Weather forecasting by computer Michael Revell NIWA

Introduction History Operational NWP system –Forecast model –Data assimilation –Verification –Interpretation and limitations of output

NWP History Wilhelm Bjerknes (1904) –Suggested integrating differential equations that describe atmosphere Lewis Fry Richardson (1922) –First attempt (WW1) –Dismal failure, but wrote method down –Estimated 64,000 people needed to do calculation Courant, Friedrichs, Lewy (1928) –Time and space steps can’t be chosen independently Radiosonde invented (1930) –Upper air data

NWP History (cont) Rossby (1930+) –Simplified version of vorticity equation Von Neuman + ENIAC (1945) –Electronic Numerical Integrator and Computer –First electronic computer Charney (1950) –First successful numerical forecast based on vorticity equation Satellite technology (1970+) –Much improved data coverage over sea (SH) Faster computers + global models + improved use of initial data ECMWF (1980+)

Numerical Weather Prediction Aim: To predict future state of atmospheric circulation from knowledge of present state by using numerical approximations to the dynamical equations

Operational NWP system Requirements: –Closed set of appropriate physical laws –Expressed in mathematical form –Accurate numerical method to integrate these equations forward in time –Suitable initial and boundary conditions (on the globe no lateral boundaries)

Closed set of appropriate physical laws Conservation of momentum (u,v,w) Conservation of energy (T) Conservation of mass (p) Conservation of water substance (r) 6 equations – 6 unknowns

Expressed in mathematical form Example: –With c a specified speed –q(x,0) a known initial condition

Accurate numerical method to integrate these equations forward in time Approximate with centred differences Giving

Initial and boundary values

An NWP cycle 1.Get first guess at current situation Usually 3 or 6 hr forecast 2.Make new observations (Generally not at model grid points) 3.Interpolate these to model grid points 4.Filter out information the model can’t resolve 5.Step the model forward (3 or 6 hrs) 6.Use this forecast to repeat from step 1.

NZLAM-VAR: Forecast-Analysis Cycle 3 h forecast 3 h forecast… 48 h forecast A ob s A bk g 0369 Time (hours) h forecast ob s A bk g ob s A bk g

Simple! So why are forecasts not perfect? Over recent years there have been dramatic improvements, but there remains 1.Model error Models now solve the conservation laws quite accurately down to the scale of the grid Still have to represent the effect of scales that the model doesn’t resolve (parameterize) –Cumulus clouds –Mixing / diffusion –Surface friction –Surface energy balance –Radiation (dependent on moisture) –chemistry These are predominantly the sources and sinks for our conservation laws

1.Model error 2.Specifying the initial and boundary conditions is still a problem – lack of good data This is being improved by remotely sensed satellite data Better methods to utilise it This has improved SH forecasts by ~ 2-3 days

Conventional Data TEMP: 12 & 24 hTEMP: 12 & 24 h PILOT: 12 & 24 hPILOT: 12 & 24 h Ships : 3 hShips : 3 h Buoys: ~6 hBuoys: ~6 h SYNOPS: 3 hSYNOPS: 3 h AMDAR & AIREPAMDAR & AIREP Brisbane Invercargill

Satellite Data TOVS / ATOVS:TOVS / ATOVS: –NOAA14 HIRS 2, 3, 4, 5HIRS 2, 3, 4, 5 MSU 2, 3, 4MSU 2, 3, 4 –NOAA15 AMSU 4, 5, 6, 7, 8, 9, 10, 11AMSU 4, 5, 6, 7, 8, 9, 10, 11 SSM/ISSM/I –1D-VAR retrievals of surface wind speed SATWINDSSATWINDS –GMS atmospheric motion vectors

Forecasts What does the output from a weather prediction model look like?

ECMWF MSLP + RH predictions

5D Visualisation – Vis5D

NZLAM: Model Domains Uses UK Met Office Unified Model and 3DVAR Data Assimilation: 12 km resolution domain –324 × 324 × 38 4 km resolution domain –600 × 600 × km

NZLAM: Model Domains Uses UK Met Office Unified Model and 3DVAR Data Assimilation: 12 km resolution domain –324 × 324 × 38 4 km resolution domain –600 × 600 × 38 2 km resolution domain –800 × 800 × 38 (Largest UM run to date – 360 Processors on Cray T3E) 4 km

NZLAM 10m Wind Forecast: 22-Jun-05:06 UTC NZLAM 10m Winds: 24 h forecast Verifying QuikSCAT 10 m winds

Microphysics: Cloud Predictions NZLAM-VAR 12 hour forecast: low, low + mid, low + mid + high “Verifying” GMS 11  m image for 16 Dec 1999, 1640 UTC

Microphysics: Rain rates

Example NZLAM Simulations

Verification How good are our models at predicting weather variables?

Temperature

Wind

Surface forecasts

Issues & Challenges Right feature, wrong place?Right feature, wrong place? “Truth” Low res. model High res. model Observations

Future Improve data coverage Increase grid resolution Improve model representation of sub grid processes How do we cope with imperfect models? –There is useful information there –How do we get at it? –Ensemble methods (probabilities) –Model output statistics (correct statistically for model biases)

Ensemble methods

Ensemble methods (cont)

Questions?