How Models and Data Assimilation of Observations Work

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How Models and Data Assimilation of Observations
Work
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• Without The Models
• Weather Prediction Is Not Possible!

Originally prepared for HCC METO 111 and
presented as a starting point of a script for
NCEP video. 9/06/2002
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To look at a current satellite or radar loop is
to view a collection of observations, not a
prediction.

• Nowcasts can be used to make short time forecasts
  of up to 12 hours, but often they are not
  accurate beyond a few hours.
• Over a beer, weather forecasters will admit and
  proclaim that to go beyond Nowcasts they need a
  model to forecast the weather accurately.
• It is the combination of the model and the MANual
  forecasts that makes NWS forecasts as good as
  they are.

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Predicting The FutureModels are based on the
idea that the atmosphere is capable of analysis
and being understood in terms of the basic laws
and concepts of physics.

• How do prediction models determine the future
  state of the atmosphere?
• Start with a simple physical system containing an
  object subject to forces.
• Think of an accelerating piano, a car, or a
  parcel (a 3-dimensional cube) of air.

A parcel of air
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A Prediction PrescriptionNewtons Law

• Acceleration change in speed divided by change
  in time force on the object times the mass of
  the object.
• The speed change the speed some time in the
  future minus the initial speed.
• The time change the time some time in the
  future minus the time initially.
• Putting it together

• a DV/Dt F / M
• DV Vf Vi
• Dt tf ti
• (Vf Vi) F / M
• (tf ti)

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A Prescription for Predicting the Future

• Rewrite and get a prediction equation by
  isolating the Speed in the future term on the
  left hand side of the equation and everything
  else on the right hand side.
• Speedfuture Speedinitially (mass X Forces) X
  the time change desired.

• In the short hand of math
• Vf Vi (F / M) X (tf ti)
• We know the mass, initial time and the desired
  time in the future for the prediction. We can
  also measure the initial speed, Vi.
• We need only know the forces, F, that are acting
  now to give the future speed, Vf !

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Our Prediction equation Vf Vi (F / M ) X
(tf ti)

• This will do for an auto or moving a piano, but
  what about predicting the state of future
  weather?
• A whole science has grown up around the methods
  used to engineer the prediction equation.

• Apply the above equation to each parcel or cube
  of air!
• Divide up the atmosphere into vertical and
  horizontal rows and columns of air cubes or
  parcels over the entire globe!
• Then apply the above equation over and over again
  in small time steps (tf ti) is small to
  predict further and further into the future.

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How to we find the Forces that are acting on the
atmosphere initially?

• The Forces can be calculated from the state
  variables of our earths observing system.
  Temperature, Moisture, Wind, Surface Pressure and
  tracers like liquid water content, ozone, etc

• We measure the state variables with observing
  instruments.

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The prediction equation is solved or integrated
forward in time.

• The prediction equation is applied to each of the
  vertically stacked and horizontally distributed
  air parcels over the globe.
• Each time resulting in a new set of parcel future
  speeds.
• There is a similar prediction equation for
  temperature, moisture, surface pressure and
  tracers, like liquid water and Ozone.

• We diagnose from the predictions of these basic
  variables other quantities, such as clouds, rain
  amount, that comprise the NWS products that are
  delivered to the public - - with adjustments made
  MANually by weather service professional
  forecasters.

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The state variables of our earths observing
system are measured from the Global Observing
System

• Number of Observations per day
• 2,765,278 (April,2002)
• RAOBS (8,964)
• (717,120)
• AIRCFT ACARS (111,726)
• RAOBS contain many measurements

• Polar Orbiting Satellite (1,582,954)
• GOES Satellite (1,182,684)
• Radar and Profiler (6,459 746)
• Ship-Buoy (15,769)

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Space and Time Scales in the AtmosphereThe
weather telescopes from Planetary to phenomena
resulting from city heat islands and river beds.

• Micro-scale, e.g., Zephyrs, Tornados

• The atmosphere appears to have distinct spatial
  and time domains
• Some weather has components of many scales at
  once, for example, a hurricane spans most scales
  from tornados to interactions between tropics and
  mid-latitudes.

Small area
Meso-scale, e.g., low level jets and severe
weather
Weather systems , e.g., Lows and Highs
Continental scales drive weather systems,
e.g., 500mb waves.
Planetary scale determines the climate, monthly
and longer, e.g., El Nino
Large Area
Long Lived Short Lived
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Big whirls have little whirls that feed on their
velocity,Little whirls have lesser whirls and so
on to viscosity. (L.. F. Richardson)

• Planetary scale determines the climate, monthly
  and longer
• Synoptic scale encompass the cyclones and
  anti-cyclones (Lows and Highs) from days to
  weeks.
• Meso-scale has meso-cyclones thunderstorm
  supercells and squall lines which last from hours
  to a day and
• Micro-Scale are phemomena smaller than 10 km such
  as a tornado or a zephyr which last from minutes
  to hours.

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The Numerical Weather Prediction System takes
account of the influence of large (small) scale
phenomena on small (large) scales

• Computers are very good at keeping track of the
  millions of calculations that need to be
  accomplished each time the prediction equation is
  iterated.
• All the scales of motion and phenomena interact
  non-linearly according to the basic laws of
  physics.
• The smallest size or minimum time that can be
  resolved is determined by the number of
  calculations that the computer can provide to
  resolve the phenomena.

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The problem is the earths observations are not
delivered from equally spaced locations or at the
same time.Clever mathematical and statistical
calculations are made to interpolate the
observations to an equally spaced grid.

• To start the integration of the prediction
  equation an analysis of the observations is done
  to interpolate the information to the model grid
  of parcels.
• Quality control of the observations to minimize
  errors is done.
• The models previous run is used as a guess and
  error statistics of the observations play an
  important role in creating optimal interpolation
  systems.

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NWS Operational Model Suite Global forecast
System is a spectral model used for aviation,
medium range forecasting and climate with

• 29,412 (32,385) complex numbers representing each
  predicting vertical level, 3-dimensional
  variable, T, U, V, q, and tracers like liquid
  water and Ozone. Twodimensional Surface
  Pressure as well as other diagnosed and fixed
  fields like sea surface temperature, snow, Ice,
  are part of the observing system initial files
  and read in at the beginning of each integration.
• The model diagnoses precipitation type and
  amount, clouds, convection and radiation.

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NWS Operational Model SuiteThe Eta Model
(Meso-Eta)

• Is a regional model convering North America with
  higher resolution resolving meso-scale phenomenon
  at 12 km and 50 levels.
• The meso-scale regional Eta model starts with
  boundary and initial conditions from a global
  model run and then uses all the observations in
  its domain to make is own analysis and improved
  high resolution forecast.
• Telescoping regional models from the global model
  is a cost effective way to get more details where
  they are needed.
• The Eta model gives the best precipitation
  predictions and is the primary forecasters tool
  for making quantitative precipitation forecasts.

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Higher resolution models will enable more
accurate prediction of meso-scale and large scale
phenomena including severe weather and special
quantities like aerosol and pollutants.

• Models can target cities and associated weather
  events, watching and warning against loss of
  property and injury, distilling the interactions
  between the largest and smallest scales for
  predicting climate, weather and ocean phenomena.
• Accuracy improvements in modeling are rewarded
  by decreasing the risk to population and
  commerce.
• The prediction system success is proven by past
  verification that they are up to the job, for
  example, in tropical cyclone and hurricane track
  prediction.