Chapter 14. Weather Forecasting

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Chapter 14. Weather Forecasting
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Weather Trivia October 14

• 1954 A farmer in the path of Hurricane Hazel
  reported that 20 of his cows seemed drunk after
  the storm. They stumbled around and could hardly
  stand up. Apparently, the cows came upon a feast
  of apples blown into a meadow by the storms
  winds. The cows got high. Their digestive
  juices worked so fast that apple juice was
  fermented rapidly, which made the cows drunk.

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Three steps in generating a numerical forecast
from a weather prediction model 1) Analysis
Determine the present state or initial
conditions, by incorporating observational data
such as 6-hourly surface and 12-hourly sounding
data onto grid points of a computer model 2)
Prediction Run the model starting from the
present state for a period of lead time to
generate a forecast for that period 3)
Prognosis Interpret the model results by
experienced forecasters
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1) Analysis Assessing the Present State

• Surface observations are taken simultaneously,
  every 6 hours at all observing stations around
  the globe
• Upper air observations are taken simultaneously
  at radiosonde stations every 12 hours
• Supplementary observations are taken from
  commercial aircraft, ships, and satellites

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Vertical Sounding Profile
Radiosonde instruments attached to balloons are
launched twice daily to profile weather variables
with height. These January 14, 1999 data show
winds veering from easterly at the surface to
southwesterly aloft.
Figure 14.5
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• The data are coded and transmitted to national
  meteorological data centres (e.g. Canadian
  Meteorological Centre in Dorval)
• The national meteorological data centres exchange
  data internationally
• The global data are screened for errors,
  projected onto model grid points, and combined
  with forecast model output for the time of the
  observations to produce the analysis the
  analysis is the best estimate of the present
  state of the atmosphere

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2) Prediction Numerical Forecast Model

• A computer model that solves the equations that
  determine the motion, temperature, humidity,
  cloudiness, precipitation in the atmosphere at
  particular grid points
• Starting from a set of initial conditions
  characterizing the atmosphere at the start of the
  forecast, the model is run to generate forecasts
  for up to about 5 days
• The model produces maps of atmospheric parameters
  such as pressure, temperature, winds at several
  heights in the atmosphere (prognostic charts)
• Specialized models may produce information about
  air quality

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Grid Points of a Model

• Over the past decades,the number of grid points
  of forecast models has increased with increasing
  computing power
• Example Number of points covering Lake Superior
  in US Weather Service models
• 1975 3 points, 6 vertical levels
• 1985 13 points
• 1992 39 points
• 2000 420 points, up to 50 vertical levels

Surface temperature of Lake Superior in a model
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Prognosis for two weather forecast models
Figure 14.1A
Figure 14.1B
Forecast of 500 mb heights generated by two
different numerical models in US
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3) Prognosis Interpreting the Model Forecast

• The forecaster uses the prognostic charts
  generated by the model as guidance to prepare a
  forecast of local weather
• Takes into account strengths and weaknesses of
  the model, and uses specialized local weather
  conditions obtained from satellite images,
  soundings, wind profilers, and weather radar data

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Figure 12.12
A basic understanding of the movement of weather
systems, and the weather associated with highs
and lows allows us to draw simple forecasts from
a weather map
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Fig. 14.10 Isallobars lines of constant 3 hr
pressure change
Lows tend to move in the direction of the fastest
pressure drops
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Figure 14.11
Mid-latitude weather systems tend to move in the
direction of the 500 mb winds at about half the
speed of the 500 mb winds
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Weather Radar

• Weather Radar measures the intensity of
  precipitation
• A Doppler radar also measures the wind speed
• and can identify regions where tornadoes may
  form
• Certain radars can also distinguish between heavy
  rain and hail

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WSR-88D Doppler Radar
Weather Surveillance Radar - 1988 Doppler, also
known as next generation radar (NEXRAD), detects
severe weather extent, movement, and
intensity. Data received by the NEXRAD unit are
processed by algorithms to assist the forecaster
in weather interpretation.
Figure 14.3
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Why are weather forecasts inaccurate?

• In spite of the power of the supercomputers,
  computing capability limits the number of grid
  points in forecast models.
• Due to a lack of understanding, many of the
  physical processes can only be represented
  approximately in the models.
• There are gaps in the observational data that are
  used to initialize the models (e.g. over the
  oceans).
• The atmosphere is inherently chaotic. The
  influence of errors in the initial measurements,
  or variations in atmospheric properties on scales
  smaller than the measurements, amplify quickly
  with time and contaminate the forecast.

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Forecasts are getting better, but . much remains
to be done
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Improvement of accuracy of 3-, 5-, 7-day forecast
of height of 500-mb surface at European Centre
for Medium-Range Weather Forecasts, UK
Northern Hemisphere
Southern Hemisphere
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Forecasts are getting better Skill of 24-hour
forecasts of precipitation that exceed 1 inch (as
measured by Threat Score) over US increases
over the period 1961-2001
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Figure shows monthly scores for 24-hour
quantitative precipitation forecast (QPF)
exceeding 1 inch for 1991-99 over US. Note
scores for summer remain low, as summer
precipitation tends to be of small spatial scale
driven by convection, and not by large scale
forcing. Also note forecasters improve model
score.
Winter months, higher score
Summer months, low score
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Chaos The Butterfly Effect

• A butterfly flapping it's wings in one area of
  the world (e.g., the Amazon) can cause a tornado
  to occur in another remote area of the world
  (e.g., midwest US)!
• The extreme sensitivity to initial conditions
  limits the predictability of weather.
• This sensitivity leads to rapid growth of
  initially small errors that are inevitable, which
  eventually contaminate forecast (chaos)
• From theory and model studies, the predictability
  limit of daily weather is about 2 weeks.

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Logistic equation

• Apparently simple numerical model of change of
  insect population with time
• Surprisingly complex behavior
• xj1 r xj (1-xj)
• xj is population at year j
• normalized to 0 lt xj lt 1
• r is a parameter to be specified (0 lt r lt 4)
• Equation gives population xj at year j, starting
  from an initial value x0

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Logistic equation (continued)

• Complex evolution of population for certain
  values of r
• Chaos the value of xj is extremely sensitive to
  the exact value of the initial value x0

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Bifurcation diagram shows the population tends
to one single equilibrium value for 1 lt r lt 3
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Population tends to 2, 4, 8, 16, . values (2-,
4-, 8-, 16-cycles and higher) as r increases to
about 3.5699457
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What happens as r gt 3.5699457 ?

• Chaos!
• The population will eventually visit every
  neighbourhood in any sub-interval of 0, 1
• The population evolution (orbit) depends very
  sensitively on the initial conditions such that
  two nearby values will eventually diverge to as
  much as two randomly chosen orbits

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Chaos starts at around r 3.5699457 resulting
in a blur of dots instead of discrete lines in
the bifurcation diagram
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In this sea of chaos, a 3-cycle suddenly appears
at r 3.82842 1 sqrt(8)!