Model Error

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Every model will have errors. Ensembles tell us the expected value of the error in a statistical sense. By examining an ensemble of model runs that each differs in some respect (differences include initial conditions or small-scale process parametrization), we can assess how the weather, acting through those changes, impacts ensemble spread and thus forecast uncertainty. As with any form of statistical forecasting, this ensemble post-processing requires that we calibrate, in this case calibrating the model spread against observed forecast errors from a large set of training cases.

Sources of Model Error

There are several sources of model error, each of which we would hope to capture with our ensemble. Below is a list of a few.

1. Nonlinear evolution of the weather pattern – making it sensitive to small errors in the initial weather analysis (3-D multivariate map) from which we start our NWP model run.
2. Poor approximation of the equations of motion by the algebraic equations to step the NWP model forward. This isn’t much of a problem with modern NWP models, as we’ve gotten pretty good at the finite difference in the math used to turn the equations of motion (a set of partial differential equations) into the model equations (a set of linear algebraic equations).
3. Poor approximation of all the physics that goes on at scales smaller than the NWP model grid (i.e., poor parametrization). The figure below shows you the smaller scale processes that I’m referring to.
   

   Visual of the small-scale processes that are smaller than NWP model grids

   Credit: U.S. DOE. 2010. Atmospheric System Research (ASR) Science and Program Plan.
   
   The processes include:
   1. short and longwave radiation,
   2. condensation and freezing of cloud droplets and various types of precipitation (e.g., rain, snow, graupel, hail, etc.),
   3. turbulent mixing,
   4. cumulus clouds (no operational forecast model has a grid fine enough to resolve all of them),
   5. transfer of heat, moisture, and momentum between the atmosphere and earth.
   These tasks are hard; thus parametrization of them in NWP models is far from perfect.

The ideal ensemble would try to capture the errors due to uncertainty in the initial conditions and those due to uncertainty in the subgrid-scale physics.

Initial Conditions

We can perturb the initial conditions of a model away from the best guess – this is called initial condition diversity. We cannot perturb the conditions by more than the uncertainty in our analysis, which results from our inability to observe the atmosphere completely. In data-rich areas that may not be much, but in data-poor areas, it could be large.

The big question is how to perturb the initial conditions. If you do it at random, the atmosphere just mixes out the fluctuation in minutes to hours. Instead, you need to perturb the initial conditions on those scales, and in those places, that the atmosphere is most likely to respond to. Below is a visual of the scales of motion in the atmosphere from microscale to climate variation.

Visual of temporal and spatial scales of motion in the atmosphere

Credit: The Comet Program.

The x-axis is the spatial scale, while the y-axis is the timescale. Generally speaking, we will focus on the mesoscale to synoptic scale for initial perturbations, as these are the most rapidly growing modes (i.e., weather patterns that are inherently unstable).

There are many ways to perturb the initial conditions, but the details are outside the scope of this course.

Physics

For each of the physics parameterizations (e.g., radiation, clouds/precipitation, turbulence, surface, cumulus, etc.) there are multiple “good” choices. Each ensemble member would have a different combination. Again, the details behind these parameterizations are outside the scope of this course. But, if you would like to see an example of how these aspects of ensemble initiations are implemented, please click here.