Forecast spectral wave model for the West Portuguese Coast

Universidade de Aveiro Departamento de F´ısica, 2020

Andr´

e Filipe

Morgado Fernandes

Avalia¸

c˜

ao de um Modelo Espectral de Previs˜

ao de

Agita¸

c˜

ao Mar´ıtima para a Costa Oeste de Portugal

[Forecast Spectral Wave Model for the West

Universidade de Aveiro Departamento de F´ısica, 2020

Andr´

e Filipe

Morgado Fernandes

Avalia¸

c˜

ao de um Modelo Espectral de Previs˜

ao de

Agita¸

c˜

ao Mar´ıtima para a Costa Oeste de Portugal

[Forecast Spectral Wave Model for the West

Portuguese Coast]

Disserta¸c˜ao apresentada `a Universidade de Aveiro para cumprimento dos requisitos necess´arios `a obten¸c˜ao do grau de Mestre em Ciˆencias do Mar e da Atmosfera, realizada sob a orienta¸c˜ao do Doutor Jo˜ao Miguel Sequeira Silva Dias, Professor Catedr´atico do Departamento de F´ısica da Universi-dade de Aveiro e do Doutor Jos´e Paulo Dos Santos Ferreira Pinto, Inves-tigador do Instituto Hidrogr´afico .

o j´uri

Presidente Prof. Doutor Jos´e Manuel Castanheira

Professor Auxiliar do Departamento de F´ısica da Universidade de Aveiro

Arguente Doutora Lu´ısa Andrade e Sousa Lamas

T´ecnica Superior do Instituto Hidrogr´afico)

Orientador Prof. Doutor Jo˜ao Miguel Sequeira Silva Dias

agradecimentos / acknowledgements

The elaboration of a master thesis is a long journey, and mine started when I managed to get an internship in Instituto Hidrogr´afico, where my interest in this field grown exponential. This interest grew due to the ex-cellent researchers of this institution, who helped me in times of need and encouraged me to work this out. First of all, thanks to my supervi-sor Prof. Dr. Jo˜ao Miguel Dias, for his help during the entire process and by providing various means for the accomplishment of my work. I would like to thank Professor / Researcher Jos´e Paulo Pinto for being available to help me on this path and to pass me all his knowledge on this field, as well as to researchers Rita Esteves and Paul Mota of the Hydrographic In-stitute, which helped me during the internship and the entire duration of this process. I also thank the entire Oceanography Department of Insti-tuto Hidrogr´afico for always be disposed to help me out with any matters I needed, specially Margarida Alves, that encouraged me to follow this path since the beginning of my interest on this field. Finally, thanks to my family and friends, who helped and instigated me to follow my goals.

Resumo Este trabalho consiste na valida¸c˜ao de um modelo espectral de 3ª gera¸c˜ao para a costa Oeste de Portugal Continental, atrav´es de uma an´alise com-parativa entre as observa¸c˜oes efectuados por b´oias ond´ografo e os resul-tados de um modelo. Em particular, pretende-se avaliar detalhadamente o desempenho do modelo sob condi¸c˜oes mais energ´eticas, a fim de pro-por poss´ıveis solu¸c˜oes e melhorias que permita prever com maior precis˜ao eventos extremos. As trˆes plataformas meteo oceanogr´aficas mantidas pelo Instituto Hidrogr´afico (IH), a b´oia Alfredo Ramalho em Leix˜oes, a b´oia MONICAN1 na Nazar´e e a b´oia mar´ıtima em Leix˜oes s˜ao os pontos de observa¸c˜ao considerados para a valida¸c˜ao do modelo. O sistema op-eracional utilizado baseia-se no modelo espectral oceˆanico WAVEWATCH III e ´e caracterizado por uma configura¸c˜ao de dom´ınio aninhado, for¸cado globalmente pelo modelo GFS produzido pelo NCEP e localmente pelo European Centre for Medium-Range Weather Forecasts (ECMWF). O m´etodo usado consiste na compara¸c˜ao entre observa¸c˜oes e resultados do modelo, usando v´arios parˆametros estat´ısticos que permitiram quan-tificar a precis˜ao do modelo. Durante condi¸c˜oes energ´eticas, as previs˜oes tˆem fortes correla¸c˜oes com as observa¸c˜oes (acima de 0.80). No geral, as previs˜oes do modelo subestimam os valores das alturas significativas das ondas de aproximadamente 0.5 m, e o modelo faz uma melhor previs˜ao quando as ondas vˆem do quadrante N-NO. Para melhorar o m´etodo de previs˜ao e a sua valida¸c˜ao, ´e necess´ario recorrer a metodologias de assim-ila¸c˜ao de dados, como por exemplo obtidos atrav´es de dete¸c˜ao remota.

Abstract This work consists in the validation of a 3rd generation spectral model for the West Coast of Portugal, through a comparative analysis between the observations made by wave buoys and the results of a model. In partic-ular, it is intended to assess in detail the performance of the model un-der more energetic conditions, to propose possible solutions and improve-ments that allow for more accurate prediction of extreme events.. The three meteo-oceanographic platforms maintained by the Hydrographic Institute (IH), the Alfredo Ramalho buoy in Leix˜oes, the MONICAN1 buoy in Nazar´e and the maritime buoy in Leix˜oes are the observation points considered for model validation. The modelling system used is based on the WAVEWATCH III ocean spectral model and is character-ized by a nested domain configuration, forced globally by the GFS model produced by the NCEP and locally by the European Centre for Medium-Range Weather Forecasts (ECMWF). The method used is to compare observations and model results, using various statistical parameters that allowed quantifying the model accuracy. During energetic conditions, fore-casts have strong correlations with observations (above 0.80). Overall, the model predictions underestimate significant wave height values of approx-imately 0.3 m, and the model makes a better prediction when the waves are from the N-NW quadrant. To improve the forecasting method and its validation, it is necessary to use data assimilation methodologies, such as obtained through remote sensing.

Contents

3 Results and Discussion 9

3.1 Normal conditions . . . 9 3.2 Energetic conditions . . . 24

4 Conclusions 38

List of Figures

2.1 Location of the buoys: nearshore Leix˜oes(a), offshore Leix˜oes (b), and

off-shore Nazar´e (c). . . 5

3.1 Comparison of significant wave height (Hs) between model results (black)

and buoy observations (blue) off the coast of Leix˜oes. . . 10

3.2 Comparison of the peak wave direction (PkDir ) between model results (black) and buoy observations (blue) off the coast of Leix˜oes. . . 10

3.3 Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) off the coast of Leix˜oes. . . 11 3.4 Comparison of significant wave height (Hs) between model results (black)

and buoy observations (blue) offshore Leix˜oes. . . 13 3.5 Comparison of the peak wave direction (PkDir ) between model results (black)

and buoy observations (blue) offshore Leix˜oes. . . 13

3.6 Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) offshore Leix˜oes. . . 14

3.7 Comparison of significant wave height (Hs) between model results (black)

and buoy observations (blue) offshore Nazar´e. . . 16

3.8 Comparison of the peak wave direction (PkDir ) between model results (black) and buoy observations (blue) offshore Nazar´e. . . 16

3.9 Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) offshore Nazar´e. . . 17

3.10 Significant wave height (Hs) scatter plot between model results and buoy

measurements in the coast of Leix˜oes. . . 19 3.11 Significant wave height (Hs) scatter plot between model results and buoy

measurements offshore Leix˜oes. . . 19 3.12 Significant wave height (Hs) scatter plot between model results and buoy

measurements offshore Nazar´e. . . 20 3.13 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements in Leix˜oes coast. . . 21 3.14 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements offshore Leix˜oes. . . 21 3.15 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements offshore Nazar´e. . . 22 3.16 Frequencies of occurence for each station considering the peak wave directions. 23 3.17 Significant wave height (Hs) scatter plot between model results and buoy

measurements in the coast of Leix˜oes. . . 27 3.18 Significant wave height (Hs) scatter plot between model results and buoy

measurements offshore Leix˜oes. . . 28 3.19 Significant wave height (Hs) scatter plot between model results and buoy

measurements offshore Nazar´e. . . 28 3.20 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements in the coast of Leix˜oes. . . 29 3.21 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements offshore Leix˜oes. . . 30 3.22 Peak wave direction (PkDir) polar histograms of model results and buoy

measurements offshore Nazar´e. . . 30 3.23 Frequencies of occurence for each station considering the peak wave

direc-tions during energetic condidirec-tions. . . 31 3.24 Bias and NRMSD representation in direction classes in the coast of Leix˜oes. . 32

3.25 Bias and NRMSD representation in direction classes in the coast of Leix˜oes. . 33

3.26 Bias and NRMSD representation in direction classes in the coast of Leix˜oes. . 33

3.27 Bias and NRMSD representation in class directions offshore Leix˜oes. . . 34

3.28 Bias and NRMSD representation in direction classes offshore Leix˜oes. . . 35

3.29 Bias and NRMSD representation in direction classes offshore Leix˜oes. . . 35

3.30 Bias and NRMSD representation in direction classes offshore Nazar´e. . . 36

3.31 Bias and NRMSD representation in direction classes offshore Nazar´e. . . 37

List of Tables

2.1 Coordinates of the three wave buoys used on this study and their exact loca-tion, depth and number of valid records . . . 6

3.1 Statistics of the coast of Leix˜oes, comparison between model results and

buoy observations for the entire period of study . . . 12 3.2 Correlations, root mean square deviation and bias comparison between model

results and buoy observations for the entire period of study in the coast of

Leix˜oes. . . 12 3.3 Statistics offshore Leix˜oes, comparison between model results and buoy

ob-servations for the entire period of study . . . 15 3.4 Correlations, root mean square deviation and bias comparison between model

results and buoy observations for the entire period of study offshore Leix˜oes. 15 3.5 Statistics offshore Nazar´e, comparison between model results and buoy

obser-vations for the entire period of study . . . 17 3.6 Correlations, root mean square deviation and bias comparison between model

results and buoy observations for the entire period of study offshore Nazar´e. . 18 3.7 Statistics of the coast of Leix˜oes, comparison between model results and

buoy observations for the entire period of study during energetic conditions. . 24 3.8 Correlations, root mean square deviation and bias comparison between model

results and buoy observations during energetic conditions for the entire

pe-riod of study in the coast of Leix˜oes. . . 25 3.9 Statistics offshore Leix˜oes, comparison between model results and buoy

3.10 Correlations, root mean square deviation and bias comparison between model results and buoy observations during energetic conditions for the entire

pe-riod of study offshore Leix˜oes. . . 26 3.11 Statistics offshore Nazar´e, comparison between model results and buoy

obser-vations for the entire period of study during energetic conditions. . . 26 3.12 Correlations, root mean square deviation and bias comparison between model

results and buoy observations during energetic conditions for the entire

Acronyms

bias Bias correction

EEZ Exclusive economic zone GFS Global Forecast System Hmax Maximum wave height Hs Significant height IH Instituto Hidrogr´afico

IPMA Portuguese Institute of the Sea and the At-mosphere

max Maximum

mean Mean

NaN Not a number

NCEP National Centers for Environmental Predic-tion

NRMSD Normalized Root mean square deviation PkDir Peak direction

r Correlation coefficient RMSD Root mean square deviation std Standard deviation

Tp Mean peak period WWIII Wave watch III

Chapter 1

Introduction

The interest in oceanic wave prediction started growing during the Second World War, due to the need to travel long distances and the practical necessity to know the sea state during landing operations on different Oceans around the world Komen et al. (1996). The main complications were to understand the random properties of the ocean surface waves and the complex mechanisms of their evolution. On another hand, the water waves with regular and permanent shapes have been studied for a long time before Mitsuyasu (2002). The base studies for the development of all the works in this field were developed by Sverdrup and Munk, that were the pioneers in suggesting a parametric description of the sea state and used empirical wind sea and swell laws Sverdrup and Munk (1947).

The next foremost step was the introduction of the concept of wave spectrum Pierson (1955), even though that’s a significant advance, it was not accepted by the majority of the scientific community, until it was found a corresponding dynamical equation that described the evolution of the spectrum Gelci et al. (1958). This was a purely empirical expression for the net source function governing the rate of change of the wave spectrum, and the introduction of the concept of spectral transport equation led to the new theories of wave generation published (Phillips (1957);Miles (1957)). In 1962, Hasselmann derived the function for the nonlinear transfer of energy in a gravity-wave spectrum Hasselmann (1962), opening the possibility to write down the general expression for the source function, entailing the three terms representing the input from the wind, the nonlinear transfer and the dissipation by bottom friction (white capping), which are used until our days Komen et al. (1996).

Wave models have been used since then, and Instituto Hidrogr´afico as been using this type of models to predict the meteo-oceanographic parameters for multiple uses along the Portuguese coast, as for example, navigation and scientific purposes. Also, they use their wave buoy network to validate the model results obtained along the coastline, either nearshore and offshore.

activities, the interest in coastal areas, as well as to the impacts of climate changes, which led to increased extreme weather conditions and risk to human lives.

In this context, extreme events are becoming a matter of interest worldwide, since in the last years the human perception of their impact as changed, and is being experienced more often on a global scale, due to some changes on Earth’s Climate. Several studies were done around the North Atlantic Ocean (northern side) with focus on storm climate trends, leading to the conclusion of the increase in storminess and in mean significant wave height between 1953 and 2009 (Bacon and Carter (1991);Wang and Swail (2001);Dowell et al. (2005); Gulev and Grigorieva (2006); Dodet et al. (2010)), as well as in cyclonic activity (Barlow et al. (1997);Geng and Sugi (2001);Gulev et al. (2001)), and a decrease of storminess on the mid and southern latitudes (Cane et al. (1997);Swail et al. (2000);Dodet et al. (2010)). Even though there are some exceptions to these results Almeida et al. (2011) stating that there’s no significant trend in the level of storminess and wave height variability on a decade timescale Group (1998). These studies are mainly focused on small scales, therefore the results may not be that accurate when comparing to large scale studies, since local wind forcing and coastal physiography may induce different results, as showed in a study revealing a wide variability between different coastal regions Nunes et al. (2009). Therefore, it’s important to perform studies with the same periods of data analyzed and for both small and large scale, since the divergences of the results can be inherited to it.

In the last years, there were several works done on the evolution of the sea state under extreme conditions and climate changes influence, such as a project developed on the Atlantic Islands Esteves et al. (2009), aiming to study the waves near the islands under mean global and seasonal conditions as well as under extreme conditions. In 2011, a study was made about the historical variation and trends in storm climate for the South Portugal Region using a method of comparison/validation, between buoy measurements and modelling results for the period 1952 to 2009, leading to a no statistically significant increase or decrease in the variability and relationships between annual number of storms and annual number of days with storms Almeida et al. (2011).

Portugal has increased its activities on the continental shelf in the last few years, since this is a very profitable area, for example on offshore oil prospection Brito et al. (2017), offshore wind farms Pacheco et al. (2017), wave energy farms Palha et al. (2010). A increase in the ship’s traffic across the entire coast was also registered, representing an increase on the risks, generating the need to develop new methods to predict the sea conditions or improve the efficiency of the ones already used. This raised the question of whether it is possible to improve wave prediction and whether the results of the models used are efficient. To improve the performance of a specific 3rd generation spectral model, especially under energetic conditions is necessary to assess it through a comparison between buoy measurements and model results. The focus of this work is on the Portuguese west coast, using buoy measurements along three different locations in order to assess the results obtained by the model Wavewatch III Tolman et al. (2002), a third-generation wave model, during normal and energetic conditions. All the necessary data was given by Instituto Hidrogr´afico(IH), since an internship was per-formed in this institute during a working semester. The modelling system was implemented

in 2002, and covers the Atlantic Ocean area and Portuguese Coast. The model was run by the IH team of the Centro Metereol´ogico e Oceanogr´afico Naval(CMETOC), responsible for ensuring the management and availability of geospatial, meteorological and oceanographic information, essential to plan and conduct Portuguese Navy operations and also the Insti-tuto Hidrogr´afico activities. The buoy measurements were provided by the Oceanographic Division responsible for the maintenance and replacement of the wave-buoys, tidal forecast, hydrographic surveys, and any work-related to oceanography. This work describes the results obtained for a period of 5 years, from 2014 to 2018.

1.1

Literature Review

The studies presented and discussed in this section are exclusively directed to model validation and assessment, aiming to understand the overall performance of a 3rd generation wave model, specifically during energetic conditions in the Portuguese West Coast. These energetic conditions are identified in wave data series and are characterized by obtaining significant wave heights higher than 4.5 m, in the Portuguese West Coast Costa et al. (2001). Wave parameters such as significant wave height, peak period and direction are required to assess a 3rd generation wave model, such as WWIII. To do so, an intercomparison between model results and observations is required, as well as applying statistical methods to the vari-ables previously mentioned Jakimaviˇcius et al. (2018). Worldwide the estimation statistical parameters used for the validation of model results are the bias, RMSD, scatter index (SI) and regression line slope Lo Re et al. (2019).

Waves reaching the Portuguese Coast are mainly generated due to atmospheric processes occurring in the middle of the Atlantic Ocean, forming swell that propagate in the form of waves until reaching the Portuguese coast.

The wave characteristics in the Portuguese West Coast during winter are defined by a high level of long periodic swell, exceeding peak periods of 18 s during several events and 20 s during four events along seven months of sampling Paillard et al. (2000).

Using data from two 3rd generation models, WAM and SWAN, Pilar et al. (2008) obtained a maximum simulated value of significant wave height of 9.18 m and a significant swell height of 8.8 m, validating the observations made by Paillard et al. (2000), as well as predominant high wave conditions from the NW and W directions.

Rusu et al. (2008) made an analysis of the average and high energetic conditions, nearshore and offshore, focusing on the Portuguese Coast for a ten years period, considering the mea-surements available from four different buoys and making a comparison with 40 days of sim-ulations from SWAN. The parameters used to validate the model used by Rusu et al. (2008) were mean significant wave heights, mean wave direction and mean peak period. The results obtained on the buoys were waves propagating from northwest/west directions, significant

wave heights of 1.21 m to 3.67 m, peak periods of 5.7 s to 9.11 s. On model results, the waves also come from northwest/west directions with significant wave heights of 1.17 m to 3.67 m and peak periods around 5.05 s to 10.5 s, showing a good correlation between them.

With the need to understand the wave climate behavior nearshore, also comes the need to predict it offshore in order to obtain boundary conditions for the nearshore simulations. Almeida et al. (2011) used two third-generation models, SWAN and WWIII, and during the entire period analyzed obtained a tendency of the wave forecasting system to underestimate the observed significant wave height, even though the accuracy of the models changes for different areas.

Esteves et al. (2010) made a characterization of extreme wave events in the Portuguese Coast, comparing the winter of 2009-2010 with the 10 years before, obtaining a non-significant increase on normal conditions but an increase on the occurrences during extreme conditions, as well as a shifting from the directions obtained before, from NW/W to W/SW.

Pinto et al. (2014) analyzed 30 years of data in Leix˜oes and Sines, aiming to understand the tendencies of some oceanographic parameters, such as mean significant height, as well as the evolution of frequencies, duration and intensity of extreme events. These studies showed an obvious difference in the climate evolution between Leix˜oes and Sines during normal con-ditions, having a positive tendency up North, and the inversion on the South, and regarding the extreme events a frequency increase on both.

Considering the actual knowledge on wave conditions along the West Portuguese Coast, the gaps that this study intends to analyze are aimed at the specific period of analysis, 2014 to 2018. Since there are no specific studies on the assessment of the spectral wave model used on the IH under energetic conditions, the necessity to assess and try to identify a possible improvement in the wave model prediction was led to the development of this study.

1.2

Thesis Structure

This study is structured into four chapters. First chapter report overall studies published in this field, introducing the history of modeling, an introduction of some research done on extreme events on North Atlantic Ocean as well as in the Portuguese coast. In section 1.1, are presented and discussed some studies developed along the Portuguese Coast related to inter-comparisons between model and buoy data, under normal and energetic conditions. Chapter two presents the description of all the methods used for the analysis of the data collected for both model results and in situ observations. In chapter 3, are presented the results as well as discussion. In chapter 4, are presented the conclusions of this work, discussed the objectives accomplished, and proposed some future research.

Chapter 2

Methods

The dataset used in this work was obtained from three different wave buoy stations, included in the wave buoy network of the Instituto Hidrogr´afico(IH). Specifically, offshore stations use Fugro Oceanor Wavesecan buoys and the nearshore station use a Datawell buoy. This is specifically designed to optimize the wave direction measurements, with internal pro-cessing of all measured parameters, real-time data transfer, high precision position tracker, and high endurance, allowing the user to set this equipment on rush environments if needed. The sampling time used to collect data was 3 hours, and during periods of 30 minutes, in case of normal conditions, while under energetic conditions the sampling is almost continuous, since a small period is necessary for real-time processing.

Figure 2.1: Location of the buoys: nearshore Leix˜oes(a), offshore Leix˜oes (b), and offshore Nazar´e (c).

The model validation with in-situ Fugro Oceanor Wavescan buoys was performed for the period from January 2014 until the end of December 2018, on the coast and offshore Leix˜oes and offshore Nazar´e. Table 2.1 shows the exact position of the three buoys used in this study, the local depth and the number of valid records for each station.

Table 2.1: Coordinates of the three wave buoys used on this study and their exact location, depth and number of valid records

Location Latitude/Longitude Depth (m) Valid Records Offshore Leix˜oes (Oceanor) 41°08.92’N/ 9°34.90’ W 1600 m 68.56 %

Offshore Nazar´e(Oceanor) 39°30.94’ N/ 9°38.24’ W 2000 m 75.53 % Nearshore Leix˜oes (Oceanor) 39°33.61’ N/ 9°12.60’ W 83 m 58.65 %

The parameters acquired by the buoys are: significant wave height (Hs), obtained through the spectral method, maximum wave height (Hmax), peak period (Tp),peak direction (PkDir), representing the direction of the most energetic waves and obtained by spectral analysis.

There are some missing data due to the occasional failure of the buoys, maintenance, transmission failure, or even damaged by energetic conditions, which can limit the results.

To assess the behavior of the third generation wave model it is crucial to understand the mean wave conditions of the study area and to do so, significant wave height, mean wave peak period, and mean peak direction are the parameters used for the purpose.

An inter-comparison between the in situ observations obtained by the buoys and the model results is essential in order to understand what’s the model performance and efficiency. The ocean spectral model WWIII is characterized by a configuration of embedded do-mains forced globally by the GFS model produced by the National Centers of Environment Prediction (NCEP) and locally by the wind fields provided by the Portuguese Institute of the Sea and the Atmosphere (IPMA). The GFS is characterized by winds (u,v ) at 10 m, ice coverage, with a resolution of 0.5° at a global scale and can forecast 144 h after the first day. Meanwhile, the data from IPMA has a resolution of 7,5’, is also predicting winds at 10 m, and only approaches the Portuguese EEZ.

IH uses specific parametrizations to run their model version and in order to obtain con-sistent results and identify specific processes, such as storms and energetic conditions, they forced a 1h time step. The results obtained are for a wide geographical area; therefore, it was necessary to interpolate the results to the points of interest shown on Table 2.1. The main purpose is to validate the performance of the wave model under energetic conditions. There-fore it’s necessary to define such conditions as a period of consecutive sea states in which Hs exceeds a predefined threshold during a minimum period of six consecutive hours, consider-ing Hs higher than 4.5 m. Model results are validated through comparisons with coincident measurements from the three points of interest (Table 2.1). The mean significant wave height (Hs), mean peak period (Tp) and mean wave peak direction (PkDir) were determined through

the following statistical parameters: bias correction (bias),maximum (max), mean mean, nor-malized root-mean-square-deviation (NRMSD), correlation coefficient (r), root mean square deviation (RMSD) and standard deviation (std).

• Bias correction,bias, biasxy = 1 N ∗ X (xi− yi) (2.1) • Mean, x, x = 1 N N X i=1 xi; (2.2) • Normalized root-mean-square-deviation, NRMSD, N RM SD = RM SD ¯ x (2.3)

• Pearson Correlation coefficient, r,

r = PN i=1(xi− ¯x)(yi− ¯y) q PN i=1(xi− ¯x)2 q PN i=1(yi− ¯y)2 (2.4) • Root-mean-square-deviation, RMSD, RMSD = r P i=1(xi− yi)2 N ; (2.5) • Standard deviation, s, s = v u u t 1 N − 1 N X i=1 (xi− x)2; (2.6)

The variables yi represent data obtained by buoy measurements, xi represent model

re-sults from WWIII and N represent the total number of items in the data series. Statistical calculations were performed on MATLAB using inherit functions as for example nanmean, mean, corrcoef, nanstd, max, etc.

After receiving the data set from IH it was necessary to do a primary treatment on both types of data. Firstly the WWIII results had to be run through a script that put together all the variables simulated by the model and save it as .txt files. Secondly, the entire results were added to have a homogeneous time step of the five years of study and to compare them with in situ observations.

The in situ observations data sets had to be rearranged together with the same process used on the model results, but since there are some missing data on the data sets it was

also necessary to introduce NaN values in the matrices when this occurs, to do a plausible comparison with the model results. This occurred due to some repairs needed on the buoy or even to improve the anchor.

To identify differences between model results and in situ observations multiple graphic representations were set for the entire period of study with no restrictions. Figures 3.1,3.2 and 3.3 show an example of Hs, PkDir and Tp for the station in the coast of Leix˜oes. Afterwards the statistical comparison was made using the statistical parameters mentioned before, obtaining the Tables 3.1, 3.2 and 3.3, as well as graphics representing dispersion (example: Figure 3.10), polar histogram (example: Figure 3.13) and frequency of occurrence (Figure 3.16).

The process was similar for the energetic conditions, even though it was necessary to implement the condition that waves must be higher than 4.5 m during a minimum period of six hours as previously mentioned. Regarding this chapter, the graphics representing the entire data set of the variables (Hs,PkDir and Tp) were not represented since they didn’t add any information to achieve our objectives. The statistical parameters were described on Tables 3.4, 3.5 and 3.6, the scatter plots (example: Figure 3.17), the polar histogram (example: Figure 3.20) and the frequency of occurrence (Figure 3.23) were also represented in order to compare both conditions with similar tables and graphics. Even though it was also necessary to represent the bias and NRMSD for several direction classes to understand from what directions the model does an accurate simulation under energetic conditions.

Chapter 3

Results and Discussion

Assessement of the model (WWIII) performance is vital to achieve a deterministic level of confidence on model results, obtained by the intercomparison of model computed parameters with observational data. Routine verifications accomplish this with in-situ buoy observations. This chapter shows two different approaches to assess the model performance, full coverage of the data, set as normal conditions, and energetic conditions whenever Hs is higher than 4.5 m and during at least six consecutive hours. It is essential to understand the model perfor-mance without any restrictions and compare the results with energetic conditions; therefore, the first section presents the results without restrictions and the second during energetic conditions.

3.1

Normal conditions

Figure 3.1 shows the comparison of significant wave heights between model results and buoy observations. It is evident from both model results and observations that mean signifi-cant wave height on Leix˜oes coast was below 3 m most of the time, increasing during periods of energetic conditions, during Autumn to Winter, essentially caused by lower pressures, hurricanes or storms coming from the North Atlantic Sea.

Figure 3.1: Comparison of significant wave height (Hs) between model results (black) and buoy observations (blue) off the coast of Leix˜oes.

Figure 3.2: Comparison of the peak wave direction (PkDir ) between model results (black) and buoy observations (blue) off the coast of Leix˜oes.

The PkDir is represented on Figure 3.2, showing the peak direction of around 300° (S-SE), and a shift occurring mostly during energetic conditions if compared to Figure 3.1. The Tp showed on Figure 3.3 also behaves as the PkDir, which was expected since the higher the waves higher the Tp on the ocean.

Figure 3.3: Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) off the coast of Leix˜oes.

In Leix˜oes coast, the max values of the Hs obtained for the buoy observations and model results were 9.67 m and 7.52 m (Table 3.1), respectively, showing a underestimation by the model predictions. Mean values are 2.32 m and 2.00 m (Table 3.1), on buoy and model results, also exhibiting the underestimation mentioned before. Regarding the std, 1.31 m and 1.09 m (Table 3.1), it is lower on the model results than on the buoy observations, demonstrating a better performance of the model related to the mean obtained.

The results obtained for PkDir are also showed on Table 3.1, and the behavior of the model compared to the buoy observations is similar as the one regarding Hs. The model underestimate the values of the mean but overestimates the max and std values.

The Tp values exhibit similar patterns to the ones obtained for the Hs, a underestimation of the mean and std, but a equal value obtained for the max.

Table 3.1: Statistics of the coast of Leix˜oes, comparison between model results and buoy observations for the entire period of study

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 2.32 1.31 9.67 2.00 1.09 7.52

Tp (s) 11.3 2.6 17.4 9.4 2.2 17.4

PkDir (°) 302 22 349 301 23 357

The correlation values obtained were represented on Table 3.2, showing a very strong correlation in the Hs between the in situ observations and the model results, a strong corre-lation of the Tp and a moderate correcorre-lation regarding the PkDir. To verify the model results accuracy, the root-mean-square deviation (RMSD ) was calculated and the results for the Hs were 0.47 m, 2.45 s for the Tp and 19.88° for PkDir, which demonstrate the slight difference between the mean predicted values and the observations. To understand the magnitude of the errors predicted by the model, the bias was calculated and the values obtained are 0.29 m for the Hs and 1.93 s for Tp, represented on Table 3.2.

Table 3.2: Correlations, root mean square deviation and bias comparison between model results and buoy observations for the entire period of study in the coast of Leix˜oes.

Variables r RMSD bias Hs 0.95 0.47 m 0.29 m Tp 0.80 2.45 s 1.93 s PkDir 0.64 19.88°

-Figure 3.4 represents the significant wave height offshore Leix˜oes, that is very similar between the model results and the buoy observations. The mean Hs was around 2 m as shown on Table 3.3. The maximum values both on the model results and on the observations had some discrepancy, even though inducing an expected very strong correlation.

The PkDir was represented in Figure 3.5, showing the mean peak direction of around 300° (S-SE), as would be expected since the stations are not very far from each other. There is also a shift occurring mostly during energetic conditions if compared to Figure 3.4 as found in Figure 3.1.

Figure 3.4: Comparison of significant wave height (Hs) between model results (black) and buoy observations (blue) offshore Leix˜oes.

Figure 3.5: Comparison of the peak wave direction (PkDir ) between model results (black) and buoy observations (blue) offshore Leix˜oes.

The Tp represented on Figure 3.6 presents the same behavior as the PkDir, higher values obtained during energetic conditions and lower during calm periods of ondulation. There are several gaps in the buoy observations, during the end of 2015 as well as missing model results for the entire period of 2014. This occurred due to some repairs needed on the buoy or even to improve the anchor.

Figure 3.6: Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) offshore Leix˜oes.

Table 3.3 reveals similar statistics than Table 3.2, which was expected since the sampling locations are not that far from each other as mentioned before. Mean values of Hs around 2 m, std of 1 m and max of 9.98 m on the observations and 7.88 m on model results.

Regarding PkDir a mean of around 305°and a std of around 30°, proving the statement previously said about both buoy observations and model results shown on 3.5.

The Tp results show a disagreement between model results and buoy observations, 2 s difference between the mean, an std of 2.3 s and 2.8 s and a significant discrepancy on the max, 17.3 s and 25.1 s, respectively.

Table 3.3: Statistics offshore Leix˜oes, comparison between model results and buoy observa-tions for the entire period of study

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 2.43 1.27 9.98 2.15 1.11 7.88

Tp (s) 11 2.8 25.1 9.1 s 2.3 17.3

PkDir (°) 305 31 359 306 27 360

Correlation, RMSD and bias are shown on Table 3.4, demonstrating a very strong corre-lation on Hs (0.94), a strong correcorre-lation on Tp (0.80), and a moderate correcorre-lation on PkDir (0.56). Comparing to the correlations obtained on Table 3.2, a similar performance of the model on all the parameters was verified for both stations.

This is also reflected on the RMSD results, 0.50 m on the Hs and 2.45 s on Tp , they are very similar as the results obtained on Table 3.2, even though there is a small difference on the PkDir (27.64°).

Concerning to the bias values, the order of magnitude is also identical as the obtained in the coast of Leix˜oes, regarding Tp but not the Hs. This indicates that even though the model performance is good, the value simulated by the model has a deviation from the buoy observation.

Table 3.4: Correlations, root mean square deviation and bias comparison between model results and buoy observations for the entire period of study offshore Leix˜oes.

Variables r RMSD bias Hs 0.94 0.50 m 0.06 m Tp 0.80 2.45 s 2.11 s PkDir 0.56 27.64°

-From the analysis of the station offshore of Nazar´e, it was possible to verify if the model results were also accurate in a point far from the two other locations. Figure 3.7 represents the Hs results and during the early year of 2014 there was no data from the buoy observations, probably due to the same issues previously referred. During the energetic seasons, it was possible to identify six peaks of maximum Hs, with the higher achieved with almost 10 m in 2017. There were some discrepancies between the model results and buoy observations which may lead to lower values of correlation afterward. The mean Hs is around 2 m as the values obtained for the stations in Leix˜oes, which were represented on Tables 3.1 and 3.3.

Figure 3.7: Comparison of significant wave height (Hs) between model results (black) and buoy observations (blue) offshore Nazar´e.

Figure 3.8: Comparison of the peak wave direction (PkDir ) between model results (black) and buoy observations (blue) offshore Nazar´e.

The PkDir is represented in Figure 3.8, showing the mean peak direction of around 300° to 310° (S-SE), as expected due to the specific wave groups that reach the Portuguese Coast propagating from the North Atlantic Ocean. There were a few points around 0° and 50° which were not found for the other stations, that may be due to the geography of the local, for instance the Nazar´e Submarine Canyon. The Tp represented in Figure 3.9 presents the same behavior as the PkDir, with higher values obtained during energetic conditions and lower during calm periods of undulation. There are several gaps in the buoy observations, during the end of 2015 as well as missing model results for the entire period of 2015.

Figure 3.9: Comparison of the peak period (Tp) between model results (black) and buoy observations (blue) offshore Nazar´e.

Table 3.5: Statistics offshore Nazar´e, comparison between model results and buoy observa-tions for the entire period of study

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 2.33 1.20 9.99 2.14 1.12 8.82

Tp (s) 11.0 2.8 22.7 9.4 2.3 19.1

PkDir (°) 310 41 360 309 25 360

Table 3.5 shows statistics identical to Tables 3.1 and 3.3, with mean values of Hs around 2 m, std of 1.1 m and max of 9.99 m on the observations and 8.82 m on model results.

than 10°, even though the mean of around 310° and the max 360° are similar. The Tp results shown a disagreement between model results and buoy observations, around 1s difference between both means, an std of 2.3 s and 2.8 s and max of 19.1 s and 22.7 s, respectively.

Overall, all the three stations present similar performance of the model when analysing the entire results for all three different variables, even though the offshore Nazar´e station shown higher values of std on the buoy observations compared to the model results and on Leix˜oes coast the std of the PkDir is higher on the model results.

The correlations obtained in offshore Nazar´e for all the variables under study (Table 3.6) were very strong on Hs, strong on Tp and weak on PkDir results. Accordingly, to the previous evaluation of the other stations, this station has a lesser correlation on the PkDir, which may be induced by the geography of the local as mentioned before.

RMSD was similar to the results obtained for previous stations, with a higher value on the PkDir, as expected. The complex structure of the Cannon may induce a decrease in the accuracy and overall performance of the model on this specific station.

The bias for all the variables bias were in the same order of magnitude as the results obtained on Table 3.2. This indicates the estimator is biased in all stations, even though on offshore Leix˜oes the order of magnitude of the Hs is smaller than the obtained on the others stations.

Table 3.6: Correlations, root mean square deviation and bias comparison between model results and buoy observations for the entire period of study offshore Nazar´e.

Buoy

Variables r RMSD bias Hs 0.93 0.50 m 0.18 m Tp 0.79 2.4 s 1.87 s

PkDir 0.37 40°

-Dispersion is the measure of the variation between variables and in the coast of Leix˜oes (Figure 3.10) the error increased with the increase of Hs, mainly when under energetic condi-tions (Hs¿4.5 m). The slope value of 0.85 indicates a positive increase of the dispersion over the mean value.

Figure 3.11, representing the station offshore Leix˜oes, indicated a lower dispersion than the one obtained on Figure 3.10, as well as a smaller slope which indicates a slower increase of the dispersion over the mean.

Figure 3.10: Significant wave height (Hs) scatter plot between model results and buoy mea-surements in the coast of Leix˜oes.

Figure 3.11: Significant wave height (Hs) scatter plot between model results and buoy mea-surements offshore Leix˜oes.

Offshore of Nazar´e (Figure 3.12), the dispersion was similar to offshore Leix˜oes (Figure 3.10, with a slope of 0.84 which indicates a strong positive linear relationship between both model results and buoy observations.

Figure 3.12: Significant wave height (Hs) scatter plot between model results and buoy mea-surements offshore Nazar´e.

In order to analyse in detail the wave direction pattern, a representation of the number of occurrences of the PkDir was developed in a polar histogram for each station. In Figure 3.13, showing the Coast of Leix˜oes, the maximum number of occurrences in the PkDir was found coming from the quadrant NW, and a few from the North quadrant, both in the model results and in the buoy observations.

Regarding offshore Leix˜oes station (Figure 3.14), the most frequent occurrences were also found for the same quadrant in the buoy observations, but for the model results there are a small shift with some waves propagating from the West quadrant.

As for offshore Nazar´e, the wave pattern was the same as for the stations mentioned above, with waves propagating from the quadrant N-W. These results confirm the expected wave patterns in the Portuguese Coast due to the important influence of the North Atlantic Ocean in the ondulation directions on the West coast.

Figure 3.13: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements in Leix˜oes coast.

Figure 3.14: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements offshore Leix˜oes.

Figure 3.15: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements offshore Nazar´e.

The number of occurrences or the regularity with which a class of the PkDir occurs was represented in a histogram (Figure 3.16) for each station for both model results and buoy observations. On Figure 3.16 (a and b) the highest frequency of occurrence were set on range directions of 280º to 330 º, on the buoy observations as well as in the model results, even though in the model results the frequency of occurrences was higher in the class of 300° to 330° compared to the buoy observations. Concerning to offshore Leix˜oes, the pattern was similar, although on the model results the frequency of occurrence is higher for the range of 280° to 330° than the represented for the buoy observations. Offshore Nazar´e the situation was similar, the buoy data showed the higher frequency of occurrence on the range of 280° to 360° and in the model results the higher frequency of occurrence was set on the class around 300° to 330° with almost 50 percent of the occurrences.

(a) Leix˜oes nearshore (b) Leix˜oes nearshore

(c) Leix˜oes offshore (d) Leix˜oes offshore

(e) Nazar´e offshore (f) Nazar´e offshore

3.2

Energetic conditions

This section shows the comparison between model results (WWIII) and buoys measure-ments during energetic conditions. Energetic conditions were established when the Hs is higher than 4.5 m, at least for a period of six consecutive hours. This requires extreme condi-tions occurring in the North Atlantic Ocean in order the wave groups travel along the ocean to reach the Portuguese coast with sufficient strength to establish energetic conditions. The results are shown through tables and graphics with statistical analysis.

Table 3.7 illustrates the statistics of Hs obtained for the coast of Leix˜oes, with max values of 9.67 m on the buoy observations and 7.52 m on the model results, revealing a underestimation by the model. Results showed that under energetic conditions the mean values of Hs are higher than 5.5 m, as during under normal conditions the mean was between 2 to 2.32 m (Table 3.1). The std was also different between both normal and energetic conditions, with lower values achieved during energetic conditions, 0.68 m and 0.97 m (Table 3.7).

The PkDir results showed on Table 3.7 revealed similar values to the mean, as the ones obtained on Table 3.1, which led to the conclusion that the peak wave directions during energetic conditions or extreme events occurring in the North Atlantic ocean were the same as during normal conditions. Comparing std during both conditions, for the energetic conditions was found a lower value that indicates a small measure of data dispersion around the sample mean than during normal conditions.

During extreme conditions the Tp are usually higher than under normal conditions, as found comparing the results obtained on Table 3.7 with those on Table 3.1. Mean values of 12.3 s on the model results and 15 s on buoy observations, lower than the values obtained under normal conditions, as well as bigger std values.

Table 3.7: Statistics of the coast of Leix˜oes, comparison between model results and buoy observations for the entire period of study during energetic conditions.

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 6.22 0.97 9.67 5.51 0.68 7.52

Tp (s) 15 2.0 18.2 12.3 1.6 17.4

PkDir (°) 300 15 331 299 12 326

The correlations between buoy observations and model results are shown in Table 3.8, with 0.60 regarding Hs, which indicates a moderate correlation. Comparing this result with normal conditions (Table 3.2), 0.95 , during energetic conditions the model predictions are less accurate due to the use of specific parametrizations/inputs as well as a model based on mean values. The model accuracy under energetic conditions was also assessed through the calculation of the RMSD, resulting in a 1.05 m deviation from the expected value. Comparing

it with normal conditions, this value is higher which induces a less accurate performance of the model for this variable during energetic conditions. The magnitude of the errors of the wave model during energetic conditions was also determined by the calculation of the bias parameter, 0.71 m, that is also significantly higher than the value obtained on Table 3.2. Once again this show that the model performance under energetic conditions is less accurate, even though it is viable for the necessities of IH, specially under normal conditions.

Statistical analysis represented on Table 3.7 for the PkDir showed a pattern similar to that described for Hs, overall, a moderate correlation between buoy observations and model results, a RMSD lower than the ones obtained on Table 3.2. Regarding the Tp, a strong correlation between buoy observations and model results, a higher RMSD and a higher bias. Comparing the correlation between normal and energetic conditions it is obvious that the model performance during energetic conditions is worst, even though the Tp correlation is similar as the obtained in normal conditions.

Table 3.8: Correlations, root mean square deviation and bias comparison between model results and buoy observations during energetic conditions for the entire period of study in the coast of Leix˜oes.

Buoy

Variables r RMSD bias Hs 0.60 1.05 m 0.71 m Tp 0.77 2.93 s 2.63 s Dir 0.62 11.97°

-Under energetic conditions the station offshore Leix˜oes showed a Hs mean of 6.01 m on the buoy observations and 5.63 m in the model results (Table 3.9), which compared with Table 3.3 are higher due to the energetic conditions analysed, which are during times of Hs higher than 4.5 m. The std is between 0.8 m and 1.06 m, showing smaller values when compared to the normal conditions (Table 3.3). These results are similar for Tp, even though the max was lower on the buoy observations than during normal conditions. This only occurred due to the analysis of energetic conditions required a period of six consecutive hours with a Hs higher than 4.5 m. PkDir has lower mean values, with a difference of around 5° from the normal conditions (Table 3.3), once again showing the impact of the North Atlantic Ocean storms in the ondulation on the Portuguese West coast. The std was lower, demonstrating a smaller deviation from the mean, comparing to normal conditions.

Table 3.9: Statistics offshore Leix˜oes, comparison between model results and buoy observa-tions for the entire period of study during energetic condiobserva-tions.

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 6.0 1.06 9.97 5.51 0.72 7.88

Tp (s) 14.1 2.1 21.3 12.5 1.6 21.3

Correlation, RMSD and bias were represented on Table 3.10, showing a strong correlation on Hs and Tp, 0.7929 and 0.8131, respectively, as well as a very strong correlation on the PkDir, 0.8766. Comparing to the results under normal conditions (Table 3.4), a similar pattern was attained . In the station of the coast of Leix˜oes lower correlation on Hs and higher correlation on Tp and PkDir.

RMSD and bias results showed a similar pattern as the one achieved on the coast of Leix˜oes. The RMSD is higher for the Hs when compared to Table 3.4 but both Tp and PkDir were lower.

The order of magnitude of bias is significantly higher for the Hs but similar when com-paring to the Tp found on Table 3.4.

Table 3.10: Correlations, root mean square deviation and bias comparison between model results and buoy observations during energetic conditions for the entire period of study off-shore Leix˜oes.

Buoy

Variables r RMSD bias Hs 0.79 0.85 m 0.55 m Tp 0.80 2.64 s 2.34 s Dir 0.88 10.86°

-Offshore Nazar´e, the statistics analysis (Table 3.11) were also similar to the results for both Leix˜oes coast and offshore Leix˜oes. With Hs mean values higher during energetic conditions, 6.03 m and 5.65 m, as well as lower std on both buoy observations and model results. This was also verified for PkDir, even though the max values obtained for Tp and PkDir were lower than during normal conditions.

Table 3.11: Statistics offshore Nazar´e, comparison between model results and buoy observa-tions for the entire period of study during energetic condiobserva-tions.

Buoy WWIII

Variables Mean Std Maximum Mean Std Maximum

Hs (m) 6.11 0.99 9.99 5.57 0.74 7.57

Tp (s) 15.2 2.2 21.8 12.63 1.9 19.1

PkDir (°) 310 18 350 309 17 341

Table 3.12 shows strong correlations between model results and buoy observations for the three variables under study, with strong correlations. Comparing with normal conditions (Table 3.6), the Hs correlation was lower, revealing a less accurate model results under en-ergetic conditions. This was also demonstrated by the RMSD results, with almost 1 m of deviation, which was almost twice the result obtained during normal conditions. The bias results also showed a higher value when comparing with normal conditions (Table 3.6) for all the variables. The correlations obtained for both Tp and PkDir were 0.8179 and 0.8846,

respectively, showing a higher performance of the model results for both, when comparing to normal conditions. The std were both lower, denoting an increase on the model performance comparing to Table 3.6.

Table 3.12: Correlations, root mean square deviation and bias comparison between model results and buoy observations during energetic conditions for the entire period of study off-shore Nazar´e. Buoy Variables Correlation RMSD r Hs 0.68 0.91 m 0.53 m Tp 0.82 2.83 s 2.53 s Dir 0.89 8.72°

-To understand the variation between buoy observations and the model results, a dispersion graphic is also presented as in the section for normal conditions. Figure 3.17, referent to the coast of Leix˜oes, shows some deviation from the mean, and also an increase of the error with the increase of Hs. This was also verified for the other two stations (Fig 3.18 and 3.19), and when compared to normal conditions, a positive linear trend was obtained for the coast of Leix˜oes (Figure 3.10) and for offshore Leix˜oes and Nazar´e (Figure 3.11 and 3.12).

Figure 3.17: Significant wave height (Hs) scatter plot between model results and buoy mea-surements in the coast of Leix˜oes.

Figure 3.18: Significant wave height (Hs) scatter plot between model results and buoy mea-surements offshore Leix˜oes.

Figure 3.19: Significant wave height (Hs) scatter plot between model results and buoy mea-surements offshore Nazar´e.

The wave direction pattern under energetic conditions was represented in Figures 3.20, 3.21 and 3.22 . The larger number of occurrences of PkDir on the coast of Leix˜oes (Figure 3.20 corresponds to waves propagating from the NW quadrant, as well as between N to NW quadrants. Both model results and observations had similar patterns, even though the buoy observations showed more occurrences propagating from the NW quadrant.

Figure 3.20: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements in the coast of Leix˜oes.

In offshore Leix˜oes, Figure 3.21, the same larger number of occurrences were identified in the buoy observations and model results, ondulation propagating from the NW quadrant and in between N to NW quadrants. There are some occurrences observed from the N to NW quadrant on the model that weren’t so high on the buoy observations due to the errors associated with the parametrizations of the model.

Offshore Nazar´e (Figure 3.22, the ondulation had similar directions, with most occurrences propagating from the NW quadrant, even though there was a slight difference between the buoy observations and the model results.

Figure 3.21: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements offshore Leix˜oes.

Figure 3.22: Peak wave direction (PkDir) polar histograms of model results and buoy mea-surements offshore Nazar´e.

Figures 3.23 (a) and (b) show the frequencies of occurrence of the PkDir on the coast of Leix˜oes during energetic conditions. On the buoy observations, a peak was identified between the ranges of 300° to 320°, with almost half of the occurrences. This is observed in the model results, even though there was a small shift to the 300° instead of between the range of 300° to 320°.

(a) Leix˜oes nearshore (b) Leix˜oes nearshore

(c) Leix˜oes offshore (d) Leix˜oes offshore

(e) Nazar´e offshore (f) Nazar´e offshore

Figure 3.23: Frequencies of occurence for each station considering the peak wave directions during energetic conditions.

Offshore Leix˜oes (Figure 3.23 (c) and (d)) shows a similar pattern, with the most frequent occurrences for the 300°, even though on the model results there were slightly higher percent-age on the highest directions. Offshore Nazar´e (Figure 3.23 (e) and (f)) the most frequent occurrences were found for the same directions as in Offshore Leix˜oes, but in the ranges of 310° to 320° and 280° to 300° the percentages were lower.

In order to assess in which direction classes the model makes a good simulation, direction class graphics with bias and NRMSD representations were made for each station. Figure 3.24 shows higher values of bias in the class of 180° to 225°, being a positive variation of Hs of almost 0.15 m in the coast of Leix˜oes. Regarding the NRMSD in the coast of Leix˜oes, the highest values were obtained on the higher classes, having differences of around 15 % between values observed and model simulations, showing a low residual variance.

Figure 3.24: Bias and NRMSD representation in direction classes in the coast of Leix˜oes.

Analysing the variable Tp on the same station, it was found that the higher bias (Figure 3.25) was on the same class as the Figure 3.24, class 180° to 225°, even though it has a negative variation of around 1 s. The NRMSD has higher values on almost all classes represented, with the highest, almost 10 %, in the class of 225° to 270°.

The analysis of Figure 3.26 shows a similar pattern of bias as the obtained on Figure 3.25. The highest value, around −40° is on the same class, 180° to 225°, and also has a negative variation. NRMSD obtained in the coast of Leix˜oes regarding PkDir was higher on the same class as the bias, 180° to 225° with almost 40 % difference.

Figure 3.25: Bias and NRMSD representation in direction classes in the coast of Leix˜oes.

Offshore Leix˜oes (Figure 3.27) the highest value of bias was in the class of 225° to 270°, even though the difference between buoy observations and the model results are in the order of 10−3. NRMSD shows a variation of almost 15 % between model results and buoy observations in the class of 315° to 360°.

Figure 3.28 shows the highest bias of around 0.04 s in the class between 225° to 270°. Regarding the NRMSD the values for each class are similar, being all higher than 4 %.

Analysing Figure 3.29, the bias of the PkDir is highest in the class of 225° to 270°, with almost −0.4° difference between buoy observations and model results. The higher value of NRMSD is also represented in the same class as bias, with almost 8 % difference between model results and buoy observations.

Concerning the station offshore Nazar´e (Figure 3.30), it was found a higher value of bias, almost 0.02 m, in the class of 225° to 270°. The NRMSD shows a different pattern, with two classes, 270° to 315° and 315° to 360°, with almost the same value, around 15 %.

Figure 3.31, representing Tp, shows a similar pattern as the obtained for Figure 3.30, with the highest value of bias in the class of 225° to 270° and several higher values of NRMSD, almost 6 %, in all the classes represented.

Figure 3.28: Bias and NRMSD representation in direction classes offshore Leix˜oes.

Analysing Figure 3.32, it was found a higher negative value of bias, around −0.4° in the same class as obtained on Figure 3.31, 225° to 270°. Regarding the NRMSD, the higher value obtained was in the class between 225° to 270°, around 4 %, even though all the other classes has similar values.

Overall, under energetic conditions the higher classes of directions has bias close to zero and also there are small values of NRMSD, showing a good quality of forecast. In some cases there are slight underestimation or overestimation of the study variables, being the higher overestimation obtained in the coast of Leix˜oes in the class direction of 180° to 225°.

Figure 3.31: Bias and NRMSD representation in direction classes offshore Nazar´e.

Chapter 4

Conclusions

This dissertation had as main objective the analysis of the performance of the model WWIII during five years of sampling, 2014 to 2018, specifically under energetic conditions in the Portuguese West Coast. An assessment of the performance of the WWIII of IH on predicting Hs, PkDir and Tp was performed by comparative analysis with buoy observations, in order to validate the use of this specific model. According to the statistical analysis of Hs, it was possible to conclude that during normal conditions the model results are very good for all stations. Regarding Tp, the performance of the model overall was good, however, PkDir analysis showed only a moderated performance. RMSD ranges of Hs were 0.35 m to 0.42 m, revealing a good accuracy of the model results. As bias with the order of magnitude between 10−6 to 10−5, allowing to conclude the small deviation from the expected value.

Model performance under energetic conditions was slightly different from normal condi-tions, specifically on the Hs analysis, where the correlation value is lower when compared to normal conditions. Taking into account the performance of the wave model (WWIII) under energetic conditions was good, but it was explicit the underestimation of the Hs results on the three stations. Concerning the performance of the model under separate class directions, it was found that the model has a better performance when the waves come from N-NO.

The assessment performed in this study showed that the wave model (WWIII) used by the IH underestimate the Hs under energetic conditions. However, the overall correlations are strong and had an error of fewer than 1 m which is good for its intended use. Therefore, during the five years of sampling, the results obtained were in agreement with the Portuguese West Coast trends.

A better way of achieving a better assessment and validation of spectral models of 3rd generation, such as WWIII, would be an assimilation of optical remote sensing satellites and field observations to predict surface indicators such as Hs. To identify specific processes or variables that are not directly observed, these method of assimilation provides a wide range of applications and can improve significantly the precision of wave models such as WWIII.

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