Prepared by Paul Quay (University of Washington) and Will Frangos (James Madison University).

Since models only approximate natural phenomena, they are inherently inexact. The mathematical description can be imperfect and/or our understanding of phenomenon may not be complete. The mathematical parameters used in models to represent real processes are often uncertain because these parameters are empirically determined or represent multiple processes. Additionally, the initial or starting conditions and/or the boundary conditions in a model may not be well known.

Despite these weaknesses, models are very powerful tools to represent natural processes. Often models are the only means we have to extrapolate to large spatial scales or predict the future. Because of their importance in the earth sciences, we try to assess model accuracy by **calibrating** and **validating** models. To help quantify the uncertainty of the model output we determine the **sensitivity** of the output to the model parameters.

## Model Calibration

The mathematical parameters in models that describe a certain process can be adjusted to obtain better agreement between model output and observations. However, the adjustment should yield a value of the parameter within its uncertainty. For example, in the modeling activity Using a mass balance model to understand carbon dioxide and its connection to global warming by R. MacKay, the growth rate of CO2 emissions from fossil fuel combustion and deforestation is adjusted to improve the fit to the observed atmospheric CO2 record.

## Model Validation

Sometimes there is an independent estimate of a certain process to which the model output can be compared. If there is good agreement between the model prediction and independent estimate, this helps validate the accuracy of the model. For example, in the activity Estimating Exchange Rates of Water in Embayments using Simple Budget Equations by K. Sverdrup and A. Duxbury, the model estimate of water exchange rates is compared to an independent estimate of water exchange derived from current meter measurements.

## Model Sensitivity

Often we want to see how model predictions respond to changes in model input, initial conditions, or parameter values. Determining the magnitude of change of the model output to changes in model input or parameters is often referred to as sensitivity tests. It is usually helpful to identify the model parameters that cause the greatest change in model output because these parameters should be constrained as best as possible. In contrast, model parameters or initial/boundary conditions that have little effect on model output can be poorly constrained and have little effect on model output. For example, in the activity What is the fate of CO2 produced by fossil fuel combustion? by P. Quay, the future concentration of atmospheric CO2 through the year 2100 is predicted for several differ scenarios of fossil fuel utilization rates during the next century.