Guidelines For Drawing Causal Loop Diagrams

Causal Loop Diagram

Business Motivation Models

David M. Bridgeland , Ron Zahavi , in Business Modeling, 2009

Causal Loop Diagrams and Management Discussion

Causal loop diagrams are useful for eliciting discussion among members of a management team. The Portia management team can dig into Figure 3.20 and (perhaps) predict how the neighborhood will evolve over time.

A causal loop diagram can also be simulated to resolve issues about how the dynamics will play out. However, causal loop diagrams are rarely simulated directly. They simply don't have enough information to resolve the uncertainties. Instead, a causal loop model is used as an intermediate step in building a system dynamics model, and the system dynamics model is simulated. Chapter 11 describes system dynamics models and simulation.

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Business Simulation

David M. Bridgeland , Ron Zahavi , in Business Modeling, 2009

Simulating Feedback

In Chapter 3 we introduced causal loop diagrams, and earlier in this chapter we examined several of these diagrams. Within a causal loop diagram are typically one or more causal loops. A causal loop is a circular chain of variables affecting one another in turn. One variable affects a second variable, which in turn affects a third variable, and the third variable then affects the first. Or perhaps the loop is longer, with five or seven variables completing the circle.

Causal loops are common in the situations modeled by business motivation simulations. In the simulation of restaurant wait times we are exploring, there are at least 10 distinct causal loops. Using the terms introduced in Chapter 3 some of these loops are reinforcing; these loops drive more and more extreme behavior. For example, as the restaurant gains customers, more people talk about it. More prospective customers learn about the restaurant through word of mouth from their friends and colleagues. Some of these prospective customers try the restaurant, and some of those samplers like it so much that they become regular customers. This in turn leads to more word of mouth and further prospective customers. The restaurant becomes more and more popular.

Other loops in our restaurant example are balancing; these loops moderate the behavior, returning the situation to some middle ground. For example, as the restaurant earns new customers and it becomes more popular, the utilization grows and the wait times increase. The increasing wait times lead to a decline in the attractiveness and fewer new customers gained. Figure 11.36 shows this balancing causal loop.

Figure 11.36. More customers lead to increased wait times, and then fewer customers

Of the nine variables in Figure 11.36, we have already explored six earlier in this chapter.

So we must define only the three remaining variables to completely model this causal loop, the three variables on the left of Figure 11.36: Enjoyed Proportion, Customers Gained, and Customers. Let's start with Enjoyed Proportion. When new people sample Zona for the first time, how many enjoy their experience enough to become customers? How many do not enjoy their experience, at least not enough to return? The proportion of people who enjoy their experience is Enjoyed Proportion. For a world-class restaurant on a good day, the enjoyed proportion might be as high as 0.80; 80 percent of the new samplers like it. For a truly awful restaurant, the enjoyed proportion can be as low as 0.0—no one likes it enough to return.

Figure 11.37 shows how Enjoyed Proportion depends on Restaurant Attr to New Custs—the attractiveness of the restaurant to new customers. As you will recall, attractiveness varies from 0—not attractive at all—to 2—highly attractive.

Figure 11.37. Restaurant attractiveness determines whether samplers return

The second undefined variable—Customers Gained—is quite simple. It is just the number of people who sampled the restaurant this week multiplied by the proportion of those samplers that enjoyed their experience:

$\text{Customers Gained}=\text{Samplers}*\text{Enjoyed Proportion}$

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31st European Symposium on Computer Aided Process Engineering

Nandita Saraf , Yogendra Shastri , in Computer Aided Chemical Engineering, 2021

2 Model development

System dynamics helps in analysing the behaviour of complex socio-economic systems due to underlaying interactions which governs the dynamics (Forrester, 1994 ). To develop a SD model, first step is to develop a causal loop diagram (CLD). It depicts causal relation that exist between variables of the system. This requires a good understanding of how two variables interact. The next step is to formulate mathematical equations which go as input to the model. The specific functional form of equation is decided based on either causal relation or historical trend. Equation parameters are estimated through fitting historical data to the proposed function. SD model developed in this work focuses on private transport vehicles in India. Important assumptions of the model are: -

1.

Ownership cost is the only decisive factor in determining the purchase demand for various vehicle options

2.

The number of vehicles and distance travelled per vehicle are always related to per capita GDP

3.

Fuel price is always related to fuel supply-demand dynamics

4.

Electricity price is considered as independent of electricity demand coming from transport sector

The CLD of the model is shown in Fig. 1. Population and GDP per capita positively influence the demand for car and two-wheeler, which is divided among various available options. Annual demand of vehicle adds to vehicle stock, which increases the fuel demand. Dynamics of fuel demand and supply impacts the fuel price. Annual fuel expense of vehicle adds to the ownership cost of vehicle, which is used in logit model to determine the annual demand for the vehicle for next time step.

Figure 1. Causal loop diagram

1 Model inputs

Car and two-wheelers ownership and annual distance travelled are the inputs to the model. From annual car and two-wheeler ownership, annual demand for cars and two-wheelers are calculated. Correlation of vehicle ownership and annual distance travelled with per capita income is represented by Gompertz function. S-shape of the function gives more realistic growth of these variables than other logistic functions. Parameter values were estimated by fitting historical data.

2 Gasoline and diesel prices

Gasoline and diesel prices are positively influenced by their respective demand and brent crude oil price (Fig. 1). Differential equations are formulated to capture the impact of the annual change in fuel demand and brent crude oil price on annual change in respective fuel prices. Annual change in fuel price for i^th time step is added to respective fuel price in i-1^th time step to get the fuel price at i^th. The equation coefficients are estimated by minimizing the sum of square of error between actual and predicted gasoline and diesel prices between 2001-2018. Calculation of fuel prices are shown in Eq. 1 and 2:

(1) $P^i=P^{i-1}+0.7224\times \frac{{\mathit{dD}}_P^i}{\mathit{dt}}+1.1772\times \frac{{\mathit{dC}}^i}{\mathit{dt}}$

(2) $D^i=D^{i-1}+0.1702\times \frac{{\mathit{dD}}_D^i}{\mathit{dt}}+0.7712\times \frac{{\mathit{dC}}^i}{\mathit{dt}}$

Where, P ⁱ and D ⁱ are gasoline and diesel prices, $\frac{{\mathit{dC}}^i}{\mathit{dt}}$ , $\frac{{\mathit{dD}}_P^i}{\mathit{dt}}$ and $\frac{{\mathit{dD}}_D^i}{\mathit{dt}}$ are annual change in brent crude oil price, gasoline and, diesel demand respectively.

3 Ethanol supply, demand and pricing

Biorefineries producing ethanol from molasses and lignocellulosic biomass have been considered. If biorefinery generates profit, it encourages more investment in the sector, thereby resulting in greater production. Impact is inverse in case sector incur a loss. Since biorefineries require high capital investment and multiple years for erection and commissioning, the model has captured the time-lag in the impact of profit/loss on the actual increase/decrease in the ethanol production using ARX time series model. The equation parameters are estimated by fitting historical data. The ethanol production equations are given by Eq. 3 and 4:

(3) ${\mathit{EP}}_M^{i+2}=0.8967\times {\mathit{EP}}_M^i+0.3224\times P_M^i+0.0307\times P_M^{i-1}$

(4) ${\mathit{EP}}_B^{i+3}=1.1365\times {\mathit{EP}}_B^i+0.3224\times P_B^i+0.0338\times P_B^{i-1}$

Where, EP _M ⁱ , EP _B ⁱ , P _M ⁱ and P _B ⁱ are ethanol production capacity in million litres and profit earned in INR by molasses and biomass based biorefineries respectively.

Literature have reported reduction in production cost of biomass-based ethanol falls within range of 15-25% as capacity doubles (van den Wall Bake et al., 2009). Based on this it is assumed that production cost will reduce by 15% for lignocellulosic ethanol. Production process of ethanol from molasses is fairly matured hence production cost is assumed constant. Ethanol demand comes from E-85 vehicle stock and mandatory blending in gasoline. Refinery gate price of ethanol is the price at which biorefineries sell their ethanol to oil manufacturing companies. If ethanol demand is higher/lower than supply then refinery gate ethanol price will have proportionate influence, as shown by negative causal relation in Fig. 1.

4 Electric vehicles and associated inconveniences

Adoption of EVs is associated with many challenges from consumers' side. The model considers two basic inconveniences, i.e., insufficient charging stations and long charging time. Insufficient charging stations lead to limited options for charging. Additionally, slow charging may further affect the desirability of an EV for a consumer. Among these, inconvenience due to lack of charging stations is considered as common for both electric car and two-wheeler as shown in CLD. This is because the charging stations would be shared by both. Inconvenience due to long charging time would be a function of their battery capacity. Hence, this would be vehicle specific. The model converts these inconveniences into monetary values and adds that to the total cost of ownership of the vehicle. Higher inconvenience results in higher ownership cost thereby reducing the demand for EVs. The inconvenience due to lack of charging stations is calculated by comparing existing number of stations with the number of stations ideally required based on electric vehicle stock. Calculation of inconvenience cost due to insufficient charging stations and long charging time is shown in Eq. 5 and 6:

(5) $I^{\mathit{CS}}=\frac{\left({\mathit{CS}}^i-{\mathit{CS}}^a\right)\ast C^{\mathit{cs}}}{{\mathit{EV}}^{\mathit{stock}}}$

(6) $I^{\mathit{CT}}=\frac{\left({\mathit{ST}}^{\mathit{car}}-{\mathit{FT}}^{\mathit{car}}\right)\ast \left(C^{\mathit{SC}}-C^{\mathit{FC}}\right)}{E_{\mathit{car}}^{\mathit{stock}}}$

where, I ^CS , I ^CT are inconvenience costs due to insufficient charging stations and long charging time, CS ⁱ , CS ^a are ideal and actual number of charging stations, C ^S , C ^SC and, C ^FC are the setup cost of station, slow and fast charger, EV ^stock and E _car ^stock are combined EV stock and electric car stock respectively. Inconvenience due to insufficient charging stations is the additional funds required to setup charging stations to meet the ideal requirement. The inconvenience due to long charging time is the fund required to pay in order to save the additional time required to charge electric car by a slow charger.

5 Ownership cost and logit model

Ownership cost of vehicle is the sum of annualised purchase price, fuel expense and, maintenance cost of vehicle. Vehicle purchase price and maintenance cost are inputs to the model. Fuel expense is determined from feedback loops of the model. Ownership cost of vehicle is negatively related to vehicle demand. Literature have used logit model to calculate purchase probability of various vehicle models in competition(Lin & Greene, 2015). Based on this the purchase probabilities n ^th vehicle option having OC _n as ownership cost is calculated using logit model as shown in Eq. 7.

(7) $P_n=\frac{e^{\frac{\mu }{{\mathit{OC}}_n}}}{\sum _{n=1}^m{e}^{\frac{\mu }{{\mathit{OC}}_n}}}$

The parameter μ in the Eq.7 is called scale parameter. It gives the statistical dispersion of probability distribution. Estimation of coefficient μ for car and two-wheelers is performed by comparing the historical sales of petrol and diesel driven vehicles.

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13th International Symposium on Process Systems Engineering (PSE 2018)

Byeonggil Lyu , ... Il Moon , in Computer Aided Chemical Engineering, 2018

3 Forecasting of Naphtha Crack

3.1 Forecasting methodology

System dynamics (SD) is a theory of problem solving based on the feedback control theory. SD uses relevant variables for the presented problem, defines the system, and models relationships among variables. It is based on the synthesis of many themes such as operating theory and system theory, control theory, information feedback theory, decision-making theory, mechanical system, and computer science. SD uses various control elements, such as feedback loops and delay times, to observe how the system reacts and responds to trends. The prediction procedure using the SD model is described in Figure 3 . The naphtha crack forecasting model is suggested based on a causal loop diagram, a quantitative model, and an old data set.

Figure 3. SD model development procedure

3.2 Forecasting model description

The forecasting model described in this section follows the model developed by our group (Lyu et al., 2017). A brief description as well as figures are introduced in this section. Following the model development procedure described in Figure 1, the forecasting model of naphtha crack is developed. First, major factors are selected by the heuristic of field engineers and the Pearson product-moment correlation coefficient (PPMCC) analysis.

(1) $p_{X,Y}=\frac{\mathit{cov}\left(X,Y\right)}{{\sigma }_X{\sigma }_Y}$

PPMCC, as expressed in Eq.(1), is a measure of linear correlation between two variables, which give values between −   1 and 1. When the PPMCC value is 1, it means that the two variables have a positive correlation, − 1 means a negative correlation, and 0 means no correlation. Following the factor selection procedure, the causal loop diagram between the selected factors is developed. Vensim, a widely used SD software, is used for modeling the naphtha crack forecasting SD model. Vensim supports drawing of the causal loop diagram and editing of interaction formula and equations. Our model and forecasting result are described in Figures 4 and 5 and Table 1.

Figure 4. SD model of the naphtha crack (Lyu et al., 2017)

Figure 5. Naphtha crack forecasting result

Table 1. Conventional supply cost

(million USD)
	Conventional
	Naphtha	Condensate	Total
t1	186.540	213.437	399.978
t2	208.487	228.560	437.047
t3	234.950	250.709	485.660
t4	242.614	251.500	494.114
t5	238.600	248.132	486.732
Ave.	222.238	238.467	460.706

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A system dynamics model for the assessment of national public–private partnership programmes' sustainable performance

Eirini Grammatiki Pagoni , Georgiadis Patroklos , in Simulation Modelling Practice and Theory, 2019

4.3 Causal-loop diagram

Fig. 3 depicts the CLD of the system under study. The structure of the CLD has been created from the relevant literature and includes all important feedbacks, concepts and decision rules of the real system. The arrows between variables (causal links) denote causal influences. The polarity '+' or '−' of each causal link indicates a positive or negative relation between the variables. A positive polarity indicates that the two variables change in the same direction, i.e., if the independent (cause) increases (or decreases), the dependent (effect) variable also increases (or decreases). A negative polarity indicates that the linked variables change in opposite directions. The causal loops are either positive (reinforcing) or negative (balancing). A negative (balancing) loop exists when a small increase (or decrease) of any variable in the loop results in a decrease (or increase) of the same variable. In positive (reinforcing) loops, a small increase (or decrease) of any variable in the loop results in an increase (or decrease) of the same variable. A brief description of the main feedback loops is given below. The CLD consists of six balancing loops (loops 1, 4, 7, 8, 10, and 11) and five reinforcing feedback loops (loops 2, 3, 5, 6, and 9). For the remainder of this paper, variable names are written in italics using underscores.

Fig. 3. Main feedback loops involving the development of national PPP programmes.

In Loop 1, PPP_Supply is controlled by PPP_Development_Rate. As PPP_Supply grows, PPP_Supply_to_Demand_Balance also grows, satisfying infrastructure demand. As PPP_Supply_to_Demand_Balance grows, PPP_Development_Rate decreases.

Loop 2 presents the positive impact of Population on PPP_Supply: as PPPs grow, economic activity through construction and operation of the services creates employment opportunities that attract more people to migrate into the country. As a result, population growth generates the necessity for more infrastructure services [48] and thus, activates the procurement of new PPP deals.

In Loop 3, PPP_Supply boosts the government's Regional_Experience and knowledge capacity in PPP practice. Experience has proven to be a critical predictor of successful future PPP arrangements [39] and therefore attracts more investments in new projects. Moreover, Regional_Experience reflects the government's reputation in its capacity to honour agreements with the private sector because positive outcomes of previous PPPs are associated with positive results of future PPPs in that country [38]. Implementing successful PPP projects requires considerable administrative capability, which can be ensured only through proper institutional and legal frameworks and long experience in the implementation of PPP projects. An institutional capacity to create, manage, and evaluate PPPs is essential to ensure that they become an effective instrument of the delivery of important services, such as infrastructure [48]. Therefore, institutional and Operational_Capacity enables further PPP development.

Loop 4 presents the impact of Population growth on Actual_Public_Revenues. As Population grows, income per capita decreases because, on a simplistic level, the average income per capita is equal to the total income (GDP) divided by the population. Consequently, Actual_Public_Revenues that result from the imposed tax on income for PPPs also increase. Actual_Public_Revenues increase the public sector's financial capacity (Public_Financial_Capacity) and its intention, i.e., decision (Public_Affordability), to procure more PPPs.

Loop 5 presents the contribution of PPP activity to economic growth. The economic output from the construction and operation of finished goods in the PPP sector adds to the GDP of the region. GDP, as a measure of wealth, increases by definition the average income per capita and therefore the public revenues collected. As in Loop 4, Actual_Public_Revenues enhance PPP development.

Loop 6 considers the employment generation obtained by PPP activity. As unemployment rates fall through the design, construction, and operational activity of projects, public trust increases, and therefore the demand risk for PPPs is decreased. Demand risk can be difficult to define and is often subject to diverse interpretations. For this study, our working definition for demand risk is the difference between the anticipated and expected levels of usage volume (Shaoul et al., 2007). As Demand_Risk increases, Actual_Public_Revenues received by public authorities grow, allowing further development of PPPs.

Loop 7 presents the adverse effect of employment generation on public budget. As the public sector operates PPP services, the associated wages increase Public_Expenses. As a result, Public_Affordability will resist further development of PPP projects.

Loop 8 describes the negative influence of Unitary_Charges on the public budget: as the public sector's commitments grow, Public_Expenses grow, causing Public_Financial_Capacity and Public_Affordability to decrease.

Loop 9 presents the positive effect that Unitary_Charges have on investors' attraction to new PPP deals. By definition, Unitary_Charges comprise the initial capital and ongoing maintenance and operation costs of a PPP project. As a benefit for the private sector, it increases the actual profitability, as well as the expected profitability, of future PPP projects. In consideration of alternative investments, the expected profitability increases Profitability and enhances the private sector's Investment_Attractiveness to new PPP deals in the region.

Loop 10 presents the negative effect that the actual construction, operation, and maintenance costs have on investors' attraction to new PPP deals.

Finally, Loop 11 considers the social behaviour in response to the expense of PPP projects. As Public_Expenses grow, public perception of future taxes that people will have to pay to their government raises public opposition to further PPP development.

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Facilitated modelling in operational research

L. Alberto Franco , Gilberto Montibeller , in European Journal of Operational Research, 2010

A related issue, and the third dimension, is the type of data requirements for building the model. Some facilitative models are mainly diagrammatic representations of the problem situation and thus have reduced quantitative data requirements (e.g. a cognitive map or a causal loop diagram), closer to the way participants think and communicate. Others, such as a multi-criteria evaluation model or a systems dynamics model do require data in quantified form (based on qualitative statements about relationships between elements of the problem) in order to build the model. The degree of quantification needed for some facilitated modelling approaches requires the OR consultant to be aware of the cognitive demands that this may impose on the participants. For example, research has shown that quantitative judgmental data can be difficult to elicit ( Budescu and Wallsten, 1985) and influenced by cognitive biases (Kahneman et al., 1982; Plous, 1993; Poyhonen et al., 2001). On the other hand, quantitative models tend to produce outputs that are less ambiguous and more amenable to further analysis (though the reduction of ambiguity may impose restrictions on the group's ability to reach agreements). Therefore the OR consultant needs to make a choice between these two conflicting modelling objectives, given the type of problem situation that the client organisation wishes to address and the abilities and competences of those participating in the modelling process.

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Applying system dynamics approach in software and information system projects: A mapping study

Eduardo Ferreira Franco , ... Marly M. Carvalho , in Information and Software Technology, 2018

5.2 How has the system dynamics approach been used in researches related to software and information system projects? (RQ2)

Based on the results obtained by the content analysis and the codification of the selected articles (see Table 7), it was observed that a significant part of the studies (46%) reached the policy design and evaluation step in the modeling process (RQ2.1).

Regarding the RQ2.2, it was possible to identify that most of the studies used simulation tools (78%) [63,65,106] and presented causal loop diagrams (61%) [16,35].

This number is slightly greater than the number of studies that applied tools such as stock and flow diagrams (36%) or model equations (37%). One explanation for this phenomenon is that a significant portion of the work uses the model proposed by Abdel-Hamid and Madnick [2] as a starting point for their research [46,107,125,126].

This finding is similar to the scenario depicted by Rahmandad and Sterman [95] where they found that only 41% of the studies they analyzed include model equations, comparing to 37% identified by the current work.

According to their purpose (RQ2.3 and "C5 – Purpose"), most of the studies were intended to broaden the understanding of the problems under study (27%), serve as a support tool for the planning activity (25%), process improvement (22%), and strategic planning (20%).

The focus of the studies (RQ2.4 and "C6 – Scope") is to analyze software development project (34%) and parts of the project cycle (31%), a small portion of the work evaluates long-term developments of products (17%), long-term organizations (14%), and multiple projects effects (8%).

Regarding the success dimensions addressed (RQ2.5 and C7 – Success Dimension), it was noted a concentration of studies exploring the dimension of system quality (73%), which mainly represent the initial phases of the construction and implementation of the software and information systems, primarily related to criteria such as time, cost and scope. Likewise, since 2005, there is an increase in the number of studies addressing the success dimensions of user satisfaction (31%) and the intention to use the system (24%).

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The characteristics of problem structuring methods: A literature review

Chris M. Smith , Duncan Shaw , in European Journal of Operational Research, 2019

5.1 Pillar 1: Systems characteristics

1.

Does the approach identify a system to model?

All of the OR approaches are clear about the system being modelled. SSM models the human activity system (Checkland & Scholes, 1990), the "modelling language used for making models of human activity systems is all the verbs in language; an indicator of logical dependency; indicators of flows, concrete or abstract" (Checkland, 1981 p. 315). SODA builds cognitive maps that are designed to represent the way in which a person defines an issue (Eden & Ackermann, 2001). The cognitive map is made up of constructs (nodes) linked to form chains (shown by arrows) of action-oriented argumentation (Eden & Ackermann, 1998). SCA builds several models that represent the interconnectedness of decisions with an aim to reduce uncertainty (Friend, 2001). VSM outlines five sub-systems that are required for an organisation to remain viable (Beer, 1981 ). SD3 draws causal loop diagrams based on mental models of a situation, which are converted into level and rate equations that can be quantitatively modelled ( Torres et al., 2017). DES models show how an entity moves through a system over time. A DEA model consists of inputs and outputs from a system of decision making units (DMUs) that are used to calculate the relative efficiency of DMUs within the system. LP models are built with constraints defining a feasible range, or convex hull. An objective function is then either maximised or minimised within this feasible range to give an optimum answer for the defined system.

2.

Does the approach model participants' subjective interpretations of the world?

SSM builds models of the human activity system, in which a purposeful system is modelled in the systems world from multiple perspectives, so subjectivity is a key feature of what is elicited (Checkland, 1981). SODA builds models from 'different subjective views of the situation as expressed through individual interviews' (Eden, 1995, p. 304). SCA models represent subjective information (Friend & Hickling, 2005). For SD3, all applications elicit participants' interpretation about the problem situation as the inputs to a model, not an objective representation of reality. VSM takes a system-in-the-world position in which the laws underpinning the model, such as requisite variety, exist (Sinn, 1998) and objectively model an external reality. DES, DEA and LP all build models of external systems that are objectively described.

3.

Does the approach seek to build a holistic understanding of the system?

SSM, SODA, SCA, VSM and SD3 all prioritise the study of whole entities before the study of parts. They codify system properties to represent how the system being studied relates to the whole. This allows decision-makers to consider systemic properties. For example, SCA uses the shaping mode to make judgments about the connectedness between one field of choice and another (Friend & Hickling, 2005). VSM analyses information flows and communication links between different parts of the system (Beer, 1981). SD3 models seek to understand the whole system, as was demonstrated by Lane et al. (2016), who sought to understand the unintended consequences of decisions.

DEA and LP do not attempt to gain a holistic understanding of the situation. These models reduce complexity by breaking the system into constituent, related parts that are formulated in a mechanistic way. The model can only give predefined answers about, for example, an optimal solution or a sensitivity analysis, without understanding how this relates to the whole.

DES is more flexible, a model often may only seek to give a mechanistic understanding of the world with a single output, such as queuing time, or it can be used in a more holistic way such as (Robinson, 2001) where efforts were made on understanding "why a particular change led to an improvement or worsening of the situation" (p. 909).

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Ten years of modeling the Deepwater Horizon oil spill

C.H. Ainsworth , ... Y. Zheng , in Environmental Modelling & Software, 2021

2 Methods

2.1 Data collection

We reviewed modeling applications since 2010 focused on studying the DWH oil spill. The literature search was based on project websites, citations, an informal Core 7B knowledge survey, and discussions with modelers, leads, and the GOMRI Research Board. We documented peer-reviewed articles, technical reports, book chapters, and conference proceedings. In a few cases, we cite GRIIDC datasets if no other published methodological or application papers from a particular model or research group could be located. In addition to the literature search, we highlight discussions from the Core 7B synthesis effort. These included a meeting of GOMRI modelers at the Gulf of Mexico Oil Spill and Ecosystem Science Conference in Tampa in 2019, a series of webinars and virtual workshops in the spring of 2019, and a series of virtual workshops in May 2020. The goal was to recognize the full range of work done by GOMRI and the impact that GOMRI has had on the state of integrated modeling. Besides this article, there are two other manuscripts resulting from the GOMRI Core 7B synthesis webinars and meetings. Solo-Gabriele et al. (2021) uses causal loop diagrams to visualize connectivity of human and natural systems. Mauritzen et al. (unpublished manuscript) uses system dynamic modeling to illustrate ecosystem connections made in integrated modeling.

We concentrated on numerical modeling. We have not documented any applications of empirical models, though many numerical models incorporate statistical methods in parameterization, simulation, and validation. There were many empirical models developed as part of GOMRI (Masi et al., 2014; McDonald et al., 2017) but these deserve their own review. Ordination, analytical models (Chiri et al., 2019; Chan et al., 2015; Kuehl 2014), and conceptual models (Zeinstra-Helfrich et al. 2015, 2016) were also not considered despite being active areas of study.

2.2 Classification of models

As we are interested in integrative modeling, we emphasize model coupling, especially across disciplines. Some models are better referred to as modeling systems as they integrate modular components. All subcomponents will be identified here. We include models that provide boundary conditions and common packages used for data assimilation (e.g. NCODA: Navy Coupled Data Assimilation system; Cummings 2005; Cummings et al., 2013). All published algorithms for model forcing, parameterization, and boundary conditions are included here as well (COARE 3.0, Fairall et al., 2003; K-Profile Parameterization KPP, Large et al., 1994; OTIS, Egbert et al., 1994).

For the purposes of categorizing the cross-disciplinary nature of DWH modeling, we considered whether applications addressed the following four scientific domains: 1) the ocean physical and chemical environment, 2) the biological system, 3) socioeconomics and 4) human health. These categories are consistent with other Core 7B Synthesis and Legacy products (https://gulfseagrant.org/oilspilloutreach). We further divided the applications into 11 categories related to the subject of the study. These categories refer to the interests of the applications and do not necessarily reflect the capabilities or most common uses of the models involved. Models may be used across many categories. The categories are: 1) circulation/mixing, 2) abiotic transport (far field), 3) oil fate, 4) biotic transport, 5) biological impacts, 6) other plume dynamics, 7) turbulence/local mixing, 8) water chemistry, 9) atmosphere, 10) oil spill response support, and 11) other. Circulation/mixing represent a wide range of hydrodynamic studies that do not include explicit particle tracking. Abiotic transport refers to the large body of work tracking reference particles. Models in this category treat particles as passive and chemically/biologically inert, but some use a multi-fraction droplet size distribution (DSD) model to affect processes such as buoyancy, deposition rate and oil fate. Oil fate models may add chemical or biological breakdown or dispersion submodels. Biotic transport of larvae or eggs implies coupling to biological models where particles can interact with other biological components (Paris et al., 2013; Bracco et al., 2019). We made particular note of models that crossed two or more scientific domains. Finally, we noted the degree to which models use field data to guide the modeling effort.

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Guidelines For Drawing Causal Loop Diagrams

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