Nathan E Cross
email: nathan.cross@mail.concordia.catt.dangvu@concordia.ca

Julie Carrier

Ronald B Postuma

Nadia Gosselin

Lisa Kakinami

Cynthia Thompson

Florian Chouchou

Thien Thanh Dang-Vu

Thanh Thien

Dang-Vu

Association between insomnia disorder and cognitive function in middle-aged and older adults: a cross-sectional analysis of the Canadian Longitudinal Study on Aging

Keywords: insomnia, cognition, aging, cohort, CLSA

Objectives: This study examined the differences in cognitive function between middle-aged and older adults with insomnia disorder, insomnia symptoms only or no insomnia symptoms, in the context of other health and lifestyle factors. Methods: 28,485 participants >45 years completed questionnaires, physical examinations, and neuropsychological testing across domains of processing speed, memory and executive functions. An 8-question instrument assessed participants' sleep, defining subjects with insomnia symptoms, probable insomnia disorder or no insomnia symptoms. The associations between these three groups and cognitive performance were examined with linear regression models adjusted for lifestyle and clinical factors.

Results: Probable insomnia disorder was identified in 1,068 participants (3.7% of the sample) while 7,813 (27.5%) experienced insomnia symptoms only. Participants with probable insomnia disorder exhibited greater proportions of adverse medical and lifestyle features such as anxiety, depression, and diabetes than both other groups. Analyses adjusting for age, sex, education, as well as medical and lifestyle factors demonstrated that adults with probable insomnia disorder exhibited declarative memory deficits (Rey Auditory Verbal Learning Test) compared to insomnia symptoms only or no insomnia symptoms.

Adults with insomnia symptoms exhibited better performance on a task of mental flexibility than both other groups.

Conclusions: These findings suggest that insomnia disorder in middle-aged and older adults is associated with poorer health outcomes and worse memory performance than adults with insomnia symptoms alone or without any sleep complaints, even after adjustment for comorbidities. The assessment of longitudinal data within this cohort will be critical to understand if insomnia disorder may increase the risk of further cognitive decline.

Statement of Significance

This study utilizes a large dataset acquired from the Canadian Longitudinal Study on Aging to compare the prevalence, clinical characteristics and cognitive function of middle-aged and older adults with probable insomnia disorder. Most previous large-sample epidemiological studies in this area have been limited by the inability to utilize clinical diagnosis of insomnia disorder at such scale and have instead focused on broad sleep measures (e.g., sleep duration, overall subjective sleep quality) or insomnia symptoms only. Indeed, compared to other adults who experience insomnia symptoms only (but do not meet criteria for insomnia disorder) or no insomnia symptoms at all, probable insomnia disorder was associated with a range of poorer lifestyle and medical outcomes, as well as impaired performances on a range of cognitive tests. After controlling for these lifestyle and medical factors, memory performances remained significantly worse in adults with probable insomnia disorder, highlighting the presence of poorer memory function in middle-aged and older individuals with insomnia disorder. This study will help to direct future analyses investigating whether insomnia disorder increases the risk of further cognitive decline longitudinally with age.

Introduction

Insomnia is one of the most common sleep disorders, estimated to affect approximately 9-10% of adults in the general population. [START_REF] Morin | Epidemiology of insomnia: prevalence, self-help treatments, consultations, and determinants of helpseeking behaviors[END_REF][START_REF] Ohayon | Epidemiological and clinical relevance of insomnia diagnosis algorithms according to the DSM-IV and the International Classification of Sleep Disorders (ICSD)[END_REF] A diagnosis of insomnia disorder is made when an individual has trouble falling asleep, staying asleep or experiences early morning awakenings more than 3 times per week, for longer than 3 months, accompanied by a subjective experience of poor sleep quality and daytime dysfunction. [START_REF] Psychiatric | Diagnostic and statistical manual of mental disorders : DSM-5[END_REF] Meanwhile, an additional 25-30% of adults may occasionally experience insomnia symptoms that do not reach the full spectrum of an insomnia disorder diagnosis, e.g. with no reported impact on daytime function. [START_REF] Morin | Epidemiology of insomnia: prevalence, self-help treatments, consultations, and determinants of helpseeking behaviors[END_REF][START_REF] Ohayon | Epidemiological and clinical relevance of insomnia diagnosis algorithms according to the DSM-IV and the International Classification of Sleep Disorders (ICSD)[END_REF] Given that sleep is implicated in multiple beneficial roles (e.g. within cardiovascular [START_REF] Jackson | Sleep as a Potential Fundamental Contributor to Cardiovascular Health Disparities[END_REF] , immune [START_REF] Asif | Human immune system during sleep[END_REF] and neural 6 systems), it is important to distinguish between insomnia symptoms and insomnia disorder in order to assess whether a full insomnia disorder phenotype is required to impact these processes leading to chronic health conditions.

Research has shown that insomnia disorder is often comorbid with psychiatric disorders such as depression and anxiety, [START_REF] Seow | Evaluating DSM-5 Insomnia Disorder and the Treatment of Sleep Problems in a Psychiatric Population[END_REF] cardiovascular disease, [START_REF] Javaheri | Insomnia and Risk of Cardiovascular Disease[END_REF] diabetes, [START_REF] Anothaisintawee | Sleep disturbances compared to traditional risk factors for diabetes development: Systematic review and meta-analysis[END_REF] and other sleep disorders such as obstructive sleep apnea. [START_REF] Beneto | Comorbidity between sleep apnea and insomnia[END_REF] Insomnia disorder has also been linked to impairments in cognitive function across a range of domains, yet studies investigating cognitive performances in clinical samples with insomnia disorder have produced mixed results, partly due to limited sample sizes, and considerable variability in study characteristics (e.g. selection criteria and assessment methods) or unmeasured confounding variables such as comordbidities. [START_REF] Altena | Sleep loss affects vigilance: effects of chronic insomnia and sleep therapy[END_REF][START_REF] Crenshaw | Slow-wave sleep and waking cognitive performance among older adults with and without insomnia complaints[END_REF][START_REF] Haimov | Chronic insomnia and cognitive functioning among older adults[END_REF][START_REF] Orff | Discrepancy Between Subjective Symptomatology and Objective Neuropsychological Performance in Insomnia[END_REF][START_REF] Varkevisser | Chronic insomnia and daytime functioning: an ambulatory assessment[END_REF][START_REF] Fortier-Brochu | Insomnia and daytime cognitive performance: a meta-analysis[END_REF] On the other hand, most large-sample epidemiological studies in this area have been limited by the inability to utilize clinical diagnosis of insomnia disorder at such scale and have instead focused on broad sleep measures (e.g., sleep duration, overall subjective sleep quality) or insomnia symptoms only. [START_REF] Cricco | The Impact of Insomnia on Cognitive Functioning in Older Adults[END_REF][START_REF] Nebes | Self-Reported Sleep Quality Predicts Poor Cognitive Performance in Healthy Older Adults[END_REF][START_REF] Kyle | Sleep and cognitive performance: crosssectional associations in the UK Biobank[END_REF][START_REF] Gildner | Associations between Sleep Duration, Sleep Quality, and Cognitive Test Performance among Older Adults from Six Middle Income Countries: Results from the Study on Global Ageing and Adult Health (SAGE)[END_REF][START_REF] Johar | Impaired Sleep Predicts Cognitive Decline in Old People: Findings from the Prospective KORA Age Study[END_REF][START_REF] Devore | SLEEP DURATION IN MIDLIFE AND LATER LIFE IN RELATION TO COGNITION[END_REF] There have only been two cohort studies that have specifically investigated probable insomnia disorder and cognitive function. [START_REF] Goldman-Mellor | Is Insomnia Associated with Deficits in Neuropsychological Functioning? Evidence from a Population-Based Study[END_REF][START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] Neither study observed any difference in cognitive function between insomnia and controls overall. However, both found that specific subgroups of insomnia exhibited cognitive deficits. One study included a representative sample of 1,037 adults all aged 38 years who had been followed from birth. This study found that of those meeting DSM-IV inclusion criteria for insomnia, only those who had also sought treatment for insomnia (defined as discussing insomnia with a health professional) exhibited deficits in tests of processing speed and verbal comprehension. [START_REF] Goldman-Mellor | Is Insomnia Associated with Deficits in Neuropsychological Functioning? Evidence from a Population-Based Study[END_REF] The other study, using a more general inclusion criterion of a complaint of insomnia with a duration ≥ 1 year from a randomly selected cohort of 678 adults, detected impaired performance in processing speed and attention tasks only among participants who displayed short sleep duration, as objectively defined by a threshold of less than 6-hours total sleep time. [START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] Taken together, this suggests that more severe phenotypes of insomnia may include cognitive impairment, however the distinction between insomnia disorder and insomnia symptoms regarding their effects on cognitive function has not been examined, particularly in older adults. Furthermore, given the range of comorbidities often concomitant with insomnia disorder, certain factors may place individuals with insomnia disorder at a greater risk of cognitive impairment. However, controlling for the effects of comorbidities and considering phenotype when assessing the association between insomnia and cognitive function has yet to be performed in a systematic way within a large sample.

Thus, the aim of this study was to determine whether an association exists between the presence of probable insomnia disorder (PID) and deficits across various cognitive domains in a large sample of middle-aged and older adults; distinct from insomnia symptoms only (ISO) and independent of relevant demographic, lifestyle and medical factors. This was addressed by utilizing the baseline data of a large-scale cohort study. We hypothesized that we would observe poorer cognitive function in adults with insomnia symptoms and insomnia disorder, compared to those without insomnia, but that these deficits would be more severe in insomnia disorder, even after accounting for medical comorbidities and lifestyle factors.

Methods

Study design and participants

The sample was sourced from the 30,097 participants who completed the baseline assessments of the 'comprehensive cohort' from the Canadian Longitudinal Study on Aging (CLSA). The CLSA is a national, 20-year, prospective cohort study, and the CLSA study design and recruitment process has been comprehensively described and published elsewhere. [START_REF] Raina | The Canadian longitudinal study on aging (CLSA)[END_REF] This large-scale cohort study collects information on the biological, medical, cognitive, psychological, social, lifestyle and economic aspects of middle-aged and older adults. Briefly, individuals were recruited through either health registration databases or random digit dialling. Eligible participants were required to be aged greater than 45 years, live within 25 or 50 km of one of 11 data collection sites (depending on the site), able to respond in English or French, and exhibit an absence of cognitive impairment at the time of testing through standardized cognitive screeners. For this particular study, further exclusion criteria included: any prior diagnosis of dementia, stroke, or major head injury resulting in a loss of consciousness >20 minutes. The final sample consisted of 28,485 individuals who met the criteria for this study.

Study participants who are part of the CLSA Comprehensive cohort were asked to provide information through questionnaires, physical examinations, neuropsychological battery and biological samples -administered per standardized protocols. Questionnaires were administered during an in-home interview. Neuropsychological data were collected during visits to data collection centres for the vast majority of participants. At-home visits were conducted when participants were unable to travel to the data collection centre (0.74%).

Sleep and insomnia measures

Measures of sleep habits were collected through structured self-report questions, that were designed for this study as part of a larger set of measures to assess physical functioning. The questions were drawn from a variety of sources [START_REF] Bastien | Validation of the Insomnia Severity Index as an outcome measure for insomnia research[END_REF][START_REF] Buysse | The Pittsburgh Sleep Quality Index: a new instrument for psychiatric practice and research[END_REF][START_REF] Ikehara | Association of sleep duration with mortality from cardiovascular disease and other causes for Japanese men and women: the JACC study[END_REF] and captured important aspects of sleep and their relation to health. The questions covered six domains: 1) participants' satisfaction with the type of sleep they were getting; 2) their reported total amount of sleep during the night ("During the past month on average how many hours of actual sleep did you get at night?"); 3) whether they were having trouble falling asleep or staying asleep; 4) whether they had trouble staying awake when they did not intend to sleep; 5) if they reported or had ever been told that they seemed to "act out their dreams" or move while sleeping, and; 6) if they experienced, recurrent, uncomfortable feelings or sensations in the legs, or urges to move their legs while sitting or lying down.

Symptoms related to insomnia were drawn from domain 3. Specifically, these were assessed via the questions: "Over the last month, how often did it take you more than 30 minutes to fall asleep?", and "Over the last month, how often did you wake in the middle of the night or too early in the morning and found it difficult to fall asleep again?" Possible responses were: Never, Less than once per week, Once or twice a week, 3-5 times/week, or 6-7 times/week.

For each insomnia symptom, participants were also asked: "To what extent do you consider your problem to interfere with your daily functioning (for example, from daytime fatigue, ability to function at work/daily chores, concentration, memory, mood, etc.)?" Possible responses were: Not at all, A little, Somewhat, Much, or Very much. They were also asked: "For how long have you had this trouble?". Finally, participants were asked: "How satisfied or dissatisfied are you with your current sleep pattern?" Possible responses were: Very Satisfied, Satisfied, Neutral, Dissatisfied, Very Dissatisfied. These questions were utilised to make a probable diagnosis of insomnia disorder based on standard diagnostic criteria from the DSM-5 3 (Supplementary Figure 1). Specifically, only participants who experienced difficulties with sleep onset or maintenance more than 3 times per week, for longer than 3 months, and additionally stated that it significantly interfered with their daily functioning were categorised as having probable insomnia disorder (PID). Any participant who experienced these symptoms with the same frequency but did not report any interference with daytime functioning were categorised as having insomnia symptoms only (ISO). All other participants were classified as having no insomnia symptoms (NIS). The specific classification of PID and ISO based on these questions is provided in Table 1, and further information on the criteria used in the classification is provided in Supplementary Figure 2.

<INSERT TABLE 1 HERE >

Cognitive performance measures

Neuropsychological testing was administered to participants by a trained interviewer.

Participants completed tests that assessed performance across three broad cognitive domains: memory, executive functions, and psychomotor speed using well-validated measures.

Declarative memory was assessed with the Rey Auditory Verbal Learning Test (RAVLT), a 15item word learning test that assesses both learning and retention. [START_REF] Lezak | Neuropsychological assessment[END_REF] The number of words recalled in one immediate recall trial (RAVLT I) and one delayed recall trial (RAVLT II, with a delay of 30 minutes) were reported.

Executive functions were assessed using the Mental Alternation Test (MAT), [START_REF] Himmelfarb | Reliability and validity of five mental health scales in older persons[END_REF] Stroop Test (Victoria version), [START_REF] Golden | The Stroop Color and Word Test: A Manual for Clinical and Experimental Uses[END_REF] Controlled Oral Word Association Test (COWAT), [START_REF] Spreen | Neurosensory Center Comprehensive Examination for Aphasia (NCCEA)[END_REF] and Animal Fluency Test (AFT). [START_REF] Himmelfarb | Reliability and validity of five mental health scales in older persons[END_REF] The MAT, is a measure of mental flexibility and processing speed, requiring participants to count aloud from 1 to 20 and say the alphabet in alternation between number and letter (i.e. 1-A, 2-B, 3-C ...) as quickly as possible for 30 seconds, with the number of items attained being the outcome. The Stroop test is a measure of mental speed, inhibition, attention, and mental control and has three parts. In the first part (Stroop1), the participant was asked to read a list of words printed in different ink colours, and in the second part (Stroop2), to name the ink color of printed symbols (X's). In the third part (Stroop 3, interference condition), names of colors were printed in mismatching colored ink, and the participant was asked to quickly name the color of the ink that the words are written in and not to read the words (e.g., say "blue" for the word "green" written in blue ink). For all parts of the Stroop test, the outcome was the time taken to complete the task.

The number of errors on Part 3 of the Stroop test was also analysed separately. The COWAT is a measure of phonological fluency or knowledge, where the participant was asked to list out as many words as possible that begin with a certain letter over three 60-second trials (using a different letter each trial, e.g. F, A then S). The AFT is a similar test of category fluency, where participants were asked to list as many names of animals as possible in one 60-second trial.

Psychomotor speed was assessed with the Choice Reaction Time (CRT) test, in which participants were instructed to touch an interactive computer screen as quickly as possible at the location of a box that appears following a 1000ms delay. All tests were scored in a standardized way in collaboration with a CLSA co-investigator who was a clinical neuropsychologist.

Demographic and lifestyle measures

Socio-demographic information, including age, sex, household income and years of formal education, was collected. The interview and questionnaire also included items measuring tobacco consumption (current and former smoking habits), as well as items measuring the amount of alcohol consumed per typical week over the past 12 months.

Medical measures

Participants self-reported whether a doctor had ever told them that they had any of a range of chronic conditions, including hypertension, neurological, anxiety, depression, cancer and chronic pain. Self-reported, clinician-diagnosed, chronic conditions have been shown to have high test-retest reliability in population-based health surveys. [START_REF] Raina | The Canadian longitudinal study on aging (CLSA)[END_REF] Medical comorbidities were not an exclusion criteria. This analytic decision enabled us conduct statistical models investigating their impact on the relationship between insomnia and cognitive function.

Trained CLSA staff also measured the height and weight of participants, in order to calculate body mass index (BMI). Patients also reported how often they found it difficult to stay awake during normal waking hours or whether anyone ever had observed them stop breathing in their sleep.

Statistical analysis

Differences in demographic and clinical characteristics between PID, ISO and NIS were assessed using ANOVA with Tukey's honest significance test, or Pearson's chi-squared tests.

The association between the three groups and cognitive function expressed continuously was examined with general linear models using the "lm" and "Anova" functions of the "stats" package in R. [START_REF]A language and environment for statistical computing[END_REF] For each cognitive outcome, three multiple regression models were created with increasing complexity. A minimally adjusted model (Model 1) adjusted for age, sex, total household income and years of education. The next model (Model 2) additionally adjusted for a range of a priori factors that were considered relevant in the context of cognitive aging. These factors included: BMI, weekly level of alcohol consumption, diagnosis of cancer, diagnosis of anxiety disorder or clinical depression, hypertension, current level of smoking, presence of chronic pain, and a report of daytime sleepiness and a witness report of breathing interruption during sleep (to provide a proxy for sleep apnea). The final model (Model 3) adjusted for everything in Model 2, in addition to a binary variable indicating whether each subject regularly ≥ 6 hours, or < 6 hours per night. This was chosen based upon previous findings that only insomnia disorder with <6h sleep exhibit cognitive impairment. [START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] All results are presented as adjusted least-squares means and 95% confidence intervals. A false discovery rate correction [START_REF] Benjamini | Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing[END_REF] to account for multiple comparisons was applied, separately for the group-level comparison of demographic and clinical characteristics, and for each regression model between insomnia group and all cognitive tests. While this approach is less conservative than other methods, type II errors are less likely, and the approach provides better control against errors originating from multiplicity."

To determine variables and interactions that significantly predicted worse cognitive performance within each group, decision tree regression was performed using the "rpart" package within R. [START_REF]An Introduction to Recursive Partitioning Using the RPART Routines[END_REF] The "rpart" package implements the Classification and Regression Trees (CART) algorithm. [START_REF] Breiman | Classification and Regression Trees[END_REF] Linear regression tree models were applied post-hoc for each cognitive outcome that were found to be significantly associated with PID in the general linear models. The variables included for decision-making in the decision tree regression were all covariates that were implemented in Model 3. The number of cross validations was set to 1000, and the minimum number of instances allowed in a node prior to a split was set to 100 (10%). The complexity parameter was set to 0 and the resulting trees were subsequently pruned to the node with the lowest x-error.

Results

Sample characteristics

The analysis cohort was comprised of 28,485 adults with a mean age 62.8 ± 10.2 years. Onequarter (25.8%, n=7,337) were aged between 45-54 years, 9379 (32.9%) between 55-64 years, 6927 (24.3%) between 65-74 years, and 4,842 (17.0%) were aged over 75 years.

Slightly more than half (51.6%, n=14,686) were females, 24,258 (85.2%) had more than 12 years of education and 95.6% were Caucasian. English was the primary language for 22,369 (78.5%) participants, while 5,390 (18.9%) spoke primarily French and 2.6% had another native language.

Sleep duration

The mean self-reported duration of total sleep time across the entire sample was 6.8 ± 1.2 hours. Sleep duration was minimally different across all age groups: 45-54 years (6.7 ± 1.2 hours), 55-64 years (6.8 ± 1.2 hours), 65-74 years (6.9 ± 1.2 hours), 75+ years (6.9 ± 1.3 hours). The majority of participants reported sleeping greater than or equal to 6 hours per night (n = 24,733, 86.8%).

Insomnia and insomnia symptoms

Across the entire sample, 13,385 (47.0%) of participants reported never experiencing sleep latency greater than 30 minutes in the past month, 10,588 (37.2%) reported sleep onset latency problems less than 3 times per week, while 4,450 (15.6%) experienced problems 3+ times per week. A third (33.2%, n=9,452) of participants reported never experiencing problems maintaining sleep, 12,230 (42.9%) reported sleep maintenance problems less than twice per week, while 6,772 (23.8%) experienced problems 3+ times per week. There were more women than men in those experiencing difficulties getting to sleep (64.7% were females of those reporting 3+ times per week) or maintaining sleep (58.7% were females of those reporting 3+ times per week, Supplementary Table 1.

< INSERT FIGURE 1 HERE >

Of the entire sample, 1,068 participants (3.7%) met the criteria for probable insomnia disorder (PID). A further 7,813 participants (27.5%) reported insomnia symptoms only (ISO) of delayed sleep onset latency or nocturnal awakenings more than 3 times per week, but did not report that this significantly impacted on their daily functioning. Most participants (19,604; 68.8%) were classified as presenting no insomnia symptoms (NIS). The prevalence of PID significantly decreased with age, with greater percentages of adults aged between 45-54 and 55-64 years reporting PID than adults aged 65-74 and 75+ (Figure 1). The prevalence of ISO did not differ across any age category.

Table 2 displays the demographic, lifestyle and medical characteristics for all groups. Almost every measure was significantly different between PID and the rest of the sample.

Particularly, participants with PID had a greater prevalence of daytime sleepiness (65.9% vs 37.0%), a greater BMI (29.0 vs 27.9 kg•m 2 ) and were more likely to be smokers (12.1% vs 6.6%). Additionally, PID participants exhibited a higher prevalence of affective disorders such as anxiety (24.8% vs 7.9%) and depression (38.3% vs 15.3%). Participants with ISO also exhibited significant demographic and lifestyle differences from those with NIS (Table 2).

< INSERT TABLE 2 HERE >

Associations between insomnia and cognitive function

The estimated marginal means for neuropsychological test scores in each group for Model 1 and Model 2 are reported in Table 3. Raw distributions of scores on all tests in each group are presented in Supplementary Figure 3, and effect sizes for each group level comparison on all tests are reported in Supplementary Table 2. After adjusting for age, sex and education (Model 1), the PID group performed significantly worse compared with participants with NIS or ISO on every cognitive test except for the COWAT and CRT.

After adjusting for other comorbidities and lifestyle factors (Model 2) the relationship between scores of PID and NIS groups were no longer significant, except for the memory recall phase of the RAVLT (3.18 vs 3.41 words, p=0.010 FDR corrected). Participants with PID also performed worse than those with ISO on the memory recall phase of the RAVLT (3.18 vs 3.42 words, p=0.010 FDR corrected). Performances on the MAT became significantly greater in those with ISO compared with the NIS group (25.23 vs 24.93 items, p=0.041 FDR corrected).

After further adjustment for whether participants had an average sleep duration of 6 hours (Model 3), all relationships from Model 2 remained. Participants with PID still had significantly worse scores than the NIS group on the memory recall phase of the RAVLT (3.17 vs 3.40 words, p=0.030 FDR adjusted). The PID group also still performed worse than those with ISO on the memory recall phase of the RAVLT (3.17 vs 3.37 words, p=0.036 FDR adjusted). The ISO group still performed significantly better on the MAT after adjusting for average sleep duration compared with the NIS group (25.14 vs 24.74, p=0.035 FDR adjusted) and PID group (25.14 vs 24.30 items, p=0.047 FDR adjusted). Differences in estimated marginal means for each group split by self-reported sleep time less than and greater than or equal to six hours are reported in Supplementary Table 3.

< INSERT TABLE 3 HERE >

Sleep onset insomnia vs sleep maintenance insomnia

Based upon the types of insomnia symptoms they reported, 63 (5.9%) PID participants reported only sleep onset symptoms, 202 (18.9%) experienced only sleep maintenance symptoms, and the majority (78.2%) reported a mix of both. Females were more likely to experience sleep onset symptoms (69.8% of those reporting sleep onset symptoms) while maintenance symptoms were more equally reported across both females and males (53% vs 47% of those reporting sleep maintenance symptoms). Additionally, there were no significant differences in performances on any cognitive test between participants with PID who reported sleep onset or sleep maintenance symptoms (Supplementary Table 4).

< INSERT FIGURE 2 HERE >

Decision tree regression of cognitive function in older adults with probable insomnia disorder

As performance on the memory component of the Rey Auditory Verbal Learning Test (RAVLT) was the only outcome to survive multivariate adjustment, a decision tree regression model was used to determine the most discriminant variables included in the multivariate model (Model 3) that predicted overall performance on this test in PID (Figure 2). The single best predictor of high performance was age <71 years. The other variables determined to be most important for higher memory recall performance in PID included: females, and having a household income of greater than or equal to $50,000.

Discussion

Utilising data from a large cohort of cognitively healthy middle-aged and elderly Canadian adults, the aim of this study was to assess the independent association between insomnia disorder and cognitive function. Symptoms that intently reflected standardized DSM-V diagnostic criteria for insomnia [START_REF] Psychiatric | Diagnostic and statistical manual of mental disorders : DSM-5[END_REF] were used to identify probable insomnia disorder, while participants who reported insomnia symptoms without complaints of daytime dysfunction were classified as exhibiting insomnia symptoms only. This allowed not only for the examination of cognitive performance associated with insomnia disorder in a large sample of adults, but also to differentiate between the effects of insomnia symptoms and insomnia as a disorder defined by complete clinical diagnostic criteria.

Following adjustment for age, sex, education and household income, adults with PID demonstrated small yet statistically significant impairments across a range of neuropsychological measures of cognitive function than adults with either ISO or NIS. This is presumably influenced by the clinical characteristics of subjects with PID, as these participants exhibited greater proportions of anxiety, depression, diabetes, smoking, daytime sleepiness and breathing stoppages during sleep (an indirect gauge of obstructive sleep apnea), in addition to greater BMI and diastolic blood pressure -all associated with cognitive impairment [START_REF] Castaneda | A review on cognitive impairments in depressive and anxiety disorders with a focus on young adults[END_REF][START_REF] Snyder | Major depressive disorder is associated with broad impairments on neuropsychological measures of executive function: a meta-analysis and review[END_REF][START_REF] Campos | Smoking and Cognition[END_REF][START_REF] Fulda | Cognitive dysfunction in sleep disorders[END_REF][START_REF] Bucks | Neurocognitive function in obstructive sleep apnoea: a meta-review[END_REF][START_REF] Cournot | Relation between body mass index and cognitive function in healthy middle-aged men and women[END_REF] and regarded as risk factors for cognitive decline. [START_REF] Norton | Potential for primary prevention of Alzheimer's disease: an analysis of population-based data[END_REF] After adjustment of these factors, regression models revealed that only performance on a test of declarative memory remained worse in participants with PID compared to participants with either ISO or NIS, thus indicating an association between insomnia disorder and memory function -independent from the other clinical characteristics of adults with insomnia disorder. Sleep has been repeatedly implicated in the consolidation of memory [START_REF] Rasch | About sleep's role in memory[END_REF] , including declarative memories. [START_REF] Hu | Sleep Facilitates Consolidation of Emotional Declarative Memory[END_REF][START_REF] Plihal | Effects of Early and Late Nocturnal Sleep on Declarative and Procedural Memory[END_REF] Additionally, worse subjective sleep quality is also associated with elevated amyloid pathology in the cerebrospinal fluid of older adults, [START_REF] Sprecher | Poor sleep is associated with CSF biomarkers of amyloid pathology in cognitively normal adults[END_REF] while amyloid burden in the prefrontal cortex has been associated with poorer impaired overnight sleepdependent memory retention. [START_REF] Mander | beta-amyloid disrupts human NREM slow waves and related hippocampus-dependent memory consolidation[END_REF] A specific deficit in older adults with insomnia disorder is thus in line with previous work relating sleep to memory consolidation.

The reasons why these effects were specific to PID and not also to those with ISO is less clear. This is possibly reflective of the criteria used to define PID, for example the requirement of a subjective report of daytime impairment specifically related to each sleep complaint. While these reports were non-specific to any particular domain, memory concerns are the most predominant cognitive complaint in older adults [START_REF] Rabin | Subjective Cognitive Decline in Older Adults: An Overview of Self-Report Measures Used Across 19 International Research Studies[END_REF] , suggesting memory complaints were common in the PID group. Thus, these subjective impairments that distinguished the PID and ISO groups may be detected in objective testing, and may partly explain why memory deficits were specifically reserved to the group with probable insomnia disorder alone. Another important distinguishing factor between PID and ISO is the recurrence and chronicity of sleep disruption. It might be the case that cognitive disturbances take time to become manifest and that the persistence of insomnia over time -as seen in insomnia disorder -is required for deficits in memory consolidation to occur.

Therefore, some degree of insomnia severity might be needed for cognitive deficits to be detected, in line with findings from other insomnia cohorts. [START_REF] Goldman-Mellor | Is Insomnia Associated with Deficits in Neuropsychological Functioning? Evidence from a Population-Based Study[END_REF][START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] While these effects are small, they are similar to effect sizes observed in other large scale epidemiological studies of insomnia symptoms. [START_REF] Kyle | Sleep and cognitive performance: crosssectional associations in the UK Biobank[END_REF] This is likely due to the heterogeneity of insomnia disorder and insomnia symptoms across large populations, in addition to the wide range of additional contributing risk factors for cognitive impairment. A meta-analysis of previous smaller case-control studies of cognition in insomnia also found that moderate impairments existed in episodic memory compared to healthy controls. [START_REF] Fortier-Brochu | Insomnia and daytime cognitive performance: a meta-analysis[END_REF] This meta-analysis additionally observed significant impairments in problem solving and working memory, which was not replicated by the current findings, however it is likely that this is reflective of the contrast in methodological characteristics (e.g. inclusion criteria, population) between this study and the smaller clinical studies included in the meta-analysis. Two previous representative cross-sectional studies both failed to observe any cognitive impairments associated with probable insomnia disorder. [START_REF] Goldman-Mellor | Is Insomnia Associated with Deficits in Neuropsychological Functioning? Evidence from a Population-Based Study[END_REF][START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] Within both studies, only certain insomnia subgroups exhibited poorer cognitive performances. In the first study of 1,037 individuals, only health-seeking insomnia subjects (n=186) performed worse on tests of processing speed and verbal comprehension. [START_REF] Goldman-Mellor | Is Insomnia Associated with Deficits in Neuropsychological Functioning? Evidence from a Population-Based Study[END_REF] However, these subjects were significantly younger (all 38 years old) than the current sample, and most treatment seeking adults had experienced cognitive capacities below population norms since childhood. In the other study of 678 subjects, who were also on average younger (mean 50 years) than the current cohort, deficits were detected on measures of processing speed, mental flexibility, and short-term visual memory solely in insomnia subjects with objective short sleep duration (<6 hours total sleep time). [START_REF] Fernandez-Mendoza | Insomnia with Objective Short Sleep Duration is Associated with Deficits in Neuropsychological Performance: A General Population Study[END_REF] The current analyses demonstrated that deficits in memory performance was not statistically related to sleep duration in the group with PID. Regression tree analysis demonstrated that age was the single best predictor declarative memory performance in adults with PID. Specifically, participants with PID aged greater than 71 years showed the poorest memory performance. These regression analyses also identified that females exhibited less impairment than males. This is unsurprising, given the strong associations that age and sex share with memory and neuropsychological functioning generally. [START_REF] Fjell | Structural brain changes in aging: courses, causes and cognitive consequences[END_REF][START_REF] Strauss | A compendium of neuropsychological tests: administration, norms and commentary[END_REF] The regression analysis also indicated that a household income greater than $50,000 was also a discriminating variable. Although the interaction between insomnia and income level have not been associated with cognitive performance before, there is evidence that females with higher income demonstrate higher memory scores. [START_REF] Lee | The relation of education and income to cognitive function among professional women[END_REF] Overall, these findings suggest that females under the age of 71 with a mid-to-high income may be better protected from the negative outcomes in memory performance associated with insomnia disorder, and that other clinical or lifestyle factors do not appear to significantly further predict memory performance within insomnia disorder.

The identification of declarative memory impairment independently associated with insomnia in older adults is particularly important in the context of cognitive decline.

Memory is one of the cognitive domains most affected in ageing and is particularly impacted in certain dementias such as Alzheimer's disease. While these current findings are limited to cross-sectional cognitive function in cognitively healthy middle-aged and older adults, the PID group also had significantly greater proportions of a range of adverse health outcomes that place them at an elevated risk for cognitive decline. For example, the PID group exhibited greater proportion of daytime sleepiness than the other groups. Evidence from clinical studies suggest that patients with insomnia do not often experience daytime sleepiness, however associations between excessive daytime sleepiness (EDS) and insomnia symptoms have previously been reported in older adults. [START_REF] Jaussent | Insomnia and daytime sleepiness are risk factors for depressive symptoms in the elderly[END_REF] Therefore, older adults with insomnia may exhibit more daytime sleepiness, which has been independently associated with risk of cognitive decline. [START_REF] Elwood | Sleep disturbance and daytime sleepiness predict vascular dementia[END_REF][START_REF] Foley | Daytime Sleepiness Is Associated with 3-Year Incident Dementia and Cognitive Decline in Older Japanese-American Men[END_REF] The assessment of longitudinal data within this cohort as it becomes available will be critical to understand if insomnia disorder may increase the risk of memory decline, or the presence of adverse risk factors for cognitive decline in ageing. Surprisingly, participants with ISO performed better than those with PID and NIS on the test of mental flexibility after adjusting for demographic, lifestyle and medical factors, as well as subjective sleep duration. This is in contrast to a large body of literature that have implicated symptoms of sleep disturbance in cognitive impairment and increased risk of cognitive decline amongst older adults. [START_REF] Spira | Impact of Sleep on the Risk of Cognitive Decline and Dementia[END_REF][START_REF] Yaffe | Connections between sleep and cognition in older adults[END_REF] However, a recent analysis of the UK Biobank reported similar findings of improved cognitive performance in adults with frequent insomnia symptoms, only after adjusting for demographic and medical comorbidities. [START_REF] Kyle | Sleep and cognitive performance: crosssectional associations in the UK Biobank[END_REF] The authors interpreted this in the context of insomnia-related hyperarousal and personality traits, however the current findings suggest that these advantages are associated with insomnia symptoms only, not insomnia disorder. The distinction in performance between insomnia symptoms only and insomnia disorder (which required a report of daytime dysfunction) implies that older adults who are subjectively less sensitive to the effects of insomnia symptoms might also demonstrate slight objective resilience in cognitive performance. However, these effects appear only after statistical adjustment for clinical characteristics, demonstrating that some characteristics of adults with ISO act as negative confounding variables. Why insomnia symptoms, particularly without any subjective report of daytime impairments, might be associated with better performance in some cognitive domains needs to be further explored.

The prevalence of PID in this sample (3.7%) was measured to be less than half of what has previously been reported in the general population (9-10%). [START_REF] Morin | Epidemiology of insomnia: prevalence, self-help treatments, consultations, and determinants of helpseeking behaviors[END_REF][START_REF] Ohayon | Epidemiological and clinical relevance of insomnia diagnosis algorithms according to the DSM-IV and the International Classification of Sleep Disorders (ICSD)[END_REF] This may be explained by the features of the sample. Firstly, the CLSA only consists of adults older than 45 years of age. In a previous cross-sectional epidemiological study from a similarly sized sample of European adults only a third of elderly subjects with a predominant complaint of insomnia received a DSM-IV diagnosis of insomnia. [START_REF] Ohayon | Epidemiological and clinical relevance of insomnia diagnosis algorithms according to the DSM-IV and the International Classification of Sleep Disorders (ICSD)[END_REF] Indeed, the prevalence of insomnia symptoms in the current sample was much higher than probable insomnia disorder, although still much lower than what has been previously reported. [START_REF] Ohayon | Epidemiological and clinical relevance of insomnia diagnosis algorithms according to the DSM-IV and the International Classification of Sleep Disorders (ICSD)[END_REF][START_REF] Liu | Sleep habits and insomnia in a sample of elderly persons in China[END_REF] Furthermore, another study also using diagnostic criteria similar to the DSM-IV reported that the prevalence of insomnia disorder in Chinese adults aged over 65 years was 8.9% -closely aligned with estimates in the general population. [START_REF] Liu | Sleep habits and insomnia in a sample of elderly persons in China[END_REF] While different estimates in insomnia prevalence may potentially arise from cultural, societal or environmental characteristics of distinct samples, these would be unlikely to account for a two-fold increase in insomnia or insomnia symptoms. A major factor that may have influenced these differences could involve the CLSA study design of including at baseline only adults with an absence of cognitive impairment, dementia or history of brain injury. Given that sleep disturbances in later life are strongly associated with cognitive decline and dementia, and insomnia often occurs following brain injury [START_REF] Viola-Saltzman | Traumatic brain injury-induced sleep disorders[END_REF] , it is plausible that much higher rates of insomnia and insomnia symptoms are present in these adults who were excluded from the current study, explaining the much lower observed prevalence of insomnia and insomnia symptoms than those from studies of the general population. The decline in insomnia disorder with age (and stability of insomnia symptom prevalence) may therefore reflect a healthy survivor-effect. Particularly, insomnia occurring less frequently in successful ageing further supports a link between sleep disorders and cognitive decline, as older adults successfully aging without cognitive impairment are less likely to have insomnia disorder. This could be supported by longitudinal data detailing the precise relationship between insomnia disorder and cognitive decline in later life.

The strengths of this study include the power achieved through such a large sample size, the inclusion of objective neuropsychological testing, and the phenotyping of insomnia disorder in comparison to insomnia symptoms only. Nevertheless, there are a few limitations that must be considered when interpreting the findings. Firstly, while insomnia disorder was measured using questions closely aligned to DSM-V criteria, these were not part of a standardized clinical interview conducted by a trained psychiatrist or sleep medicine specialist. For example, the question surrounding sleep satisfaction might have been interpreted in different ways by different participants (e.g. refreshing sleep vs satisfaction with time of sleep onset or offset). Therefore, PID cannot be regarded as a definite inperson diagnosis of insomnia disorder, however such a diagnosis is unlikely to be achieved in such a large study. Secondly, while proxy measures of the presence of sleep apnea (daytime sleepiness and witnessed apneic events) were available and included in the models, objective information surrounding any sleep disorders, or the use of sleeping medication, were not available and thus could not be incorporated into these analyses. These data come from a specific study on healthy aging, and screening out cognitive impairment at baseline may have attenuated the associations between insomnia and cognition. As such these findings cannot be generalised to younger adults with insomnia under the age of 45, or older adults with moderate-to-severe objective cognitive impairments. Additionally, all the neuropsychological findings were of small magnitude.

However, given that these data come from a cohort specifically chosen for the absence of any objective cognitive impairment, the fact that significant differences in memory performance were still able to be detected demonstrates the sensitive relationship between insomnia and memory in ageing. This relationship may become stronger and more prevalent as cognitive function declines in the elderly. Finally, these findings are cross-sectional, and do not track the time course of cognitive function in insomnia in later life, which will need to be investigated to understand the distinct relationship between insomnia and cognitive decline. This highlights the benefit of longitudinal studies such as the CLSA to explore such factors for healthy ageing.

In conclusion, these findings suggest that insomnia disorder in cognitively healthy middle aged and older adults is associated with deficits in a range of cognitive domains, which is likely due to the demographic and clinical characteristics of adults with insomnia. After adjustment for these variables, adults with probable insomnia disorder exhibited decreased performance specifically on a test of declarative memory. This was distinguishable from insomnia symptoms only, and detectable despite the inclusion of adults without any identified cognitive impairment only. While small, these findings highlight the importance of distinguishing insomnia disorder from insomnia symptoms when considering cognitive function. The longitudinal relationship between insomnia disorder and memory decline now needs to be further explored in middle aged and older adults.

Figure 1 .

 1 Figure 1. Percentage of adults reporting probable insomnia disorder (PID) or insomnia symptoms only (ISO) across age brackets. *p<0.05 **p<0.01 ***p<0.001

Figure 2 .

 2 Figure 2. Decision tree regression model for performance on the delayed recall phase of the Rey Auditory Verbal Learning Test (RAVLT) in PID. Each node of the tree reflects the mean score on the test and percentage of the sample for each group split by the preceding variable.

Figure 1 Figure 2

 12 Figure 1

Table 1 .

 1 Criteria used for categorisation into probable insomnia disorder (PID) and insomnia symptoms only (ISO).

	Criteria for PID	Criteria for ISO

Sleep onset >3x per week OR Sleep maintenance >3x per week AND Interferes with daytime function ≥ "Much" AND Has been present >3months AND Satisfaction with sleep quality < "Neutral" Sleep onset >3x per week OR Sleep maintenance >3x per week AND Interferes with daytime function < "Much"Table 2 .

 2 Demographic, clinical and lifestyle characteristics of participants with probable insomnia disorder (PID), insomnia symptoms only (ISO) and no insomnia symptoms (NIS). Center for Epidemiologic Studies Depression Scale; BMI = body mass index; BP = blood pressure. Tukey's honest significance test or χ 2 test, as appropriate. All analyses are

	Diastolic BP, mmHg	2	74.8 10.4	73.9 9.9	73.7 10.0	0.001	0.012	0.181
	CESD = FDR		adjusted	to	correct	for	multiple	comparisons.
				Probable Insomnia	Insomnia Symptoms	No Insomnia Symptoms	PID Vs ISO	PID Vs NIS	ISO Vs NIS
					Disorder (PID)	Only (ISO)	(NIS)
					(n = 1068)	(n = 7813)	(n = 19604)	P	P	P
	Age, years SD			59.75 ± 9.15	62.82 ± 10.27	62.93 ± 10.22	<0.001	<0.001	0.747
	Females, %			64.5	58.3	48.2	<0.001	<0.001	<0.001
	Primary Language
	English			80.5	79.7	78.0	0.555	0.059	0.003
	French			16.1	18.1	19.4	0.135	0.011	0.015
	Caucasian, %			93.6	96.1	95.5	0.001	0.007	0.033
	>12 years education, %	82.7	84.0	85.8	0.002	<0.001	<0.001
	Income
	<$20,000		12.1	6.1	4.1	<0.001	<0.001	<0.001
	$20,000-$50,000	25.8	22.4	20.0	0.017	<0.001	<0.001
	$50,000-$100,000	30.4	32.2	33.5	0.277	0.049	0.049
	$100,000-$150,000	15.0	17.7	19.2	0.033	0.001	0.008
	$150,000+	10.4	15.1	16.9	<0.001	<0.001	<0.001
	BMI, kg•m	2 SD			28.99 6.1	27.93 5.34	27.88 5.08	<0.001	<0.001	0.747
	Smoker, %				12.1	7.4	6.2	<0.001	<0.001	0.030
	Alcohol >4 times per week, %	17.4	26.8	26.3	<0.001	<0.001	0.016
	Anxiety disorder, %		24.8	9.7	7.1	<0.001	<0.001	<0.001
	Current or history of Depression,%	38.3	18.2	14.0	<0.001	<0.001	0.816
	Taking antidepressant medication	22.9	7.9	7.1	<0.001	<0.001	<0.001
	CESD, score SD			11.1 6.2	6.6 4.8	4.3 4.1	<0.001	<0.001	<0.001
	Breathing stops in sleep, %	24.6	13.4	13.5	<0.001	<0.001	0.839
	Daytime sleepiness %	65. 9	41.7	34.9	<0.001	<0.001	<0.001
	Chronic pain, %			59.1	40.7	31.2	<0.001	<0.001	<0.001
	Cancer, %				14.5	16.1	14.9	0.206	0.747	0.017
	Diabetes Mellitus, %	14.0	9.9	8.4	<0.001	<0.001	<0.001
	Systolic BP, mmHg	2		120.4 16.3	121.1 16.7	120.9 16.6	0.631	0.370	0.660
									35

Acknowledgments

This research was made possible using the data/biospecimens collected by the Canadian Longitudinal Study on Aging (CLSA). Funding for the Canadian Longitudinal Study on Aging (CLSA) is provided by the Government of Canada through the Canadian Institutes of Health Research (CIHR) under grant reference: LSA 9447 and the Canada Foundation for Innovation. This research has been conducted using the CLSA Baseline Comprehensive Dataset version 4.0, under Application Number 160607. The CLSA is led by Drs. Parminder Raina, Christina Wolfson and Susan Kirkland.

Disclosure Statement

The authors have no conflicts of interest. NC is funded by the Fonds de Recherche du


Ryan Smith

Frédéric Dias
email: frederic.dias@ucd.ie

Gabriele Facciolo

Thomas Brendan Murphy

Pre-Computation of Image Features for the Classification of Dynamic Properties in Waves

Keywords: Breaking waves, Optical flow, Convolutional Neural Networks, Image Classification

The use of convolutional neural networks (CNNs) in image classification has become the standard method of approaching computer vision problems. Here we apply pre-trained networks to classify images of non-breaking, plunging and spilling breaking waves. The CNNs are used as basic feature extractors and a classifier is then trained on top of these networks. The dynamic nature of breaking waves is exploited by using image sequences to gain extra information and improve the classification results. We also see improved classification performance by using pre-computed image features such as the optical flow between image pairs to create new models in combination with infra-red images. The inclusion of the dynamic information improves the classification between breaking wave classes. We also provide corrections to the methodology from the article from which the data originates to achieve a more accurate assessment of performance.

Introduction

Large ocean waves carry huge amounts of energy which can be dissipated through a process known as breaking. One example of breaking is when an overturning of the crest causes a collapse and a breakdown to turbulence. The breaking process releases large amounts of energy in the dissipation of the kinetic energy of the wave through this turbulence. Understanding the breaking process, exchange of gases and energy in waves at various scales is of great importance to improving models of ocean-atmosphere interactions such as weather and climate models [START_REF] Deike | Capillary effects on wave breaking[END_REF][START_REF] Deike | Air entrainment by breaking waves[END_REF]. The dissipation of large amounts of energy through turbulent breaking is also of interest in coastal engineering applications where waves may slam into cliffs or man-made coastal structures.

The dissipation of energy at small length-scales creates difficulty in modelling breaking waves, as they interact with the air above the surface in the breaking process, creating large and small bubbles through a turbulent air entrainment [START_REF] Lubin | Are breaking waves, bores, surges and jumps the same flow?[END_REF][START_REF] Lim | Experimental study on plunging breaking waves in deep water[END_REF]. Breaking waves being turbulent, it is a complex two-phase process at the free surface where by overturning waves generate bubbles and jets of water plunging back into the wave create vortices which increase the mixing further. Current numerical methods make great simplifications/assumptions about the fluid flow at which point the details in the breaking process may be lost [START_REF] Shi | On optical flow techniques applied to breaking surges[END_REF] and what happens after breaking is largely unresearched as numerical methods are unable to simulate the process on large scales.

Ocean waves are difficult to recreate in the laboratory due to the different salinity, temperature and thus density gradients throughout the fluid. The waves are usually generated mechanically and do not experience the same breaking or spraying as ocean waves generated by wind. It is desirable then to study breaking waves so that it is feasible to measure turbulent quantities and determine characteristics of these waves in a real world setting. Examples are the breaking threshold, a criterion that distinguishes breaking waves from non-breaking waves and the spreading of breaking through the wave.

To overcome these challenges new methods are being pursued to extract dense or detailed information from ocean waves in real time using video data. A large video database of waves allows for a thorough analysis of breaking waves using image processing and modern computer vision techniques. The collected image data can also be used in the training of deep learning models for classification [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF], clustering, segmentation and prediction of wave characteristics [START_REF] Choi | Real-time significant wave height estimations from raw ocean images based on 2D and 3D deep neural networks[END_REF]. Such models can be used in further processing the image data collected to automatically detect, track and estimate quantitative wave properties.

We have applied image processing algorithms to breaking wave image data to probe what extra information can be gained from this approach of analysing fluid flows and in particular breaking waves. The main technique used on the dataset is optical flow [START_REF] Horn | Determining optical flow[END_REF][START_REF] Sánchez | TV-L1 Optical flow estimation[END_REF], which calculates the displacement of pixels between a pair of images. One of the difficulties is the discontinuous nature of breaking waves and the fact that these algorithms have been developed to deal with typically more rigid objects and motions. Thus it may prove necessary to use images from video at high resolution and high frequency to be able to resolve the details in the motions.

Related Works

Advances in the field of machine learning (ML) and increased processing power of computers over the last two decades have seen ML incorporated into almost every quantitative research field.

Fluid dynamics and oceanography have been no different, with applications from the simulation of fluids [START_REF] Fukami | Super-resolution reconstruction of turbulent flows with machine learning[END_REF] to flow optimisation and control [START_REF] Brunton | Machine Learning for Fluid Mechanics[END_REF]. Image processing and computer vision techniques have also shown great promise in oceanographic research where both classical algorithms and deep learning approaches have been implemented to process large amounts of image data to produce three dimensional depth maps [START_REF] Benetazzo | Measurements of short water waves using stereo matched image sequences[END_REF][START_REF] Fedele | Space-time measurements of oceanic sea states[END_REF][START_REF] Gallego | A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves[END_REF], wave tracking [START_REF] Stringari | A novel machine learning algorithm for tracking remotely sensed waves in the surf zone[END_REF], classification and segmentation of waves [START_REF] Stringari | Deep neural networks for active wave breaking classification[END_REF][START_REF] Stringari | Remote Sensing Observations of Dominant Breaking Waves in Intermediate to Deep Water from a Lighthouse During Storm Conditions[END_REF] and wave height estimations [START_REF] Choi | Real-time significant wave height estimation from raw ocean images based on 2D and 3D deep neural networks[END_REF][START_REF] Buscombe | Optical wave gauging using deep neural networks[END_REF].

Infra-red provides somewhat of an advantage for the study of breaking waves when using images due to small temperature fluctuations which are recorded by the infrared camera at the breaking region [START_REF] Jessup | Defining and quantifying microscale wave breaking with infrared imagery[END_REF]. These temperature fluctuations manifest as streaky patterns on the back of plunging waves [START_REF] Jessup | Infrared remote sensing of breaking waves[END_REF] and can be detected with the feature extraction in modern convolutional neural networks.

The infra-red cameras are also less sensitive to the reflection of light from the sun on the sea surface than traditional visible wavelength cameras. Using infra-red cameras does however come with limitations in image resolution and observation distance.

Optical flow in fluids research has also been used to analyse the motion of fluids in laboratory wave tanks [START_REF] Shi | On optical flow techniques applied to breaking surges[END_REF][START_REF] Zhang | Application of local optical flow methods to high-velocity free-surface flows: Validation and application to stepped chutes[END_REF] and to improve the results from Particle Image Velocimetry (PIV) [START_REF] Quénot | Particle image velocimetry with optical flow[END_REF][START_REF] Corpetti | Fluid experimental flow estimation based on an optical-flow scheme[END_REF]. Attempts to constrain the variational equations of optical flow with fluid mechanics equations has shown increased accuracy in some cases [START_REF] Heitz | Variational fluid flow measurements from image sequences: synopsis and perspectives[END_REF][START_REF] Liu | Fluid flow and optical flow[END_REF][START_REF] Wang | An analysis of physics-based optical flow[END_REF].

Video classification algorithms where both raw frames and optical flows are combined to help with the classification task have also been explored [START_REF] Ng | Beyond Short Snippets: Deep Networks for Video Classification[END_REF] and shown to give increased performance over the same algorithms without the additional optical flow information. Although the cited article uses a more complex Long-Short-Term-Memory (LSTM) network architecture, which was not implemented for our experiments as we use only two frames compared to a longer video sequence, they explore the usefulness of additional optical flow information. However it is noted that optical flow on its own in a case of noisy video frames can show degraded classification performance in comparison to just raw image frames.

Materials and Methods

Data collection

The data used for this project is from Buscombe and Carini [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF] in which they used a multitude of popular pre-trained CNNs as basic feature extractors for infra-red (IR) images of breaking waves in order to classify them. Details of the data acquisition can be found within the cited paper. The dataset consists of 9996 images split among three different wave classes: nonbreaking, plunging and spilling waves. The IR images were taken at a resolution of 640 by 480 pixels and are downsampled to a resolution of 299 by 299 for the CNN feature extractions. The dataset is highly imbalanced and contains relatively few examples of the plunging breakers: with 9996 total images, 208 are plunge, 2354 spilling and 7434 non-breaking wave images. Consecutive sample frames from each one of the wave classes are shown in Fig. 1.

As documented in Buscombe and Carini [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF], the images were captured using a thermal infra-red camera in November of 2016 at a US Army Corps of Engineers Field Research Facility in Duck, North Carolina, USA. The camera was angled at 45 • to the sea surface and mounted on a pier at the research facility. The images were sampled continuously at 10 frames per second while a Light Detection and Ranging device (LIDAR) measured the sea surface elevation in the same field of view. The wave height, as measured by the LIDAR, varied between 0 and 5.94 meters during the 10.5 hour acquisition period. The sequences vary in length from 7 frames to over 700 frames in a sequence (shorter sequences typically belonging to the plunge and spill breaking waves, while nonbreaking sequences are much longer). The distribution of pixel intensities was used to determine if the image contained a breaking wave. The type of breaking wave detected in these images was then manually classified by examining the patterns in front of and behind the breaking region. We made several changes to the dataset after finding errors in the manual classification which are described in subsection 3.2. Further details of camera and LIDAR specifications are available in the cited paper.

Our proposal is to achieve better results on the classification task by incorporating some of the dynamical information from the waves using the optical flow methods described in the following sections. In the original paper, the authors claim to have a high precision and recall on each of the classes (after augmentation F 1 scores ≈ 92 for all classes) but in a further analysis we found flaws with their dataset and model. The metrics used to assess the models were significantly degraded after correction of the dataset problems described in subsection 3.2. Thus, we aim to improve upon the corrected results by inclusion of the dynamical information. The wave movement is difficult to observe in the non-breaking case. However the breaking waves (spilling and plunging) show turbulent white-water effects which are picked up well by the infra-red (IR) camera. These white-water patterns contain distinctive identifying markers for the type of breaking that occurs. In the spilling case the breaking occurs more slowly and the white-water spreads over the back face of the wave. To contrast this in the plunging wave there is more structure to the back of the wave as the breaking happens more suddenly and crashes in front of the wave.

Nonbreaking Spilling

Nonbreaking Spilling

Plunging

Figure 2. Samples of calculated optical flows using TV-L 1 for each of the given classes. The optical flows are calculated using the sample IR images in Figure 1 and their respective next frame. The difference between the non-breaking and breaking classes is clear while the differences between spilling and plunging classes are more subtle but the extended "white water" region can be seen in the spilling optical flows.

Dataset Corrections

During the investigation several issues were identified with the dataset that was originally proposed to be used. Firstly in going through the original authors code, it was noted that the dataset splitting into training and testing sets was randomised. As the data was sequential (video images at 10 frames per second) it essentially meant that the authors' model was training on images that were one tenth of a second away from the testing images and in most cases the model saw images either side of the test image. Thus to sort the dataset correctly we separated the images into discrete waves based on the filename (i.e. group images xxx110 xxx120 and xxx130 into wave 1 for the class they belong to).

The grouping of the images into waves revealed another problem with the dataset: misclassified images. The grouping method described above revealed some waves in the classes contained only one or two images, but a file search for the images that would surround these revealed images of the same wave put into a different class (e.g. found spill/xx30, spill/xx50 but plunge/xx40). This is a clear mislabelling of the dataset as the waves do not change class and back again within 0.2 seconds. Each of these corrections was manually verified.

Once the data was sorted correctly, we tested the original authors best model and found it was significantly less accurate and the original logistic regression model did not perform well even on training data. One of the proposed reasons for this under-performance is the large class imbalance in the dataset and the fact that there are very few samples of the plunging breaking waves. Thus, the model is unable to find a distinguishing feature between the spilling waves and the plunging waves before over-fitting to the training set. It is cautioned to not randomly split sequential data like this which is highly dependent on the previous observation when splitting into training and testing datasets. This will give false results in regard to the models ability to generalise as the testing set contains near identical examples to the training set.

Optical flow

Motion analysis in image processing can be reduced to three main groups of problems: motion detection, object tracking and location and the derivation of 3D properties from 2D projections acquired at different points in time [START_REF] Sonka | Image processing, analysis and machine vision[END_REF]. In this section we are concerned with tracking the motions of individual pixels in a pair of images. In this way we calculate the displacement of pixels from the first image to the second; this is optical flow.

The optical flow between a pair of successive images is the apparent motion of the objects appearing in the two frames [START_REF] Sonka | Image processing, analysis and machine vision[END_REF]. Thus the optical flow is a vector field of the displacements of pixels and provides a mapping from the first image to the second image. Errors in this mapping can be caused by the following features: occlusion where the movement of objects blocks other objects in the second image, a lack of texture (high gradients in the pixel intensity) on the objects, or sudden brightness shifts such that tracking the motion becomes difficult.

A variety of techniques for calculating the optical flow field exist including classical methods and methods using convolutional neural networks (CNN) for the estimation of optical flow. Classical methods include variational techniques like the Horn-Schunck optical flow [START_REF] Horn | Determining optical flow[END_REF] which minimises an energy functional over the images, yielding a dense (for each pixel) vector field of displacements.

These techniques are based on the assumption that displacements are only one or two pixels in size, thus pyramid or multi-scale approaches are implemented which allow the detection of larger motions.

The multi-scale method downsamples the image to calculate a rough optical flow to be used as a base approximation for each increase in resolution back to the original resolution. This is often referred to as a coarse-to-fine optical flow estimation.

The CNN based methods are instead trained to estimate the motion fields in a more "black box" manner by providing many example images and their ground truth optical flows. A CNN model then learns to detect the textures within the images, and the change in location of these textures between the images thus producing an optical flow field. The ability to generalise is then dependent on the variety of textures and objects in motion in the images used for training the CNN. Datasets used for this training create an artificial optical flow by overlaying objects in the images and moving them from one frame to the next, in this way they know the "ground truth" optical flow.

We have selected two optical flow (OF) methods for use in this study; a classical method TVL 1 [9, [START_REF] Zach | A duality based approach for realtime TV-L1 optical flow[END_REF][START_REF] Wedel | An improved algorithm for TV-L1 optical flow. Statistical and Geometrical Approaches to Visual Motion Analysis[END_REF][START_REF] Monzón | Robust Discontinuity Preserving Optical Flow Methods[END_REF] and a CNN based method SPyNet [START_REF] Ranjan | Optical Flow Estimation using a Spatial Pyramid Network[END_REF][START_REF] Niklaus | A Reimplementation of SPyNet Using PyTorch[END_REF]. The details of the OF algorithms can be found in the respective articles along with working implementations. Fig. 2 shows the optical flow (computed with TVL 1 ) corresponding to the sample frames shown in Fig. 1.

Training and classification metrics

For the feature extraction, we use different pre-trained image classification models from the Tensorflow Python library. The top (fully connected) layer of these networks was removed so that a vector of features was outputted. This feature vector is then saved for each image or image pair. For comparison with the original paper [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF], we then trained the same logistic regression (LR) model on these feature vectors. A new fully connected layer was found to give no significant improvement over the LR model although more samples of the plunging class or more aggressive data augmentation could boost the performance of the neural network but this was not pursued here. The images were downsampled to the appropriate size for each respective CNN architecture (based on what they had originally been trained on) for optimal feature extraction. We trained several different models of which some take two or three images as the inputs. For the multi-image inputs we process each image with the CNN and combine the feature vectors together before training the classification model. Stacking the inputs on top of each other and processing these with the CNNs was found to produce inferior results. This result is likely because the channels in these pre-trained CNNs corresponded to the red, green and blue features but extracting all those channel features on each grayscale image gave more useful information. We trained an IR, OF, IR+IR and IR+OF models, where IR stands for infra-red and OF stands for optical flow image inputs. The addition represents the concatenation of the feature vectors with IR+IR being two consecutive infra-red images.

The metrics used for the evaluation of the classification predictions are described below, with the inclusion of two more metrics than in the Buscombe and Carini paper. The models were assessed using five different metrics on the classes: Precision (Pr), Recall (Re), F1 score (F1), Informedness [START_REF] Youden | Index for rating diagnostic tests[END_REF] (In) and the Brier score [START_REF] Brier | Verification of forecasts expressed in termps of probability[END_REF] (Bs) and each is defined in terms of the true and false positive (TP, FP) and true and false negatives (TN, FN) as follows:

Pr = TP TP + FP , Re = TP TP + FN , F1 = 2 Pr × Re Pr + Re In = TP TP + FN + TN TN + FP -1, Bs = 1 N N ∑ t R ∑ i (p ti -l ti ) 2 ,
where in the Bs the sums are over all N samples and all R classes, p ti represents the predicted probability for sample t and class i and l ti is then a vector with a 1 in the position indicating the true label. It thus measures the mean square difference between the predicted probability and the actual labels and thus a lower Bs is better. The informedness score estimates the probability of making an "informed decision": a score of 1 indicates a perfect classifier while a score of 0 indicates random decisions.

Results

Classification

After fixing the problems with the original dataset (see subsection 3.2), we use the original authors methods as a new baseline measure for our results. The best model from the [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF] paper is a logistic regression model fit to features extracted by a pre-trained MobileNet_V2 [START_REF] Howard | Efficient convolutional neural networks for mobile vision applications[END_REF]. We found the MobileNet_V2 CNN to perform much worse than using the features extracted from the Xception [START_REF] Chollet | Xception: Deep Learning with Depthwise Separable Convolutions[END_REF] pre-trained CNN. All model results below are from features extracted by the Xception network and a logistic regression fit. From Table 1 we can see that the optical flow of the images can be used in the classification task and it provides results comparable to using a single image. However the best results came from using the two IR images or a combination of the IR images and the optical flow. The extra information from the use of two images does not affect the nonbreaking classifications significantly, but it does have a positive impact on the spill and plunge classifications. In our experiments we also observed that the image augmentation implemented (rotation, zoom, crop) does not help when using the optical flow and in some cases it decreases performance. The SPyNet model shows difficulty in extracting the features to differentiate the two breaking types (plunge and spill). The CNN's output for calculating optical flow was seen to produce inaccurate and overly smooth flows on these images and thus performs slightly worse than the TV-L 1 model. The probabilities of each class obtained from the models are visualised in Fig. 4.

We also tabulate the errors from each of these metrics to make it more clear where exactly the best improvements in our models are. In Table 2 we give these improvements as percentages relative to the baseline IR model. It is clear that most models have performed significantly better in most metrics when compared to the single IR input model. The IR+TV-L 1 model reports the majority of largest improvements (indicted by the bold text).

Misclassifications

In this section we present the analysis of some misclassifications and confusion matrices in Fig. 3 of the models on testing (unseen) data both with and without augmentation applied. This allows for quick visual identification of misclassifications by looking at the off-diagonal terms in the confusion matrices.

For the confusion matrices, each row corresponds to a true label and each column corresponds to the predicted label. Higher performance corresponds to a darker main diagonal in the matrix. We observe that all models perform well on the non-breaking waves, with IR and the SPyNet OF having the largest errors on spilling waves (approximately 19 and 10 percent of spilling waves classified as non-breaking respectively). The TV-L 1 OF and the combined IR+OF (TV-L 1 ) are the best performing models at separating plunging waves from spilling waves. The majority of misclassifications occur as a wave is just entering or exiting the frame when it is reasonable to be incorrect.

Discussion

We have explored the use of optical flow features for the classification of breaking wave images.

This was tested on an image classification task to gain improved classification of sequences of IR images of breaking waves compared to only using a single IR image. After an initial exploration of the original dataset, the original analysis was found to be flawed. A large class imbalance exists, Our experiments have focused on the inclusion of temporal features in the data used to train the models. This gives a significant reduction in errors when compared to the baseline, single infra-red image input, model. In contrast to Buscombe and Carini [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF], who have quantified the performance of different pre-trained network feature extractions, our focus was thus on the data input to the networks.

As opposed to the results in table 1 of [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF], we detected and removed a selection bias within the data split caused by the high correlation of the training and testing data when randomly selected. Our results give a baseline which corresponds to Buscombe and Carini's results for the Xception network when the selection bias is removed and all the models, with the exception of the SPyNet based optical flow, have shown significant improvements over the baseline model. Further our results show that our application of optical flow as input to a pre-trained CNN has reduced errors on the classification task but similar to Ng et al. [START_REF] Ng | Beyond Short Snippets: Deep Networks for Video Classification[END_REF] noisy optical flows lead to a deteriorated performance as with the SPyNet results.

An analysis of the misclassified cases of the models shows that most misclassifications occur at the beginning or end of the image sequences where the type of wave is unclear. The gains on identifying both the plunging and spilling waves from using the optical flow can be achieved also by using the two IR images and applying the feature extraction on these. Further improvements may be possible with more regularisation or more aggressive data augmentation, in combination with more complex models, for better performance on the plunging samples. The dataset was deemed insufficient to train more complex neural networks or fine-tuning without over-fitting and adapting of the SPyNet optical flow network was abandoned after it failed to produce accurate optical flows on the images.

The inclusion of Optical Flow into the features for the classification task improved the results on the plunging wave category, and a combination of optical flow and IR images gave the best results on the spilling waves.

In future work, a higher quality dataset in terms of clearer and higher resolution images, but also in terms of a better balance of the breaking wave classes, will make the classification task and training of more complex models easier. Distinctive patterns in wave breaking can be identified but capturing the temporal evolution of wave properties through a sequence of images remains a challenge.

Investigation of how breaking evolves over time and an understanding of how it affects the free surface is crucial to provide accurate parameterizations for numerical forecasting systems.

Conclusions

The introduction of optical flow to incorporate temporal features leads to significant increase in a models ability to distinguish between plunging and spilling waves. The novel application of optical flow (TV-L 1 and SPyNet) and sequential images to breaking wave to infer temporal features yields significant performance gains as evident from both Table 2 and in Fig. 3 where errors are reduced by up to 60%. Moreover, our use of sequential images has shown that improved performance was achieved in nearly every metric for each model tested versus a baseline result obtained using only a single infra-red image. The addition of image augmentation to boost the number of image samples available for training of models leads to further increases with models that have raw infra-red images as inputs (IR, IR+IR and IR+OF models), whereas degradation of performance is seen where only optical flow is the input (TV-L 1 and SPyNet models). This observation is inline with those of Ng et al. [START_REF] Ng | Beyond Short Snippets: Deep Networks for Video Classification[END_REF] where they conclude the decrease is because of insufficient detail in the optical flow images which is exacerbated by cropping or augmentation.

Figure 1 .

 1 Figure 1. Samples of wave dynamics for each of the given classes. The image sequences span a time-frame of 1.0, 0.4 and 0.4 seconds for the non-breaking, spilling and plunging sequences respectively.The wave movement is difficult to observe in the non-breaking case. However the breaking waves (spilling and plunging) show turbulent white-water effects which are picked up well by the infra-red (IR) camera. These white-water patterns contain distinctive identifying markers for the type of breaking that occurs. In the spilling case the breaking occurs more slowly and the white-water spreads over the back face of the wave. To contrast this in the plunging wave there is more structure to the back of the wave as the breaking happens more suddenly and crashes in front of the wave.

Figure 3 .

 3 Figure 3. Confusion matrices for each of the tested models. The true class is in each row and the predicted class in each column.

Figure 4 .

 4 Figure 4. The evolution of probabilities for each class from some of the tested models. The horizontal axis corresponds to the image in the sequences. We see that the gain from the optical flow method in the classification of plunge images comes at the cost of uncertainty in the spill cases. A Brier score of 0 indicates a correct classification and total confidence in the classification i.e. the probability of that class is 1. Sudden spikes or changes in predictions are mostly from start and ending of image sequences where waves are only starting to enter the frame or almost entirely out of frame.

Table 1 .

 1 Metrics for tested models. For each metric (column) the best score for each class is indicated by the bold text. Higher scores are better for all metrics except for the Brier score where a score of 0 indicates perfect predictions and confidence. Results for models using augmented data are in parenthesis.

	Model	Class	Precision	Recall	F 1 score	Informedness Brier score
	IR	Non-breaking 0.97 (0.96) 0.94 (0.93) 0.95 (0.95)	0.87	0.09
		Plunge	0.33 (0.30) 0.42 (0.47) 0.37 (0.37)	0.41	0.97
		Spill	0.80 (0.79) 0.85 (0.83) 0.82 (0.81)	0.79	0.22
	TV-L 1	Non-breaking 0.98 (0.98) 0.96 (0.96) 0.97 (0.97)	0.90	0.06
		Plunge	0.32 (0.30) 0.59 (0.57) 0.42 (0.39)	0.58	0.70
		Spill	0.85 (0.85) 0.86 (0.85) 0.85 (0.85)	0.81	0.22
	SPyNet	Non-breaking 0.97 (0.97) 0.96 (0.96) 0.96 (0.96)	0.87	0.06
		Plunge	0.15 (0.14) 0.46 (0.46) 0.22 (0.22)	0.43	0.92
		Spill	0.84 (0.84) 0.76 (0.76) 0.80 (0.80)	0.72	0.33
	IR + IR	Non-breaking 0.98 (0.97) 0.96 (0.95) 0.97 (0.96)	0.89	0.08
		Plunge	0.39 (0.34) 0.43 (0.49) 0.41 (0.40)	0.42	1.01
		Spill	0.84 (0.82) 0.89 (0.87) 0.86 (0.84)	0.83	0.24
	IR + TV-L 1	Non-breaking 0.98 (0.98) 0.97 (0.97) 0.98 (0.98)	0.90	0.05
		Plunge	0.43 (0.36) 0.41 (0.46) 0.42 (0.40)	0.48	0.91
		Spill	0.88 (0.88) 0.92 (0.91) 0.90 (0.89)	0.86	0.12

Table 2 .

 2 The table below gives first the Infrared errors as a reference in section (a). The rest of the rows within section (b) contain the relative % improvement over the simple IR input model. Each error (except for Brier score) is calculated as 1score, where the score is the value reported in Table1. For the Brier score, since a lower score is best, we leave it as is. The percentages reported are the improvements in respective errors for the models, so a high positive % indicates a large improvement in the metric (reduced error). The best improvements are once again highlighted in bold text.

				(a)
				Errors
	Model	Class	Precision	Recall	F 1 score Informedness Brier score
	IR	Non-breaking	0.03	0.06	0.05	0.13	0.09
		Plunge	0.77	0.58	0.63	0.59	0.97
		Spill	0.20	0.15	0.18	0.21	0.22
				(b)
		Relative Improvements over IR Model Errors
	TV-L 1	Non-breaking +33.33%	+33.33%	+40.0%	+23.08%	+33.33%
		Plunge	-1.49%	+29.31%	+7.94%	+28.81%	+27.84%
		Spill	+25.0%	+6.67%	+16.67%	+9.52%	0.0%
	SPyNet	Non-breaking	0.0%	+33.33%	+20.0%	0.0%	33.33%
		Plunge	-26.87%	+6.9%	-23.81%	+3.39%	+5.15%
		Spill	+20.0%	-60.0%	-11.11%	-33.33%	-50.00%
	IR+IR	Non-breaking +33.33%	+33.33%	+40.0%	+15.38%	+11.11%
		Plunge	+8.96%	+1.72%	+6.35%	+1.69%	-4.12%
		Spill	+20.0%	+26.67% +22.22%	+19.05%	-9.09%
	IR+TV-L 1	Non-breaking +33.33%	+50.0%	+60.0%	+23.08%	+44.44%
		Plunge	+14.93%	-1.72%	+7.94%	+11.86%	+6.19%
		Spill	+40.0%	+46.67% +44.44%	+33.33%	+45.45%

Acknowledgments:

The authors would like to thank Jean-Michel Morel for his advice throughout the project.

Conflicts of Interest:

The authors declare no conflict of interest.

Funding: This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant number 18/CRT/6049 and through MaREI, the SFI Research Centre for Energy, Climate, and Marine (Grant number 12/RC/2302). We also wish to acknowledge the European Research Council (ERC-2019-AdG 833125-HIGHWAVE) and Insight, the SFI Research Centre for Data Analytics (Grant number SFI/12/RC/2289).

Data Availability: The code used to produce these results is available from github.com/ryan597/ Precomputation-of-features--classification. The data and extracted features for all models using the data split method in section 3.2 is available at doi.org/10.5281/zenodo.5361958. The original dataset split used in [START_REF] Buscombe | A data driven approach to classifying wave breaking in infrared imagery[END_REF] is also freely available at github.com/dbuscombe-usgs/IR_waveclass.

Author Contributions: RS proposed the use of optical flow and using multiple frames to improve the classification. RS carried out the experiments and wrote the draft article. FD and BM oversaw and gave feedback on the drafts, GF gave feedback on the drafts and further suggestions for improvement.