The daily averages of Fe concentration and solubility at the surface from four models were used for a comparison with the ambient measurements over the oceans (fig. S1 and table S2) (10, 21, 23, 24, 26, 37, 4143, 49, 50, 5259). When the field data uncertainties were not available, regional averages of relative SDs (SD divided by the average number of replicates) were used to estimate the SDs of the measurements. Mineral dust and biomass burning emissions are highly episodic and exhibit seasonal and interannual variability (5). It is, therefore, problematic to compare the monthly mean values of model estimates with the field data from different times of year, or different years. Moreover, the field observations have shown relatively high solubility at low concentration in aerosols influenced by combustion sources (2426). Thus, aerosols at high atmospheric concentration can be more representative of mineral dust aerosols, while mixed aerosols from different sources, i.e., dust and combustion aerosols, may be more representative at low atmospheric concentration. This suggests that modeled Fe concentrations should be consistent with the measurements to assess the relative contribution of each source. However, direct association of model estimates to a specific cruise track and time period can introduce biases when used as a reference for larger regions and different time periods. The maximum likelihood method has been operationally implemented to atmospheric data assimilation systems to estimate the state of the atmosphere from observations and models. Therefore, the MLEs of Fe concentration, sa, with error variance, σa2, were derived from the measurements, so, and a priori daily estimates modeled in the same month as the measurements, sb, with corresponding error variances, σo2 and σb2,σb2σo2+σb2 × (sosb)(1)σa2=σo2σb2σo2+σb2(2)

Using the probability function of the MLEs of Fe concentration assuming a normal distribution (MATLAB function), the weighted averages and SDs of Fe concentration and solubility were calculated. The a posteriori data were used as simulated estimates for the comparison with the measurements when MLEs of Fe concentration fell within ±2σo of the measurements (fig. S1 and table S2).