# Measuring Carbon in Cities and Their Buildings through Reverse Engineering of Life Cycle Assessment
## 1 Introduction
In the case of buildings, it comprises the construction phases, while operational carbon links to the use phases [24; 28]. Embodied carbon is reported as Global Warming Potential (GWP). The Environmental Protection Agency (EPA) states [29; 30]: \"The Global Warming Potential (GWP) was developed to allow comparisons of the global warming impacts of different gases. Specifically, it is a measure of how much energy the emissions of 1 ton of a gas will absorb over a given period of time, relative to the emissions of 1 ton of carbon dioxide (CO\({}_{2}\))\". The standard for the calculation methods of carbon emissions generated in the life cycle of a building [19; 23; 24; 31] establishes that for the embedded carbon emission, life cycle assessment (LCA) is a widely accepted approach. LCA is defined by the International Standard ISO 14040 [31] as \"the compilation and evaluation of the inputs, outputs, and the potential environmental impacts of a product system throughout its life cycle\". In its \"Integrated Product Policy\" document, the European Commission underlined the need for consensus in LCA methodologies and more consistent data. As a result, initiatives were launched to this point [23; 32; 33]. For the study case of this document, the LCA tool LCAByg [34] was used for the GWP values calculation. The LCA calculation process behind LCAByg and other LCA tools [35] shows high interoperability with other design, calculation, modeling, reverse engineering, machine learning, and coding tools [36; 37]; thus, the method chosen in this paper [34; 38; 39], using LCAByg (2023), MatLab ([[https://www.mathworks.com/products/matlab.html](https://www.mathworks.com/products/matlab.html)]([https://www.mathworks.com/products/matlab.html](https://www.mathworks.com/products/matlab.html))) and Excel (2023) tools, is coherent with that objective. Most importantly, a future application of this method approach to other sustainability indicators, design variables, sustainability assessments, and reverse engineering tools--for instance, the economic factor, as other recent research documents study, is possible. In them, monetary values and their corresponding environmental inputs/outputs are analyzed with methods such as (EIO)-based methods of LCA evince [40]. Building LCA studies have often concentrated on a specific variables of the building [40] or on each stage of the life cycle of the building separately [41]; few have addressed the entire building over its whole life cycle due to the difficulties of acquiring accurate input data (building material quantities, building performance indicators) [42]. Design tools such as Building Information Modelling (BIM) and LCA Carbon calculation tools [41] allow for the avoidance of this barrier [42], offering add-ons/plugins to this end. Likewise, this paper's method can be helpful as a prediction/target seek/optimization/design (P/T/O/D) function add-on/plugin to design tools. The effect of building design on carbon emissions is currently well understood by academics around the globe, who have also conducted extensive research in this area using machine learning or similar tools, although limited to specific aspects such as:  
1. Studies for prediction, scope, also for carbon footprint [43], and optimization [44; 45; 46], or modeling/digital twins for design and energy [47; 48; 49; 50; 51]. Those are studies mainly focused on energy performance, design comparison for a building, parametric design, or optimization of a building for specific parameters. 2. Studies for cost-sustainability analysis: Carbon-cost related, Sustainable assessment cost prediction through neural network, Artificial Intelligence (AI) Cost-Carbon tools [52; 53]. 3. Studies based on a comparison between a design solution and a reference solution named conventional solution, usually defined in construction catalogs [54]. 4. Studies for the measurement of carbon in cities, for instance, through surveys and multi-country life cycle assessment techniques or other accounting principles [55; 56].