An estimated 0.5–1 billion people globally have inadequate intakes of selenium (

Selenium (

Atmospheric deposition is an important source of

Since

Atmospheric chemistry modeling studies have been applied to other trace elements to predict atmospheric lifetimes and spatial patterns of deposition. For example, atmospheric mercury models were developed more than 2 decades ago

Since the atmospheric

Until recently, most sensitivity analyses of atmospheric chemistry models consisted of local methods, principally the one-at-a-time (OAT) approach. In the OAT approach, the model is initially run with a set of default parameters to yield a “reference” simulation. Multiple sensitivity simulations are then conducted, so that for each simulation one parameter is perturbed from the reference set at a time. The influence of these perturbations on the model output of interest would then be analyzed. However, this approach may be flawed because it only considers the first-order response of the model to each parameter, ignoring interactions that might exist between parameters

There are several recent examples of atmospheric chemistry studies that included a global sensitivity analysis. The sensitivity of cloud condensation nuclei number density to input parameters in an aerosol model was investigated at the local (geographic) scale

This study focuses on the construction of the first global atmospheric

SOCOL-AERv2 is a global CCM that includes a sulfate aerosol microphysical scheme

The sulfate aerosol model AER

For the simulations in this study we use boundary conditions for the year 2000. Sea ice coverage and sea surface temperatures are prescribed from the Hadley Centre dataset

Scheme of the atmospheric

We included the

To determine which

Description of

Atmospheric

We conducted a literature review to develop the model's chemical scheme of the

Rate constants of

The photolysis of gas-phase

As nonvolatile species, oxidized inorganic and organic

One limitation of using SOCOL-AER for the

Estimation of unknown

To conduct the sensitivity analysis of our

We restricted the scope of our sensitivity analysis to parameters that have been implemented in the model as part of the

Probability distributions of the model input parameters selected for the sensitivity analysis.

The

Five

Uncertainties in our calculated

For the sensitivity analysis, we do not alter the spatial distribution of

Spatial distribution of

The available speciation information for

Regarding the speciation of volcanic

The accommodation coefficient represents the probability that a gas-phase oxidized

SOCOL-AER only includes sulfate aerosol, lacking other aerosol types (e.g., dust, sea salt, organic aerosol) that may also transport

To determine a reasonable range for the emission magnitude of additional aerosol particles, we analyzed the particle emission inventories from the AEROCOM I project

The creation of surrogate models requires a set of training runs with the full SOCOL-AER model. The values of the input parameters are varied simultaneously between training runs, so that interactions between parameters can also be detected. A Latin hypercube design is used to draw

The initial conditions file for the training runs was created from a previous 10-year spinup of the model under year 2000 conditions. The atmospheric mixing ratios of

All relevant

In polynomial chaos decomposition, the output variable

PCE coefficients are generally calculated by least-square regression

When the dimension is large, regression techniques that allow for sparsity, i.e., by forcing some coefficients to be zero, are favored. In this work, we consider least-angle regression as proposed in

The accuracy of the PCE in representing the full SOCOL-AER model is evaluated with a cross-validation metric named the leave-one-out (LOO) error,

To improve the accuracy of the approximation, we applied post-processing steps to the construction of PCE models (Table

The cross-validation approach would usually remove the need for an independent validation dataset, saving computational expense. However, to evaluate the post-processing steps applied to the surrogate models, we also produced an independent validation dataset of 50 SOCOL-AER runs. The parameters for these runs were chosen by enriching the training experimental design to create a pseudo-Latin hypercube of 450 runs, ensuring that the distance between the validation runs and existing training runs is maximal.

Summary of methods to construct surrogate models and calculate Sobol' sensitivity indices of the SOCOL-AER output parameters.

A Sobol' sensitivity index represents the fraction of model variance caused by the parametric uncertainty of a certain input variable or the interaction between multiple variables

The total Sobol' index (

Other studies have emphasized the computational expense of conducting a sensitivity analysis for all grid boxes in a chemistry–climate model

To summarize categories of input variables, we aggregate the Sobol' indices of several input parameters to yield a total Sobol' index for that category. For example, we summarize the total dummy aerosol effect by summing the total Sobol' indices of the dummy aerosol radius, emission magnitude, and latitude. It would anyways be difficult to separate the effects of the dummy aerosol input parameters since they are correlated inputs in the experimental design. The second-order indices involving two dummy aerosol input parameters may be double-counted with this method. However, since these indices are small (

In order to estimate distribution statistics (mean, standard deviation, quantiles) of the output variable, we resample each surrogate model 40 000 times. We also use these 40 000 samples of the parameter space to calculate relationships between input parameters and output variables. To visualize marginal relationships between a certain input parameter and the output, we replace the value of the input parameter in the 40 000 samples by a fixed value and calculate the mean and variance of the surrogate model output. Repeating this step with other evenly spaced values in the input parameter range, we can produce the univariate relationship between the model output and the input parameter.

We decided to compare SOCOL-AER results with measurements of

Previous studies measuring

From the 400 training runs of SOCOL-AER, we created PCE models of the global and annual mean total

Distribution of the atmospheric

In order to identify the input parameters that drive the variability in the simulated

Sensitivity indices of the most important parameters (

Several of the most influential input parameters for the

Relationships between the atmospheric

After

Relationship between the atmospheric

The other inputs have minor impacts on the global

Surrogate models for

Map of the mean

Maps of the total Sobol' indices of emission parameters and the accommodation coefficient for total

Figures

It is also important to note which input parameters do not influence

Although other parameters may play a role in certain grid boxes, the emission parameters are most important on the global scale, evidenced by their higher mean total Sobol' index (Fig.

Maps of the total Sobol' indices of reaction rate constants and dummy aerosol parameters for total

Bar plot summarizing the importance of the input parameters to total

With surrogate models of wet

Figure

Through our consideration of model uncertainties related to

The results of the sensitivity analyses raise an obvious question: why do the input parameters that influence the atmospheric

It must be noted that our simulations were performed only for the year 2000 and focused on uncertainties in the

The global sensitivity analyses in this paper provide clear next steps for atmospheric

Comparison of wet deposition flux measurements (Table

The ultimate motivation for studying biogeochemical

Now that it includes

The SOCOL-AER code is available upon request from the authors, after users have signed the ECHAM5 license agreement:

The supplement related to this article is available online at:

AS, TP, and LHEW initiated the project of studying the atmospheric

The authors declare that they have no conflict of interest.

Thanks are due to Severin Gysin for his work on sensitivity analysis in a

This research has been supported by the ETH Zurich (grant no. ETH-39 15-2).

This paper was edited by Frank Dentener and reviewed by four anonymous referees.