Factors determining the robustness of AOT40 and other ozone exposure indices

The robustness problem is considered for mathematical indices that describe the adverse effects of vegetation exposure to ozone. It is shown that some of them may demonstrate infinitely high sensitivity of the exposure estimate to small variations of ozone concentrations or internal parameters of specific functional. In particular, for the accumulated exposure over a threshold of 40 ppb (AOT40) index such conditions are not extraordinary, but rather describe quite often situations in remote areas in Northern Europe. Taking into account inevitable uncertainties in both calculated and observed ozone concentrations, a high sensitivity of ozone impact indices results in an instability of the exposure estimates and creates problems in their use. Theoretical consideration of the problem enabled to formulate the necessary and sufficient conditions for the limited sensitivity of a time-integrating index. An example of a modified AOT formulation fulfilling the obtained criteria and hence not experiencing the sensitivity problem is considered.