| Data assimilation and forecasting the weather (!) |
| Eugenia Kalnay | |
| and many friends | |
| University of Maryland |
| Content |
| Forecasting the weather - we are really getting betterÉ | |
| Why: Better obs? Better models? Better data assimilation? | |
| Intro to data assim: a toy example, we measure radiance and we want an accurate temperature | |
| Comparison of the toy and the real equations | |
| An example from JMA comparing 4D-Var and LETKF (a type of Ensemble Kalman Filter) |
| Typical 6-hour analysis cycle |
| The observing system a few years agoÉ |
| Typical distribution of observations in +/- 3hours |
| Typical distribution of observations in +/- 3hours |
| Model grid points (uniformly distributed) and observations (randomly distributed). For the grid point i only observations within a radius of influence may be considered |
| Some statisticsÉ |
| Some comparisonsÉ |
| Slide 10 |
| Comparisons of Northern and Southern Hemispheres |
| Satellite radiances are essential in the SH |
| More and more satellite radiancesÉ |
| Intro. to data assimilation: a toy example |
| Assume we have an object, a stone in space | |
| We want to estimate its temperature T (oK) accurately by measuring the radiance y (W/m2) | |
| that it emits. We have an observation model: | |
| We also have a forecast model for the temperature | |
| We will derive the data assim eqs (KF and Var) for this toy system (easy to understand!) | |
| Will compare the toy and the real huge vector/matrix equations: they are the same! |
| Toy temperature data assimilation, measure radiance |
| Toy temperature data assimilation, measure radiance |
| Toy temperature data assimilation, measure radiance |
| Toy temperature data assimilation, variational approach |
| Toy temperature data assimilation, variational approach |
| Typical 6-hour analysis cycle |
| Toy temperature analysis cycle (Kalman Filter) |
| Toy temperature analysis cycle (Kalman Filter) |
| Summary of toy system equations (for a scalar) |
| Summary of toy system equations (cont.) |
| Summary of toy system equations (cont.) |
| Equations for toy and real huge systems |
| Interpretation of the NWP system of equations |
| Interpretation of the NWP system of equations |
| Summary of NWP equations (cont.) |
| Comparison of 4-D Var and LETKF
at JMA T. Miyoshi and Y. Sato |
| Comparison of 4-D Var and LETKF
at JMA T. Miyoshi and Y. Sato |
| Comparison of 4-D Var and LETKF
at JMA T. Miyoshi and Y. Sato |
| Comparison of 4-D Var and LETKF
at JMA 18th typhoon in 2004, IC 12Z 8 August 2004 T. Miyoshi and Y. Sato |
| Comparison of 4-D Var and LETKF
at JMA RMS error statistics for all typhoons in August 2004 T. Miyoshi and Y. Sato |
| Summary |
| Data assimilation methods have contributed much to the improvements in NWP. | ||
| A toy example is easy to understand, and the equations are the same for a realistic system | ||
| Kalman Filter (too costly) and 4D-Var (complicated) solve the same problem (if model is linear and we use long assimilation windows) | ||
| Ensemble Kalman Filter is feasible and simple | ||
| It is starting to catch up with operational 4D-Var | ||
| Important problems: estimate and correct model errors & obs. errors, optimal obs. types and locations, tuning additive/multiplicative inflation, parameters estimation,É | ||
| Tellus: 4D-Var or EnKF? In press | ||
| Workshop in Buenos Aires NovÕ08 | ||