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A LITTLE HISTORY

DAVID BURRIDGE

with thanks to Adrian Simmons, Deborah Salmond, Terry Davies, Andy Malcolm, Andrew Staniforth and other colleagues

Vilhelm Bjerknes’ 1904 paper:

“Das Problem der Wettervorhersage, betrachtet vom Standpunkteder Mechanik und der Physik” 

which enunciated the basic principles of theprinciples of the computation of atmospheric evolution and thereby the science of weather prediction

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The details set out in Richardson’s 1922 book:

WEATHER PREDICTION

BY NUMERICAL PROCESS

CharneyFjörtoft

von Neumann

The advent of:

• the electronic computer

• rational approximation of the governing equations

Charney, Fjörtoft and

von Neumann (1950):

Numerical integration of

the barotropic vorticity

equation

1954 – NWP operational (for two weeks) in Sweden

Tellus, 2, 237-254

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Milestones in general circulation modelling Phillips (1956) – The first general circulation

experiment

Smagorinsky (1963) – Hemispheric primitive-equation general circulation model (hydrostatic)

Mintz (1965) – Global primitive-equation model

M b t l (1965) I l i f i t Manabe et al. (1965) – Inclusion of moist processes

Miyakoda et al. (1972) – Hemispheric medium-range forecasts

Pieter Brueghel the Elder

NWP with the hydrostatic Primitive Equations

A Source of inspiration

Time stepping?

Time filtering?Conservation (laws)Mass; energy;potential enstrophy……?

Resolution?

Boundary conditions?

Resolution?

My Sources/heroes of inspiration – Akio Arakawa & André Robert

Aliasing?

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Primitive equations

φ – latitudeλ - longitude

Fλ - “Physics”Fφ – “Physics”

Equation of continuity

Hydrostatic balance; w determined by the continuity equation and is the vertical velocity required to maintain hydrostatic balance

φ yQ – “Physics”

Equation of continuity

First law of thermodynamics

Gas law

Arakawa’s five latitude‐longitude horizontal grids ‐ with conservative finite differences for the spatial derivatives

φ represents –Pressure, temperature, humidity …;U d V h i t lU and V – horizontal wind components

Over time, the C-grid (a Voroni arrangement) has become the most popular –conservation of mass ();

geostropic adjustment (); can be designed to have good nonlinear stability characteristics (low aliasing)(); semi-implicit time-differencing ()

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Vertical co‐ordinates and grid systems

Z - Height co-ordinates; cut through the surface

Hydrostatic model one to one relation between p and z

the surface

P -Pressure co-ordinates; cut through the surface

σ(P/Ps)- sigma co-( s) gordinates; cut through the surface

Explicit time‐stepping – linear advection

Up-stream -dissipative for h tshort waves

Leapfrog – not dissipative but needs a time-filter)

Lax-Wendroff -di i ti fdissipative for short waves

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Implicit time‐stepping – Gravity Waves

Explicit schemes require very short time-steps

Implicit schemes remove this constraint

Requires a solver (for essentially a three-dimensional Poisson equation) to determine U and H at the new time-step so the wind speed constrains the time-step instead of c.

Pole problems – c‐grid

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Spectral ModelsRepresentation of grid point valuesin terms of functions - Spherical Harmonics

Ym,n (λ,μ)Spherical Harmonics

T

R

No differencing errors; generally no pole problem; solver trivial because spherical harmonics are eigenfunctions of the Laplacian; uniform resolution; can be non-aliased if the underlying grid is chosen appropriately (generally was but not now!)

Spectral, semi-implicit modellingFollowing developments made in the late 1960s and early 70s by Robert, Orszag, Eliasen, Machenhauer,

…

with Daley, Hoskins & Simmons, and others in the slipstream 

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Global NWP is established1974: NMC (USA) operational with 2.5o grid and 9 levels

1979: ECMWF operational with 1.875o grid and 15 levels

1980: NMC (USA) goes spectral

1982: The Met Office and US Navy go global

1983: ECMWF goes spectral

Time-stepping – semi-Lagrangianremoving the time-step constraint(another key contribution from André Robert)André Robert)

OR

a = departure point; d = arrival point

No time-step constraint

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Global operational models (2010/11)Centre Model

ECMWF (Europe) TL1279 (~16km) L91

Met Office (UK) 25 km L70

Meteo France TL798c2.4 L70(10km on W Europe)p

DWD (Germany) 30 km L60

HMC (Russia) T169 L31

NCEP (USA) T574 L64 (7.5)T254 L64 (16)

Navy(USA) T319 L42

CMC (Canada) (0.45°x0.3°) L80

CPTEC (Brazil) 20 km L96CPTEC (Brazil) 20 km L96

JMA (Japan) TL959 L60

CMA (China) TL959 L60

KMA (South Korea) 40 km L50

NCMRWF (India) T382 L64

BoM (Australia) ~40 km L70

Spectral = 8Grid points = 6

Large improvements in forecasts have stemmed from better data assimilation and observations

Data assimilation and reanalysis (proposed by Roger Daley in 1983 for monitoring impact of changes to forecasting system) ‐ improvement from 1980 to 2000 comes mostly from improvement to f iforecasting system Improvement since 2000 comes from improvement to forecasting system and to observations

Adrian Simmons ‐ 2012

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Error of 36h NMC 500hPa height forecasts for North America (Shuman, 1989)

Anomaly correlation of ECMWF 500hPa height forecasts

NWP is a real success story

and the heroes of the 1970s and the intellectual capital they built up still provides major elements of the numerical treatments of the dynamics employed in current operational forecasting systems.

Jaguar: World’s most powerful computer

Peak performance 2 3 petaflopsPeak performance 2.3 petaflops

System memory 300 terabytes

Disk space 10 petabytes

Disk bandwidth 240 gigabytes/second

System power 7 MW

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Simulated Satellite ObservationsECMWF predictions (T1279, ~15 km)

and Meteosat observations

Challenges - many of which are essentially modelling challenges

Clouds, diurnal cycle of precipitation, stable boundary layer, realistic,

characterization of the land surface, tropical convection e.g. MJO, blocking….

Address by: Address by:

- increasing accuracy through higher resolutions

- better cloud microphysics (rain, snow, aerosols….) - more comprehensive land surface (vegetation, lakes, snow cover….) - unification of clear and cloudy boundary layers with deeper convection - improvements in turbulent mixing and dissipation (shears, surface drag etc) - using innovative observational datasets

- ??????????

Data assimilation at very high resolutions and the effective assimilation of

more exotic variables such as rain, clouds, aerosols, constituents

Addressing the increasingly severe computational scalability issues

Global NWP in ‘the grey zone’ 5/10 km in the coming decade

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Met Office N512L70 – 7 day forecast

N512 forecast run

solver

advection

atmos_physics2

atmos_physics1

updates

end TS diags

diffusion

dumps

sw ap_bounds

stash

ECMWF 36r3 – T1279 L91 Forecastrun on 48 nodes

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Summary (very personal of course)

Process Met Office ECMWF

Data Assimilation ~22% ~30%

Deterministic FC ~28% ~20%

EPS ~50% ~50%

Heroes of the 1970s provided the basis for most of the numerical treatments of the of the dynamics used in current operational weather prediction models.

Dynamics requires typically more than 50% of the computational time of operational weather prediction models (the efficiency of models may become more important when Ensemble Kalman Filtering is adopted for data assimilation)  

The requirements for improved numerical treatments of the dynamics requires study in view of the increasing complexity of modelling

More efficient and probably better dynamical treatments are required ‐meso‐scale  modelling will provide major challenges.

TTHANK YOU

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Large improvements in forecasts have stemmed from better data assimilation and observations

Data assimilation and reanalysis (proposed by Roger Daley in 1983 for monitoring impact of changes to forecasting system) ‐ improvement from 1980 to 2000 comes mostly from improvement to f iforecasting system Improvement since 2000 comes from improvement to forecasting system and to observations

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Large improvements in forecasts have stemmed from better data assimilation and observationsReanalysis applies a fixed modern data assimilation system to multiyear sets of observations.  Proposed by Roger Daley in 1983 for monitoring impact of changes to forecasting systemchanges to forecasting systemData assimilation and reanalysis ‐Improvement from 1980 to 2000 comes mostly from improvement to forecasting system Improvement since 2000 comes from improvement to forecasting system and to observations

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