Mapping Existing Modelling Approaches to Maritime Decarbonisation Using Latent Dirichlet Allocation

Abstract

While for a long time reluctant to take action over the climate emergency at hand, the maritime shipping industry is now addressing the pressing need to decarbonise. Within this context, numerous modelling approaches and associated tools have emerged, with the aim of either reducing shipping emissions directly or facilitating decision-making around the sector’s transition. This paper explores the use of topic modelling—specifically Latent Dirichlet Allocation (LDA)—as a means of identifying the trends in these existing modelling approaches to maritime decarbonisation. The use of topic modelling is proposed as a means of overcoming challenges inherent to both the chosen field of study and wider shipping industry, namely significant heterogeneity and fragmentation. LDA is shown to provide an effective means of mapping this particular research field, with four topics identified as principal thematic trends. The results obtained may serve to ascertain where future research in sustainable shipping can most effectively intervene.

1. Introduction

The maritime shipping industry today is responsible for 80% of freight transport worldwide and approximately 3% of global greenhouse gas (GHG) emissions [1]. These are primarily comprised of carbon dioxide (CO₂), methane (CH₄) and nitrous oxide (N₂O) gases, although shipping also accounts for significant sulphur oxides (SO_x), nitrogen oxides (NO_x) and particulate matter (PM) emissions [2]. With growth expected to increase at a yearly rate of 1.3% over the coming years, shipping emissions could be responsible for between 5 and 9% of global GHG emissions by 2050 [1] according to various economic and energy scenarios [2]. In 2023, the International Maritime Organisation (IMO) therefore revised its Initial GHG Strategy of 2018 with a new objective of net-zero shipping emissions “by or around 2050” [3]. While this renewed objective is not sufficiently ambitious with regard to meeting the 1.5 °C global warming target set out by the Paris Agreement of 2015 [4], it has nevertheless compounded the industry with a regulatory imperative to decarbonise for which drastic actions must now be taken industry-wide.

Within this context, the role of modelling approaches can be thought of as twofold. Indeed, models can either act as emission reduction measures in their own right or mitigate the complexity of the transition by providing a means of testing and defining strategies for future implementation. Today, numerous such models exist and continue to emerge, principally as either papers from the scientific research sphere or as digital solutions from commercial providers. Recent years in particular have been marked by a surge in the number of models developed. The latter can in part be attributed to the growing awareness of the decarbonisation imperative worldwide and gradual implementation of GHG emission regulations. In addition, the potential now seen in the practice of modelling as a legitimate facilitator for the implementation of sustainable policy and practice has undoubtedly played a part.

The aim of this paper is to explore the potential of topic modelling—and specifically Latent Dirichlet Allocation (LDA) [5]—as a means of identifying and reviewing the principal themes explored by existing modelling approaches to maritime decarbonisation. The motivations underlying this objective are severalfold. Firstly, a review of existing modelling approaches to maritime decarbonisation has yet to be provided. It is however thought that reviewing existing approaches is necessary to ascertaining where future research can intervene to make industry efforts to decarbonise as comprehensive and effective as possible. Thus, the initial premise for this paper is defined. Secondly, in attempting such a review, it is observed that certain characteristics of our chosen field of study render finding a basis for comparison between different modelling approaches particularly complex. Yet crucially, a certain degree of comparability between modelling approaches is considered necessary to establishing a coherent review. The use of topic modelling is thus introduced as a means of undertaking this review in such a way as to overcome the particular challenges posed by the specificities of our chosen field of study.

In this way, the following paper begins to address the gap within the existing literature as to the need for a review of modelling approaches to maritime decarbonisation, by exploring how that review might be undertaken. The methodology employed does not aim to be exhaustive but to demonstrate the potential of topic modelling for this particular task. The results obtained nevertheless enable a preliminary mapping of the thematic trends addressed by current modelling approaches to maritime decarbonisation.

This paper is divided into five sections. Section 2 gives an overview of the related literature and the research questions determined as a result. In Section 3, the methodology employed for the application of topic modelling to 200 modelling approaches is described, before moving to a presentation and discussion of the results obtained in Section 4. A conclusion and summary of future research perspectives are given in Section 5.

2. Background and Literature Review

The following section addresses the related literature, establishing the need for a review of existing modelling approaches to maritime decarbonisation. The decision to explore the use of topic modelling as a way of undertaking this review is then explained in relation to literature from other research fields, such as the wider energy transition and information science.

To the authors’ knowledge, no previous attempts have been made at exploring the use of topic modelling to review existing modelling approaches to maritime decarbonisation. In fact, only a limited number of attempts at reviewing modelling approaches to maritime decarbonisation or similar exist at all. Where such reviews do exist, they have often focused on models treating specific aspects of maritime decarbonisation, such as surveys of modelling approaches to routing and voyage optimisation [6,7] or efficient ship hull and energy system design [8,9]. These have employed various methods, including drawing on the use of the Scopus database [6,8,9], conducting bibliometric analyses of scientific research articles [6,9] and developing taxonomies for the classification of articles within their respective fields [6]. The highly specific nature of these reviews has allowed for in-depth appraisals of different modelling approaches and classification by variables and/or scenarios considered, for example [7]. In addition, as the number of maritime digital solution start-ups has grown, so several studies have sought to review the commercial products available and chart the dynamics of this rapidly expanding market area. While these provide descriptive overviews of the principal categories of solutions available and their application potential [10,11], these are not systematic analyses and aim principally at providing a general overview of digitalisation as a pathway to decarbonisation.

The need for a review of modelling approaches to maritime decarbonisation is thus made quickly apparent. Deciding on how to undertake this review, however, remains a challenge. For indeed, if the recent proliferation of modelling approaches to maritime decarbonisation is undoubtedly positive in that it points to an increasing level of engagement with the need to decarbonise, the significant differences between the models developed in form, function and scale have almost come to reflect the often-cited fragmented nature of the maritime industry itself [12]. While this level of heterogeneity between modelling approaches is not necessarily a disadvantage in itself, it makes finding a basis for comparison between them rather more complex. Indeed, whereas reviews treating specific aspects of maritime decarbonisation can develop taxonomies based on a select number of model characteristics due to high levels of comparability within a particular category, the same cannot be said of our field of study. Instead, we must find common ground for comparison and classification between vastly different models, such as a wind propulsion technology simulation tool [13] and a GIS decision-support framework for the design of a zero-emission coastal shipping network in Greece [14].

The above challenge is of course not unique to our field. In their review of trends in tools and modelling approaches to the wider energy transition, Chang et al. [15] noted the difficulties posed by the methodological gap in the technical terminology used to describe modelling approaches to the energy transition. To bridge this gap, they chose to design a questionnaire based on earlier work by Connolly et al. [16]. They then distributed this questionnaire to model developers, thereby establishing a common terminology and framework for the evaluation of modelling approaches and thus facilitating their inter-comparison [15]. A similar approach was in fact initially attempted for our study. However, it was quickly felt that this might limit the number of models considered since data availability would depend entirely on the willingness of model developers to respond. As a reference, Chang et al. received 54 complete responses of the 137 models initially identified [15]. In addition, to design their questionnaire, Chang et al. were able to build on 42 earlier reviews of modelling approaches to the energy transition [15]. The framework they put forward in their questionnaire was therefore based on a more common understanding of the forms an energy transition model can take. With no precedent to build upon in our case, it was felt that applying this same methodology would mean imposing a framework on an as yet uncharted field of study. It was thus concluded that a bottom-up approach to reviewing modelling approaches to maritime decarbonisation might perhaps be more pertinent.

It is in light of the above challenges and specificities inherent to our field of study that it was decided to consider topic modelling as a means of facilitating a review of modelling approaches to maritime decarbonisation. Most crucially, since by addressing the language used to describe modelling approaches as a means of reviewing them, we find common ground for comparison in what is today a largely varied and expanding field. While it is not suggested that topic modelling is the only way of doing so, its application potential to reviewing modelling approaches to maritime decarbonisation is believed to warrant exploration.

An unsupervised strand of Natural Language Processing (NLP), topic modelling has been applied extensively since the 1990s [17] to extract latent variables from large datasets [18]. It follows two principal assumptions; namely, that each document within a corpus of texts can be represented as a distribution over a set of topics, with each topic itself, a distribution over a set of words [19]. Topic models are then used to infer this statistical structure for a given set of texts, with the statistical nature of the results obtained facilitating quantitative analysis and graphical visualisation. Today, several different types of topic models exist, with the recent emergence of Large Language Models (LLMs) in particular allowing for further developments with regard to text representation [19]. The following can thus be identified as the principal categories of topic models available today [19]: Non-Negative Matrix Factorisation [20], Latent Semantic Indexing [17], Probabilistic Latent Semantic Indexing [21,22], Latent Dirichlet Allocation [5], Correlated Topic Models [23,24], Lda2Vec [25], BERTopic [26] and Top2Vec [27].

While topic modelling has been applied extensively to various different kinds of datasets, it is only recently that the potential of topic modelling for assisting researchers in writing literature reviews has been explored. Asmussen and Moller in particular provided a framework for doing so [28]. Here, the authors chose to use LDA, noting its status as the preferred topic modelling method and number of previous applications, as well as the speed and relative ease with which LDA can be applied to large text corpora [28]. In addition, they found LDA to be particularly well-suited to applications in research, since the preprocessing, tuning and evaluation stages of LDA require a certain level of knowledge from the user as to the corpus’ subject domain [28]. A researcher, they note, is particularly well-suited to making these choices since they will often know the subject domain addressed by the texts they seek to review [28]. Our decision to use LDA in turn was based on the above work by Asmussen and Moller [28] and on its high potential for comparison with other LDA-based studies due to the method’s status as the preferred topic modelling method [18,19]. That is not to say that LDA does not have its shortcomings. Indeed, while LDA has improved on the performance of algebraic topic modelling methods such as LSA, it has several faults (assumption of word, document and topic independence, for example) and requires intensive optimisation with regard to hyperparameter estimation [18]. More recent methods have in fact either sought to address such shortcomings and/or explore the integration of new text representation methods to capture contextual word embeddings [19], with LDA nevertheless remaining a “benchmark” reference [18]. Since our aim here is not necessarily to apply the best performing topic modelling method, but to explore the application potential of topic modelling more generally to the task of reviewing existing modelling approaches to maritime decarbonisation, it was thus decided to use LDA for this initial exploration. Further work will, however, expand on the latter by applying other more recent and advanced methods to compare their respective performances on this corpus.

Thus, having identified a gap in the existing literature with regard to the need for a review of modelling approaches to maritime decarbonisation and the choice of a pertinent methodology to do so, the following sections will explore the application of LDA to this task.

3. Materials and Methods

An overview of the methodology employed for this study is given in Figure 1 with more detailed descriptions provided below.

It was decided in the first instance to focus on modelling approaches for maritime decarbonisation as emerging from the academic research sphere, since technical documentation for these is widely available in the form of scientific research articles. Articles were selected for analysis using the Web of Science (WoS) database, largely regarded as both highly specific and comprehensive [29]. The following exact search query was used in WoS (all databases): TS = (decarbonisation OR decarbonization) AND TS = (maritime OR shipping) AND TS = (tool OR model OR modelling OR decision-aid OR decision-tool OR decision-support). TS is the advanced search field tag for topic in WoS, meaning the search for the specified terms is made in the title, abstract, author and keyword fields for each record. Refining to articles only, the above search query resulted in the selection of 200 scientific research articles for analysis [8,13,14,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226]; the obtained corpus was not subsequently modified in any way. It should be noted that the aim was not for this corpus to be exhaustive but rather for it be representative. With articles drawn from 45 countries, 30 different WoS research areas and published in 85 different journals between 2012 and 2024, the corpus of modelling approaches to maritime decarbonisation extracted was deemed varied and diverse.

The selected articles were then cleaned in preparation for LDA. It was decided here to use only the abstracts of each article for LDA analysis, since these were thought to contain the most significant points from each article. Moreover, a research article will often include introductory and literature review sections which may mention themes outside the thematic scope of the model it proposes. Thus, an article proposing an alternative fuel selection framework [128] might still describe international GHG regulation and/or operational reduction measures in setting the context for the work presented, even if the latter is entirely concerned with the use of alternative fuels [128]. Using the entire articles for LDA in these cases could therefore have skewed both the thematic clusters obtained and associated per-text topic distributions. While this decision had has its limitations, since an abstract cannot capture the depth and detail of an entire article, it was thought prudent at this stage to base our analysis on the abstracts and explore their its application to entire articles in further work.

The abstracts for each of the 200 articles were thus extracted for analysis. Then, using the Python libraries Gensim (4.4.0) [227] and NLTK (3.9.1) [228], each abstract was lowercased and tokenised, with both punctuation and English stopwords removed. Tokenisation here refers to the process of splitting a text into tokens (here, individual word “strings”) in preparation for NLP [227]. English stopwords are words such as ‘the’ or ‘of’ which are considered of little semantic value to the texts and therefore omitted. Subject-specific stopwords such as ‘maritime’ or ‘shipping’ were also removed; these were also considered of little semantic value since their use within each article was an initial criterion for selection within the WoS database in the article selection stage. No further custom stopwords were set since it has been shown that removing extensive custom stopwords is of little benefit to model inference and can at worse skew topic modelling results [229]. In a final cleaning step, each token was then stemmed to root form. A total of 174,824 tokens remained following this data preprocessing stage, with 3001 of them unique.

While LDA is an unsupervised method, certain hyperparameters must still be set by the user. These include the number of topics, and the Dirichlet priors α and β, which determine, respectively, the distribution of topics for a given document and the distribution of words for a given topic. In this instance, the default settings provided by the Gensim library were used for both Dirichlet priors [227] since setting α and β values requires a priori knowledge of distributions within the corpus that we did not presume to have at this stage of our analysis. The use of default settings here was moreover deemed sufficient in light of the exploratory nature of the task at hand. With regard to the number of topics, the optimal choice is somewhat complex and varies according to the corpus and analysis aims. A lower number of topics will, for instance, lead to a more general overview, with a higher number of topics providing a more detailed analysis [28]. Moreover, while it is possible to evaluate a topic number choice based on the calculation of a Coherence or Perplexity score, the level of ambiguity intrinsic to human semiotics means human input is often necessary to evaluate NLP model results [230].

The latter was also noted by Asmussen and Moller, for example, who choseto determine the topic number for their analysis semantically, as opposed to using statistical or predictive evaluation methods [28]. To do so, they ran the LDA model with different topic numbers and evaluated the results by asking an expert in the corpus’ subject domain to assess the validity of the different topic groupings obtained [28]. A similar approach was applied in this study, although the quantitative evaluation of our results was also considered. Thus, the LDA model was run using a range of different topic numbers, with Coherence and Perplexity scores also calculated. Then, drawing on our own knowledge of the maritime decarbonisation research field, the results were semantically evaluated for the entire range of topic numbers by the authors. The latter involved ascertaining the coherence of the topic clusters obtained in relation to the types of emission-reduction measures and solutions identified by recognised studies [2,3,12,231,232]. Here, a compromise was made between the degree of semantic interpretability and the Coherence and Perplexity scores obtained, resulting in the choice of four as the preferred number of topics. Indeed, while considering four topics results in only the third-best coherence and perplexity scores for the range of examined topic numbers, the semantic coherence of the topics obtained was considered superior to when topic numbers achieving better scores were applied. In addition, since the aim of the analysis was to provide a general overview of the trends within modelling approaches to maritime decarbonisation, a lower number of topics was considered most appropriate at this stage. It should be noted that these results were additionally evaluated by three independent experts in the field who deemed the four topic clusters obtained to be semantically coherent. The above means of determining a topic number is of course subjective, and while reasonable within the context of our analysis aims, will be explored in further work.

With both preprocessing and hyperparameter selection stages complete, a dictionary of unique tokens and a matrix of unique term prevalence were created to serve as parameters to the LDA modelling module provided by Gensim [227]. The generative process of LDA as described by Blei et al. is then the following [5]. For each document w of N words in a corpus of M texts, and with K the number of topics:

• Choose N~Poisson (ξ);
• Choose θ~Dir (α);
• For each of the N words w_n;
• Choose a topic z_n~Multinomial (θ);
• Choose a word w_n from p (w_n|z_n, β), a multinomial probability conditioned on the topic z_n.

From the above generative process, a distribution of words for each of the four topics and a distribution of topics for each of the 200 abstracts were obtained.

4. Results and Discussion

The following section is comprised of the results obtained from the application of the methodology detailed above, their discussion and their exploration. It is divided into two sections as per the two types of results obtained from LDA topic modelling: per-topic word and per-text topic distributions.

4.1. Per-Topic Word Distributions

For each topic, the distribution of words gives the probability of each word belonging to that particular topic. Exploring these keywords and their respective weights within each topic is essential not only to assessing the validity of the results obtained as to their domain coherence but also to determining appropriate descriptions for each topic cluster. For while LDA can infer a distribution of words for each of a given number of topics, it does not describe or provide topic titles. To do so, the user must assess model results as informed by their own knowledge of the corpus’ subject domain [28]. To this end, the top ten most important keywords per topic from our results are pictured in bar charts in Figure 2, with the terms with the highest probabilities of belonging to a particular topic being its most defining keywords.

An initial assessment of these results was undertaken, as informed by our own knowledge of the recognised categories of emission-reduction measures available for application to the maritime shipping industry. These can be classified in different ways, but are generally considered as being either concerned with a ship’s energy-saving operation or its propulsion power and/or energy source(s) [231]. Examples of energy-efficiency measures include the use of air lubrication or hull performance monitoring, while the use of biofuels or wind energy addresses the need for alternative propulsion power sources [12]. The use of policy is moreover identified as one of the principal means of reducing shipping’s GHG emissions at the wider industry level through the introduction of subsidies, emissions price and/or quantity control mechanisms, for example [12]. Thus, the following can be deduced. Topic 1 seems concerned with the implementation of operational measures as a means of reducing shipping emissions. Its defining tokens point to the universally recognised idea that the optimisation of current vessel usage (performance, routing, port calls, etc.) can afford significant savings in fuel consumption, reducing emissions as a result. Topic 2 is defined by the two very specific tokens ‘hydrogen’ and ‘ammonia’ and a more overarching reference to ‘fuel’. It is therefore ascertained that topic 2 refers to the uptake of alternative (‘green’) fuels (‘power’) and the strategies (‘storage’, ‘system’, ‘cost’) required to do so. Topic 3, meanwhile, is more difficult to define. Based principally on the tokens ‘sector’, ‘polici’ and ‘industri’, however, it is thought to refer to the definition and application of emission-reduction policy. Finally, topic 4 is similarly somewhat difficult to define due to the lack of specificity in some of its defining tokens, but it is thought here to be concerned with the design and management strategies of ship energy systems based on the combination of tokens ‘system’, ‘electr’, ‘engine’ and ‘combust’, as well as ‘energi’, ‘fuel’ and ‘power’.

Sievert and Shirley argue that the above approach to interpreting topics based solely on their keyword distributions is insufficient and suboptimal since the most common words within the corpus will often be given a high probability of belonging to multiple topics, which makes differentiating between them more complex [233]. Instead, they propose a method for ranking terms within a topic called relevance whereby they calculate a weighted average of the logarithms of a term’s probability and its lift, given a weight parameter λ [233]. The lift is the ratio of a term’s probability within a topic to its marginal probability across the corpus, as defined by Taddy [234]. The relevance is then incorporated into an interactive tool Sievert and Shirley provide for the visualisation of LDA model results [233].

The latter is used to create the intertopic map and bar chart shown in Figure 3. Here, each circle is a topic represented in two-dimensional space as a result of multidimensional scaling. The distance between circles corresponds to their degree of similarity, while the area of each circle represents the chosen topic’s relative prevalence within the corpus [234]. Thus, the following can be noted. Firstly, for this corpus, topic 3 is shown to be the most prevalent, although this is perhaps to be expected since it is the least specific of the four. Secondly, the overlap between topics 2 and 4 points to the connectedness between ship energy system type and power source, while the relative proximity between topics 2 and 3 can be interpreted as reflecting the oft-remarked idea that the mainstream usage of alternative fuels in the near future will have to be facilitated by policy. Indeed, at current prices their implementation is simply non-economical and will need to be incentivised by the introduction of pertinent policy [12]. In this sense, it is perhaps unsurprising to note the relative distance between topic circles 1 and 3, since operational measures need not be incentivised as much by policy due to the financial savings they afford in terms of reduced fuel consumption. These observations are further confirmed through the use of Hellinger [235] and Jaccard [236] distances, as well as Cosine Similarity, to provide quantitative estimates of topic similarity. The strong correlation between topics 2 and 4 is particularly noted, as is the level of dissimilarity between topics 1 and 3. The relative proximity of topics 1 and 4, as well as 2 and 3, is highlighted by the use of Hellinger distance and Cosine Similarity in particular.

In Figure 3, the relevance weight parameter λ is set to 1 and topic keywords are therefore ranked according to the probability distribution obtained from the original LDA model run. A key aspect of the interactive visualisation tool developed by Sievert and Shirley is that it allows the user to vary the λ values used between 0 and 1 to facilitate the interpretation of the topic clusters obtained [233]. To explore whether modifying the relevance using pyLDAvis in this way may enrich the interpretation of our results based solely on the per-topic word distributions initially obtained, the top three keywords for each topic with λ = 0.5 and λ = 0 are recorded below (

Table 1. Top three keywords per topic for λ = 1, λ = 0.5 and λ = 0.

Topic Number	λ = 1	λ = 0.5	λ = 0
1	perform, oper, port	perform, port, oper	percentag, observ, schedul
2	hydrogen, fuel, ammonia	hydrogen, fuel, storage	infrastructure, advantage, element
3	sector, polici, use	sector, polici, climat	country, aviat, freight
4	energi, fuel, engin	energy, engin, system	heat, load, pump

).

Of course, testing only three λ values in this way does not enable us to ascertain the optimal weight parameter and resulting relevance for ranking topic keywords. The latter is not necessarily the objective at this stage, but will be investigated in further work. Instead, it is sought here to investigate whether variations in λ may enrich the topic interpretations made above and based solely on Figure 2.

Thus, in tracking the changes in the top three keywords for each topic across the chosen λ values, the following can be observed. Firstly, there is little change in the defining keywords when λ is changed from 1 to 0.5; the keywords are the same for topic 1, with only one change for topics 2 to 4, although the order in which the words are ranked does change across all four topics. When λ is set to 0 however, all three topic keywords change across all topics. While the topic keywords when λ = 0 are in keeping with what is determined from Figure 2 as to the general focus of each topic, these seem too specific to draw from in deciding on topic titles.

Setting λ to 0.5 seems more pertinent to our analysis. Indeed, it can be noted, for instance, that when λ = 0.5 as opposed to 1, the keywords ‘use’ and ‘fuel’ are lost from topics 3 and 4, but ‘fuel’ remains a defining keyword for topic 2. If we consider Figure 2, it can be observed that both ‘fuel’ and ‘use’ are in the top ten keywords of all four topics and are two of the most prevalent tokens within the corpus. This is somewhat unsurprising since it is widely agreed that two of the principal pathways to maritime decarbonisation are the optimisation of vessel operational usage and the introduction of alternative fuels. However, the fact that their importance in defining topics 3 and 4 changes with the relevance confirms the opinion put forward by Sievert and Shirley that assessing keyword distributions at λ = 1 can make correct interpretation more difficult, since the most frequent terms tend to be ranked as most important [233]. Conversely, the fact that ‘fuel’ remains nearly as important to defining topic 2 when λ is changed to 0.5 reinforces the assessment made from Figure 2 that this topic is concerned with the introduction of alternative fuels. In addition, it is interesting to note that the importance of ‘ammonia’ to topic 2 decreases with λ and is instead replaced by ‘storage’ within the top three, but that ‘hydrogen’ remains the topic’s most defining keyword, followed by ‘fuel’. We might consider here whether lowering λ from 1 in this way does actually improve the topic’s interpretability, since the relative importance of a subject-specific term is here shown to decrease, whereas that of the more overarching and frequent token ‘fuel’ remains unchanged.

On the whole, however, the relative importance of topic keywords and the ways in which the top-ranked keywords change with λ and the resulting relevance confirms the initial observations made from Figure 2 as to each topic’s principal theme. Based on our analysis using the combined approach explored above, each topic is attributed a title (

Table 2. Topic cluster titles based on model results assessment and use of pyLDAvis.

Topic	Title
1	Operational emission-reduction measures and usage optimisation
2	Alternative fuel choice and implementation strategies
3	Emission-reduction policy creation and application
4	Ship energy system design and management strategies

). Having assessed these topic clusters in this way, we move now to exploring their combinations within each of the 200 individual models.

4.2. Per-Text Topic Distributions

The distribution of topics at the individual text level is of interest for two reasons. Firstly, the consensus in the maritime shipping industry and associated research spheres is that no single measure can at this stage decarbonise maritime shipping on its own and that achieving decarbonisation will therefore require the application of several existing emission-reduction measures simultaneously [12,231]. In considering per-text distributions, it is thought that we may thus identify some of the combinations in which the simultaneous application of such measures has been explored. Secondly, it is considered that identifying these combinations is pertinent to considering where future research and modelling approaches must intervene to make wider efforts to decarbonise as effective as possible.

To this end, Figure 4 is created using the per-text topic distributions obtained above. Drawing on related work by Duplan [237], a conventional t-Distributed Stochastic Neighbour Embedding (t-SNE) plot [238] of our results is added to by making each one of the 200 data points a pie chart showing its individual topic distribution. In this way, the degree of similarity between modelling approaches can be visualised both in terms of the topics they address and the proportions in which they do so.

As in the intertopic distance map created using pyLDAvis (Figure 3), the obtained results are presented here in two-dimensional space, by reducing the topic distribution of each text from four to two dimensions in a matrix of pairwise similarities [238]. Again, the points closest together are the most similar, and conversely. The added pie chart feature means an idea of each data point’s high-dimensional topic distribution is retained despite having to reduce these dimensions to plot them in 2-D space.

In so doing, the following can be observed. The majority of modelling approaches consider more than one topic. This is particularly evident in modelling approaches considering topic 1, which is consistently combined with one or more of the other three topics. This both points to the essential role that operational measures can play in reducing emissions, especially in the short-term, but also to their limitations with regard to achieving deep decarbonisation in the long-term. For while operational measures such as routing and speed optimisation may effectively reduce emissions, applying only operational measures such as these cannot possibly compensate for the use of Heavy Fuel Oil (HFO) as a principal fuel source, for example. This perhaps explains why topic 1 is so often combined with the other three types of measures here. There are also instances of modelling approaches considering only one of topics 2–4. A cluster of models focusing solely on topic 3 is particularly notable and perhaps suggests a divide between researchers addressing maritime decarbonisation from a social sciences (policy) perspective and other engineering approaches to the matter, hence this cluster of topic 3-centred models. It is thought that it would be of interest to investigate this cluster further and that it is an example of where the methodology proposed in this paper might allow for the clustering of a highly heterogeneous field into smaller sub-groups for further analysis.

In terms of the other combinations visible here, few models are shown to address solely topics 1 and 2 or topics 1 and 3 together, but topics 2 and 3 are regularly considered simultaneously as are topics 3 and 4 and topics 1 and 4. These combinations reflect the necessity of enabling and incentivising the implementation of alternative fuels (topic 2) through policy (topic 3) and the consequent adaptation of ship energy systems (topic 4), as well as the need to optimise the usage (topic 1) of both new and existing energy systems (topic 4). The number of models considering both topics 3 and 4, and therefore the link between policy and ship energy system design and management, is perhaps less obvious, and it is a sub-group of modelling approaches that warrants further investigation. Between the sub-groups of data points combining topics 1 and 3 and topics 1 and 2, the modelling approaches that address the full range of topics can be observed. These are primarily concentrated around the topic 1 and topic 4 clusters, perhaps suggesting a tendency within these areas to engage with the challenges of maritime decarbonisation from a broader industry perspective. It is interesting to note that the number of modelling approaches addressing maritime decarbonisation from a pluri-disciplinary perspective (all four topics) within our corpus is relatively small.

The observations made here carry the following implications. Several configurations of topic combinations are now well-defined; either because they present obvious links because of their interdependence (topics 2 and topics 4) or due to their ease of applicability and high compatibility with other types of measures (topic 1). A cluster of topic 3-only approaches suggests the necessity of further integrating policy considerations within engineering-focused approaches (topics 1, 2 and 4) and vice-versa. Finally, the relative lack of approaches considering the issue from a truly pluri-disciplinary perspective (all four topics) is particularly significant with regard to future technological and policy developments. Indeed, it is oft remarked that the industry’s decarbonisation will only be achieved through the application of several types of emission-reduction measures simultaneously and that sustainable solutions must therefore be multifaceted to be comprehensive [12]. It is thus particularly striking that in light of this context, such a gap should appear within our corpus. Such a gap is surely an example of one future research must seek to fill.

5. Conclusions and Future Research Perspectives

The maritime shipping industry has shown growing engagement with the pressing need to decarbonise in the face of global climate change, with the introduction of an initial GHG policy in 2018 and its revision in 2023. In parallel, significant growth has been observed in the number of modelling approaches developed with the aim of addressing and facilitating maritime decarbonisation. This paper has explored the potential of topic modelling—and specifically Latent Dirichlet Allocation (LDA)—as a means of mapping and reviewing these existing modelling approaches.

Principal findings can be summarised as follows. The use of LDA entails a focus on the language used to describe different modelling approaches to maritime decarbonisation as a basis for comparing them. In so doing, the difficulties posed to comparison by significant levels of heterogeneity and fragmentation between modelling approaches are overcome, to provide an initial map of this field’s defining thematic trends. While the related literature has reviewed specific and more homogeneous groups of modelling approaches to maritime decarbonisation, this paper has addressed the need for an overarching review of modelling approaches to maritime decarbonisation and explored how such a review might be undertaken. In testing the use of LDA on 200 article abstracts drawn from the WoS database, four topics have been identified as the driving themes addressed by existing modelling approaches to maritime decarbonisation. These four topics are operational and usage optimisation, alternative fuel choice and implementation strategies, emission-reduction policy creation, and ship energy system design and management strategies. The above is in keeping with the principal categories of solutions identified as possible pathways to maritime decarbonisation in the related literature [2,3,12,231,232].

A key contribution is the graph provided in Figure 4 showing each of the 200 modelling approaches, the degree of similarity between them and the extent to which they address each of the four topics. This latter graph carries perhaps the most significant implications of the work undertaken here. For indeed, it is thought that visually charting the thematic dynamics of our field may help ascertain where future research in sustainable shipping must intervene to make efforts to decarbonise as concerted and effective as possible. It is for instance notable in Figure 4 that few approaches address all four topics simultaneously, although it is largely recognised that decarbonising the maritime industry will require a multifaceted and pluri-disciplinary approach [12]. The latter is an example of a gap which future research must seek to fill. In visually revealing such gaps, it is shown that the clusters and trends identified here may help guide future research directions. Finally, the analytical framework proposed above may be applied to further types of datasets to add to the findings provided in Figure 4. Where this particular paper has focused on modelling approaches as emerging from the scientific research sphere, the focus on language as a basis for comparison means commercially available tools for maritime decarbonisation may be integrated into our analysis, despite a lack of available and detailed documentation. It is thought, for instance, that this analytical framework may be applied to the language used to describe commercially available tools in patent databases or directly on digital providers’ websites. Indeed, the former would be particularly compatible with the methodology developed since the advanced search modules of patent databases often resemble that of the WoS database, with abstracts moreover provided for each patent. With regard to commercial approaches, several modifications would have to be made to the current methodology. Challenges here would include developing an appropriate advanced search strategy and standardising which abstract-equivalent parts of a provider’s website might be extracted or scraped for each commercialised approach. However, once this is established, the focus on language as a means of classification within the developed methodology would enable the comparison of these modelling approaches despite their different sources and forms of presentation. The results obtained in this way could enrich the overview of modelling approaches to maritime decarbonisation provided and enable a detailed appraisal of wider industry trends as well as academic/commercial interactions and transfer.

Several limitations to our approach and their potential consequences on our results should be noted. The decision to focus on language as a means of classifying mathematical models, for instance, is approximate; such an approach cannot be entirely comprehensive or representative of the scientific methodology behind each model. As a result, our conclusions cannot for example match the level of detail provided by Chang et al. in their analysis of modelling approaches to the wider energy transition and their respective methodologies [15]. Moreover, LDA is neither the most recent nor advanced topic modelling method, and the methodology applied here was largely based on the use of default parameters. Future work should therefore include the application and comparison of several different types of modelling methods, considering, in particular, new text representation methods to capture contextual word embeddings [19]. A sensitivity analysis will also need to be carried out to improve our choice of Dirichlet priors and hyperparameter tuning methodology. Indeed, the use of default symmetrical priors for α in particular has potentially negatively impacted topic coherence if we look to related studies as to the impact of Dirichlet prior choice [240]. The use of part-of-speech filtering should also be explored; it is thought the latter could enrich our analysis in considering only tokens of categories of the highest semantic value. Potential changes to the initial advanced search strategy applied to the WoS database should also be explored. As it currently stands, the keywords used in this advanced search were defined by the authors following what they viewed to be a modelling approach to maritime decarbonisation. The latter is inevitably biassed, and the advanced search terms warrant further investigation to ensure that the corpus is as representative as possible of this field of research. It is for example surprising that relatively few articles addressing the use of wind propulsion were selected following the advanced search, despite the fact that wind propulsion has often been identified as one of the most promising and immediately actionable pathways to maritime decarbonisation [241]. Finally, the clusters identified in this paper should be analysed according to data such as publication date, journal or country to provide further insights.

Overall, it can nevertheless be concluded that inferring the topic structure of a dataset of modelling approaches to maritime decarbonisation through LDA provides an effective means of mapping the dynamics and research trends of this largely varied and expanding field.