Separating demand reduction from accounting intensity in building renovation: A logarithmic mean Divisia analysis of an anonymised nonresidential case

Large reductions in reported building carbon emissions can conceal opposing changes in useful demand, delivered-energy intensity and effective emissions intensity. This paper applies additive logarithmic mean Divisia index decomposition to one baseline and six cumulative renovation packages from a confidential energy consultancy report. The identity g = u × (e/u) × (g/e) separates reported carbon intensity per floor area into useful-demand intensity, a final-to-useful energy ratio and effective carbon per unit final energy. The decomposition is exact for the positive model outputs and does not require an arbitrary residual allocation. Between the baseline and the final package, the useful-demand contribution is approximately −44.57 kg CO2/(m² year), while the energy-ratio and effective-carbon contributions are +0.55 and +0.05 respectively. Their sum reproduces the net reported reduction of approximately 43.97 kg CO2/(m² year). Before the photovoltaic package, the offsetting ratio contributions are larger. The final photovoltaic transition leaves useful demand unchanged and produces negative contributions in both accounting ratios. Direct endpoint and chained decompositions close to the same total but allocate it differently, illustrating the importance of stating the comparison path. The factors are descriptive accounting ratios, not separately identified physical efficiencies or causal effects of individual measures. The study provides a reproducible interpretation of modelled renovation emissions while distinguishing mathematical closure from measurement validation and from lifecycle carbon assessment.