Forecasting Models

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Forecasting Models
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Numerical Weather Prediction (NWP)

• A numerical model is a computer program designed
  to simulate some real system.
• When a numerical model is used in meteorology to
  forecast the weather the process is called
  numerical weather prediction (NWP).

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NWP Model Basics

• NWP Models are based on the laws of physics.
• Equations based on those laws are integrated
  forward in time to simulate changes in the
  atmosphere.

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NWP Model Basics (Cont.)

• Even with the current generation of computer
  technology it is impossible to simulate all of
  the important processes that occur in the
  atmosphere..

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NWP Model Basics (Cont.)

• A parameterization is used in order to estimate
  the effects of important processes that cannot be
  predicted directly by the model.
• A parameterization estimates the effect of a
  process using variables that can be predicted by
  the model.

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NWP Model Basics (Cont.)

• For example, most models cannot predict
  individual clouds, yet predicting the effects of
  clouds and the precipitation they produce is a
  primary goal of NWP.
• Thus, most NWP model include a cloud
  parameterization that attempts to predict the
  effect of clouds based on the other variable
  predicted by the model.

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NWP Model Basics (Cont.)

• Thus, it is necessary to simplify (the word model
  in this sense means a simplified version of
  reality) the real atmosphere when it is simulated
  by the model.

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NWP Model Components

• Input Data
• Initialization
• Model
• Model Output (Post-processing)

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Input Data

• Surface observations
• Rawinsonde observations
• Satellite data
• Radar data
• Profiler observations
• Aircraft observation

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Initialization

• Initialization is the process of taking data and
  preparing it for input into a numerical model.
• Data are from different sources,are taken at
  different times and may contain errors.

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Initialization (Cont.)

• The initialization process must blend together
  the data from the different sources into a
  consistent data set that accurately represents
  the state of the atmosphere.

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Initialization (Cont.)

• Some initialization schemes use the short-term
  (3, 6 or 12 hours) forecast from the previous
  model run as a first guess about the status of
  the atmosphere.

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Initialization (Cont.)

• The initialization then adds in data at
  appropriate times and places and nudges (i.e.
  modifies) the previous model forecast as it
  integrates up to the current time.
• The result of the initialization is a physically
  consistent data set that is used as the initial
  conditions for the NWP model.

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Initialization (Cont.)

• Quality control identifies obvious errors in
  input data.
• Data assimilation combine data from different
  sources.
• Generate initial analysis fields (i.e. conditions
  at time t0 in forecast run).

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NWP Model

• Integrates forward in time to produce the NWP
  forecast of the atmospheric variables.
• Because the equation are highly nonlinear, they
  cannot be integrated analytically to produce an
  exact solution.

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NWP Model (Cont.)

• In order to solve the equations they are
  approximated numerically (often using a truncated
  form of a series expansion to represent the
  derivatives in the equations).
• The use of a truncated series introduces
  truncation errors into the model.

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NWP Model (Cont.)

• Suppose we have a simple advection model of the
  form
• ?u/?t u (?u/?x)
• rate of change with time of u equals advection of
  u in x-direction.

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NWP Model (Cont.)

• ?u/?t u (?u/?x)
• could be approximated as
• ?u/?t u (?u/?x)

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NWP Model (Cont.)

• Compute u (?u/?x)t0 based on the initial data
  at time t0.
• Let ?u/?tt1 u (?u/?x)t0
• Integrate forward in time
• ut1 ut0 ?u/?tt1 ?t
• Compute u (?u/?x)t1 based on the forecast for
  time t1.
• Let ?u/?tt2 u (?u/?x)t1

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NWP Model (Cont.)

• ut2 ut1 ?u/?tt1 ?t
• Repeat steps until desired forecast time is
  reached.

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Model Output

• Numerical Models generate files that contain the
  model forecasts.
• Post-processing of the forecasts is performed to
  generate graphical products that can be viewed
  individually or looped to view a sequence of
  forecasts.

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Model Output Statistics (MOS)

• The model forecasts are sometimes used as input
  to programs that generate Model Output Statistics
  (MOS) which are model-based statistical
  forecasts for specific locations.

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MOS (Cont.)

• MOS equations are developed by a statistical
  analysis of the forecast and observed variables
  most closely related to the desired forecast of
  dependent variable at a point on the surface of
  the Earth.

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MOS (Cont.)

• For example
• T3hrs a bX1 cX2 dX3 eX4
• where X1, X2, X3 and X4 are independent variables
  identified during the statistical analysis of
  past data, and a, b, c, d, and e are coefficients
  based on the statistical analysis.

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NWP Model Types

• One way to differentiate between numerical models
  divides them into
• Grid point models and
• Spectral models.

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Grid Point Models

• Grid point models solve the basic equations and
  make forecasts for specific points on the surface
  of the Earth and in the atmosphere.
• Grid point models often use a Taylor series
  expansion approximate derivatives.

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Grid Point Models (Cont.)
N
E
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Grid Point Models (Cont.)

• A point in a grid point model is supposed to
  represent the areal average of a grid box around
  that point.

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Grid Point Models (Cont.)

• A grid point models horizontal resolution is
  defined as the average distance between adjacent
  grid points with the same variable.

Horizontal Resolution
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Spectral Models

• Spectral models attempt to forecast the movement
  and changes of amplitude of ridges and troughs of
  different wavelengths that make up the
  atmospheric geopotential height pattern.
• Spectral models often use a Fourier series
  expansion to approximate horizontal derivatives.

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Longwave Pattern
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Shortwave Pattern
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Combined (actual) Pattern
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Spectral Models (Cont.)

• The horizontal resolution in spectral models is
  indicated by the T number, which indicates the
  maximum number of waves used to represent the
  global pattern.

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Spectral Models (Cont.)

• Spectral models truncate their numerical
  approximation at T waves. Thus, they cannot
  explicitly forecast systems produced by waves
  with wavelengths shorter than the T wave.

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Spectral Models (Cont.)

• The minimum wavelength is the wavelength of the
  smallest system that can be forecast explicitly
  by a spectral model.
• minimum wavelength 360/T

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Vertical Resolution

• The vertical resolution of a model refers to the
  number of levels and the ability of the model to
  reproduce the structure of the atmosphere.
• A model with more vertical levels has a greater
  vertical resolution and will represent the
  vertical structure of the atmosphere better.

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Vertical Resolution (Cont.)
Higher Vertical Resolution
Lower Vertical Resolution
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Vertical Coordinates

• Height, z
• Pressure, p
• Sigma, s p/psurface
• Eta, ?
• Isentropic, ?

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Height as a Vertical Coordinate

• Advantages intuitive, easy to construct
  equations
• Disadvantage difficult to represent surface of
  Earth because different places are at different
  heights.

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Pressure as a Vertical Coordinate

• Advantages easy to represent the top of the
  atmosphere (i.e. p0) and easy to incorporate
  rawinsonde data.
• Disadvantage difficult to represent the surface
  of the Earth because the pressure changes from
  one point to another on the surface.

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Sigma as a Vertical Coordinate

• Advantages easy to represent the top and bottom
  of the atmosphere.
• s 0 at the top of the atmosphere.
• s 1 at the Earths surface.
• Disadvantage errors can result in calculation
  of the horizontal pressure gradient force in
  areas with steep slopes.

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Sigma as a Vertical Coordinate (Cont.)
(?p/?x)z
(?p/?x)s
s 0.9
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Eta as a Vertical Coordinate

• Eta is also called the stepped mountain
  coordinate. It was created in the 1980s in an
  attempt to reduce the errors that sometimes
  occurred when the horizontal pressure gradient
  force was computed using sigma.

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Eta as a Vertical Coordinate (Cont.)

• ?s pr(zs) pt/pr(z0) pt
• where
• pr(zs) is the pressure in the standard atmosphere
  at height zs
• pt is the pressure at the top of the atmosphere
• pr(z0) is the pressure at sea level in the
  standard atmosphere (1013.25 mb)

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Eta as a Vertical Coordinate (Cont.)
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Eta as a Vertical Coordinate (Cont.)

• Advantage improves calculation of horizontal
  pressure gradient force.
• Disadvantage does not accurately represent the
  surface topography.

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Isentropic Coordinates

• Isentropic coordinates refers to the use of
  potential temperature, ?, as the vertical
  coordinate.
• When the atmosphere is stable and unsaturated, ?
  will increase with height.

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Isentropic Coordinates (Cont.)

• Advantages
• ? surfaces are nearly horizontal in the mid and
  upper troposphere, and
• ? is constant during adiabatic processes.

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Isentropic Coordinates (Cont.)

• Disadvantages
• Diabatic processes such as radiative transfers,
  latent energy exchanges and thermal advection are
  not isentropic and ? will not be constant.
• ? surfaces tend to intersect the ground at sharp
  angles.

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Isentropic Coordinates (Cont.)
? is constant surface
? surface intersects ground
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Boundary Conditions

• Operational meteorological models may contain two
  types of boundary conditions.
• Vertical boundary conditions
• Lateral boundary conditions

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Vertical Boundary Conditions

• Vertical boundary conditions specify the
  relationships used to define the magnitudes of
  forecast variables at the top and bottom of the
  numerical model (e.g. at the top of the
  atmosphere and at the Earths surface).

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Alternate Way to Classify Models

• Global models generate predictions over all
  parts of the Earths surface.
• Regional models generate predictions over some
  limited section of the Earths surface (e.g.
  North America or the continental U.S.).

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Lateral Boundary Conditions

• Lateral boundary conditions refer to the
  relationships used to specify the magnitudes of
  forecast variables at the horizontal edges of a
  models domain.
• Since global models cover the entire Earths
  surface, there is no need for lateral boundary
  conditions in global models.

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Lateral Boundary Conditions (Cont.)

• Since regional models only cover a limited
  portion of the Earths surface lateral boundary
  conditions are necessary to specify the
  conditions at the horizontal edges of the models
  domain.

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Lateral Boundary Conditions (Cont.)
N
E
Regional Model Domain
Low
Significant Weather System initially outside
model domain.
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Lateral Boundary Conditions (Cont.)

• Since regional models only cover a limited
  portion of the Earths surface, significant
  weather systems could move into the region from
  outside the model domain during the forecast
  period.

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Lateral Boundary Conditions (Cont.)

• The regional model needs to be supplied with
  information about these weather systems in order
  to produce useful forecasts.
• The lateral boundary conditions can be used to
  specify the impacts of the weather systems as
  they enter the model domain.

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Lateral Boundary Conditions (Cont.)

• Regional models often use lateral boundary
  conditions supplied by forecasts from global
  models.
• For example, the North American Mesoscale (NAM
  model uses lateral boundary conditions supplied
  by the Global Forecasting System (GFS) model.