[DRAFT] New: the PlanZero glossary

Table of Contents:

• Introduction
• Glossary Overview
• Computation and Simulation
  • Time Series
  • Dynamic Element
  • Simulation
  • Scenario
• Modelling National Emissions
  • Emissions and Costs as Critical Success Factors
  • Strategies: broad activities that could be pursued, or not
  • Barriers: connecting strategies to outcomes
  • National Emissions Model
• Conclusion

Introduction

PlanZero has been accumulating a lexicon since its first post, but in modelling Bovaer adoption, it became clear to me that the project was entering a new phase. I struggled to explain, in that post, what I had done; the first draft was very long and difficult to follow. Not only did the writing need re-working, but PlanZero's implementation itself needed reworking, in order to function with the degree of conceptual clarity that I wanted to offer in writing about how it worked. This is the second of two follow ups, which complete the rewrite. The first follow-up post (About this project...) introduced, among other things, the "Draft Status" to offer a mechanism for this level of re-writing, and this post aims to bring the conceptual clarity that was missing from that first draft. This post announces a new glossary page, and explains the glossary terms relating to modelling. There are already more terms in the glossary than are explained here (almost fifty, including terms relating to data sources, climate organizations, and source code version control). I'll amend some previous posts to link to the glossary as appropriate, and call out glossary additions in new posts going forward.

This post is organized around three top-level content sections. The first one is an overview of the new glossary. The second one is about how PlanZero models work at a computational level, in terms of time series, dynamic element, simulation, and scenario. This section explains how dynamic elements define recurrent mathematical definitions (expressed in Python programming), how those definitions define time series, and how simulation of a set of dynamic elements produces a set of time series called a scenario. It is the closest thing to technical documentation that exists on the website to date, and might feel like low-level irrelevant details to some readers; if that's you, feel free to skip ahead to the next section on emissions modeling.

The third section is about how PlanZero models work at a semantic level, as models of emissions and economic activity, in terms of e.g. drivers, emission factors, subsidy programs, emission contributions, strategies, and barriers. This section explains how PlanZero models the computation of national emissions, as well as the possible effects of new technologies and government programs. Bovaer adoption, as the first worked example, has driven many design choices here. As the set of strategies grows, I expect the modelling framework to grow too, but this is how it works for now.

Glossary Overview

As of the writing of this post, PlanZero's glossary defines and cross-references the following 58 terms:

The terms were chosen somewhat ad-hoc based on my recollection of key topics from posts to date. Terminology of emissions and greenhouse gases links to A Model of Greenhouse Gas Emissions, from January 21. Terms relating to IPCC, Paris Agreements, UNFCC, CNZEAA and so on link to The Paris Agreement and the CNZEAA. Several terms relating to NIR modelling e.g. NIR, NGGI, NEUD, NRCan, ECCC link implicitly and/or explicitly to NIR-modelling posts I've been writing over the past few months. Terms relating to git and GitHub relate somewhat to the previous "About This Project..." post, but also aim to provide some onboarding documentation to future readers I hope to have, who might be interested in collaboration on this project. The glossary also defines terms that have been used implicitly in the recent post on Bovaer Modelling, such as Model, Scenario, Simulation, Strategy, Barrier, and KPI. The glossary also defines key terms of the computational modelling framework that underlies PlanZero's simulation results, such as Time Series, Dynamic Element, and Scenario, because they are so closely related to the modelling terms, and they may some day be useful as preliminary developer documentation.

I haven't written about how PlanZero works before, and writing about how it worked made me think about how it worked, which made me realize that it should work better. Writing this glossary post, has, consequently, been one of the largest efforts of any post written to date. Among many changes (see GH PR #78) the most impactful is probably the conceptual clarification of Scenario and Simulation, which has led to improved visualizations, as well as the improved handling of KPIs (see below), which have enabled much better visualization of the impact of strategies. Visualizing and analyzing the impacts of strategies is one of the core capabilities that PlanZero needs to be good at, so I think the effort was time well spent. The rest of this post introduces the computational and modelling terms in narrative form, so that their entries in the glossary can be reasonably short, and link to this post for more context.

Simulation Framework

This section introduces the simulation system used in PlanZero, which involves four concepts:

• time series, which contain the data of time-varying quantities (such as e.g. temperature, or annual emissions)
• dynamic elements, which implement rules for the evolution of time series data
• simulation, which is the computational act of rolling out time series forward in time
• scenarios, which are the result of simulation

Time Series

A time series represents a time-varying quantity in some unit of measure. PlanZero posts have used time series objects already to represent just about everything that was plotted as a function of time, e.g. both the various sectoral emissions of greenhouse gases in the NIR, and the attempts to reconstruct them. The key attributes of a time series are:

• a set of what numeric values the series takes
• a set of times marking when the series takes these values
• a unit of measure for the values
• an interpolation mode, indicating how to interpret the value for times other than the enumerated ones.

Time series are important in PlanZero because they are the basis of simulation. PlanZero simulates scenarios by repeatedly figuring out what the next value in each time series should be. The figuring-out of the next value is done by dynamic elements, which we'll talk about next.

Time series always have an associated unit of measure, as guard against programming and modelling errors. Unit conversion is a notorious source of error in systems that are difficult to test. One recent high-profile example is the loss of the Mars Climate Orbiter in 1999. PlanZero uses Python's pint package to handle units. PlanZero has also introduced additional units of measure, such as cattle, farms, CAD, kg-of-${\mathrm{C}\mathrm{O}}_2\mathrm{e}$, in order prevent, for example, adding rates of cost per head of cattle to a rate of cost per farm. Several programming errors so far in PlanZero development have been caught by this mechanism.

The time series interpolation mode is a mechanism that is partly for convenience and partly for error prevention. There are currently two interpolation modes. The value of a time series at times other than those explicitly mentioned is either

• "current", defined to be the most recent value of the series
• "no interpolation", which leaves such values undefined

If one of the time series represents an annual total though, it should have the second type of interpolation. To see why, consider the e.g. annual total ${\mathrm{C}\mathrm{H}}_4$ emissions for Quebec. It makes sense to represent annual totals as time series because there is a total for each year, at least over some period. However, the total represents a time integral of emissions over a certain period, typically January 1 to Dec 31; we can associate that total with a time within each year (such as the beginning or the end), but the intention for such totals is to handle them with precision, and the total was not meant to apply to other times of the year. The rules of time series arithmetic in PlanZero are that "no interpolation" tends to spread: adding a "no interpolation" time series to a "current" interpolation time series results in a "no interpolation" time series defined at the intersection of times where the argument time series were defined. Sometimes, after an elaborate computation, this intersection of times with an associated value is a smaller set than expected. It's usually a programming error on my part, that I meant to interpret some of the time series more broadly, but having to do this kind of debugging and fix it by choosing a specific point in the implementation logic at which to introduce more points or a "current" interpolation, results in implementation logic that I'm more confident in.

These mechanisms don't guarantee a model is good, but they do help ensure that a simulation result reflects the intended modelling assumptions.

Dynamic Element

If time series are like the tables of numbers you in spreadsheet columns, PlanZero's dynamic elements are like the formulas that define spreadsheet cells. Dynamic elements define time series; they associate time series with names (unique identifiers), and implement logic that defines the times and values of each time series. All of the modelling elements in PlanZero models, which define the time series shown in various charts etc., are dynamic elements. The logic for defining time series in a dynamic element is of two kinds:

• initialization, defining some time series regardless of other dynamic elements or time series in a simulation
• recurrence, updating those time series by reading values from other dynamic elements and time series

Dynamic elements are meant to be loosely coupled, in the sense that you can define a simulation from any set of dynamic elements. This modularity helps with testing, because a dynamic element can be simulated on its own or with a small set of related ones, to verify its behaviour quickly and comprehensively. This design pattern comes with a danger though, which is that if simulating any set of dynamic elements does something, then the fact of many dynamic elements producing a scenario through simulation offers no evidence that the scenario reflects what it is supposed to model. Generally, it is hard to verify that a large system of variables governed by modular logic is behaving as it should. PlanZero helps produce sound models at a computational level by supporting modular testing, and could validate that, for example, unused time series are deliberately unused.

Initialization

With initialization logic, a dynamic element creates time series (singular or plural) without reference to other dynamic elements or their time series. It declares all of the time series that it intends to read from once they are defined, and it declares the ones it intends to write. Only one dynamic element is allowed to write to each time series, but it can can read from many. I think of these time series (to which a dynamic element writes) as belonging to that dynamic element; when I refer to a dynamic element's time series, I am referring to these time series to which it defined, and to which it is able to write. When declaring an intention to read a time series, a dynamic element must also declare whether it intends to read the exactly-current value, or just historical values. This is important for scheduling the recurrence computation, the topic of the next section. The initialization also defines the first time at which the recurrence logic will be required, in order to extend its time series.

Recurrence

A dynamic element's recurrence logic serves to update its time series to the present moment of an in-progress simulation. Any recurrence logic required for simulation of time series up to some point in time is scheduled to run after all of the dynamic element initialization. After initialization, all of the time series are ready for reading, so that recurrence logic in each dynamic element can read from any time series defined by any dynamic element. These reads may only be of the past or present, and may only be of the present for the time series declared to be needed for exactly-current reads. Recurrence calculations are used to define time series that may change differently depending on what other dynamic elements are involved in a simulation. At the end of each recurrence calculation, the recurrence logic must report whether (and when) the recurrence should run again if the simulation continues to that point.

Exactly-current reads are special, because it means that the dynamic element writing to the other one must update the value of that other time series first, before this dynamic element reads the value. This exactly-current reading can also create mutual dependency: two dynamic elements can define variables and declare that they need to read one another's variables all at exactly-current time. The PlanZero simulation engine will refuse to simulate anything in such a situation, one or the other of the dynamic elements will need to relax its requirement to read the exactly-current value from the other.

Simulation

Simulation in PlanZero is the computational process of turning set of dynamic elements into a set of time series covering a period of time, called a scenario (more on scenarios next section). Simulation begins with the initialization logic of each dynamic element, which, together, define all of the time series in a scenario. After initialization, the simulation algorithm has (1) each time series defined (if only for the earliest times and values), and (2) the next time each time series could be defined, by appealing to the recurrence logic of its owner. The current simulation algorithm then simply steps forward in chronological order, updating each time series until the whole time period required for the simulation has been covered.

I believe it is possible to evaluate dynamic elements more efficiently by not always going in strictly chronological order, and sometimes evaluating multiple time points at once, but the implementation is not simple. There's a note about it in this github issue.

Scenario

A PlanZero scenario is the set of time series that result from simulation, which are fully specified by times and values until the end time of the simulation. When visualizing a simulation within the Simulations pages on this site, it is the scenario data that are used to draw the various figures and to compute various statistics.

Modelling National Emissions

The purpose of PlanZero is to model future scenarios, and to explore strategies for how Canada might achieve a net-zero economy. I think of this modelling as being a combination of strategic management, machine learning, and numerical optimization. Numerical optimization may perhaps some day play a role in optimizing the use of a large set of strategies, but that day is still some ways off. Machine learning may perhaps be useful in establishing good baselines for strategy evaluation, and I'd like to explore it in near-term future work. For now though, this section uses concepts from strategic management to explain how PlanZero models are organized and presented via the "Simulations" pages of this site.

Strategic management, to quote wikipedia, "involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessment of the internal and external environments in which the organization operates." If we consider Canada as an organization, the federal government has, among its many goals and initiatives, set a goal to achieve net-zero by 2050 (earlier post, government site). The word "goal" has a common-sense definition, but in the context of governmental planning and legislation, it is also appropriate to interpret it more technically. For PlanZero, the technical definition leads goals to play a precise role in its modelling framework.

Academics and practicing managers have developed numerous models and frameworks to assist in strategic decision-making, but for the formal modeling elements in PlanZero, I chose to draw from "The Executive's Guide to Facilitating Strategy" by Michael Wilkinson (published 2011, which I'll refer to as EGFS). In the terminology of the EGFS, an organization's SMART goals (Specific, Measurable, Achievable, Relevant, and Time-bound) should be broken down during a planning process into three conceptual kinds of thing: barriers, critical success factors, and strategies. All of these things map onto elements of PlanZero models, and the mapping helps to explain how a PlanZero model can represent a plan for e.g. Canada's National Emissions.

PlanZero posts about replicating NIR estimates (such as "Enteric Fermentation: Emissions Calculations") have included sections with these names (barriers, critical success factors, strategies), and informal thoughts aligned with the EGFS definitions in the table above. The modelling framework in this post introduces the PlanZero definitions in the rightmost column, as dynamic elements and time series. I believe that by organizing time series and dynamic elements according to these labels, PlanZero models will be easier to communicate.

The next subsections explain how the EGFS concepts of critical success factor, barrier, and strategy can be formalized in terms of time series and dynamic elements, and used in that way to structure and interpret scenario simulations for the purpose of evaluating strategies.

Emissions and Costs as Critical Success Factors

Critical success factors are introduced in EGFS as "key conditions that must be created to achieve one or more objectives" and the articulation of critical success factors is recommended as a prelude to building strategies. In PlanZero, there is a specific objective: the objective is to reduce emissions as much as possible for each IPCC sector, even producing negative emissions as applicable, and to achieve net zero emissions by 2050. PlanZero does not include explicitly-formalized critical success factors in its models, but if they were formalized, I expect they would be formalized as a triplet of

• a time series, e.g. ${\mathrm{C}\mathrm{O}}_2\mathrm{e}$/yr for an IPCC sector, greenhouse gas, and province / territory
• a target value range
• a target time range

At some point, PlanZero may include explicit critical success factors in order to determine automatically whether or not (or with what probability) a model achieves net-zero by 2050. For now, no model comes close, so no automatic assessment is required.

Coming back to Performance Indicators (KPIs), specific KPIs have been formalized as being important to PlanZero models. The three types of base KPI in PlanZero are

• drivers, which are measures of activity or stock, and which are associated with a province or territory
• emission factors, which are factors of proportionality between drivers and greenhouse gases, specific to an IPCC Sector, which may be associated with a specific province or territory
• subsidy factors, which are factors of proportionality between drivers and dollar amounts, which are associated with real or hypothetical public funding programs

For example, in the case of enteric fermentation (see this earlier post approximating the enteric fermentation emissions) the emissions calculation can be approximated as the product of two terms (ignoring ruminants other than cattle): number of cattle, and average methane emitted per head of cattle. These two terms correspond to two base KPIs:

• number of cattle (a driver)
• average amount of methane emitted per head of cattle per unit time (an emission factor)

These KPIs are now used to illustrate the effect of strategies, on the one currently-implemented strategy page here (Scale Bovaer).

Strategies: broad activities that could be pursued, or not

Strategies are defined in EGFS as "broad activities required to achieve a goal, create a critical condition, or overcome a barrier." In PlanZero, strategies are dynamic elements that influence barriers (see below) to affect KPIs such as emissions and costs. PlanZero barriers and strategies are both dynamic elements in PlanZero. The difference between them is that PlanZero strategies should be optional, whereas barriers should not. PlanZero strategy [dynamic] elements are meant to represent real-life strategies that could be pursued, or not pursued; including a strategy in a model means pursuing it, and not-including that strategy in the model should mean not-pursuing it. The effect of a strategy can be determined by simulating a model with the strategy included, and then again without including it, and comparing the two scenarios. PlanZero performs this comparison (called Ablative Analysis) automatically to produce charts and analysis for strategies in a simulation. What counts as a "broad activity" in EGFS is the only kind of activity reflected in PlanZero. Detailed planning of how to pursue a strategy in real life is beyond the scope of PlanZero modelling.

Barriers: connecting strategies to outcomes

Barriers are defined in EGFS as "existing or potential challenges that hinder the achievement of one or more objectives". In PlanZero, barriers are the dynamic elements that do almost all of the modelling work; they define time series for various physical, economic, ecological, or social factors, they relate these time series to one another, and they relate them as well to critical success factors such as emissions and costs. PlanZero barrier [dynamic] elements don't just aim to model challenges and hinderences, they collectively represent all of the modelled relationship between strategies and objectives. Barrier dynamic elements model, e.g.

• how fast strategies will take effect
• what costs / profits are expected
• what will happen in the meantime before / as they work
• how will strategies affect one another

National Emissions Model

A National Emissions Model, sometimes what I just call a "model", is a set of dynamic elements that register time series as drivers and emissions factors, so that when they are simulated, the resulting scenario includes emissions of the kind that are reported in the National Inventory Reports. If a model attempts to be predictive of the future, these emissions time series are its predictions. The dynamic elements that register drivers and emissions factors are barrier elements, so for that reason barrier elements are required in a national emissions model. A national emissions model does not need any strategies.

I would like to illustrate national emissions models, but they are hard to show. The following diagram is a first attempt at drawing a part of PlanZero model. It looks only at the use of Bovaer model, looks only at one kind of cost, looks only at the effect on one IPCC Sector, and ignores that separate time series are defined for each of several cattle types, as well as most provinces and territories. Still it begins to show something of the kind of dependency relationship that flows through from strategies, through barriers, to emissions and costs. Perhaps some day, this sort of visualization can be used to explore implemented models rather than simplified caricatures.

    flowchart TD
    DE_scale[["Scale Bovaer (Strategy)"]] --> TS_frac_on_bovaer
    TS_frac_on_bovaer(["Fraction of cattle on Bovaer (Time Series)"]) --> DE_cattle_enteric_emissions
    DE_cattle_enteric_emissions["Cattle Enteric Emission Rates (Barrier)"] --> TS_cattle_emfacs
    TS_cattle_emfacs(["Emission factor: annual methane per cattle type (Time Series)"])
    DE_limit["Limit Bovaer Adoption (Barrier)"] --> TS_farmers_open_to_bovaer
    TS_farmers_open_to_bovaer(["Driver: Farmers open to Bovaer (Time Series)"]) -.->|Scale Bovaer does not use current value| DE_scale
    TS_frac_on_bovaer --> DE_limit
    TS_frac_on_bovaer --> DE_purchase_cost
    DE_purchase_cost["Bovaer Purchasing (Barrier)"] --> TS_bovaer_cost
    TS_bovaer_cost(["Cost: Annual Bovaer per cattle type (Time Series)"])

Since the PlanZero site usually uses simulations to investigate national emissions models, I sometimes use the terms interchangeably, even though they refer to distinct conceptual levels. As of writing, the "Simulations" tab of the site lists two items, which correspond to two models. The first one, NIR2025, comprises a single barrier that initializes time series corresponding to the data from the 2025 National Inventory Report. That dynamic element has no recurrent logic, so the time series do not change after year 2023. The second one, Scaling, incorporates the NIR2025 data for all but two sectors (Enteric Fermentation, and Industrial Processes / Other Product Manufacture and Use), which are defined instead according to the model presented in modelling Bovaer adoption.

Conclusion

This post has introduced PlanZero's modelling and simulation framework in terms of computational elements (time series and dynamic elements) and in terms of strategic management (critical success factors, barriers, strategies). The post brings with it a new tab at the top of the PlanZero website: a glossary listing these terms, as well as several other terms that have come up in previous posts (e.g. NIR, NEUD, Net Zero). The two previous posts, still in draft, which introduced the Bovaer strategy and which presented the analogy of posts as revision announcements, have been updated with glossary links and expanded to include the more-detailed ablative analysis made possible by the drivers and emissions factors now used by barrier elements. From now on, this glossary can provide a basis of general documentation, and save me having to repeat definitions across posts (and you, dear reader, from having to read them).

As of the authoring of this post, the modelling terms defined here now guide and inform the charts and page layouts in the model visualization section of the site, which is now, as per the new terminology, called "Simulations". In the analysis of strategies, the charts now visualize the breakdown of emissions changes by sector, and the breakdown of subsidy costs by program and payee. In the analysis of simulations by IPCC sectors, it is possible to see a breakdown by contribution (the product of a driver and an emission factor). This style of visualization aims for alignment with the style of thinking at work in the preparation of e.g. the ECCC-maintained National Inventory, and the NRCan-maintained NEUD. In the "Scaling" simulation, only the "Enteric Fermentation" sector is structured in this way as of writing, but in future posts I will incorporate the per-sector models built for previous posts into this unified system.

Before I incorporate the per-sector models though, I would like to make a post about predictions. I will continue to use enteric emissions and cattle as the working example, and compare two ways to make predictions about them based on historical patterns and trends, rather than hypothetical strategies. Assuming that goes well, I'll follow up with posts making similar kinds of predictions for other sectors studied in previous PlanZero posts. The result will be a new "Extrapolation" model carrying on current trends, and a better baseline against which to evaluate possible strategies in the "Scaling" model.

Until next time,

- James Bergstra

P.S. Link longevity and deprecation

In working on the glossary, I renamed most of the analysis pages from "Scenarios" to "Simulations", and then to "Models". Naturally, this has changed many urls, and I decided I'm okay with that. Candidly, there are many things that could change about the site, and I cannot commit to maintaining every url that ever worked. The general solution to retrieve an old version of the site would be to retrieve the source from GitHub, find the version of interest, and either link to content directly on GitHub and/or host some specific version of the site.

The exception to this general rule, is the posts. I do intend to ensure those urls are persistent, and the posts do not substantially change (for non-Drafts). This policy has been added to the About page: Page Post, and Link Lifetime and Durability.

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