SHADOWING IN THE ATMOSPHERE

Ross Lieb-LappenChris Danforth

Forecasting Challenges

• Uncertainty in the initial state

• Chaos: sensitive dependence on initial conditions

• Model error

Trajectory of the System Truth

Forecast of the System Truth

Improving the Forecast

Our Model

Image: Nick Allgaier

Forecasting Methodology

• Ensemble forecasting

• Lorenz ‘96 Model

• Define new ensemble members

• Inflation of forecast ellipsoid

FXXXXdtdX jj jjj 121 )(/

advection dissipation

external forcing

Controlled Inflation• Only in contracting directions • Within climatological span of particular variable

• Maintain appropriate ratio with neighboring values

Model Success

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

Time

Err

orDifference between Truth and Forecast

Acknowledgments

Advisor:Chris Danforth

Nick Allgaier Kameron Harris

Singular Value Decomposition

-4 -3.5 -3 -2.5 -2

4

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

Variable 1

Var

iabl

e 2

Definition of new ensemble members