Budget-constrained sensor placement for methane plume inversion under sparse satellite revisits: a computer-science evaluation of emission-attribution error in national inventory audits

National methane inventories increasingly rely on satellite-constrained plume inversion, yet the placement of a fixed sensor budget across a landscape of sparse satellite revisits determines how much of the resulting emission-attribution error is reducible and how much is structural. the present analysis formalises budget-constrained sensor placement as a submodular maximisation problem over a plume-inversion error functional, derives a greedy placement rule with a (1 - 1/e) approximation guarantee under a monotone submodular surrogate, and characterises the conditions under which the surrogate diverges from the true attribution error. The analysis is methodological and theoretical: no field deployment is reported. A worked evaluation on a computed plume field calibrated to published satellite revisit statistics shows that the greedy rule recovers between 71 and 88 per cent of the oracle placement gain across budget levels, while the residual attribution error is dominated by revisit sparsity rather than by sensor count. Inventory audits should report a placement-attributable error component separately from a revisit-attributable component, because conflating the two leads auditors to over-attribute residual uncertainty to instrumentation and under-attribute it to orbital sampling. The contribution is a formal decomposition of emission-attribution error into placement-reducible and revisit-structural parts, together with a placement algorithm whose guarantees are stated relative to that decomposition.