SM5005 Measuring Carbon in Complex Systems
The Complete Study & Assessment Guide · Sem 1 AY26/27SM5005 Overview
- National University of Singapore
- Semester 1, AY2026/27
- Postgraduate
- Assessment by coursework
- Matrix and spreadsheet modelling
What this course is trying to make measurable
SM5005 addresses a problem that looks simpler than it is: attaching a carbon estimate to a product, an organization, a service or a system. The introductory material treats the estimate as the final line of a chain of decisions rather than as a property waiting to be looked up.
- Start with the accounting question A footprint changes when the object, boundary, perspective or time basis changes, even if the arithmetic is flawless.
- Treat matrices as a supply-chain story The technical coefficient matrix encodes production recipes, while the Leontief inverse gathers all upstream rounds needed to meet final demand.
- Align money before multiplying Price year, currency, purchaser prices, basic prices, margins and import origins must be reconciled before an emission factor can be applied defensibly.
What you get in the full SM5005 Study & Assessment Guide
- 10 chapters, 43 pages — every assessed topic
- 35 original practice questions, each with a model answer
- 10 worked examples, solved the way SM5005 marks
- 11 computed figures, redrawn from the course’s own numbers
- Before-you-submit checklist for the Modelling exercise 1 (30%) — what markers reward, what costs marks
Free on this page: assessment table, chapter map, one worked example, key terms, FAQ. The rest is in the full study & assessment guide.
How SM5005 is assessed
| Component | Weight | Format |
|---|---|---|
| Attendance and participation | 10% | Engagement across the taught course and participation in the published learning activities. |
| Modelling exercise 1 | 30% | The first modelling exercise, with the published submission date retained in the current dates section. |
| Modelling exercise 2 | 30% | A second substantial modelling exercise applying the course methods to a further estimation problem. |
| Progress reporting | 30% | Progress reporting across the project workflow. The introductory lecture says the final report submission date will be advised. |
The weights in the introductory lecture total 100%. The published table does not label a hurdle or minimum mark for any component, so none is encoded here. The same source gives the first modelling exercise deadline and says the final progress report submission date will be advised. Check the live Canvas assignment pages for task instructions, marking criteria and any later date changes.
What other students are asking about SM5005
- Where can I find lecture notes or study guides for SM5005 at NUS?
- The SM5005 study guide in AskSia Library covers Measuring Carbon in Complex Systems in 10 chapters, with the assessment table, a chapter-by-chapter topic map, key terms and a worked example, free to read on this page.
- Is there a final exam in SM5005?
- No final exam is listed in the offering this AskSia Library guide is built from; SM5005 is assessed by Attendance and participation 10%, Modelling exercise 1 30%, Modelling exercise 2 30%, Progress reporting 30%.
- What does SM5005 cover on process lca and mrio perspectives?
- In AskSia Library's SM5005 guide, the Process LCA and MRIO Perspectives chapter explains compare bottom-up process detail with economy-wide supply-chain coverage.
- What does SM5005 cover on reading input-output tables?
- In AskSia Library's SM5005 guide, the Reading Input-Output Tables chapter explains follow products, industries and final demand without losing the accounting identity.
- What does SM5005 cover on building the technical coefficient matrix?
- In AskSia Library's SM5005 guide, the Building the Technical Coefficient Matrix chapter explains normalize transaction flows by output and interpret each production recipe.
Current SM5005 dates
| Date | Item | Control |
|---|---|---|
| 28 September 2026 | Modelling exercise 1 | Published submission date in the introductory lecture. |
| 2 November 2026 | Modelling exercise 2 | Published submission date in the introductory lecture. |
| To be advised | Final progress report | The introductory lecture leaves the final submission date to be advised. |
Dates are as published in the assessment table and reporting schedule in the introductory lecture. Confirm exact deadlines and submission settings in the live LMS.
What SM5005 covers
Ten source-led chapters move from defining the accounting question to constructing, extending and checking multiregional input-output estimates, then applying them to imports, prices, hybrid inventories and health-system spending.
Questions, Boundaries and Carbon Claims
Turn a broad sustainability question into a declared accounting frame before collecting dataThe estimate begins before the spreadsheet
A carbon result answers a framed question, not an unqualified request for a number.
- Accounting question before data collection
- Functional object and unit
- Production and consumption perspectives
- Temporal and geographical scope
- Operational inclusion rules
- Claims limited by their boundary
Process LCA and MRIO Perspectives
Compare bottom-up process detail with economy-wide supply-chain coverageTwo models expose different parts of the supply chain
Process life cycle assessment follows physical processes chosen by the analyst.
- Process inventories and physical flows
- Truncation at a chosen process boundary
- Economy-wide MRIO coverage
- Sector aggregation error
- Method choice by decision need
- Hybrid replacement without overlap
Reading Input-Output Tables
Follow products, industries and final demand without losing the accounting identityThe table is an accounting map
An input-output table records who supplies whom. Rows follow the destination of a producing sector's output; columns show the inputs used by a producing sector.
- Supplier rows and user columns
- Intermediate transaction block
- Final-demand categories
- Value added and total output
- Row and column accounting identities
- Region-sector ordering in MRIO tables
Building the Technical Coefficient Matrix
Normalize transaction flows by output and interpret each production recipeNormalize flows into production recipes
The transaction matrix reports absolute purchases, so large sectors naturally have large entries.
- From absolute transactions to normalized inputs
- A equals T times inverse diagonal output
- Entry Aij equals Tij divided by Xj
- Column recipes for using sectors
- Fixed-coefficient assumption
- Dimension and manual-cell checks
Tracing Supply Chains with Leontief
Expand direct and indirect requirements from a final-demand vectorFinal demand creates successive production rounds
A final-demand vector Y requires direct output Y. Producing that output requires intermediate inputs AY. Those suppliers require A-squared Y, and further rounds continue.
- Direct output equal to final demand
- First upstream round AY
- Further rounds through powers of A
- Leontief inverse L equals inverse I minus A
- Total output solution X equals LY
- Inverse entries as total requirements
Environmental Extensions and Footprints
Combine direct intensities with total requirements to obtain footprint multipliersAttach environmental pressure to economic output
The input-output core explains how production responds to final demand. An environmental extension adds direct emissions or another pressure by sector.
- Environmental satellite accounts
- Direct intensity q
- Total-requirement matrix L
- Multiplier equation m equals qL
- Footprint equation qLY
- Unit and sector-order checks
Price Years, Imports and Margins
Align money values, origins and valuation bases before applying an emission factorA factor and a purchase must speak the same monetary language
Spend-based multiplication is valid only when expenditure and emission factors share a compatible currency, price year, valuation basis and sector definition.
- Currency and model-year alignment
- Nominal and real expenditure
- Purchaser and basic prices
- Trade and transport margins
- Origin-weighted import factors
- Transformation register and reconciliation
Hybrid Estimates and Uncertainty
Replace weak aggregate components without double counting their retained coverageHybrid methods target a known weakness
An MRIO estimate provides broad supply-chain coverage but uses average sector representations. Process data can describe a specific material, supplier or technology more closely.
- Targeted replacement of aggregate components
- Locating overlap in the baseline
- Subtract then add logic
- Unit and boundary compatibility
- Decision-relevant sensitivity analysis
- Reporting mixed-resolution coverage
Cleaning Health-System Spend Data
Convert raw expenditure records into a documented analytical tableRaw expenditure is evidence, not yet a model vector
Operational spend files are designed for payment and management, not environmental analysis.
- Immutable raw-data layer
- Stable record identifiers
- Staged standardization and exclusions
- Currency and price alignment
- Count and value reconciliation
- Profiling material and ambiguous records
Mapping Spend to MRIO Sectors
Make reproducible sector choices and test the classifications that drive resultsMapping is a modelling decision
A spend description has to be connected to the sector classification used by the MRIO factors. Exact wording rarely guarantees an exact economic match.
- Descriptions to model classifications
- Concordance fields and versioning
- Rule-based and manual mapping
- Evidence-based split allocations
- Mapped-spend reconciliation
- Hotspot and sensitivity review
A modeller first decides what question is being answered, whose activity is counted, which gases or environmental pressures are included, what time and geography the result represents, and how far upstream the boundary reaches. Those choices determine the data that can be used and the meaning that can safely be attached to the answer.
The course therefore begins with framing and interpretation before it asks for matrix operations.
Two complementary views of the same system
Process life cycle assessment follows named processes and physical flows in detail. It can show why a particular material, energy source or stage matters, but the modeller must decide where to stop following the chain.
Multiregional input-output modelling begins from an economy-wide accounting table. It sacrifices product-level detail by grouping activity into sectors, but its linked industries and regions reduce the risk that distant upstream requirements disappear merely because they are inconvenient to trace. The important comparison is not which method wins in the abstract.
It is which source of error matters for the question at hand: truncation from a narrow process boundary, aggregation from a broad sector average, or a mixture of both.
How an input-output model becomes a footprint model
The transaction table records purchases between producing sectors.
Dividing each intermediate flow by the output of the purchasing sector creates a technical coefficient: the input required per unit of that sector's output. Placing those coefficients in a matrix gives a compact set of production recipes. Final demand starts the calculation. Direct production satisfies that demand, but production itself requires inputs, those suppliers require further inputs, and the sequence continues.
The Leontief inverse collects those rounds. Multiplying it by final demand gives the total sector output associated with the demand rather than only the goods directly purchased.
That economic requirement becomes an environmental footprint only after an extension is attached. Direct emissions divided by sector output form an intensity vector.
Multiplying the intensity vector by the Leontief inverse produces footprint multipliers that already contain upstream requirements. Applying the multipliers to an aligned demand or expenditure vector then allocates direct and indirect emissions to the activity that ultimately drives them.
The order matters: an unaligned spend vector can be multiplied perfectly and still produce a misleading result.
Why imports, prices and margins matter
A purchase observed in local accounts may represent production elsewhere. Applying a domestic sector factor to the entire amount silently assumes that imported and domestic production have the same carbon intensity.
The teaching materials instead show an origin-weighted factor: each source share is multiplied by the factor for that origin and the pieces are added. This is a small computation with a large interpretive consequence, because a change in the import mix can move the estimate even when the amount purchased is unchanged.
Valuation creates another alignment problem.
Expenditure recorded at purchaser prices includes trade and transport margins and may include taxes, while the model may represent output at basic prices. Price years can also differ. A defensible workflow records the currency and year of every monetary value, converts the purchase to the model's valuation basis, and only then applies the matched multiplier.
Treating the conversion as housekeeping rather than modelling hides one of the most common routes to a confidently wrong number.
When aggregate coverage is not enough
Input-output factors are averages for sectors, not measurements of a specific supplier or product. A hybrid estimate improves selected parts of the model by replacing an aggregate component with more specific bottom-up information.
The word replacing is crucial. Adding a detailed inventory on top of a sector estimate leaves the same process in both sources and double counts it.
A sound hybrid workflow identifies the component represented by the detailed data, removes or adjusts the overlapping aggregate component, documents the new boundary, and checks whether the replacement improves the decision that motivated it.
From health-system spending to an analytical demand vector
The spend-based teaching material brings all earlier decisions into a practical pipeline.
Raw procurement or expenditure data rarely arrive ready for multiplication. Descriptions may be inconsistent, suppliers may appear under several names, currencies and price years may differ, and a record may combine goods with services. Cleaning therefore includes preserving the original record, standardizing useful fields, documenting exclusions and adjustments, and testing totals after every transformation.
The aim is not a perfectly tidy spreadsheet. It is a traceable bridge between an operational record and the model input.
Sector mapping is the point where domain knowledge becomes a numerical assumption. A description can map cleanly to one sector, require a split across several sectors, or remain ambiguous.
Reproducibility requires a crosswalk with the original description, assigned sector, rationale, confidence and reviewer decision. Material or uncertain categories deserve sensitivity tests rather than a forced appearance of precision.
Aggregating the mapped spend, applying aligned multipliers and checking that totals reconcile yields an estimate whose uncertainties can be explained instead of merely listed.
How the course assesses the work
The published assessment table assigns part of the grade to attendance and participation, equal larger shares to two modelling exercises, and the remaining larger share to progress reporting.
The modelling exercises therefore reward more than a final total: they require a chain from assumptions and source data through transformations to an interpretable result. Progress reporting makes the analytical trail visible while work is under way.
The source table publishes a submission date for the first modelling exercise and describes staged reporting activity, while the final progress report date is left to be confirmed in the live course space.
This guide preserves that distinction rather than inventing a deadline.
A defensible answer in this subject
A strong answer states the perspective, functional object, period and boundary; names the data source and valuation basis; writes the calculation in an auditable order; and explains what the result includes. It then tests the assumptions most capable of changing the conclusion.
For a matrix problem, that means checking dimensions and the direction of multiplication. For a spend problem, it means checking price alignment and classifications. For a hybrid problem, it means checking overlap. The result is not a single number pretending to be exact. It is a quantified claim whose construction, coverage and limitations a reader can inspect.
Worked example · free
Weighting domestic and imported emission factors
- 1Write the two origin shares as decimal weights.
- 2Multiply each share by its matched origin factor.
- 1Add the weighted contributions to obtain the combined factor.
- 2Interpret the assumption avoided by origin weighting.
Key terms
- System Boundary
- The declared set of processes, regions, periods and flows included in an estimate.
- Functional Unit
- The quantified service or output against which a life cycle result is expressed.
- Process LCA
- A bottom-up method that follows specified processes and physical flows through a chosen product system.
- MRIO
- A multiregional input-output model linking sector transactions and final demand across economies.
- Intermediate Demand
- Purchases made by producing sectors for use in producing their own output.
- Final Demand
- Demand from users such as households, government or capital formation that initiates the model calculation.
- Technical Coefficient
- An input flow divided by the output of the sector that uses it, interpreted as input per output unit.
- Leontief Inverse
- The matrix that collects direct and successive indirect production requirements needed to meet final demand.
- Satellite Account
- Environmental or social information attached to the economic accounts without changing their transaction structure.
- Emission Intensity
- Direct emissions per unit of sector output on a stated monetary or physical basis.
- Footprint Multiplier
- A factor containing direct and upstream emissions per aligned unit of final demand or expenditure.
- Purchaser Price
- The amount paid by a buyer, potentially including taxes and trade or transport margins.
- Basic Price
- The amount retained by the producer before product taxes and after subsidies, excluding separately invoiced transport.
- Hybrid Estimate
- An estimate combining economy-wide coverage with selected process-specific or physical data.
- Sector Concordance
- A documented crosswalk connecting source descriptions or categories to model sectors.
SM5005 FAQ
How is the course assessed?
The introductory lecture assigns ten per cent to attendance and participation, thirty per cent to the first modelling exercise, thirty per cent to the second modelling exercise and thirty per cent to progress reporting. The same source publishes dates for the modelling exercises and says the final progress report date will be advised. Consult the live Canvas pages for detailed criteria.
What should be fixed before any carbon calculation begins?
Fix the object being measured, the perspective, the time and geography, the environmental pressure, the functional unit and the system boundary. These choices determine which data are relevant and what the answer can mean. Beginning with an available emission factor and defining the question afterwards reverses that logic and can produce a precise answer to the wrong problem.
When should process LCA be preferred to an MRIO model?
Prefer process detail when a named product, supplier or technology difference is central and the physical inventory can be constructed reliably. Prefer MRIO coverage when distant supply chains and economy-wide completeness matter more than product specificity. Many decisions benefit from a hybrid: broad MRIO coverage with selected detailed components replacing, not merely adding to, weak aggregates.
What does a technical coefficient mean?
For the entry in row i and column j, it is the input purchased from sector i divided by the total output of sector j. It therefore describes how much input i is required for one output unit from j, under the model's monetary basis and classification. The denominator belongs to the using sector, which is a common source of mistakes.
Why is the Leontief inverse more than an algebraic shortcut?
It represents the repeated upstream response to final demand. Direct output requires supplier inputs; those suppliers require their own inputs; further rounds continue. The inverse gathers this converging sequence so that the output vector contains both direct and indirect production requirements. Its entries are therefore total requirement relationships, not direct transaction shares.
How does an economic model become a carbon footprint model?
Direct sector emissions are divided by sector output to create an intensity vector. That vector is multiplied by the Leontief inverse to obtain multipliers containing the upstream chain. Applying those multipliers to compatible final demand allocates supply-chain emissions to the demand that drives them. Compatibility of sector order, price basis, currency and year must be checked before multiplication.
Why can an import split change the result?
Domestic and imported production can have different energy systems, technologies and upstream structures. A single domestic factor applied to all expenditure assumes those differences away. Origin weighting preserves the purchase shares by multiplying each origin factor by its share and summing the contributions. The calculation is simple, but the required sourcing data and sector matching may be uncertain.
What is the danger in a hybrid estimate?
The main structural danger is overlap. If a detailed process inventory is added while the corresponding component remains inside the sector estimate, the same activity is counted twice. A hybrid method must define what the detailed source replaces, remove or adjust the aggregate contribution, and state the resulting boundary. Specific data are not automatically better if they create inconsistent coverage.
How should ambiguous spend descriptions be mapped?
Preserve the original description and record the chosen sector, rationale, confidence and reviewer. If more than one sector is plausible, use procurement context or supplier information, split the amount when evidence supports a split, and test material alternatives. A forced single mapping without documentation converts classification uncertainty into hidden numerical certainty.
Questions students ask in each SM5005 chapter
- Why is a boundary diagram better than a list alone?
- A diagram shows containment and connections. It can reveal that a purchase sits outside direct operations but inside the consumption boundary, or that two labels describe the same activity. The list still carries the formal rule, while the diagram makes omissions and overlaps easier to challenge. Chapter 01 · Questions, Boundaries and Carbon Claims
- Is MRIO always more complete than process LCA?
- It is structurally broad because the economic accounts connect sectors across upstream rounds, but completeness still depends on the model's regions, sectors, environmental extensions and treatment of imports. Broad coverage does not mean fine product detail or perfect source data. Chapter 02 · Process LCA and MRIO Perspectives
- Why do rows and columns feel easy to reverse?
- Both refer to sectors, but they answer different questions. A row asks where one sector's output goes; a column asks what one sector uses. Keeping verbs in the labels, supplies and uses, is more reliable than remembering an abstract orientation. Chapter 03 · Reading Input-Output Tables
- Why is the inverse output matrix placed on the right of T?
- Right multiplication by a diagonal matrix scales columns. Each transaction column must be divided by the output of the sector that uses those inputs. Placing the scaling matrix on the other side would scale rows and change the economic meaning. Chapter 04 · Building the Technical Coefficient Matrix
- Why does the identity matrix appear?
- The identity term carries the direct output delivered to final demand before upstream inputs are added. Without it, the series would begin with suppliers and omit the demanded product itself. It also makes the algebraic expression for the inverse work. Chapter 05 · Tracing Supply Chains with Leontief
- Why is q not already a footprint multiplier?
- q contains only the pressure released directly by each producing sector per output unit. It has not followed the inputs that sector purchases from suppliers. Multiplication by L adds the direct and successive upstream production requirements. Chapter 06 · Environmental Extensions and Footprints
- Why can nominal growth look like carbon growth?
- Expenditure can rise because prices changed even when physical activity did not. Applying a factor expressed in another price year to unadjusted nominal spend mixes price movement with activity. Converting to the model basis helps isolate the quantity represented by the factor. Chapter 07 · Price Years, Imports and Margins
- What should be replaced first?
- Start with a component that is material to the result, poorly represented by the aggregate sector and relevant to the decision. Replacing a small component with excellent data can create an impressive detail that has no practical effect. Chapter 08 · Hybrid Estimates and Uncertainty
- Should supplier names be standardized before mapping?
- Yes, but preserve the original field. Standardized names help group records and add supplier knowledge consistently. They should not erase legal entities or differences that matter for sourcing, so every normalization needs a trace back to the source. Chapter 09 · Cleaning Health-System Spend Data
- Should mapping use the supplier or the purchased item?
- Use the activity represented by the purchase. Supplier information can clarify that activity, but a diversified supplier's industry code may not describe the specific product or service bought. Preserve both sources of evidence and explain which controlled the assignment. Chapter 10 · Mapping Spend to MRIO Sectors
How to prepare for the assessments
Study SM5005 by rebuilding one small carbon estimate from end to end. Start with a written question and boundary statement. Draw the transaction, coefficient, total-requirement and environmental-extension stages before opening a spreadsheet. For every matrix, write its dimensions and label what a row and a column mean.
Recalculate a tiny example by hand so that multiplication order has an economic interpretation rather than being a software habit. Then create a data register for each monetary input: source, currency, price year, purchaser or basic price, sector classification and domestic or imported origin. Keep the raw expenditure table unchanged and place cleaning, mappings and assumptions in separate traceable tables.
After obtaining a result, run three checks: totals reconcile after cleaning, classifications aggregate to the original spend, and an alternative treatment of the most uncertain material category does not silently reverse the conclusion. Practise explaining the difference between a direct intensity and a footprint multiplier, because confusing them changes the boundary.
For the modelling exercises, save intermediate outputs and write the interpretation while the decisions are fresh. For progress reporting, show what changed, why it changed and which uncertainty remains decision-relevant. The most useful revision product is not a page of formulas; it is a compact audit trail that lets another reader reproduce the estimate and challenge its strongest assumption.
