**5. Suicide prevention via social media usage**

As has been reiterated severally, and with good reason, Social media have changed the world as we have come to know it, and this includes the mental health of the populace. The potential detrimental, stressor and suicidal capacity of social media use has been largely investigated and somewhat accepted. Dissimilarly, however, the potential use of online social media in suicide prevention is only in its infancy as it is only recently started accruing mainstream attention.

Logically, preventing any menace will center majorly on efforts to handicap its perpetrating factors, and in the same vein, involve an in-depth understanding of its underlying mechanism and attempting to impede it at any and several stages in its evolution.

Almost all cases of successful and failed suicidal attempts have a Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) psychiatric illness. Mood disorders, principally major depressive disorder and bipolar disorder are associated with about 60% of suicides [26–28].

Consequently, any efforts at using social media to avert suicide must cater for mental health broadly; increasing its awareness, diagnosis and treatment alongside providing a means to access appropriate help.

Nowadays, in the age of the internet, young people can effortlessly access and share content across the globe in the snap of a finger using varying platforms including but not exclusive to collaborative projects (e.g. Wikipedia and social bookmarking), blogs and microblogs (e.g. Twitter), content communities (e.g. YouTube), social networking sites (e.g. Facebook, WhatsApp), virtual game and social worlds [29]. These avenues can and have been used by youth to find out about suicide and varying means of perpetrating it as well as making suicide pacts with other distressed individuals. Alas, fortunately, this provides an opportunity to find and intervene early if someone expresses suicidal intent as well as an avenue for people who have felt suicidal in the past to help persons currently feeling so.

In a small-scale internet survey administered by Robinson et al. they noted that respondents had identified social media as an avenue to provide support and equally receive help as relating to suicide, with the respondents acknowledging increased feelings of well-being by being able to help and support suicidal persons; the latter further accentuating previous reports that social media users found the ability to help therapeutic in and of itself. This beneficial reversibility of roles provided by social media is not applicable in one-on-one therapy. Another immense advantage of social media also highlighted by respondents was the potential to intervene swiftly if and when persons expressed suicidal intent online. Two previous studies cited this as a unique benefit of social media [30, 31]. One of these reports [31] described a successful intervention in a suicide attempt following the posting of a suicide note on Twitter.

A more representative and personal experience is shared by Reidenberg, the Executive director of the United States-based prevention organization Suicide Awareness Voices of Education (SAVE) [32].

Daniel Reidenberg was scanning Facebook for his suicide-prevention organization on a Friday evening in the spring of 2014 when he noticed the post of a clearly suicidal young widow who had declared the intent to take her life and that of her baby. As he had a wealth of experience working with Facebook and other digital companies on the prevention of suicide, he knew exactly what to do: he contacted Facebook's safety center. Although, there was no indication in the post of the woman's location, he knew Facebook would still be able to find her, and that they did in very few minutes. Facebook employees determined the woman had posted her message from an Internet café in a small village in South America. They contacted the local police. Holding a picture from the woman's Facebook page, police officers walked through the village. Within ten minutes of leaving the café, the police found were able to find her and get her into a hospital and get her childcare [32].

With 2 billion people using social media and 500 million people posting on Facebook alone, there is "a lot of opportunity for intervention and prevention," says Reidenberg. "It's critical that everyone starts looking at this new era with technology being involved in the field of suicide prevention. It isn't just going to a doctor's office any longer—it is that 'plus'."

"In a few short years since some of the big social media companies began meeting periodically at Facebook's California head office in 2011 to brainstorm about what to do, the world's largest social network has rolled out a direct intervention. In 25 of the 50 American states, when a user posts a message on Facebook containing a phrase that its algorithms flag as indicating suicidal thoughts or intentions, a banner

#### *Social Media and Suicide DOI: http://dx.doi.org/10.5772/intechopen.92160*

pops up on the user's page. Friends viewing the post can also click on an icon that reports the message, sending it to the Facebook safety centre to review" [32].

The automatic banner asks whether the user needs help and provides the number of the National Suicide Prevention Lifeline. Facebook then contacts the user and offers to connect him or her to the distress line. The message includes tips and links to support videos aligned with best prevention practices. Facebook may also freeze the user's page until the person in distress has interacted with the support applications. The program is billed to be expanded to the entire country and is even said to piloted in some undisclosed countries [32].

A psychiatrist has said that Facebook's program raises a 'thorny' issue as users can post content they don't intend to act on. Reidenberg acknowledged that companies are wrestling with the privacy issue, but he reminded the audience at the International Association for Suicide Prevention's annual conference in Montréal, Quebec, that once someone posts anything on a social media site—even if it's personal health information—it is no longer private [32].

## **6. Novel approaches to suicide prevention**

Current efforts at suicide prevention center largely on reducing suicidal desire among individuals hospitalized for suicidality or being treated for related psychopathology. Such efforts have yielded evidence-based treatments, and yet the national suicide rate has continued to climb [33]. The contrast between the robust evidence base for several treatments and the continually increasing suicide rate points toward a vital disconnect between the primary problem and the tools we are using to address it [33].

Rightly so, new frontiers and novel approaches to suicide prevention are emerging by the day. One such compelling proposal was made by Michael et al. [33], who propose that this disconnect is heavily influenced by an unmet need to consider population-level interventions aimed at reducing the capability for suicide.

HIV death rates peaked in 1965, necessitating the need for national-level intervention strategies. However, one that was noted to have been quite effective was the needle exchange program whose aim was to reduce needle sharing, which at the time was the main means of contracting the disease. It also provided an avenue for counseling and health education on safe sex and intravenous drug use. A similar approach was employed to drastically reduce the incidence and prevalence of lung cancer by aggressive public education, increased taxation of cigarette companies, policies limiting places where smokers could publicly smoke as well as the introduction of cigarette filters. By the same token, vehicular accidents were massively reduced by laws imposing the use of seatbelts, child passenger safety and bans on alcohol consumption whilst driving.

Drawing from these largely successful interventions that quelled major public health concerns, Michael et al. resolved that a similar population-level means restriction approach be undertaken. They postulate that achieving a position of strength as regards suicide prevention will stem from a more adept understanding of the mechanism underpinning various aspects of suicide risk. A recent metaanalysis by Franklin et al has shown no increased predictive value of the past few decades of research examining traditional risk factors of suicide. Besides, research has shown that lots of people who think about taking their own lives, never do and the great majority who do try do not die by suicide. The failure of these traditional methods has led to a new approach in suicidology, "ideation to action framework", which has heralded the various psychological theories of suicide. Foremost and oldest amongst these theories is the interpersonal theory of suicide.

The interpersonal theory of suicide (ITS) [34] posits that individuals are at greatest risk of suicide ideation when they feel a sense of burdensomeness to others, lack a sense of belonging, and feel hopeless that these states will change. Although, the ability to make a suicidal attempt is acquired through exposure to painful and provocative events, such as experiences that heighten individuals' pain tolerance and fearlessness about death. Examples of such painful and provocative events include starvation [35], risky illegal behaviors [36], and combat [37]. Additionally, research has indicated that genetic factors may influence individuals' capability for suicide [38]. Conclusively, both suicidal ideation and suicidal capacity must be present for suicidal behavior to ensue [33]. O'Connor's Integrated Motivational– Volitional Model of Suicidal Behavior (IMV) [39] is another suicidal theory influenced by the ITS. Both the IMV and ITS have been empirically tested and supported [40]. Klonsky and May [41] have proposed and empirically tested the most recent of theory within the ideation to action framework, the Three-Step Theory (3ST).

All three theories posit that suicidal intent and suicidal capacity must be present for suicide to ensue. Although defined somewhat differently across each theory, they posit that for a suicidal or lethal attempt to occur, suicidal capacity must be in play. It is important to note that capacity is not in and of itself pathological, in actual fact it is beneficial and can be adaptive in the right circumstances. For instance, increased comfort with blood would prove beneficial to emergency doctors and nurses, likewise, an increased fearlessness of death would enable soldiers to complete a dangerous mission. However, in conditions where persons with an elevated capacity for suicide also experience danger and an increased suicidal desire, the odds for a fatal suicidal attempt increase substantially. Consequently, this offers a promising opportunity for the development of broader-scale national level preventive interventions that target suicidal capacity, even in individuals who deny suicidal thoughts. The most prominent example of such approaches currently in practice, albeit sporadically, is means safety [33]. Novel as this may seem, it's actually an age long, veritably tested and acknowledged measure as evinced by the significant reduction in suicide rates following reduced packaging and access to drugs known to be lethal in high doses, restriction of access to suicide hotspots (bridge barriers), detoxification of gas, ban on popular insecticides frequently used to execute suicide. This effect was witnessed in 2006 in Israel as the Israeli defense Force prevented soldiers from taking their firearms home over the weekend having noted that firearm suicide was high over weekends. As much as a 40% reduction was noted in suicide rates amongst soldiers aged 18–21 following the intervention. Literature, scientific and historical, is fraught with successful campaigns of means restriction/safety. Decreased access to and safe use/storage of lethal means might represent an opportunity to address an important aspect of the capability for suicide without diminishing the ability of individuals to succeed in their chosen professions and environments [33].

A reasonable concern among individuals first hearing about means safety is the possibility that limiting access to one specific method for suicide will simply result in individuals dying by another method. Importantly, this argument has been largely refuted by available research [33]. In his review of means restriction and means substitution research, Daigle [42] found little evidence in favor of means substitution, Similarly, Sarchiapone et al. [43] also examined the effect of broadscale means safety efforts and found that means substitution was uncommon across a variety of methods.

The overwhelming evidence for means restriction and safety, as a means of suicide prevention, lends credence to the recommendation that it be promulgated into law. Whilst a few countries have passed laws and regulations encouraging means restriction, most are yet to. Social media advocacy can be a veritable tool to

#### *Social Media and Suicide DOI: http://dx.doi.org/10.5772/intechopen.92160*

ensure legislation of means restriction and safety globally, public education on the importance of the subject matter and ultimately shift public perception and cultural views on means safety.

Another budding and promising endeavor for the cause of suicide prevention, presented by recent advancements in science and technology, is 'big data'. Generally, big data is high-volume, high-velocity and high-variety data usually in its raw inedited format and coming from diverse sources. This large data set potentially offers scientists and researchers alike, the access to an unprecedented sample size to experiment and test hypothesis and published data. More so, analytics of text, images, videos, audio and social media information can be used to extract information, patterns, relationships and diversities which can in turn be used to predict suicide risk in varying demographics the world over. Additionally, this may also impel the development of online and app-based interventions to extend even to persons who are unawares of their suicidal capacity. One such app is Therapeutic Evaluative Conditioning, TEC, which aims to alter an individual's association with suicidal behavior. Although, caution has been advised with its use, it exemplifies the burgeoning opportunities the use of big-data will afford the world in preventing suicide.


**5. Conclusions**

This article is an attempt to understand multiple pathways for a particular disease state to manifest in different phenotypes. Each particular phenotype having a distinct immune function abnormality requiring a precise targeted treatment. Unless we understand the immune interplay among different phenotypes of a single disease, it may not be possible to address the underlying immune function abnormality for achieving better outcomes.

*Immunosuppression and Immunomodulation*


for the revised model for log-transformed data. The subscripts *j* denote the sampled parameters in iteration *j*. When using log-transformed data, the predictions are retransformed back to the original scale before the loss functions are calculated, i.e. the losses are on the same scale and should in principle be comparable although it is acknowledged that the comparison

*n* ∑ *j*=1 �

One alternative loss function where the squared prediction errors have been weighted according to the actual observed significant wave height is also employed. A weight of size *Z*(*x*) is included in order to give greater emphasis on prediction errors at locations where large significant wave heights are observed. Hence, an alternative loss function as given in eq.

*Z*(*x*) − *Z*(*x*)∗

*j* �2 ⎤ ⎦

*Z*(*x*) − *Z*(*x*)∗

*j* = *μ*(*x*)*j* + *θ*(*x*, *t*)*j* + *M*(*t*)*j* + T(*t*)*j* + *εz*(*t*)*j* (15)

*j* are taken as the estimated value of *Z* given the samples for all model

*j* �2 ⎤ ⎦

*μ*(*x*)*j*+*θ*(*x*,*t*)*j*+*M*(*t*)*j*+T(*t*)*j*+*εY*(*x*,*t*)*j* (16)

1 2

1 2

at location *x* in iteration *j* of the MCMC simulations.

*La* =

*Z*(*x*)∗

*Z*(*x*)∗ *j* = *e*

for the basic and extended models and

⎡ ⎣

large in this case.

14 is calculated.

The predictions *Z*(*x*)∗

The basic model is found to perform reasonably well on the monthly maximum significant wave height data, with posterior estimates of the mean spatial field, *μ*(*x*), ranging from 6.1 to 7.3 meters over the area. The variability was greater in the north-south direction than in the east-west direction, which is reasonable. The expected contributions from the space-time dynamic part, *θ*(*x*, *t*) were between -1.1 and 1.8 meters and the expected seasonal contributions correspond to an annual cyclic variation of about ± 2.5 meters.

The component of most interest in this chapter, however, is the contribution from the long-term trend component T(*t*), which is included to model any long-term effects, possibly related to global climate change. According to the linear model, an expected increase in monthly maximum significant wave height of 69 cm is estimated over the data-period. The 90% credible interval ranges from 45 - 94 cm, i.e. the complete interval is positive. These posterior trend contributions are illustrated in figure 6. The black line corresponds to the mean sampled T(*t*), whereas the red lines correspond to the expected contribution *γt* as well as the 90% credible interval of the mean. The green line corresponds to no trend and it is clearly seen that the model detects a significant increasing trend in the wave climate.

In order to estimate future changes of the wave climate, possibly due to climate change, the estimated linear trend is extrapolated towards the year 2100. Hence, assuming that the identified long-term trend persists over 100 years, this would correspond to an expected increase in monthly maximum significant wave height of 1.6 meters over 100 years, with a 95% credibility of an increase of at least 1.0 meter.

#### **6.2. Revised model - log-transformed data**

Also the revised model, applied on the log-transformed data, seems to perform rather well on the monthly maximum data. The normal probability plots of the residuals suggest that the model revision is an improvement compared to the basic model, but the estimated losses are somewhat greater.

The expected contributions from the *μ*(*x*)-field are between 1.76 and 1.95, but the interpretation is different. *eμ*(*x*) is now a multiplicative factor for the monthly maximum significant wave height at location *x*, varying between 5.8 and 7.0 over the area. The mean

**Figure 6.** Estimated temporal trends of the North Atlantic wave climate; basic model

contributions from the space-time dynamic part, *θ*(*x*, *t*) corresponds to factors between 0.70 and 1.4 for different times and locations. Hence, this component contributes from -30% to +40%. The seasonal component corresponds to a factor 0.68 for calm seasons and 1.5 in rough seasons.

**Figure 7.** Estimated temporal trends of the North Atlantic wave climate; log-transformed model

With the extended model, the stochastic relationship between significant wave height and atmospheric levels of CO2 is exploited together with future projections of CO2 trends in order to obtain estimates of future trends in the wave climate. Expectantly, the estimated trends should be similar to the trends estimated with the basic model, but future projections can be obtained from various CO2 projections and may differ from the extrapolated linear trends. It is noted that for the extended model, the long-term trend contribution does not necessarily start at 0 for t=0, but in the results presented herein, necessary adjustments have been made so that the long-term trend effectively starts at 0. For extracting the expected trends over the period 1958-2001, the long-term trend is adjusted to be 0 in 1958 and for the future projections towards 2100, the trend contribution is adjusted to start at 0 in 2001. This does not affect the relative trend between two points in time, but is accompanied by a similar but opposite

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 495

The contributions from the adjusted time-independent field, *μ*(*x*), varies between 6.3 and 7.5 meters over the area, and this is in reasonable agreement to the estimates obtained from the basic model. The short-term dynamic contribution from *θ*(*x*, *t*) varies from -1.1 to 1.9 meters and the mean seasonal contributions lie between ± 2.66 meters, which also agrees well with

The contribution from the long-term trend, possibly due to climate change, is shown in figure 8, corresponding to an expected increase of 59 cm over the period. This is somewhat lower than the estimated trend from the basic model, but still agrees fairly well. The 90% credible interval ranges from 16 to 92 cm increases in monthly maximum significant wave height.

**6.3. Extended model with regression component**

adjustment of the mean spatial field.

the estimates obtained from the basic model.

The mean estimated long-term trend from the linear model corresponds to a factor about 1.07 over the data-period. The 90% credible interval ranges from 1.03 to 1.12. For typical monthly maximum significant wave heights of, say, 5 and 8 meters respectively, this corresponds to expected increases of about 36 and 57 cm. However, for more extreme sea states, say significant wave heights of 10 or 15 meters respectively, corresponding expected increases would be 70 cm and more than 1 meter respectively. Overall, these trends are somewhat smaller than the trends estimated from the non-transformed data, but the trends pertaining to extreme conditions are greater. A QMLE-estimate for bias correction ([18]) due to retransformation has been adopted and is incorporated into the estimates above, see [39]. The estimated expected long-term trends with 90% credible interval are shown in figure 7 on the original, i.e. re-transformed scale.

Also the estimated trends obtained from the log-transformed data were extrapolated in order to obtain an estimate of future trends in the wave climate. Over 100 years, the expected future increase in monthly maximum wave height corresponds to a factor of 1.15, with a 95% credibility of a trend factor larger than 1.04. Assuming such trends to persist and valid for average monthly maximum sea states of 5 and 8 meters in calm and rough seasons, the expected increase is about 75 cm and 1.2 meters respectively. However, for more extreme sea states, with significant wave height of, say, 10 and 15 meters, expected increases would be 1.5 and 2.3 meters respectively towards the year 2100.

#### **6.3. Extended model with regression component**

14 Climate Change

**Figure 6.** Estimated temporal trends of the North Atlantic wave climate; basic model

seasons.

the original, i.e. re-transformed scale.

and 2.3 meters respectively towards the year 2100.

contributions from the space-time dynamic part, *θ*(*x*, *t*) corresponds to factors between 0.70 and 1.4 for different times and locations. Hence, this component contributes from -30% to +40%. The seasonal component corresponds to a factor 0.68 for calm seasons and 1.5 in rough

The mean estimated long-term trend from the linear model corresponds to a factor about 1.07 over the data-period. The 90% credible interval ranges from 1.03 to 1.12. For typical monthly maximum significant wave heights of, say, 5 and 8 meters respectively, this corresponds to expected increases of about 36 and 57 cm. However, for more extreme sea states, say significant wave heights of 10 or 15 meters respectively, corresponding expected increases would be 70 cm and more than 1 meter respectively. Overall, these trends are somewhat smaller than the trends estimated from the non-transformed data, but the trends pertaining to extreme conditions are greater. A QMLE-estimate for bias correction ([18]) due to retransformation has been adopted and is incorporated into the estimates above, see [39]. The estimated expected long-term trends with 90% credible interval are shown in figure 7 on

Also the estimated trends obtained from the log-transformed data were extrapolated in order to obtain an estimate of future trends in the wave climate. Over 100 years, the expected future increase in monthly maximum wave height corresponds to a factor of 1.15, with a 95% credibility of a trend factor larger than 1.04. Assuming such trends to persist and valid for average monthly maximum sea states of 5 and 8 meters in calm and rough seasons, the expected increase is about 75 cm and 1.2 meters respectively. However, for more extreme sea states, with significant wave height of, say, 10 and 15 meters, expected increases would be 1.5 With the extended model, the stochastic relationship between significant wave height and atmospheric levels of CO2 is exploited together with future projections of CO2 trends in order to obtain estimates of future trends in the wave climate. Expectantly, the estimated trends should be similar to the trends estimated with the basic model, but future projections can be obtained from various CO2 projections and may differ from the extrapolated linear trends.

It is noted that for the extended model, the long-term trend contribution does not necessarily start at 0 for t=0, but in the results presented herein, necessary adjustments have been made so that the long-term trend effectively starts at 0. For extracting the expected trends over the period 1958-2001, the long-term trend is adjusted to be 0 in 1958 and for the future projections towards 2100, the trend contribution is adjusted to start at 0 in 2001. This does not affect the relative trend between two points in time, but is accompanied by a similar but opposite adjustment of the mean spatial field.

The contributions from the adjusted time-independent field, *μ*(*x*), varies between 6.3 and 7.5 meters over the area, and this is in reasonable agreement to the estimates obtained from the basic model. The short-term dynamic contribution from *θ*(*x*, *t*) varies from -1.1 to 1.9 meters and the mean seasonal contributions lie between ± 2.66 meters, which also agrees well with the estimates obtained from the basic model.

The contribution from the long-term trend, possibly due to climate change, is shown in figure 8, corresponding to an expected increase of 59 cm over the period. This is somewhat lower than the estimated trend from the basic model, but still agrees fairly well. The 90% credible interval ranges from 16 to 92 cm increases in monthly maximum significant wave height.

**Figure 7.** Estimated temporal trends of the North Atlantic wave climate; log-transformed model

**Figure 8.** Estimated temporal trends of the North Atlantic wave climate; model with CO2 regression

**Figure 9.** Estimated future trends in the North Atlantic wave climate for two emission scenarios

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 497

**Figure 10.** Estimated future trends in the North Atlantic wave climate with credible intervals

projections.

discussed herein are presented in table 2.

differences are, as would be expected, related to the long term temporal trend and the future

The models may also be compared by way of the loss functions for short-term prediction. The estimated losses corresponding to the two loss functions for each of the model alternatives

It is observed that both the models fitted to the original data are associated with lower losses compared to the model for log-transformed data. However, it is noted that comparison might not be fair for predictions made on log-transformed data so it does not necessarily mean that the revised model performs worst. Furthermore, the extended model with a CO2 regression

One of the main motivations for including the CO2 regression component into the model was to facilitate future projections. Hence, projections of future significant wave heights are made from two future scenarios for CO2 levels, referred to as the A2 and B1 scenario respectively. The corresponding projected trends of significant wave height are illustrated in figure 9, and it can be seen that scenario A2 yields future projections corresponding to an increase of 5.4 meters and the B1 scenario corresponds to an increase of 1.9 meters towards 2100 compared to the year 2001. The large difference between the two projections is due to the different CO2 levels projected by the two scenarios. However, both the projected trends are considerably larger than the one obtained from extrapolating the linear trend obtained from the basic model.

The expected future projections including 90% credible intervals are illustrated in figure 10. The credible intervals are calculated from the credible intervals of the distribution of (*γ*, *η*) and do not include the uncertainty due to *ε*T. For scenario A2, the 90% credible interval at year 2100 corresponds to increases in monthly maximum significant wave height over the 21 century ranging from 2.7 meters to 8.1 meters. For scenario B1, the corresponding credible interval covers a range between 1.2 to 2.6 meters increase from 2001 to 2100.

#### **6.4. Model comparison**

A crude comparison of the different model alternatives can be carried out by comparing the resulting posterior estimates of the model parameters (see [38–40]). By doing so, it is observed that the spatial features of the model seem to be barely affected by the model alterations. Since the model extensions were only related to the temporal trend, this is reassuring. The seasonal part of the model also seems to behave similarly over the model alternatives. Hence, the main

16 Climate Change

**Figure 8.** Estimated temporal trends of the North Atlantic wave climate; model with CO2 regression

the basic model.

**6.4. Model comparison**

One of the main motivations for including the CO2 regression component into the model was to facilitate future projections. Hence, projections of future significant wave heights are made from two future scenarios for CO2 levels, referred to as the A2 and B1 scenario respectively. The corresponding projected trends of significant wave height are illustrated in figure 9, and it can be seen that scenario A2 yields future projections corresponding to an increase of 5.4 meters and the B1 scenario corresponds to an increase of 1.9 meters towards 2100 compared to the year 2001. The large difference between the two projections is due to the different CO2 levels projected by the two scenarios. However, both the projected trends are considerably larger than the one obtained from extrapolating the linear trend obtained from

The expected future projections including 90% credible intervals are illustrated in figure 10. The credible intervals are calculated from the credible intervals of the distribution of (*γ*, *η*) and do not include the uncertainty due to *ε*T. For scenario A2, the 90% credible interval at year 2100 corresponds to increases in monthly maximum significant wave height over the 21 century ranging from 2.7 meters to 8.1 meters. For scenario B1, the corresponding credible

A crude comparison of the different model alternatives can be carried out by comparing the resulting posterior estimates of the model parameters (see [38–40]). By doing so, it is observed that the spatial features of the model seem to be barely affected by the model alterations. Since the model extensions were only related to the temporal trend, this is reassuring. The seasonal part of the model also seems to behave similarly over the model alternatives. Hence, the main

interval covers a range between 1.2 to 2.6 meters increase from 2001 to 2100.

**Figure 9.** Estimated future trends in the North Atlantic wave climate for two emission scenarios

**Figure 10.** Estimated future trends in the North Atlantic wave climate with credible intervals

differences are, as would be expected, related to the long term temporal trend and the future projections.

The models may also be compared by way of the loss functions for short-term prediction. The estimated losses corresponding to the two loss functions for each of the model alternatives discussed herein are presented in table 2.

It is observed that both the models fitted to the original data are associated with lower losses compared to the model for log-transformed data. However, it is noted that comparison might not be fair for predictions made on log-transformed data so it does not necessarily mean that the revised model performs worst. Furthermore, the extended model with a CO2 regression

of the trend is explored, extreme loads are considered and this makes these assumptions less troublesome; this simplification is considered acceptable for extremes but neither for fatigue calculations nor specification of operational criteria when lower sea states are of importance.

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 499

The marginal distribution of significant wave height is normally not sufficient for load and response calculations of marine structures; the joint distribution of several metocean parameters is required. As a minimum, the joint distribution of significant wave height and

The above trends were extracted from the corrected ERA-40 data (C-ERA-40) over an area in the North Atlantic. Due to lack of information about wave period in the C-ERA-40 data, the joint distribution of significant wave height and wave period used for load calculations are based on the ERA interim data set3 for a particular location. However, that location is contained within the area considered by the C-ERA-40 data and is assumed representative for the whole area. Furthermore, main features of the C-ERA-40 and ERAInterim data sets are similar, and it is assumed that any bias would be similar in the two data sets. The long-term trends obtained in the present study are therefore incorporated in the established joint distribution of significant wave height and wave period based on the ERAinterim data. It has previously been proposed to model the marginal distribution of significant wave height, *Hs*, according to a 3-parameter Weibull distribution and the conditional distribution of the wave period, *T*, conditional on the significant wave height, as a log-normal distribution ([4, 26]). Hence, the joint distribution of significant wave height and wave period will be the product of a Weibull and a log-normal distribution given *Hs* (eq. 18) according to the Conditional Modelling Approach (for several met-ocean parameters see [2, 3]). The 3-parameter Weibull distribution was first applied to describe significant wave height by [29].

*fHs*,*T*(*h*, *t*) = *fHs* (*h*)*fT*|*Hs*

period will obviously change, so this assumption seems reasonable.

 *x* − *γ α*

*β*−1 *e* −( *x*−*γ α* ) *β*

and *β* (shape), as shown in eq. 19.

*f*(*x*) = *β α*

3 Website: http://www.ecmwf.int/research/era/do/get/era-interim

It is assumed that the trend in the significant wave height corresponds to a modified marginal distribution for the significant wave height, but that the distribution of wave period, conditional on the significant wave height, remains unchanged. It is noted that even though the conditional distribution is assumed unchanged, the marginal distribution of the wave

The 3-parameter Weibull distribution is parametrized by the parameters *γ* (location), *α* (scale)

It is assumed that the distribution of the significant wave height after the trend has been added can be approximated by a 3-parameter Weibull distribution with the same shape parameter, i.e. that the trend can be modelled as a modification of the location and scale parameters of

(*t*|*h*) (18)

*x* ≥ *γ* (19)

**7.1. Conditional modelling of joint metocean parameters**

wave period is needed.

**Table 2.** Model comparison: Standard and weighted loss functions

component yields the lowest losses, which indicates that this is an improvement compared to the basic model. The differences are small, however, and the estimated losses cannot be used to reliably distinguish between the models, which all seem to describe the data reasonably well.

## **7. Potential impact of climate change on ship structural loads**

If indeed the future wave climate will become rougher, as predicted by the models presented herein, this might have an impact on the safety of maritime transportation, since ships are then likely to experience greater environmental loads. Extreme environmental loads represent a serious hazard to ship operations and any increasing trends might thus lead to higher risk, if not properly accounted for in design and operational procedures.

Having identified a trend in the significant wave height data, it would therefore be of great interest to consider how such results could be related to the calculation of future environmental loads and responses on ships and other floating structures. Trends in the ocean wave climate will obviously also be important for offshore and coastal structures, and the results can generally be applied also to offshore and coastal structures design. However, if applied to fixed installations, location specific data should be used; North Atlantic data are used only for ship design. For the purpose of this study, the trends towards 2100 estimated from the basic model and the extended model with a CO2 regression component and scenario B1 will be assumed. It will be investigated how to relate such trends to the calculations of ship structural loads and responses. It is emphasized that potential influence of such trends on structural design, as was discussed in [8] is not considered explicitly herein. Results pertaining to any other projection period, such as 30 or 40 years ahead in time, could also easily have been used.

The trends estimated above correspond to an addition, 100 years ahead in time, with mean 1.6 meters and standard deviation 0.39 meters from the basic model and mean 1.9 meters and standard deviation 0.65 meters from the extended model adopting the B1 scenario. The mean and standard deviation of the climatic trend contribution will be denoted by *μct* and *σct* when stemming from the basic model and *μB*1 and *σB*1 when estimated by the extended model with scenario B1, respectively, i.e. an additive trend, T ∼ (*μ*·, *σ*2 · ) will be assumed.

$$\begin{array}{ll} \mu\_{\rm cf} = 1.6m & \sigma\_{\rm cf} = 0.39m\\ \mu\_{B1} = 1.9m & \sigma\_{B1} = 0.65m \end{array} \tag{17}$$

It is noted that the climate trend is estimated from monthly maxima although it is applied to the whole body of the *Hs* distribution (the marginal distribution of significant wave height). Thus the revised *Hs* distribution is more representative for high values of *Hs*. When the impact of the trend is explored, extreme loads are considered and this makes these assumptions less troublesome; this simplification is considered acceptable for extremes but neither for fatigue calculations nor specification of operational criteria when lower sea states are of importance.

#### **7.1. Conditional modelling of joint metocean parameters**

18 Climate Change

**Model alternative** *Ls Lw* Basic model 2.576 2.691 Revised model (log-transform) 3.346 3.412 Extended model (CO2 regression) 2.562 2.674

component yields the lowest losses, which indicates that this is an improvement compared to the basic model. The differences are small, however, and the estimated losses cannot be used to reliably distinguish between the models, which all seem to describe the data reasonably

If indeed the future wave climate will become rougher, as predicted by the models presented herein, this might have an impact on the safety of maritime transportation, since ships are then likely to experience greater environmental loads. Extreme environmental loads represent a serious hazard to ship operations and any increasing trends might thus lead to higher risk,

Having identified a trend in the significant wave height data, it would therefore be of great interest to consider how such results could be related to the calculation of future environmental loads and responses on ships and other floating structures. Trends in the ocean wave climate will obviously also be important for offshore and coastal structures, and the results can generally be applied also to offshore and coastal structures design. However, if applied to fixed installations, location specific data should be used; North Atlantic data are used only for ship design. For the purpose of this study, the trends towards 2100 estimated from the basic model and the extended model with a CO2 regression component and scenario B1 will be assumed. It will be investigated how to relate such trends to the calculations of ship structural loads and responses. It is emphasized that potential influence of such trends on structural design, as was discussed in [8] is not considered explicitly herein. Results pertaining to any other projection period, such as 30 or 40 years ahead in time, could also easily have been

The trends estimated above correspond to an addition, 100 years ahead in time, with mean 1.6 meters and standard deviation 0.39 meters from the basic model and mean 1.9 meters and standard deviation 0.65 meters from the extended model adopting the B1 scenario. The mean and standard deviation of the climatic trend contribution will be denoted by *μct* and *σct* when stemming from the basic model and *μB*1 and *σB*1 when estimated by the extended model with

*μct* = 1.6*m σct* = 0.39*m*

It is noted that the climate trend is estimated from monthly maxima although it is applied to the whole body of the *Hs* distribution (the marginal distribution of significant wave height). Thus the revised *Hs* distribution is more representative for high values of *Hs*. When the impact

· ) will be assumed.

*μB*1 = 1.9*m σB*1 = 0.65*m* (17)

**7. Potential impact of climate change on ship structural loads**

if not properly accounted for in design and operational procedures.

scenario B1, respectively, i.e. an additive trend, T ∼ (*μ*·, *σ*2

**Table 2.** Model comparison: Standard and weighted loss functions

well.

used.

The marginal distribution of significant wave height is normally not sufficient for load and response calculations of marine structures; the joint distribution of several metocean parameters is required. As a minimum, the joint distribution of significant wave height and wave period is needed.

The above trends were extracted from the corrected ERA-40 data (C-ERA-40) over an area in the North Atlantic. Due to lack of information about wave period in the C-ERA-40 data, the joint distribution of significant wave height and wave period used for load calculations are based on the ERA interim data set3 for a particular location. However, that location is contained within the area considered by the C-ERA-40 data and is assumed representative for the whole area. Furthermore, main features of the C-ERA-40 and ERAInterim data sets are similar, and it is assumed that any bias would be similar in the two data sets. The long-term trends obtained in the present study are therefore incorporated in the established joint distribution of significant wave height and wave period based on the ERAinterim data.

It has previously been proposed to model the marginal distribution of significant wave height, *Hs*, according to a 3-parameter Weibull distribution and the conditional distribution of the wave period, *T*, conditional on the significant wave height, as a log-normal distribution ([4, 26]). Hence, the joint distribution of significant wave height and wave period will be the product of a Weibull and a log-normal distribution given *Hs* (eq. 18) according to the Conditional Modelling Approach (for several met-ocean parameters see [2, 3]). The 3-parameter Weibull distribution was first applied to describe significant wave height by [29].

$$f\_{H\_{\rm s}T}(h\_{\prime}t) = f\_{H\_{\rm s}}(h)f\_{T|H\_{\rm s}}(t|h) \tag{18}$$

It is assumed that the trend in the significant wave height corresponds to a modified marginal distribution for the significant wave height, but that the distribution of wave period, conditional on the significant wave height, remains unchanged. It is noted that even though the conditional distribution is assumed unchanged, the marginal distribution of the wave period will obviously change, so this assumption seems reasonable.

The 3-parameter Weibull distribution is parametrized by the parameters *γ* (location), *α* (scale) and *β* (shape), as shown in eq. 19.

$$f(\mathbf{x}) = \frac{\beta}{a} \left(\frac{\mathbf{x} - \boldsymbol{\gamma}}{a}\right)^{\beta - 1} e^{-\left(\frac{\mathbf{x} - \boldsymbol{\gamma}}{a}\right)^{\beta}} \qquad \qquad \qquad \mathbf{x} \ge \boldsymbol{\gamma} \tag{19}$$

It is assumed that the distribution of the significant wave height after the trend has been added can be approximated by a 3-parameter Weibull distribution with the same shape parameter, i.e. that the trend can be modelled as a modification of the location and scale parameters of

3 Website: http://www.ecmwf.int/research/era/do/get/era-interim

the 3-parameter Weibull distribution. A simulation study confirms that this is a reasonable approximation. With these assumptions, the modified parameters due to the long-term trend can be calculated so that the modified Weibull distribution has the correct expectation and variance, resulting in the modified parameters in eqs. 20-21.

$$\gamma \rightarrow \gamma' = \gamma + \mu\_{ct} + \Gamma \left(\frac{1}{\beta} + 1\right) \left[a - \sqrt{a^2 + \frac{\sigma\_{ct}^2}{\Gamma\left(\frac{2}{\beta} + 1\right) - \Gamma\left(\frac{1}{\beta} + 1\right)^2}}\right] \tag{20}$$

$$\mathfrak{a} \rightarrow \mathfrak{a}' = \sqrt{\mathfrak{a}^2 + \frac{\sigma\_{\mathfrak{c}t}^2}{\Gamma\left(\frac{2}{\beta} + 1\right) - \Gamma\left(\frac{1}{\beta} + 1\right)^2}}\tag{21}$$

The 3-parameter Weibull distribution was fitted to significant wave height data for one location from the ERA-40Interim data and the estimated parameters together with the modified parameters as a result of adding the projected long-term trends (over 100 years) are given in table 3. The corresponding mean and standard deviation of the distributions are also given.

**Table 3.** Fitted and modified parameters for the 3-parameter Weibull distribution for significant wave height

It is observed that the mean of the modified distribution is changed quite drastically, whereas there is only a slight increase in the standard deviation as a result of adding the climatic trend with uncertainties.

The conditional distribution of wave period is modelled as a log-normal distribution where the parameters are modelled as functions of significant wave height, as shown in eqs. 22-23. By assumption, this conditional distribution is not expected to change due to climatic trends, and the parameters *ai* and *bi* for *i* = 1, 2, 3 are estimated from the data. The resulting joint densities of the original and the modified distributions for significant wave height, H*s*, and zero-up-crossing period, *Tz*, are illustrated by the contour plots in figure 11 (on the same scale). It is noted that *Tz* is one of several ways of describing the wave period, *T*.

$$\mu\_{\rm f} = E[\ln T\_{\rm z} | H\_{\rm s} = h\_{\rm s}] = a\_1 + a\_2 h\_{\rm s}^{a\_3} \tag{22}$$

**Figure 11.** Contour plots of the joint distribution of significant wave height and zero-up-crossing period; Fitted distributions (top left) and modified distributions with trends estimated from the basic model (top

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 501

When specifying design criteria as well as carrying out load and response assessment for marine structures a full long-term load and response analysis can be applied, or alternatively, the environmental contour concept outlined in [48] can be used (IFORM). The latter is a valid, simplified and rational method of estimating extreme conditions and is recommended by DNV ([16]). The idea is to define contours in the environmental parameter space (usually *Hs*, *Tz*) within which extreme responses with a given return period should lie. It requires determination of the joint environmental model of sea state variables of interest. It should be noticed that the contours are found by relating sea state variables to the standard normal variables, an assumption that may affect their accuracy. Furthermore, adding the trend introduces a dependency between the sea states at subsequent times, but the effect this might have on the return values have been ignored in this study. Presumably, since the variability of the estimated trend is small in comparison to the variability of sea states, this effect is not

Figure 12 shows the environmental contour lines of H*s* and T*z* for the North Atlantic location considered in the present study. The 1, 10, and 25-year return period levels calculated by IFORM are shown for the fit to the original ERAInterim data and for the corrected fits where the long-term trends are included. The 3-parameter Weibull distributions for *Hs* given in table 3

right) and the extended model with the B1 scenario (bottom)

very great.

$$
\sigma\_l = \text{sd}[\ln T\_z | H\_s = h\_s] = b\_1 + b\_2 e^{b\_3 h\_s} \tag{23}
$$

#### **7.2. Case study: Impact of long-term trends on the load assessment of an oil tanker**

As an illustrative example, load characteristics will be calculated for an oil tanker of 250 m length and 40 m width with the same characteristics as the one reported in [5].

20 Climate Change

the 3-parameter Weibull distribution. A simulation study confirms that this is a reasonable approximation. With these assumptions, the modified parameters due to the long-term trend can be calculated so that the modified Weibull distribution has the correct expectation and

The 3-parameter Weibull distribution was fitted to significant wave height data for one location from the ERA-40Interim data and the estimated parameters together with the modified parameters as a result of adding the projected long-term trends (over 100 years) are given in table 3. The corresponding mean and standard deviation of the distributions are also given.

Fitted distribution 2.776 1.471 0.8888 3.401 1.737 Modified parameters (Basic model trend) 2.846 1.471 2.393 4.969 1.781 Modified parameters (Extended model / B1) 2.965 1.471 2.613 5.296 1.855 **Table 3.** Fitted and modified parameters for the 3-parameter Weibull distribution for significant wave

It is observed that the mean of the modified distribution is changed quite drastically, whereas there is only a slight increase in the standard deviation as a result of adding the climatic trend

The conditional distribution of wave period is modelled as a log-normal distribution where the parameters are modelled as functions of significant wave height, as shown in eqs. 22-23. By assumption, this conditional distribution is not expected to change due to climatic trends, and the parameters *ai* and *bi* for *i* = 1, 2, 3 are estimated from the data. The resulting joint densities of the original and the modified distributions for significant wave height, H*s*, and zero-up-crossing period, *Tz*, are illustrated by the contour plots in figure 11 (on the same scale).

*μt* = *E*[ln *Tz*|*Hs* = *hs*] = *a*1 + *a*2*ha*3

As an illustrative example, load characteristics will be calculated for an oil tanker of 250 m

*σt* = *sd*[ln *Tz*|*Hs* = *hs*] = *b*1 + *b*2*e*

**7.2. Case study: Impact of long-term trends on the load assessment of an oil**

length and 40 m width with the same characteristics as the one reported in [5].

It is noted that *Tz* is one of several ways of describing the wave period, *T*.

*σ*2 *ct*

�2 (21)

*αβ γ* E[*Hs*] sd[*Hs*]

*s* (22)

*b*3*hs* (23)

⎤ ⎥ ⎥ ⎦

(20)

Γ � 2 *β* + 1 � − Γ � 1 *β* + 1 �2

variance, resulting in the modified parameters in eqs. 20-21.

Γ � 2 *β* + 1 � − Γ � 1 *β* + 1

� 1 *β* + 1 � ⎡ ⎢ ⎢ ⎣ *α* − ����� *α*2 +

> *σ*2 *ct*

*γ* → *γ*� = *γ* + *μct* + Γ

����� *α*2 +

*α* → *α*� =

height

**tanker**

with uncertainties.

**Figure 11.** Contour plots of the joint distribution of significant wave height and zero-up-crossing period; Fitted distributions (top left) and modified distributions with trends estimated from the basic model (top right) and the extended model with the B1 scenario (bottom)

When specifying design criteria as well as carrying out load and response assessment for marine structures a full long-term load and response analysis can be applied, or alternatively, the environmental contour concept outlined in [48] can be used (IFORM). The latter is a valid, simplified and rational method of estimating extreme conditions and is recommended by DNV ([16]). The idea is to define contours in the environmental parameter space (usually *Hs*, *Tz*) within which extreme responses with a given return period should lie. It requires determination of the joint environmental model of sea state variables of interest. It should be noticed that the contours are found by relating sea state variables to the standard normal variables, an assumption that may affect their accuracy. Furthermore, adding the trend introduces a dependency between the sea states at subsequent times, but the effect this might have on the return values have been ignored in this study. Presumably, since the variability of the estimated trend is small in comparison to the variability of sea states, this effect is not very great.

Figure 12 shows the environmental contour lines of H*s* and T*z* for the North Atlantic location considered in the present study. The 1, 10, and 25-year return period levels calculated by IFORM are shown for the fit to the original ERAInterim data and for the corrected fits where the long-term trends are included. The 3-parameter Weibull distributions for *Hs* given in table 3 and the conditional log-normal distribution for *Tz* have been used in the analysis. As expected, the modification of the distribution for significant wave height moves the environmental contours upwards and to the right. Furthermore, the long-term trend correction has narrowed the contours and increased the maximum 1, 10 and 25-year return *Hs* and related *Tz*.

is noted that similar calculations have not been done for the A2 scenario, but the effect would presumably be even larger for such a worst-case trend. Furthermore, the potential effect of the modified environmental contours on the structural loads is highly ship-dependent and even though the loads were found to increase significantly for this particular ship, it does not

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 503

The models presented in this chapter aim at modelling the effect of climate change on the North Atlantic wave climate, and all model variations agree that the ocean wave climate has become rougher and is likely to become even rougher towards the next century. In [41], the models have been fitted to data for 11 other ocean areas around the globe with increasing

Different emission scenarios have been assumed in the extended model to obtain different future projections of the wave climate, and it has been seen that adopting an extreme emission scenario, such as the A2 scenario, corresponds to predicting extreme future trends in significant wave height. With a more moderate emission scenario, such as B1, the resulting future projections are still larger than the extrapolation of observed recent trends, as predicted by the basic model. As for any future climate predictions, uncertainties are large and it is difficult to determine which predictions are best. According to the two loss functions utilized in this study (eqs. 13-14), the extended model seems to represent an improvement in describing the data at hand but this does not necessarily mean that the projections from this model are more reliable than the others; significant uncertainties are also related to the CO2 scenarios proposed by IPCC. However, the extended model may adopt different CO2

scenarios and investigate their effects on the trends in the future ocean wave climate.

An implicit assumption inherent in the extended model is that there is stochastic dependence between atmospheric CO2 levels and the ocean wave climate, and also that this relationship will remain essentially the same in the future. It is assumed that an increase of greenhouse gases in the atmosphere will increase the temperature and put more energy into the weather systems, leading to more powerful storms and wind fields. This might again change the ocean wave climate, since it is well known that ocean waves are generated by wind and air pressure gradients. This is obviously a simplification, and it is possible to refine the model with different layers of dynamics and relationships, e.g. including projections of wind or pressure fields as explanatory variables in the model. Notwithstanding, it is argued that the physics underlying the wave generation process is inevitably implicit in the data, and when applying the models to a particular data set any such physical effects would unavoidably be incorporated by way of the data. On the other hand, the stochastic models are affected by data

Comparing the projections obtained with the different Bayesian hierarchical space-time models with previous studies, it is seen that apart from the predictions pertaining to the A2 scenario, the projections are comparable to those made for the North Atlantic in e.g. [12, 14, 15, 19, 42–44]. The uncertainties are large, the estimated 90% credible intervals correspond to about ± 50% of the expected projections, and the intervals generally overlap. It should also be kept in mind that the trends predicted herein pertain to the monthly maxima

necessarily generalize to all types and sizes of ships.

**8. Discussion**

trends predicted also for 9 of these.

uncertainties and possible biases.

**Figure 12.** Environmental contour lines for the ERAInterim data derived from the original data (top left) and modified with the climatic trend over 100 years from the basic model (top right) and from the extended model with the B1 scenario (bottom)

The 25-year stress amplitudes for the considered oil tanker have been calculated in the 25-year sea states (*Hs*, *Tz*) given by the environmental contour lines. A 3-hour sea state duration and a Rayleigh distributed stress process in a short-term sea state (see [5]) have been assumed in the calculations. Table 4 includes the results of the analysis for the original joint (*Hs*, *Tz*) fit and the modified ones, taking the estimated 100-year long-term trends into account. The response characteristics obtained using the original (*Hs*, *Tz*) fit to the ERAInterim data are referred to herein as a Base Case and only relative increases in comparison to the Base Case are given in table 4.

**Table 4.** 25-year extreme load characteristics

As seen in table 4 incorporation of the long-term trend in the *Hs* distribution has increased the 25-year stress amplitude significantly and also the zero-crossing response period has been increased. The 25-year stress amplitude has increased by 7% or 10% while the zero-crossing response period has increased by 2% due to the estimated long-term trend over 100 years. It is noted that similar calculations have not been done for the A2 scenario, but the effect would presumably be even larger for such a worst-case trend. Furthermore, the potential effect of the modified environmental contours on the structural loads is highly ship-dependent and even though the loads were found to increase significantly for this particular ship, it does not necessarily generalize to all types and sizes of ships.

## **8. Discussion**

22 Climate Change

and the conditional log-normal distribution for *Tz* have been used in the analysis. As expected, the modification of the distribution for significant wave height moves the environmental contours upwards and to the right. Furthermore, the long-term trend correction has narrowed

**Figure 12.** Environmental contour lines for the ERAInterim data derived from the original data (top left) and modified with the climatic trend over 100 years from the basic model (top right) and from the

The 25-year stress amplitudes for the considered oil tanker have been calculated in the 25-year sea states (*Hs*, *Tz*) given by the environmental contour lines. A 3-hour sea state duration and a Rayleigh distributed stress process in a short-term sea state (see [5]) have been assumed in the calculations. Table 4 includes the results of the analysis for the original joint (*Hs*, *Tz*) fit and the modified ones, taking the estimated 100-year long-term trends into account. The response characteristics obtained using the original (*Hs*, *Tz*) fit to the ERAInterim data are referred to herein as a Base Case and only relative increases in comparison to the Base Case are given in

Base case 1.0 1.0 Modified fit - Basic model 1.07 1.02 Modified fit - Extended model / B1 1.10 1.02

As seen in table 4 incorporation of the long-term trend in the *Hs* distribution has increased the 25-year stress amplitude significantly and also the zero-crossing response period has been increased. The 25-year stress amplitude has increased by 7% or 10% while the zero-crossing response period has increased by 2% due to the estimated long-term trend over 100 years. It

Stress amplitude (MPa) Response period (s)

extended model with the B1 scenario (bottom)

**Table 4.** 25-year extreme load characteristics

table 4.

the contours and increased the maximum 1, 10 and 25-year return *Hs* and related *Tz*.

The models presented in this chapter aim at modelling the effect of climate change on the North Atlantic wave climate, and all model variations agree that the ocean wave climate has become rougher and is likely to become even rougher towards the next century. In [41], the models have been fitted to data for 11 other ocean areas around the globe with increasing trends predicted also for 9 of these.

Different emission scenarios have been assumed in the extended model to obtain different future projections of the wave climate, and it has been seen that adopting an extreme emission scenario, such as the A2 scenario, corresponds to predicting extreme future trends in significant wave height. With a more moderate emission scenario, such as B1, the resulting future projections are still larger than the extrapolation of observed recent trends, as predicted by the basic model. As for any future climate predictions, uncertainties are large and it is difficult to determine which predictions are best. According to the two loss functions utilized in this study (eqs. 13-14), the extended model seems to represent an improvement in describing the data at hand but this does not necessarily mean that the projections from this model are more reliable than the others; significant uncertainties are also related to the CO2 scenarios proposed by IPCC. However, the extended model may adopt different CO2 scenarios and investigate their effects on the trends in the future ocean wave climate.

An implicit assumption inherent in the extended model is that there is stochastic dependence between atmospheric CO2 levels and the ocean wave climate, and also that this relationship will remain essentially the same in the future. It is assumed that an increase of greenhouse gases in the atmosphere will increase the temperature and put more energy into the weather systems, leading to more powerful storms and wind fields. This might again change the ocean wave climate, since it is well known that ocean waves are generated by wind and air pressure gradients. This is obviously a simplification, and it is possible to refine the model with different layers of dynamics and relationships, e.g. including projections of wind or pressure fields as explanatory variables in the model. Notwithstanding, it is argued that the physics underlying the wave generation process is inevitably implicit in the data, and when applying the models to a particular data set any such physical effects would unavoidably be incorporated by way of the data. On the other hand, the stochastic models are affected by data uncertainties and possible biases.

Comparing the projections obtained with the different Bayesian hierarchical space-time models with previous studies, it is seen that apart from the predictions pertaining to the A2 scenario, the projections are comparable to those made for the North Atlantic in e.g. [12, 14, 15, 19, 42–44]. The uncertainties are large, the estimated 90% credible intervals correspond to about ± 50% of the expected projections, and the intervals generally overlap. It should also be kept in mind that the trends predicted herein pertain to the monthly maxima

#### 24 Climate Change 504 Climate Change – Realities, Impacts Over Ice Cap, Sea Level and Risks An Illustration of the Effect of Climate Change on the Ocean Wave Climate - A Stochastic Model 25

and the maxima might experience a greater change than moderate sea states, as also suggested in e.g. [49]. The A2 scenario can be construed as a worst case scenario and is important to consider from a precautionary perspective. Nevertheless, even stronger trends were predicted in [31], albeit for an area in the Pacific ocean.

question. Nevertheless, an important prerequisite for making well-founded decisions is reliable predictions of the future effect of climate change. The stochastic model presented in this chapter aims at contributing to this discussion by providing a model for predicting the effect of climate change on the ocean wave climate. Such an effect could again have practical implications on many areas of society, most notably related to marine and coastal management. It is acknowledged that the models represent a simplification of reality, as inevitably all models do, and that there is potential for improvements to the models. Nonetheless, it is believed that the study presented herein is an important contribution to the scientific debate on the effects of climate change, and it is a hope that it can spur further debate and motivate further research into the effects of climate change on the future ocean

An Illustration of the Eff ect of Climate Change on the Ocean Wave Climate - A Stochastic Model 505

The authors want to express their thanks to Dr. Andreas Sterl at KNMI for kindly providing the significant wave height data used in this analysis and for clarifying some issues discovered when investigating the data. Thanks also to Dr. Pieter Tans for kind permission to use the NOAA ESRL CO2-data. Furthermore, thanks to the Norwegian Meteorological Institute for providing the ERAInterim data. The data on future projections of atmospheric concentration of

[1] Arena, F. & Pavone, D. [2009]. A generalized approach for long-term modelling of

[2] Bitner-Gregersen, E. & Haver, S. [1989]. Joint long term description of environmental parameters for structural response calculation, *Proc. 2nd International Workshop on Wave*

[3] Bitner-Gregersen, E. & Haver, S. [1991]. Joint environmental model for reliability calculations, *Proc. 1st International Offshore and Polar Engineering conference (ISOPE 1991)*,

[4] Bitner-Gregersen, E. M. [1988]. Appendix: Joint long term distribution of Hs, Tp, *Probabilistic Calculation of Design Criteria for Ultimate Tether Capacity of Snorre TLP*, Madsen,

H.O., Rooney, P. and Bitner-Gregersen, E. Det Norske Veritas Report No. 87-31. [5] Bitner-Gregersen, E. M., Cramer, E. H. & Løseth, R. [1995]. Uncertainties of load characteristics and fatigue damage of ship structures, *Marine Structures* 8: 97–117. [6] Bitner-Gregersen, E. M. & de Valk, C. [2008]. Quality control issues in estimating wave climate from hindcast and satellite data, *Proc. 27th International Conference on*

extreme crest-to-trough wave heights, *Ocean Modelling* 26: 217–225.

The International Society of Offshore and Polar Engineering (ISOPE).

wave climate.

**Acknowledgments**

**Author details**

**10. References**

*University of Oslo, Norway*

Elzbieta M. Bitner-Gregersen *Det Norske Veritas, Norway*

*Hindcasting and Forecasting*.

CO2 were obtained from the IPCC.

Erik Vanem, Bent Natvig and Arne Bang Huseby

It should be stressed that even though the models detect trends in the data, it does not necessarily mean that the trend is a direct consequence of anthropogenic climate change. It might be a result of decadal natural variability, as discussed in e.g. [9], and wave climate variability has been reported to be considerable on different temporal scales ([17]). Great care should therefore be taken when interpreting the meaning and the origin of this trend, even though the correlation between anthropogenic CO2 emissions and the wave climate are found to be strong in this study.

One practical implication of the predicted changes in the ocean wave climate due to global climate change is that the structural loads and stresses on ships and other marine structures might increase notably in the future. A case study indicates increases of up to 10% over the current century. This is not negligible, and it is therefore recommended to carefully consider and take into account the potential impact of climate change in the design and construction of ocean going ships to avoid jeopardizing the safety of future maritime operations.

## **9. Conclusions**

This chapter has been concerned with the potential impact of global climate change on the ocean wave climate and, consequently, on the risk of maritime transportation. A Bayesian hierarchical space-time model that has been developed to model the effect of climate change on the ocean wave climate has been presented. Different versions of the model have been discussed and they all agree in a non-negligible positive trend in the monthly maximum significant wave height over a selected area of the North Atlantic ocean. Estimated expected additive trends towards 2100 range from 1.6 - 5.4 meters and expected multiplicative trends in the order of 15% are predicted. Assuming an average monthly maximum significant wave height of 7.5 meters, the estimated trends related to the B1 and A2 scenarios correspond to centurial increases of 25% - 72%, which are indeed significant. However, the uncertainties are large, and 90% credible intervals for the expected trends range from 1.2 to 2.6 meters for the B1 scenario and 2.7 to 8.1 meters for the A2 scenario.

One of the advantages of using a stochastic model is that estimates of the uncertainties are given explicitly. These are important when future projections are to be incorporated in risk analyses or utilized in probabilistic load calculations as illustrated by an example in this chapter. The case study reveals that the effect of the predicted trend in the ocean wave climate on environmental loads of ships is far from being negligible, and that this may need to be taken into account in design and construction of ships. Obviously, a roughening of the ocean wave climate also has the potential to severely impact other areas of society as well, related to maritime, offshore and coastal activities. Combined with sea level rise and other possible effects of climate change, coastal areas throughout the globe may be seriously affected.

How to adapt to climate change is one of the most important questions in society today. It is a political question and perhaps a moral question as much as it is a scientific question. Nevertheless, an important prerequisite for making well-founded decisions is reliable predictions of the future effect of climate change. The stochastic model presented in this chapter aims at contributing to this discussion by providing a model for predicting the effect of climate change on the ocean wave climate. Such an effect could again have practical implications on many areas of society, most notably related to marine and coastal management. It is acknowledged that the models represent a simplification of reality, as inevitably all models do, and that there is potential for improvements to the models. Nonetheless, it is believed that the study presented herein is an important contribution to the scientific debate on the effects of climate change, and it is a hope that it can spur further debate and motivate further research into the effects of climate change on the future ocean wave climate.

## **Acknowledgments**

24 Climate Change

and the maxima might experience a greater change than moderate sea states, as also suggested in e.g. [49]. The A2 scenario can be construed as a worst case scenario and is important to consider from a precautionary perspective. Nevertheless, even stronger trends were predicted

It should be stressed that even though the models detect trends in the data, it does not necessarily mean that the trend is a direct consequence of anthropogenic climate change. It might be a result of decadal natural variability, as discussed in e.g. [9], and wave climate variability has been reported to be considerable on different temporal scales ([17]). Great care should therefore be taken when interpreting the meaning and the origin of this trend, even though the correlation between anthropogenic CO2 emissions and the wave climate are found

One practical implication of the predicted changes in the ocean wave climate due to global climate change is that the structural loads and stresses on ships and other marine structures might increase notably in the future. A case study indicates increases of up to 10% over the current century. This is not negligible, and it is therefore recommended to carefully consider and take into account the potential impact of climate change in the design and construction of

This chapter has been concerned with the potential impact of global climate change on the ocean wave climate and, consequently, on the risk of maritime transportation. A Bayesian hierarchical space-time model that has been developed to model the effect of climate change on the ocean wave climate has been presented. Different versions of the model have been discussed and they all agree in a non-negligible positive trend in the monthly maximum significant wave height over a selected area of the North Atlantic ocean. Estimated expected additive trends towards 2100 range from 1.6 - 5.4 meters and expected multiplicative trends in the order of 15% are predicted. Assuming an average monthly maximum significant wave height of 7.5 meters, the estimated trends related to the B1 and A2 scenarios correspond to centurial increases of 25% - 72%, which are indeed significant. However, the uncertainties are large, and 90% credible intervals for the expected trends range from 1.2 to 2.6 meters for the

One of the advantages of using a stochastic model is that estimates of the uncertainties are given explicitly. These are important when future projections are to be incorporated in risk analyses or utilized in probabilistic load calculations as illustrated by an example in this chapter. The case study reveals that the effect of the predicted trend in the ocean wave climate on environmental loads of ships is far from being negligible, and that this may need to be taken into account in design and construction of ships. Obviously, a roughening of the ocean wave climate also has the potential to severely impact other areas of society as well, related to maritime, offshore and coastal activities. Combined with sea level rise and other possible effects of climate change, coastal areas throughout the globe may be seriously affected.

How to adapt to climate change is one of the most important questions in society today. It is a political question and perhaps a moral question as much as it is a scientific

ocean going ships to avoid jeopardizing the safety of future maritime operations.

in [31], albeit for an area in the Pacific ocean.

B1 scenario and 2.7 to 8.1 meters for the A2 scenario.

to be strong in this study.

**9. Conclusions**

The authors want to express their thanks to Dr. Andreas Sterl at KNMI for kindly providing the significant wave height data used in this analysis and for clarifying some issues discovered when investigating the data. Thanks also to Dr. Pieter Tans for kind permission to use the NOAA ESRL CO2-data. Furthermore, thanks to the Norwegian Meteorological Institute for providing the ERAInterim data. The data on future projections of atmospheric concentration of CO2 were obtained from the IPCC.

## **Author details**

Erik Vanem, Bent Natvig and Arne Bang Huseby *University of Oslo, Norway*

Elzbieta M. Bitner-Gregersen *Det Norske Veritas, Norway*

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## *Edited by Bharat Raj Singh*

The Earth is the only planet in our solar system that supports life. The complex process of evolution occurred on Earth only because of some unique environmental conditions that were present: water, an oxygen-rich atmosphere, and a suitable surface temperature. Climate change refers to a statistically significant variation in either the mean state of the climate or in its variability, persisting for an extended period (typically decades or longer). Thus, it requires field of attention towards reduction in the rise in atmospheric temperature, by controlling emitted greenhouse gases into the atmosphere in order to preserve natural resources and by introducing new technologies on alternative fuels. This book presents the fundamental effect on the origin of climate change, impacts over ice cap, melting of Arctic ice, rise in sea level and related technologies that can be implemented to cultivate our land for agriculture, growing forestation to reduce the impact of temperature rise and disaster on human being as well as on other livelihood. This also need to strive for novel policies that world leader should adopt.

Climate Change - Realities, Impacts Over Ice Cap, Sea Level and Risks

Climate Change

Realities, Impacts Over Ice Cap,

Sea Level and Risks

*Edited by Bharat Raj Singh*

Photo by hopsalka / iStock


*Edited by Mani T. Valarmathi*

Stromal cells are connective tissue cells of any organ, and they support the function of the parenchymal cells of that particular organ. Stromal/stromal stem cells are fundamentally a heterogeneous population of cells with contradictory differentiation potential depending upon their environmental niche. Stromal cell biology is not only intriguing, but equally stromal cell ontogeny *in vivo* remains challenging. In recent years there has been substantial advances in our understanding of stromal cell biology, especially stromal cell isolation, characterization, differentiation, and interactions in physiological (epithelial–stromal interactions) as well as pathophysiological (stromal– cancer interactions) contexts. In addition, stromal cells are also utilized more and more as a therapeutic tool not only in the field of gene therapy but also in the translational field of tissue engineering and regenerative medicine. Therefore, the goal of this book is to consolidate the recent advances in the area of stromal/stromal stem cell biology covering a broad range of interrelated topics in a timely fashion and to disseminate that knowledge in a lucid way to a greater scientific audience. This book will prove highly useful for students, researchers, and clinicians in stem cell biology, developmental biology, cancer biology, pathology, oncology, as well as tissue engineering and regenerative medicine. This quick reference will benefit anyone desiring a thorough overview of stromal cell structure, function, and its therapeutic implications.

ISBN 978-1-78984-984-4

Stromal Cells - Structure, Function, and Therapeutic Implications

Published in London, UK © 2019 IntechOpen © defun / iStock


Preface

Macular degeneration is one of the leading causes of blindness. The devastating effect of this blinding disease becomes more obvious as people age. Leaps and bounds of innovations and inventions have increased patient quality of life and have helped many patients regain lost vision in neovascular age-related macular degeneration (AMD). However, the therapeutic options for the more prevalent variety of macular degeneration, atrophic or "dry" AMD, are lacking.

This book is a collection of chapters that focus on the disease state of macular degeneration, issues related to the diagnosis and management of AMD, treatment considerations, and vision rehabilitation. The introductory chapter sets the tone for the book with general issues related to AMD pathogenesis. The section on diagnosis and management talks about using optical coherence tomography to aid clinical management as well as highlights the importance of discussing with patients the concept of health promotion and issues related to good diet and supplementation for atrophic AMD. The next section delves into anti-vascular endothelial growth factor therapy (anti-VEGF), which is the standard of care in AMD, and new modalities of drugs under development for the disease. One would hope that with early management and interventions we could potentially avoid the need for low vision and vision rehabilitation, but this remains an aspiration for now. Thus, the final section discusses vision rehabilitation and new strategies and advances in this area.

A multi-author edited book is never complete without contributions from experts in the field. I am grateful to all the contributing authors and the reviewers that helped shape this book. A special thanks goes to Author Service Manager Ms. Romina Rovan at IntechOpen for her tireless efforts in seeing this book to completion. Most importantly, I am grateful to my family and my dear wife Payal, and my kids Ved and Jash, who allowed me to dedicate myself to scientific pursuits. Payal, Ved, and Jash, you are truly the support that enables me to do all that I do and for that I am grateful.

> **Pinakin Gunvant Davey** Western University of Health Sciences, Pomona, California, USA

Section 1 Introduction