# Evaluating Uncertainties in Marine Biogeochemical Models: Benchmarking Aerosol Precursors
## 2 Methods
Our tuning parameter (\(\alpha\)) is currently set at unity, but could be modified as needed:  
\[S=e^{-\alpha\epsilon} \tag{1}\]  
The mean state analysis in IOMB employs area weighting over a region (\(\Omega\)) of choice. The package computes an integral mean value (\(\overline{v}\)) over space and time. The variable of choice \(v(t,x)\) represents a discontinuous function of constants in space and time, where the temporal domain is the initial time (\(t_{0}\)) and final time \(\left(t_{f}\right)\) intervals, and the spatial domain is the combination of areas within cell boundaries:  
\[\overline{v}=\int\limits_{\Omega}{((\frac{1}{t_{f}-t_{0}})\int\limits_{t_{0}}^ {t_{f}}v(t,x)dt)d\Omega} \tag{2}\]  
Using monthly mean files of a chosen variable, we compute the temporal and spatial mean for the overlapping time interval \(\left(t_{0},\ t_{f}\right)\) and region (\(\Omega\)) between the predicted (\(P\)) output from ESMs and the observational (\(O\)) datasets. We therefore interpolate on a common grid cell before computing the bias (\(B\)) on overlapping cells:  
\[B(x)=\frac{1}{t_{f}-t_{0}}\int\limits_{t_{0}}^{t_{f}}(P(t,x)-O(t,x))dt \tag{3}\]  
The temporal and spatial distribution of the results is limited by that of the observations, as model data outside of the referenced dataset spatial bounds are truncated and computed as complementary estimates to show complete accountability. A spatial bias plot is presented in the results section, since the aggregate in Equation (3) could be misleading when values are near zero. Model spatial variability is also computed using the standard deviation, RMSE, and Pearson correlation. Details on the subtlety of our scoring methodology are discussed in a related manuscript currently under review [59]. Observational datasets are either three or four-dimensional with the depth dimension limited to the ocean top layer (0-10 m). Options are also available for the quantification of various assessments such as the seasonal cycle and interannual variability. However, these features are not fully considered in the present analysis due to limitations of the observational datasets. Other potential global analyses that could be performed with IOMB/ILAMB can be found in the documentation for the parent package [10]. For demonstration purposes, we work initially from current understanding of the familiar, major nutrients in the surface ocean. We demonstrate the ability of IOMB to evaluate model outcomes for nitrate and net primary production, and then use DMS as a proxy for volatile organic compounds (VOCs). This is accomplished as follows: critical observational datasets are called upon to analyze the behavior of contemporary climate system models as they attempt to simulate the recent past (Table 1). Observation datasets in IOMB can be obtained from [[https://ilamb.ornl.gov/IOMB-Data/DATA/](https://ilamb.ornl.gov/IOMB-Data/DATA/)]([https://ilamb.ornl.gov/IOMB-Data/DATA/](https://ilamb.ornl.gov/IOMB-Data/DATA/)). A dynamic feature of this benchmarking package is that multiple referenced datasets could be used for the analysis, but we are making use of one per variable in this initial confrontation. We are currently expanding metrics in the package to include uncertainty quantification in the flux of aerosol precursors to the MBL. Our initial attempt is to validate surface ocean DMS concentrations relative to the most up-to-date climatology, which is the Lana dataset obtainable from [PERSON] et al. [14] ([[http://www.bodc.ac.uk/](http://www.bodc.ac.uk/)]([http://www.bodc.ac.uk/](http://www.bodc.ac.uk/))). The gridded monthly climatologies of the Lana dataset are the standard product used as input to climate models. The data is provided on a \(1^{\circ}\times 1^{\circ}\) resolution for periods between March 1972 and February 2009. Our DMS analysis is centered between 1978-2008, as most of the data used for the climatology were generated between these years.