Model Structure

C.Scale calculates whole life carbon emissions

C.Scale integrates embodied, operational, and landscape carbon emission assessment into a single model. By taking a 'whole carbon' view, C.Scale prevents burden shifting and ensures that a project has the information necessary to target the most impactful carbon reductions.

C.Scale uses GWP-100 characterization factors.

Calculating Embodied Carbon

For each contributor ii, embodied emissions are assessed with the following expression:

Assessed emissionsi= Axici{Assessed\ emissions}_i=\ A\ast x_i\ast c_i

Where A is the total building area, xix_i is the quantity of the contributor ii per building area, and cic_i is the carbon intensity per unit of the contributor ii.

For example, a 10,000 square foot building may use 4 pounds of reinforcing steel per square foot of floor area, and the reinforcing steel may have a carbon intensity of 500 grams (0.5 kilograms) of carbon dioxide-equivalent emissions per pound of steel (values for illustrative purposes only). Taking the product of these three hypothetical quantities yields the contribution of reinforcing steel to that building’s embodied carbon emission:

10,000 sf4 lbs rebarsf0.5 kg CO2elb rebar=20,000 kg CO2e10,000\ sf\ast4\ \frac{lbs\ rebar}{sf}\ast0.5\ \frac{kg\ CO_2e}{lb\ rebar}=20,000\ kg\ CO_2e

In each section of its model, C.Scale sums the assessed emission of many individual contributors. While simple summation is acceptable in some cases, some materials will be replaced before the target date. For these materials, the emissions are assigned to the year(s) in which they’re replaced, and a multiplier is added to the total summation. The total embodied emissions assessed by C.Scale are represented by this expression:

Total\ embodied\ carbon\ emissions=\ \sum_{i=1}^{n}\ A\ast x_i\ast c_i\ast(1+r_i)\

For n number of contributors to the embodied emissions, where A is the total building area, xix_i is the quantity of the contributor ii per building area, cic_i is the carbon intensity per unit of the contributor ii, and rir_i is the number of replacements of the contributor ii before the target date.

Calculating Operational Carbon

The operational emissions of the project are assessed annually and summed across all years before the target date. The equation is similar to the equation for embodied emissions, with two key differences: first, the quantity x is substituted for the energy use intensity (EUI) e; second, the equation is a double summation, once across all the fuel types in the building and again across all years between the building’s completion and the target year. The total operational emissions assessed by C.Scale are represented by this expression:

Operational carbon emissions= t=1m j=1o AetjcjOperational\ carbon\ emissions=\ \sum_{t=1}^{m}\ \sum_{j=1}^{o}\ A\ast e_{tj}\ast c_j

For m total years between the building’s completion and the target year and across o fuel types, where A is the total building area, etje_{tj} is the energy use per building area (EUI) in year tt of fuel jj, and ctjc_{tj} is the carbon intensity per energy unit in year tt of fuel jj.

Carbon emissions associated with electricity are derived from NREL's Cambium model. Onsite fossil fuel use is assumed to be natural gas. The carbon emissions of natural gas are assessed with a 2.4% leakage rate. Fuel oil emissions account for N20 and CH4 emissions. Characterization of non-CO2 emissions is determined with the GWP100 factors published in IPCC AR6.

Refrigerant Emissions

In C.Scale, fugitive emissions from refrigerant leakage are categorized as operational emissions. They are counted in life cycle stage B1.

Calculating Stored and Avoided Carbon

In C.Scale, landscaping and the use of structural timber contribute to biogenic carbon storage. Carbon storage in structural materials is assessed once in the first year of the project, and landscape sequestration is assessed each year. Biogenic carbon sequestration is evaluated with the following expression:

Carbon Storage=xiCi+ t=1m AkCkCarbon\ Storage=x_i\ast C_i+\ \sum_{t=1}^{m}\ A_k\ast C_k

Where xix_i is the amount of carbon-sequestering timber structural material ii, CiC_i is the carbon sequestration per unit ii,AkA_k is the area A of carbon-sequestering planting type k, and CkC_k is the carbon sequestration in year tt per area of planting kk.

The generation of excess energy by an onsite solar photovoltaic array displaces the generation an equivalent amount of electricity from the utility grid. This is calculated as follows:

Avoided carbon emissions= t=1m etctAvoided\ carbon\ emissions=\ \sum_{t=1}^{m}\ e_{t}\ast c_{t}

Where ete_{t} is the excess energy in kWh generated in year tt and ctc_{t} is the carbon intensity of the electrical grid per unit demand in year tt. This method assumes that there is no curtailment of PV production, and that the carbon emissions of grid electricity when solar energy is produced is substantially similar to the annual average emissions. In locations with a high proportion of solar on the grid, curtailment is likely and skepticism of C.Scale's calculation of avoided emissions is warranted.

C.Scale is a time series model

In the built environment, it is essential to understand the time value of carbon. To this end, C.Scale uses time series data to analyze carbon emissions across a building's life. For each year in the analysis period (defined by the project's time horizon), C.Scale estimates all emissions occurring in that year.

In the first year, the following emissions are always calculated:

  • Embodied emissions in construction materials (life cycle stages A1-A3)

  • Construction site emissions (life cycle stages A4-A5)

  • Storage of biogenic carbon in timber structural components (life cycle stage D)

In each year, the following emissions are always calculated:

  • Operational carbon emissions from onsite fossil fuel use (life cycle stage B6)

  • Operational carbon emissions from onsite electricity use (life cycle stage B6)

  • Emissions from landscape maintenance, when applicable (life cycle stage B2)

In only some years, the following emissions are always calculated:

  • Replacement and refurbishment of hardscape (life cycle stages B3-B5)

  • Replacement and refurbishment of the building envelope (life cycle stages B3-B5)

  • Replacement and refurbishment of interior fit-out (life cycle stages B3-B5)

  • Replacement and refurbishment of MEP and PV systems (life cycle stages B3-B5)

C.Scale customizable and extensible

C.Scale is built as a series of modules, each connected to the others and tasked with a specific set of calculations. These modules are added or expanded in response to the requests of users.

The C.scale model's assumptions and background data can be overriden or refined through additional inputs. This allows for the addition of project-specific data where it is available while maintaining the C.Scale model for calculating all other parts of the project's carbon footprint. For more information on how this works, check out our Swagger docs or reach out for a conversation.

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