Meteorology Weather and Climate Weather Forecasting 2

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MeteorologyWeather and Climate Weather
Forecasting 2

• Ruth Doherty CREW 303
• Ruth.Doherty_at_ed.ac.uk

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The forecast process

• 1. Gather observations for the globe to define
  the current state of the atmosphere
• Collect observations
• Perform quality control
• 2. Use these observations in a model that
  describes how the the atmosphere changes with
  time
• Data assimilation
• 3. Take this as the current state of the
  atmosphere and run the same model into the future
  
• Stop after 24, 48, 72 hours and interpret weather
  forecast!

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Observation types-surface dataTemperature,
humidity, pressure, wind
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Observations- important points

• In a 6-hour period receive gt100,000 observations
  of
• Temperature, wind speed and direction,surface
  pressure, humidity
• For some data types transformation performed
• e.g. radiances ? temperatures
• Data types have different geographical coverage,
  vertical structure and temporal distribution
• Surface observations are sparser coverage in SH
• Only certain data types give vertical profiles,
  satellite data have problems with vertical
  resolution

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Quality control 2. assign errors

• Assign errors to data retained
• Calculate observation error which depends on data
  type/instrument
• Calculate background error error at a given
  location dependent on synoptic situation (fast or
  slow moving systems) and data coverage
• Observational error and background error combined
  ? error estimate

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Data assimilation

• Observations and their error estimates are
  assimilated into the model
• Interpolate observations onto model horizontal
  and vertical grid
• Combine latest observations with
  previousbackground forecast
• Perform adjustments

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2. Combine new observations with previous forecast

• adjusts the model background field -the forecast
  from the previous model run- towards the new data
  received from observations
• Include observational errors to determine how
  reliable these new data are
• Process is very complex (adjustments often
  needed) and known as variational analysis
• Data assimilation can take 30 of the
  computational effort

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An analysis of the current state of the
atmosphere

• We now have the best possible estimate of the
  current state of the atmosphere on a regular grid
  over the whole world.
• This is called an analysis
• The process of making the forecast can now begin

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Conclusions

• Weather forecasts are based on numerical models
  of the atmosphere
• Used routinely for over 30 years
• Observations are numerous and come from a wide
  variety of sources
• Data assimilation schemes are very complex and
  can take 30 of the computational effort
• Create an analysis of the current state of the
  atmosphere then can forecast into the future

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Lecture 2 Weather Forecasting 2

• a) Model representation of the atmosphere
• Horizontal and vertical grid, boundary conditions
• b) Modelling physical processes-parametrisations
• c) Fundamental model equations-dynamics
• d) Model calculations
• e) Computational instability
• f) Other types of models
• No substantial material in Ahrens Meteorology
  Today but see
• www.metoffice.com/research/nwp/numerical/index.htm
  l,
• www.ecmwf.int/products/forecasts/guide/

ON HANDOUT
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Components of a numerical model
ON HANDOUT
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Numerical Weather Prediction (NWP) models

• All NWP models are based on the same set of
  governing dynamical equations
• They differ in the grids they use to represent
  the atmosphere
• They differ in the representation of physical
  processes
• They differ in how their dynamical equations are
  solved

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a) Model representation of the atmosphere 1
model grids

• NWP models solve their equations on a horizontal
  and vertical grid using finite difference
  techniques
• Grid resolution varies amongst different models
• UK met office horizontal grid0.83 longitude
  (432 columns) and 0.56 latitude (325 rows) -
  60km in mid-latitudes
• Vertical grid of 38 levels which are much closer
  at the surface where the atmosphere is most
  complex
• Model time steps generally of 20 minutes for
  computations of physics

ON HANDOUT
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Horizontal grid- UK met office NWP model
Each grid square represents an area of 60 km in
the mid-latitudes
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Vertical grid constant height surface

• NWP models use a variety of types of vertical
  grids

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Vertical grid constant pressure surface
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Vertical gridthe most common

• sigma coordinate (p/ps)

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Model representation of the atmosphere 2 Surface
boundary conditions

• Surface fields or model boundary conditions that
  are needed
• Land-sea mask
• Elevation and orography
• Vegetation and soil type
• Sea surface temperature and sea ice
  concentrations

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b) Modelling physical processes

• Parametrisation ? approximation of physical
  process numerically
• Required for physical processes occurring on
  scales that are too small to be directly seen
  or resolved by the numerical model i.e. less than
  60km (see later)
• surface properties (these can vary largely over
  a 50km region e.g. different vegetation coverage)
• Cloud amounts
• Parametrisations make assumptions due to
• computational restraints
• lack of fully understanding the processes
  involved.
• The effect of these processes are formulated in
  the model in terms of known grid -scale or state
  variables (i.e. temperature, humidity, pressure)

ON HANDOUT
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Physical parametrisations

• Model physical parametrisations required for
• Radiation (surface properties/clouds vary on
  scales finer than 50km)
• Surface and sub-surface processes- heat, moisture
  and momentum transfer from the surface (affected
  by vegetation, varies greatly near the surface
  cannot be represented in single vertical model
  layer)
• Clouds and precipitation (as above)
• Orographic (Gravity-wave) drag- effects of
  mountains
• http//www.metoffice.com/research/nwp/numerical/ph
  ysics/index.html,http//www.ecmwf.int/products/for
  ecasts/guide/Parametrization_of_physical_processes
  .html

ON HANDOUT
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Physical parameterisations
Processes that occur on scales less than 60km
or vary greatly at the surface-atmosphere
interface
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c) Model equations-state variables

• Model equations are solved between grid points
  every time step to calculate rates of change of
• Horizontal winds- U (W E) and V (N-S)
• Temperature, T
• Humidity, q
• Pressure, P
• Finite difference technique? approximate
  continuous changes in atmospheric behaviour using
  a fixed horizontal distance (between two grid
  points 60km ) and fixed time period (time step
  20 minutes)

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Dynamical Equations

• Horizontal forces
• Pressure gradient force (PGF)
• Coriolis force (CF)
• Friction

• So-called 6 primitive equations
• Describe rates of change
• Horizontal equations of motion -Newtons 2nd law
  or conservation of momentum
• Thermodynamic equation- 1st Law or conservation
  of energy
• Continuity equation- conservation of mass
• Water vapour equation conservation of moisture
  (evaporation/condensation)
• Relations between variables
• The hydrostatic equation (relationship between
  the density of the air and the change of pressure
  with height)
• Ideal gas law or equation of state

PV nRT
ON HANDOUT
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d) calculations
?u -u ?u -v ?u - 1 ?P f v F(u) (NB
simplified, 2D) ?t ?x ?y ? ?x

• Example rate of change of u at a point over
  time
• Advection of u by the wind at that point
• West-East PGF at that point
• CF turning the North-South wind at that point
• Friction at that point
• U is in many terms on the right hand side- a
  non-linear equation
• Use finite difference techniques to solve
  equations

ON HANDOUT
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New variables calculated

• In addition to state variables T, q, P e.g.
• Vertical velocity
• Cloud water
• precipitation
• Soil temperature
• Many more

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Example typical model grid

• 0.56o x 0.83o latitude-longitude grid
• 325 x 432 points
• 38 vertical layers
• Total number of points 38 x 325 x 432
• 5,335,200, say 5,000,000

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Example

• For ?t 1200 secs
• Approx 6 equations each requiring 10 calculations
  at all grid points
• 60 x 5,000,000
• 300,000,000 per time step
• 24 hour forecast
• needs 72 time steps
• so needs 21,000,000,000 calculations!

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e) Stability Condition

• CFL (Courant, Friedrichs, Lewy) criterion
• Speed of fastest winds in model lt grid spacing /
  time step
• u lt ?x/ ?t
• Must be true for the fastest moving system
  supported by the model
• Fastest wind speeds 50ms-1 (110mph)
• For ?x 60,000m
• ?t must be 1200 seconds (20 minutes)

ON HANDOUT
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f) Types of models

• NWP models- grid or spectral models
• Coupled Atmosphere (NWP)-Ocean Model
• lower resolution UK Met office model -2.5o x3.75o
  73 rows by 96 columns,19 vertical levels ?250km
  in the mid-latitudes
• Used for seasonal forecasting
• Used for future climate simulations with
  increasing CO2 concentrations
• More on these models in lectures 3 and 4

ON HANDOUT
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Computing power changes

• Recently -24 hour forecast with UK met office
  model on NEC computers takes 7 minutes!
  (5,000,000,000,000 calculations)

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Conclusions

• Numerical Weather Prediction models solve
  dynamical equations on a model grid
• These models use parametrisations to represent
  sub-grid scale processes
• Fundamental set of governing equations-
• These calculate changes in state variables
  between grid points finite difference method
• Instability criteria requires sensible choice of
  model grid square size and model time step per
  calculation
• Much improved resolution over the last few
  decades

ON HANDOUT