Meteorology Weather and Climate Weather and Climate Prediction1

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Meteorology Weather and ClimateWeather and
Climate Prediction1

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

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Lecture 3 Weather and Climate Prediction 1

• Not in Ahrens Meteorology Today
• Why is a forecast not accurate?
• Measuring the accuracy and reliability of a
  forecast
• Despite improvements why is a forecast still not
  accurate?
• Chaos theory
• Ensemble and seasonal forecasting

• http//www.ecmwf.int/products/forecasts
  (/guide/ and /seasonal),
• The Physics of Atmospheres Houghton ch13
  (JCM QC880)

ON HANDOUT
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Modelling physical processes

• Parametrisation approximation of physical
  process numerically
• Parametrisations are required for physical
  processes in the atmosphere occurring on scales
  that are too small to be directly seen or
  resolved by the numerical model, typically less
  than 50km,
• These are called sub-grid scale processes

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Physical parameterisations
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Dynamical Equations

• So-called 6 primitive equations
• Describe rates of change of u,v,T,q
• 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
• Equations are non-linear use finite difference
  techniques

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Stability Condition

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

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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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Conclusions

• Numerical models solve dynamical equations on a
  model grid and need physical parametrisations to
  represent sub-grid scale physical processes
• Computational effort in models depends on
  resolution, time step and forecast period
• Inappropriate choices can cause instability
• Much improved resolution over the last few
  decades

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Why are forecasts not perfect?

• a) The observed current state of the
  atmosphereanalysis is not known accurately
  enough
• b) The grid size is too large for representing
  the atmosphere-parameterisations need to be used
  for sub-grid scale processes and these are not
  exact
• c) The model equations are non-linear

ON HANDOUT
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Inaccuracies in the analysis

• Despite quality control and adjustments
  inaccuracies can occur in the analysis
• Sparse or lack of data over considerable time and
  areas
• Good data influences the analysis the wrong way-
  can happen when a weather system is only
  partially covered by observations
• An analysis error may only lead to a forecast
  failure in a dynamically sensitive region e.g.,
  cyclone forming region

ON HANDOUT
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Forecast and Actual

• Forecastforecast for 600pm based on
  observations that were assimilated in the model-
  to produce an analysis (global picture of the
  current state of the atmosphere) at 1200 noon
• Actual Analysis for 1200 noon based on
  observations assimilated into the model at noon?
  best guess for reality

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Is this a good forecast?

• Temperature forecast
• Forecast Actual
  Analysis

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Comparing forecasts statistics

• Statistical tests compare each grid box value in
  the forecast and the actual analysis and provide
  a summary result for the whole field or map. Two
  test used are
• Root-mean-square (rms) difference
• This is a measure of the absolute difference
  between the forecast and the actual field or map
• Anomaly correlation
• This is a measure of the similarity in patterns
  across
• the field or map, irrespective of the absolute
  difference

ON HANDOUT
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RMS errors of surface pressure compared with
analyses from observations

• Improvements in model dynamics and physics and
  resolution- improvement in forecast skill

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How long are forecasts reliable for?

• Large rms error or small anomaly correlation
  implies an unreliable forecast
• but is it of any use at all?
• A forecast still has some reliability if it is
  better than the
• Persistence forecast
• Climatology

ON HANDOUT
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Typical forecast accuracy
Forecast error
Climatology Persistence Typical NWP
0
1
2
3
4
5
6
7
8
9
10
Days into forecast
ON HANDOUT
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Still unpredictable-chaos theory

• The atmosphere is still unpredictable
• Edward Lorenz, 1963 pioneer of chaos
• Non-linear equations can be chaotic
• The equations are exact but their solutions are
  very sensitive to the initial values
• We can never model the atmosphere perfectly Very
  small differences between the forecast and real
  world can grow to very large errors over time
  making the forecast unreliable
• Similarly, two slightly different forecasts for
  the same time that use the same observations but
  with slightly different observation errors can
  diverge over time
• The physics of Atmospheres- Houghton ch 13 (JCM
  QC880)

ON HANDOUT
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Lorenz model predictable state -little change
e.g. slow moving pressure system

• Two points (forecasts or forecast and reality)
  stay close together

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Lorenz model less predictable state- diverging
rapidly
e.g. deepening depression
e.g. Warm and wet
e.g. Cold and sunny
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Lorenz model unpredictable state- massive
divergence
e.g. birth of a depression
e.g. Cold and sunny
e.g. Warm and wet
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Forecast period spatial coverage

• The longer the forecast period the more spatial
  information needed, since weather systems further
  away from the forecast region will influence the
  weather in the forecast region

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Regions of sensitivity
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Ensemble forecasts

• We can use chaos theory to gain confidence in the
  accuracy of forecasts
• Requires an ensemble or group of forecasts (20
  to 50)
• Each forecast uses slightly different initial
  conditions e.g. different random errors included
• Identify characteristic weather regimes and how
  often they occur
• Identify regions where the forecasts diverge as
  low confidence or unlikely forecasts

ON HANDOUT
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Example-Ensemble forecasting
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Example-Spaghetti diagrams 500hPa Z
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Seasonal forecasting

• Ensemble forecasting can also be used to make
  longer term seasonal forecasts for some areas of
  the globe
• They are probabilistic forecasts
• But how are these meaningful if forecasts are not
  reliable past 10 days?
• Because of atmosphere-ocean interactions. Some
  ocean processes are predictable over longer
  timescales (see later)

ON HANDOUT
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East African Rainfall

• UK met office forecasts of the East African short
  rains (October to December)
• Use 40 ensembles

• 5 categories- very wet, wet, average, dry, very
  dry
• Most forecasts within one category of the actual
  category

ON HANDOUT
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Conclusions

• Numerical weather prediction is a chaotic process
• Accuracy of forecast depends on accuracy of
  initial state
• Since observations will always contain some
  error, there will always be a limit to
  predictability
• Best estimate for a single forecast at present
  10 days
• Ensemble forecasting can extend this to 2 weeks
• Beyond two weeks forecasters mostly use ensemble
  forecasting combined with coupled ocean
  atmosphere models to make probabilistic forecasts

ON HANDOUT