MIUU), and scientists are in the process of coupling the wave model to an atmospheric regional climate model (Rossby center regional climate model, RCA). Output from the new version of WAM has to be validated. It will also require some verification of the model set ups. In 1993, Romeiser presented the first, full one year period, validation of the WAM model as a global model (Romeiser, 1993). The result was relatively good in general, over the northern hemisphere. The RCA-WAM coupled model system, at MIUU, will be used over the Baltic Sea as a tool to improve the understanding of wave influence on the exchange of momentum, latent heat and other parameters, between the ocean surface and the atmosphere. The gravity waves generated by the wind are thought to be very important in the climate processes, and play a large role in the global exchanging process of heat, energy, gases and particles (aerosols) between the oceans and the atmosphere.

To be able to run the WAM model, wind forcing from an atmospheric model is required. The model is forced by a wind field at 10 meters height. In this study winds directly from ERA-40 reanalysis and from a downscaling of ERA40 with a regional climate model (RCA) will be used.

The main goal of this study is to assess how well the waves are hindcasted by WAM. In order to do this, the output from the model is compared with measured data from the Swedish Meteorological and Hydrological Institute (SMHI) and MIUU buoys from six different locations in the Baltic Sea. The validation is made by comparing the model output with buoy data. The validation of the model focuses on six different periods, each of them covering one full month.

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2. Theory

2.1 Wave theory

A gravity wave may be represented as a sinusoidal movement as shown in Figure 1. It is the gravity that forces the surface back to its original level when for example the wind has caused a displacement away from the mean surface level. The result is an oscillating motion where kinetic energy is transformed into potential energy as the wave propagates.

Figure 1: A sinusoidal wave (from USACER, (1973)).

A good way to characterize waves is to use the wave period, T. The wave period is the time it takes for a wave crest and a wave trough to pass a fixed point, the duration of one cycle. The ordinary gravity wave has a wave period between 1 and 30 seconds (WMO, 1998).

When observing the sea surface one can believe that the ocean surface contains waves that move in the same direction and that they have been created at the same place. As a matter of fact, the sea surface may be regarded as a sum of many different sinusoidal waves. It can be compared with a huge column with many layers on top of each other where every layer represents one wave. This can be seen in Figure 2.

Figure 2: The column of layers where each layer represents a

sinusoidal wave (from Pierson et al., (1955)).

Each layer, with one sinusoidal wave, has a different frequency, direction, amplitude and phase.Each frequency and direction describes a wave component and each component has

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an associated amplitude and phase. Furthermore, all these layers may have been generated in different places.

The waves which are directly connected to the wind are often called wind sea. When waves propagate away from the place where they were generated and no longer are affected by the wind forcing that created them, they are called swell (the wind does not longer transport energy into the waves).Swell can not only carry forward a great amount of energy, but also transport momentum. One can believe that, because of the energy transport, voluminous amount of water would also be transported, but this is not the case. One single water particle does not have a big forward movement, actually it is a very small motion.

Figure 3: Stokes drift (WMO, 1998).

When a wave passes a water particle, the particle moves up and down. When the particle is in the trough (Figure 1) it moves a little bit backwards and at the crest (Figure 1) it moves slightly forward. During the time the wave is passing by, the particle describe a circle in a vertical plane (cross section). But the water particle does not return to the same spot it started, it actually moves a bit to the same direction as the wave travels. This small distance is called the “Stokes drift” or the wave induced current (Stokes, 1847), see Figure 3:

The group velocity, , is defined as the velocity at which energy is transferred along a group of waves (WMO, 1998):

(1)

Where c is the wave phase speed defined as:

(2)

and is the circle frequency and is the wave number.

Waves are affected by the depth, they changes as they begin to feel the bottom. Only the period remains constant. In order to be effected by the bottom the depth has to be approximately less than half of the wavelength. As waves move towards shallow waters,

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they will be refracted, causing a change in the direction of propagation. An example is illustrated in Figure 4.

Figure 4: Refraction: waves are affected by the

bathymetry and may change its direction when moving against shallower water (WMO, 1998).

Refraction occurs since waves in deeper water moves faster than waves in shallow waters. This can be shown by Snell’s law:

(3)

where is the angle between a wave front and a local isobath (a line of constant depth) for the deeper part and for the shallower part, is the depth in deep water and is the depth in the shallower area. is the group velocity for the shallower part.

When a validation of a wave model is to be made the main wave parameter to evaluate is the significant wave height, Hs, the mean height of 1/3 of the highest waves.

Another parameter used to describe waves is the peak period, :

(4)

where fP is the spectral peak frequency (the frequency at which the spectral function is at a

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2.2 The WAM model

The WAM model is a state of the art third generation wave model (Komen et al., 1994). It is characterized by its way of taking into account the effect of time-varying current. It is coupled dynamically with a hydrodynamic model and can handle wave-wave interaction and dissipation (Booij, 1997). The most important difference between a second- and a third- generation model is that the last one includes an explicit source term for the nonlinear interactions and that the model solves the equation without any former assumptions on the shape of the wave energy spectrum.

The WAM model was developed by the WAMDI group during the 80’s because it turned out that the wave models that were present at that time did not give a good description of the sea state. Another reason for the group to improve the existing model was that the computers had improved a lot during the last years and were by then capable to solve more advanced equations (ECMWF, 2003).

Since the first implementation of the model in 1988, there have been several improvements. The WAMDI group and other teams have three times released a new version of the model (Bender, 1995). The original version was called WAM-cycle 1 and from this one they later updated it to WAM-cycle 2, 3 and 4. The changes which were made between the first three versions had nothing to do with the physics, only the code in the program was modernized and made more efficient. When the fourth edition was released, some changes in the model physics were introduced. The main improvement was concentrated on the coupling between the sea state and the air flow. At first the model contained a parameterization that handled this, but when the fourth edition came out the WAMDI group included a dynamic coupling between wind and sea to deal with the problem (Bender, 1995).

After cycle 4, the WAMDI group was disestablished and the model was no longer in the process of evolution by this group. However, there has been some upgrading of the model in various aspects, different changes at different institute. Each department or group that uses this wave model is changing it so that their special requests and needs are satisfied. The WAM model calculates both the swells and the wind sea.

2.2.1 Deep water

The WAM model solves a spectral equation for describing the two-dimensional wave spectrum, the spectral energy balance equation:

(5)

where is spectral wave energy density, depending on wave frequency, , wave direction, , position, , and time, . Equation 5 describes the loss, gain and shifting of energy and the equation is valid for deep water with no refraction and no significant current. The so called source functions, on the right hand side in Equation 5, describe the wind input, , nonlinear transfer, , and dissipation due to white-capping, .

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Sin is the input by the wind. It is scaled in terms of friction velocity, (WAMDI, 1988)

and is defined as:

(6)

where is wave growth described by:

(7)

and is density of air and water respectively and θ is the direction of propagation (measured clockwise relative to true north).

describes the non linear source term. The weekly non-linear, resonant, wave-wave interaction process is responsible for the transfer of energy along the wave spectrum (WMO, 1998), from higher to lower frequencies (Figure 5).

Figure 5: Transport of energy from higher to lower frequencies.

It is believed that this process is responsible for the downshift in peak frequency, as a wind sea develops into a mature sea. The final result will be a sharper spectrum with a well defined peak for mature seas. The sharper spectra can be seen in Figure 5, as well as the spectra for the wind sea. Hasselmann et al. (1992) proposed a discrete interaction operator parameterization to deal with this term.

Sds describes the loss of energy in terms of dissipation (Komen et al., 1994):

(8)

where:

(9) is the mean frequency. E describes the total energy and can be written as:

(10)

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(11)

is a theoretical value of for a Pierson-Moskowitz spectrum (WAMDI, 1988) and may by expressed by:

(12)

2.2.2 Shallow water

For shallow waters one extra term is added to Equation 5, because of the influence by the depth:

(13)

where Sbf is the energy loss due to bottom friction and percolation:

(14)

where and D is the depth. For shallow water, the other

source terms also need to be rewritten so they have a depth dependency. The non linear term is almost the same as in deep waters, what brings them apart is a scaling factor R (ECMWF, 2004):

(15) where is the mean wave number and R is defined as:

(16)

2.2.3 Numerical aspects

The model solves the spectral energy balance equation at each grid point. It is possible to get model results on a specific point that does not coincide with a gridpoint. The model interpolates the results between the nearest four gridpoints into the new point (Figure 6).

Figure 6: Interpolation between four gridpoints to get the results in point not corresponding to the actually

gridpoints.

After solving the equation, the output from the model is a 2D spectrum at each grid point. The 2D spectra is actually a matrix (N*M) where N is the number of directional bins (usually 24) and M is the number of frequency bins (usually 25, logarithmically spaced). There are 25 frequency bins and 24 direction bins.

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The model uses a fully implicit scheme for the source function integration in time. The time step has to be greater than the time it takes for the highest frequencies to adjust to the dynamic equations. The most useful implicit scheme for advection and refraction turned out to be the first order upwinding scheme (ECMWF, 2004).

2.3 Statistics

For the validation of the model some basic statistical parameters were used. The standard deviation of any parameter x, is defined as:

(17)

where N is the total number of observations, the value from the model and the observations.

The root mean square, , describes the magnitude of a varying quantity. It is defined as:

(18)

where .

The bias shows the tendency of a data set (a model output in this case) to a specific behavior. It defines as:

(19)

A large bias value means that the model has a tendency to consistently forecast on a specific way (under- or overforecast), whereas a small bias indicates of a more random or dispersive behavior.

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3. Model setup and data analysis

The friction velocity is the physical parameter of importance. Therefore, the model ought to be forced by the friction velocity, but also because of the fact that the surface stress was expressed by the friction velocity when the model were about to be developed (ECMWF, 2003). So, it would have been better to use the friction velocity in this project to force the model, but this parameter is probably determined with great uncertainty in ERA40 reanalysis and RCA climate model.

In this study the wind applied to force WAM was extracted from the ECMWF ERA-40 reanalysis. There will also be cases with RCA data. Romeiser, 1993, used the wind stress to force WAM. It was calculated by multiplying the wind speed at a height of 10 m with a drag coefficient depending only on the wind speed.

Figure 7: The location of the

wave measurement sites.

3.1 Model implementation of the Baltic Sea

The model was set-up for the Baltic Sea, for a domain bounded by the meridians 52ºN and 68ºN and by the parallels 4ºE and 34ºE. The model domain was assumed to be a closed basin on all its extension, with no wave energy exchange with the open ocean. This is, of course, a perfect assumption for the buoys located inside the Baltic Sea, but only a reasonable assumption for the buoys on the west coast of Sweden, SMHI4 and SMHI5. The bathymetry for the model runs was extracted from the etopo2 2 minute worldwide

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bathymetry data base (National Geophysical Data Center, 2001). From this data base an interpolation to the different grid points was done using the pre-processing tools of met.no (Norwegian Meteorological Institute). The same interpolation was done with the wind data, so that both the wind and the bathymetry data would coincide at each grid point. The grid point spacing was 0.25 degrees and WAM was run with a 60 seconds integration time step. The model output was set up for every full hour and the time used on the model was UTC (coordinated universal time). The two-dimension spectral boundaries were fixed with 25, logarithmically spaced, frequency values, and with a 24, 15 degrees spaced, direction bins (resolution). The model was run with a cold start for all the periods where the spin-up time was estimated to be 2 days.

3.2 Buoy data

Two different types of buoys were selected for the validation: Waverider and Seawatch. The Seawatch type of buoy can collect directional wave data as well as meteorological and oceanographic parameters; air pressure and temperature, wind speed and direction, wave height and period (Barstow et al, 1994). A Waverider buoy is used only to measure wave parameters and it is used more frequently than the Seawatch. The buoys are run and owned by SMHI (SMHI1-SMHI5) and FIMR (Finnish Institute of Marine Research). The FIMR buoy is named MIUU1 in the present study. They are listed in Table 1 and the locations of these buoys are shown in Figure 7. Four of the buoys are located in the Baltic Sea and two of them are located on the west coast of Sweden (SMHI4 and SMHI5).

Table 1: The different buoys and its location.

Buoy ID Location Water Depth Type

SMHI1 59⁰ 09⁰ 19⁰ 08⁰ 29 m Waverider SMHI2 58⁰ 56⁰ 19⁰ 10⁰ 90 m Seawatch SMHI3 56⁰ 04⁰ 16⁰ 41⁰ 25 m Waverider SMHI4 57⁰ 13⁰ 11⁰ 34⁰ 70 m Seawatch SMHI5 57⁰ 36⁰ 11⁰ 38⁰ 25 m Waverider MIUU1 57⁰ 25⁰ 19⁰ 03⁰ 36 m Waverider

As could be seen in Table 1, there is two Seawatch buoys and four Waveriders in this study. The Waveriders are often on a depth of 30 m and the Seawatcher on the depth of 70-90 m.

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3.3 Meteorological forcing

The ERA-40 data base is a global atmospheric reanalysis that contains atmospheric and ocean parameters for the period September 1957 to August 2002 (Kållberg et al., 2005). It was completed in 2003 and the data is divided in three different sections where each section includes data with similarities in data sources. The objective of the ERA40 project was to create a high quality analyses for the past four decades that should be available for scientific community everywhere on the earth. ERA-40 has generated a data set of about 45 years that has given a new opportunity for scientist to have a better view over the global circulation of the atmosphere and the global change.

In order to generate the database the ECMWF operational global model was used, but also satellite and In-Situ data. Analyses were produced daily at 00Z, 06Z, 12Z and 18Z, data assimilation with a six hourly cycling. This analyze is then used as a background field in the next assimilation.

The wind at 10 m in ERA-40 was used in this project to force WAM for period 1 to 3. It is also used in the other buoys, but it will instead be a downscaling of ERA40 with a regional climate model (RCA).

3.3.2 RCA

The RCA is the regional atmospheric climate model from the SMHI Rossby Center. It is a hydrostatic, primitive equation model and is a modified version of the international HIRLAM limited area model. The model has a resolution of 44 km and the parameters evaluated by the model are for example the horizontal wind components, temperature, specific humidity and cloud water (Rummukainen et al., 2001). RCA is used over the Baltic Sea and is useful in studies of regional effect of the climate. The model uses an Eulerian advection and a leapfrog semi-implicit time integration scheme and has a time step of 30 minutes (Jones et al., 2002). RCA is taking into account if there is land or if there is water in each gridpoint. In terms of ice, the model is treating this as land.

In 2002, the quality of the RCA model improved a lot. Between 2000 and 2002 a new version of the model was developed. It was released in 2002 (Jones et al., 2002). The changes included a new land surface scheme, some treatment of clouds and radiation, and improvement of the numerics. RCA is coupled to an ocean model, in the Baltic Sea, called the Rossby Centre Ocean model (RCO). The coupled system is called RCAO.

3.4 Hindcast periods

The periods that the model will be evaluated for can be seen in Table 2. These individual periods where all chosen for different reason; both autumn and winter is represented and different types of weather (stormy and calm) and wave regimes (high and low) are present. For periods 1-3 WAM is forced both with ERA-40 and RCA. There was, unfortunately, no data from ERA40 the last three periods. So these periods, 4 to 6, are only forced with RCA winds.

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Table 2: The periods used for each buoy.

Period SMHI 1 SMHI 2 SMHI 3 SMHI 4 SMHI 5 MIUU 1 1 Feb 1996 X X X 2 Feb 1997 X X 3 Dec 1999 X X 4 Sep/okt 2003 X X X 5 Dec 2004 X 6 Jan 2005 X X

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4. Results

This section describes the verification results for significant wave height, direction and peak period.

4.1 Period 1

There was a really cold winter this year (1996) in Sweden. Some cyclones in the Baltic Proper were really intense and created high waves, higher than the average. This high waves can be seen in Figure 8, especially in SMHI3 (Figure 8b). SMHI5 does not have these high waves due to the fact that this buoy is on the west coast of Sweden (the cyclones were most intense in the Baltic Sea during this period).

Figure 8: Comparison between model and observation February 1996, significant wave height.

5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] a) SMHI1 1996-02 Buoy Model-ERA40 Model-RCA 5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] b) SMHI3 1996-02 Buoy Model-ERA40 Model-RCA 5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] c) SMHI5 1996-02 Buoy Model-ERA40 Model-RCA

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The model output forced by ERA40, displays a wave top around day 10 on SMHI5 (Figure 8c) that are lacking out in both the observations and the model output forced by RCA. This can be due to the model or the data, there is maybe something wrong with the observation or perhaps the model output is incorrect. The most reasonably reason is the last one due to the fact that ERA is the only one displaying this wave top. After this day, however, the waves are better captured by the model when forcing it with ERA40 (SMHI5). Actually, in both SMHI1 and SMHI5, the results are better with ERA40 (Figure 8a and 8c) and the hindcasts follows the observations approximately good.

The period had some days with relatively high waves, especially in the Baltic Proper (SMHI3 buoy), as mention earlier. Generally, wave models are having a hard time to reproduce the higher waves. Between day 15 and day 23, SMHI3 indicates rather high waves. Despite this, WAM gives a reasonable good hindcast during these days.

Note that Figure 8 shows a significant underestimation for the wave height throughout the whole period.

4.2 Period 2

Before one of the warmest summer ever since 1858 in the Baltic Sea 1997, came a very cold period in February. Because of the relatively high wind speed for the season, the waves reached high values. The model output during this period is compared with observations from buoys in Figure 9. Both SMHI1 and SMHI3 demonstrate high waves, as expected. The mean of the significant wave height is around 2 m.

Figure 9: Comparison between model and observation February 1997, significant wave height.

5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] a) SMHI1 1997-02 Buoy Model-ERA40 Model-RCA 5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] b) SMHI3 1997-02 Buoy Model-ERA40 Model-RCA

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From period 2 there is only information from two different buoys. One of them shows obviously incorrect values (Figure 9a), this is not a realistic wave height variability. Broman et al. (2006) showed in there thesis that during February 1997, the significant wave height for SMHI1 did not correspond to the present wind field that was observed (Broman, 2006). One can see in Figure 9a that the fluctuation of the buoy measurements, do not represents a natural image of the sea state. With this knowledge, this buoy is not useful in the discussion whether the model gives a good hindcast or not for this period. The outcome from SMHI3 (Figure 9b), on the other hand, is really useful and shows that the model achieve high-quality results.

Both ERA40 and RCA slightly underestimate the wave height. But between day 17 and 22 the model output with ERA40 capture the variability in the observations much better than RCA. So, for this specific period, ERA40 are better than RCA.

4.3 Period 3

In December one can expect rather high waves, 1999 was no exception. Actually, it was higher waves than the normal average because in this period a huge storm hit the coast of Denmark. The storm had attenuated a little bit when it reached the Baltic Sea, but was still pretty strong.

Figure 10: Comparison between model and observation December 1999, significant wave height.

The statement of high waves during this period is confirmed by Figure 10. The model is having some problem with this, it underestimates the highest waves. The quality of the hindcast decreases slowly with increasing wave height. Both ERA40 and RCA do not

5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] a) SMHI1 1999-12 Buoy Model-ERA40 Model-RCA 5 10 15 20 25 30 0 1 2 3 4 5 6 7 Time [days] H e ig h t [m ] b) SMHI5 1999-12 Buoy Model-ERA40 Model-RCA

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capture a wave top around day 7 in Figure 10a. The underestimation is quite big for both of them.

There is a difference though between the hindcasts run with the ERA40 wind field and the hindcasts run with WAM using the RCA climate model. RCA are slightly better when talking in terms of SMHI5 (Figure 10b).

4.4 Period 4

Figure 11 shows that the waves are rather low in the beginning of the month this year (September 2003). However, at the end of the month, the waves are getting a little bit higher. This is very typical because the autumn is approaching more and more and with the autumn comes the low pressure systems as well. They are crossing Sweden in its pattern over the earth, with relatively high wind speed. This creates high waves.

Period 4 has been used in a campaign in the Baltic Sea, called Baltic Sea Swell Experiment (BASE). The weather situation during this period was quite variable with variability in wind speed and wind direction. Big changes in sea surface temperature were observed as well, from 16.5˚ in the beginning to 13.0˚ in the end of the period (Högström et al., 2008). Because of this variability and the hasty change in temperature, it is interesting to investigate this period.

Figures 11-13 illustrate the result for the fourth period. As said before, one can expect a little bit higher waves at the end of the month. The model has captured this month varying height quite well, but misses, in this period as well, some of the highest waves. Around day 11 in SMHI2 (Figure 11a) and day 23 in SMHI5 (Figure 11b), the model do not capture the wave peaks so good. They are underestimated by WAM. Actually, the model overall underestimates the height of the waves.

Because of the relatively small wave height, the model should not have a problem to hindcast them properly. Unfortunately, the result is quite bad for the MIUU1 buoy (Figure 11c). The model output is not acceptable, it is not even close in showing the same wave height as the observations. The observations indicate the low waves in the beginning of the month and the high waves in the end. So, the most likely reason, is that it is something wrong with the model output.

When considering the direction, one can see in Figure 12 that the model only gives a rough picture of the sea state, the results are not good. The peak period (Figure 13) is a little bit better, but still not well.

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Figure 11: Comparison between model and observation September 2003, significant wave height.

5 10 15 20 25 30 0 2 4 6

Time [days]

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Figure 12: Comparison between model and observation September 2003, direction.

Figure 13: Comparison between model and observation September 2003, peak period.

5 10 15 20 25 30 0 100 200 300

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4.5 Period 5

The mean of the significant wave height was measured to 7.7 meters on the east coast of Sweden and the highest wave had the magnitude of 14 meters during this period (December 2004) (Broman et al., 2006). Unfortunately, there are only buoy observations from SMHI4 this period. This buoy is on the west coast, so Figure 14 do not show that high values in terms of wave height.

The significant wave height in Figure 14 is really good, with the exception of two wave peaks between day 25 and day 30. The model underestimates the waves during these days and some other time as well. Although it uses to be difficult to achieve a high quality result when comparing direction and peak period between buoy measurements and models hindcasts, Figure 15 and 16 illustrate that there is an acceptable agreement between the hindcasted values and the data from the buoy, both for direction and peak period. Noteworthy in Figure 16 is a rather strange thing from the model around day 29. This is not a reasonably result.

Figure 14: Comparison between model and observation December 2004, significant wave height.

Figure 15: Comparison between model and observation December 2004, direction.

5 10 15 20 25 30 0 1 2 3 4 5 6 7

Time [days]

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]

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20

Figure 16: Comparison between model and observation December 2004, peak period.

4.6 Period 6

During period 6, a powerful and intense cyclone approached the coast of Sweden. When it reached land, at least 17 people died and many houses lost their electricity. Wind speed with the magnitude of 26 m/s was measured in Denmark. The waves reached a height (significant wave height) of 10 m (Broman et al., 2006). The storm was called Gudrun in Sweden.

Figure 17: Comparison between model and observation January 2005, significant wave height.

5 10 15 20 25 30 2 4 6 8 10

Time [days]

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21

Unfortunately, there is not much data from the buoys at this specific period. SMHI4 only contains one data set of 15 days for the direction and the significant wave height. However, the model captured these parameters very well during this few days. The model output follows the observations well and displays the same variability, see Figure 17a and 18a.

The model output for the MIUU1 buoy, on the other hand, does not capture the values from the observations very well. Actually, in Figure 17b, the result is a catastrophe for the significant wave height. The peak period is a little bit better, but still not good (Figure 19).

Figure 18: Comparison between model and observation January 2005, direction.

Figure 19: Comparison between model and observation January 2005, peak period.

5 10 15 20 25 30 0 100 200 300

Time [days]

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22

5. Model skills

To get a better overview of how good the qualities of the hindcasts are, statistical parameters have been used. The only wave parameter showing in the following pictures is the significant wave height, due to the importance of this parameter. In Figure 20 and Figure 21, the different periods are mark with P1, P2, P3, P4, P5 and P6.

5.1 ERA40

In section 5.1 one can see the qualities on the hindcast when using ERA40 reanalysis. Data from SMHI1, SMHI3 and SMHI5 were available during these periods (period 1 to 3).

Figure 20: Comparison of significant wave height between model and buoy (ERA40).The gray dots

indicate all the values from the model and the buoy, the black dashed line indicates the total linear regression, all periods for this buoy, and the gray lines show the different periods. Hs is here in meters.

0 2 4 6 0 1 2 3 4 5 6 7 Hs (obs) H s (m o d e l) SMHI1 ERA40 a) P1 P3 Total 0 2 4 6 0 1 2 3 4 5 6 7 Hs (obs) H s (m o d e l) SMHI3 ERA40 b) P2 P3 Total P1 0 1 2 3 4 0 1 2 3 4 Hs (obs) H s (m o d e l) SMHI5 ERA40 c) P1 P3 Total

23

In Figure 20 the result for ERA40 are presented, each buoy in separate picture. The dashed black line shows the total linear regression for all the periods and the dashed gray line shows the different periods. The gray dots are the observations relatively to the model and the black line is showing when the correlation coefficient is one (this is because the viewer should have something to compare the results with).

In all of these buoys in Figure 20, WAM underestimate the significant wave height, some periods are better and some are worse. The quality of the hindcasts decreases with increasing wave height. This is a consistent phenomena through all the periods in Figure 20. The total linear regression is approximately the same for all the buoys. There is no indication for one place where the model achieves better. So, it is not any differences between the oceans in the east of Sweden and the oceans in the west of Sweden, the quality of the model output is roughly equal. Worth to mention is that period 1 is always better than period 3.

Table 3 shows the values of the total bias, root mean square and the standard deviation. These parameters are very useful in a validation of a model. The bias indicates due to the negative value that the model gives a lower value than the observations. Consequently, the model underestimates the waves, as already noted earlier, for all the buoys. The root mean square, on the other hand, shows that the scattering is different from one buoy to another. In SMHI1, the scattering is not that high, as it is in SMHI5. This can also be seen in Figure 20a and Figure 20c, by looking at the dots. The value of the root mean square in the two buoys is 0.61 for SMHI1 and 0.64 for SMHI5. Consequently, a 0.06 difference.

Table 3: Total bias, root mean square and standard deviation for every buoy (ERA40).

bias rms std

SMHI1 -0.27 0.61 0.54

SMHI3 -0.15 0.78 0.77

SMHI5 -0.15 0.64 0.62

So, when WAM is used with ERA40, a significant negative bias is found with respect to the buoy data. The trend of WAM is to underestimate the significant wave height, which is in agreement with Figure 20. Average bias is -0.19 and the average rms is 0.79.

5.2 RCA

This section shows the result when WAM is forced with the RCA climate model. In contrast to earlier section 5.1, all the periods have been run with RCA. Here, the results are not that consistent as in section 5.1, some periods are much better than the other ones (Figure 21). Both SMHI1 and SMHI3 are really bad in terms of how much it underestimates the wave height. However, when comparing the scattering, SMHI1 is a little bit better.

24

Figure 21: Comparison of significant wave height between model and buoy (RCA).The gray dots indicates

all the values from the model and the buoy, the black dashed line indicates the total linear regression, all periods for this buoy, and the gray lines show the different periods. Hs is here in meters.

0 2 4 6 0 1 2 3 4 5 6 7 Hs (obs) H s (m o d e l) SMHI1 RCA a) P3 Total P1 0 1 2 3 4 0 1 2 3 4 Hs (obs) H s (m o d e l) SMHI2 RCA b) P5 0 1 2 3 4 0 1 2 3 4 Hs (obs) H s (m o d e l) SMHI3 RCA c) Total P2 P1 0 1 2 3 4 5 0 1 2 3 4 5 Hs (obs) H s (m o d e l) SMHI4 RCA d) P6 P5 Total 0 1 2 3 0 0.5 1 1.5 2 2.5 3 Hs (obs) H s (m o d e l) SMHI5 RCA e) P4

25

As could be seen in Figure 21 the waves, in general, are underestimated by WAM. Only one buoy in one period indicates the opposite (SMHI4 period 6). Another, very obviously thing in Figure 21 is that the quality of the hindcasts decreases with increasing wave height. These phenomena can be seen through all of the periods, Figure 21 and Figure 20 as well.

When looking at Figure 21c and Figure 20b, the earlier statement in section 4.2 that ERA40 is better than RCA in period 2 in SMHI3 is confirmed. The same figure (21c), is also showing that period 1 do not represent the waves properly, see also Figure 8b which is illustrating the significant wave high during this period. SMHI5 however, is actually good and confirms the statement in section 4.4 that the model underestimates the height of the waves, even in terms of low waves (this period did not have so high waves).

When forcing WAM with RCA, the differences between the model output on the west coast and the model output on the east coast of Sweden are notable. The buoys west of Sweden (SMHI4 and SMHI5) are better, both in terms of the scatter but also in how much the model underestimate relative the observations. SMHI2, for example, underestimates the wave height more than SMHI4, see Figure 21, and SMHI5 is better than SMHI1. However, SMHI2 is not bad, it underestimates the waves just as match as SMHI5. The difference in rms between the west coast and the east coast is 0.38, and the difference in bias is 0.14. This shows that it is better results on the west coast.

Table 4: Total bias, root mean square and standard deviation for every buoy (RCA).

Bias rms std SMHI1 -0.53 0.93 0.77 SMHI2 -0.40 0.53 0.35 SMHI3 -0.13 1.05 1.04 SMHI4 -0.17 0.55 0.52 SMHI5 -0.16 0.37 0.33

The wave model has a bias of -0.28 (on average) and an rms error of 0.78 (on average) and is extremely bad in two of these buoys (SMHI1 and SMHI3). This leads to a quite misleading result of the average bias and rms. If one not includes these two buoys the values changes to -0.24 for the bias and 0.48 for the rms. And this is, of course, a better result, especially for the rms.

The bias in SMHI3 indicates of a quite good result (-0.13). Unfortunately, the rms is showing the opposite. In Figure 21c one can see that the dots are really scattered. So, the bias can sometimes be rather misleading.

26

6. Discussion

Significant wave height, direction and peak period from MIUU1 in Period 6 (Figures 17, 18 and 19), are really bad described by the model. This was also shown in Period 4, Figures 11, 12 and 13. Due to the lack of data (only period 6 and 4), no clear conclusion can be drawn on the quality of the model when comparing with data from this buoy. Noteworthy is that when FIMR uses this buoy for different aspects, they get good results (Olsonen, 2008). One possible reason that the result from this buoy is not as good as the other buoys can be the location. The site of the buoy is close to Östergarnsholm in the west. Due to the low resolution of the model and the distance from land in the west, the output from the model is bad. SMHI4 and SMHI5 are also near the coast, but they have the coast to the east. The most common wind direction is from the west and this is why this phenomenon only shows up in MIUU1.

In this study, two different type of buoys have been used; Seawatch and Waverider. SMHI2 and SMHI4 are both Seawatch buoys, and the other ones are Waveriders. When comparing the result in Figure 20 and 21 for the different type of buoys, one can see that it is a marginal difference between does. Figure 21d are displaying the best result, in terms of the rate of underestimation, and this is a Seawatch buoy. The difference are small but still a defference worth mention. The scatter is, in fact, also a little bit better for the Seawatch buoys. The value of the root mean square shows this in table 3 and 4. Only SMHI5 is better than both SMHI2 and SMHI4.

6.1 Significant wave height

It was found that, over all in Figures 20 and 21, the significant wave height is underestimated by the model. The bias in Table 3 and Table 4 indicate this as well. The average of the bias is -0.24 and this strengthens the statement of underestimating. Wingeart (2001) did a verification of the WAM model in 2001 and found out that the model, in most cases, underestimated the energy measured by the buoys (Wingeart, 2001). The underestimating can have something to do with the resolution of the model. If the resolution would have been better, maybe the significant wave height would have been better predicted. Cavaleri and Bertotti showed this in 2002 (Cavaleri and Bertotti, 2002). They found out that when increasing the resolution it leads to an improvement of the result. Unfortunately, the bias does not disappear on the highest resolution (about 25 km). In this thesis the resolution are rather small (45 km), so one can expect underestimation. Generally, the model has a hard time to capture the higher waves. For these waves, the model shows a significant underestimation. Woge et al, 2002, got the result that high waves were underestimated as well. They also found out that low waves were overestimated. In Figure 20 and Figure 21 one can see that this agrees, for the lowest waves, in this study. The low waves are, consequently overestimated by the model in this study.

The result from SMHI1 and SMHI3 are, as mention earlier, not good with RCA and SMHI2, SMHI4 and SMHI5 only have one or two periods each with RCA. Because of

27

this, it is hard to draw a conclusion weather the model achieve good results or not with RCA. Still, one conclusion can be drawn about the quality of the RCA data in the first two periods (1996 and 1997), it is not good. These two periods are not well described by the model, see Figure 21ac, Figure 8a and Figure 9a. The underestimation is extremely high and the scatter is not acceptable.

The Danish meteorological institute did a verification of the WAM model in 2002 (Woge et al., 2002). The significant wave height gives reasonable results and was underestimated and the hindcast quality decreases slowly with increasing significant wave height. By comparing the result from Woge et al. with the result in this thesis one can see that the quality of the WAM model is quite consistent everywhere. There is a slightly underestimation and increasing rate of this with increasing wave height.

6.2 Direction and peak period

From the significant wave height in Figure 11 one can draw the conclusion that the wind velocity was not very high during this period (the height of the waves depends on the strength in the wind). In terms of low wind velocity, direction of the wind can vary a lot. This can be seen in Figure 12; the observed waves are often shifting its direction. Due to this high variability in time, WAM can have a hard time to hindcast all of this small fluctuations. When taking this into account, the quality of the hindcast for the direction is reasonable. This can be confirmed with the other buoys and periods shown in Figure 15 and Figure 18. The peak period is not that reasonable. Many fluctuations in the observed peak period are not so well captured by the model. One can even speculate if there is something strange with the observations, especially from MIUU1 in period 4 (Figure 13), due to the fact that it has so many fluctuations.

When not including the statement of variability in direction, the results are not good for this parameter.

6.3 ERA40 vs. RCA

Both ERA40 and RCA show a systematic increase of the underestimation with increasing wave height. RCA seems to be much better after 1997, see Figure 21. The periods after 1997 are resonably in showing the wave height, but also in terms of the scattering. The scattering are more important to know than the mean rate of underprediction. This is due to the fact that the most important thing for the output is to be coherent. The root mean square is a way to see how the scatter varies. The mean of the root mean square for ERA40 and RCA are 0.79 respectively 0.78. So, it is really a marginal difference between these two. It is a more significant difference when one, instead, look at the bias. The mean of the bias for ERA40 and RCA are -0.19 respectively -0.28. So, the output from the model forced with ERA40 is better.

Other then the two first periods with RCA, there is no indication of one period with better results. All periods are good in some of the buoys and bad in others.

28

7. Conclusions

The WAM model has been studied to verify how well it describes the waves in the Baltic Sea. This has been done by comparing the output from the model with observations from buoys, located in the Baltic Sea and on the west coast of Sweden. The study is built on three different parameters; significant wave height, direction and peak period. The final conclusions for this study are:

For the significant wave height the result is, over all, rather good if one does not include the MIUU buoy.

A consistent phenomena through all the buoys are a slightly underestimation. What was shown was that the rate of the underestimation increases with increasing wave height.

Model output around the MIUU1 buoy is not useful, it is too misleading. This is probably due to the resolution of the model.

If one comparing the model output when WAM is forced with the RCA climate model and when it is forced with ERA40 reanalysis, the differences between them are notable but not large. ERA40 shows a slightly better bias. For the root mean square, on the other hand, the results are almost the same for both of them. There are some differences between the east coast and the west coast of Sweden,

when forcing the model with RCA. The output is slightly better with RCA on the west coast. On the contrary, with ERA40 the result is very consistent.

The quality of the hindcast for the direction and the peak period, in contrast to the significant wave height, is not that good. The results are not bad, but it only gives a rough picture of the sea state.

When comparing this study to other similar thesis, the quality of the WAM model seems to be quite consistent everywhere.

In order to be able to use WAM in scientific matter later on, there has to be some

improvement to make the model more efficient. The results from this study are not good enough, especially not for the direction and the peak period. A way to develop the model would be to change the resolution, the resolution in this study is too small.

29

Acknowledgement

Especially thanks to Ph.D. student Alvaro Semedo for helping me with MATLAB and supporting me with many useful ideas. I would also like to thank my supervisor Anna Rutgersson for the help with my writing.

Thanks to Barry Broman (at SMHI) and FIMR for providing me with data from the different buoys.

I also would like to thank Ylva, Malin and my sisters Johanna and Maria for reading my thesis and providing me with useful suggestions for improvement of the text. Furthermore, a big thanks to my classmates and to Tordh for the support and encouragement during this semester.

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Sweden, Hanna Ridefelt

Nr 71 Trilobite biostratigraphy of the Tremadoc Bjørkåsholmen Formation on Öland, Sweden, Åsa Frisk

Nr 72 Skyddsområden för grundvattentäkter - granskning av hur de upprättats, Jill Fernqvist

Nr 73 Ultramafic diatremes in middle Sweden, Johan Sjöberg

Nr 74 The effect of tannery waste on soil and groundwater in Erode district, Tamil Nadu, India A Minor Field Study, Janette Jönsson

Nr 75 Impact of copper- and zinc contamination in groundwater and soil, Coimbatore urban

areas, Tamil Nadu, South India A Minor Field Study, Sofia Gröhn

Nr 76 Klassificering av Low Level Jets och analys av den termiska vinden över Östergarnsholm , Lisa Frost