Large language models are increasingly used for quantitative work in the environmental sciences, yet existing evaluations score only final answers, leaving calculation process unobserved. Here we introduce AtmosCoder-Bench, an execution-grounded benchmark that makes the calculation process visible. Built through a transferable semi-automated pipeline (436 problems, 3,910 variants, 7,029 graded quantities), every problem is validated to be unambiguous and human-solvable, with uniquely verifiable answers. We find that (i) multiple-choice formats inflate measured accuracy by at least 12 percentage points; (ii) many failures arise not from missing knowledge but from models failing to apply known formulas and constraints consistently throughout multi-step computation; and (iii) even frontier models remain weak when task-specific conditions invalidate familiar methods, often reverting to canonical solution patterns rather than adapting methods to the relevant physical regime, leaving expert oversight essential.