ISORROPIA-MCX: Enabling Sensitivity Analysis With Multicomplex Variables in the Aerosol Thermodynamic Model, ISORROPIA

Sensitivity analysis with atmospheric chemical transport models may be used to quantify influences of specific emissions on pollutant concentrations. This information facilitates efficient environmental decision-making regarding emissions control strategies for pollutants that affect human health and public welfare. The multicomplex step method (MCX) is a sensitivity analysis approach that enables calculation of first- and higher-order sensitivities of a nonlinear algorithm with analytical accuracy. Compared to the well-known finite difference method, the MCX method is also straight-forward to compute yet does not suffer from precision errors due to subtracting numbers with common leading digits and eliminates the requirement of tuning the step size. The aerosol inorganic equilibrium thermodynamic model, ISORROPIA, which treats ammonium, chloride, nitrate, sodium, sulfate, calcium, potassium, and magnesium, was augmented to leverage the multicomplex step method (ISORROPIA-MCX) to analyze the influence that the total amount of a pollutant has on concentrations partitioned into different phases. This enables simultaneous calculation of the first-order, second-order, and cross-sensitivity terms in the Taylor Series expansion when evaluating the impact of changes in input parameters on an output variable, increasing the accuracy of the estimated effect when the functions are nonlinear. ISORROPIA encodes highly nonlinear processes which showcases the computational advantages of the multicomplex step method as well as the limitations of the approach for fractured solution surfaces. With ISORROPIA-MCX, the influence of total concentrations of aerosol precursors on aerosol acidity are evaluated with cross-sensitivity terms for the first time. Plain Language Summary Models of the atmosphere allow various stakeholders to understand how one element of this complex system influences outcomes of interest, such as air pollutant concentrations. One atmospheric process that impacts estimates of the burden of disease from air pollution is the formation of aerosols, which are small liquid or solid particles suspended in the air. Some inorganic gases such as nitric acid and ammonia move to these particles under certain conditions characterized by temperature, relative humidity, and the concentrations of other pollutants. This process is described in atmospheric models by the thermodynamic equilibrium model ISORROPIA. Until now, an efficient method has not been available to calculate the way a change in the total concentration of any given species would influence the partitioning between liquid and gas phases of the model output, which includes concentrations of up to eight aerosol species as well as the aerosol acidity and liquid water content. Here, the implementation of multicomplex numbers in ISORROPIA is shown to provide an efficient way of calculating the influence of an input concentration on all of the output, including aerosol acidity, in a single, augmented model execution.