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Numerical Weather Prediction
and Data Assimilation
David Schultz, Mohan Ramamurthy,
Erik Gregow, John Horel
What is a model?
• Resource: Kalnay, E., 2003: Atmospheric Modeling, Data
Assimilation and Predictability
• model: tool for simulating or predicting the behavior of a
dynamical system such as the atmosphere
• Types of models include:
– heuristic: rule of thumb based on experience or common sense
– empirical: prediction based on past behavior
– conceptual: framework for understanding physical processes
based on physical reasoning
– analytic: exact solution to “simplified” equations that describe the
dynamical system
– numerical: integration of governing equations by numerical
methods subject to specified initial and boundary conditions
What is Numerical Weather
Prediction?
• The technique used to obtain an objective
forecast of the future weather (up to
possibly two weeks) by solving a set of
governing equations that describe the
evolution of variables that define the
present state of the atmosphere.
• Feasible only using computers
A Brief History
• Recognition by V. Bjerknes in 1904 that forecasting
is fundamentally an initial-value problem and basic
system of equations already known
• L. F. Richardson’s (1922) attempt at practical NWP
• Radiosonde invention in 1930s made upper-air
data available
• Late 1940s: First successful dynamical-numerical
forecast made by Charney, Fjortoft, and von
Neumann
• 1960s: Edward Lorenz shows the atmosphere is
chaotic and its predictibility limit is about two weeks
NWP System
• NWP entails not just the design and
development of atmospheric models, but
includes all the different components of an
NWP system
• It is an integrated, end-to-end forecast
process system
Data Assimilation
Components of an NWP
model
1. Governing equations
• F=ma, conservation of mass, moisture, and thermodynamic
eqn., gas law
2. Numerical procedures:
• approximations used to estimate each term (especially important
for advection terms)
• approximations used to integrate model forward in time
• boundary conditions
3. Approximations of physical processes
(parameterizations)
4. Initial conditions:
• Observing systems, objective analysis, initialization, and data
assimilation
Model Physics
• Grid-scale precip. (large scale condensation)
• Deep and shallow convection
• Microphysics (increasingly becoming
important)
• Evaporation
• PBL processes, including turbulence
• Radiation
• Cloud-radiation interaction
• Diffusion
• Gravity wave drag
• Chemistry (e.g., ozone, aerosols)
Grid spacing (resolution) defines the
scale of the features you can simulate
with the model.
Good Numerical Forecasts
Require…
• Initial conditions that adequately represent the state of
the atmosphere (three-dimensional wind, temperature,
pressure, moisture and cloud parameters)
• Numerical weather prediction model that adequately
represents the physical laws of the atmosphere over the
whole globe
Sources of error in NWP
• Errors in the initial conditions
• Errors in the model
• Intrinsic predictability limitations
• Errors can be random and/or systematic
errors
Sources of Errors - continued
Initial Condition Errors
1
2
3
4
5
6
Observational Data Coverage
a Spatial Density
b Temporal Frequency
Errors in the Data
a Instrument Errors
b Representativeness Errors
Errors in Quality Control
Errors in Objective Analysis
Errors in Data Assimilation
Missing Variables
Model Errors
1 Equations of Motion Incomplete
2 Errors in Numerical
Approximations
a Horizontal Resolution
b Vertical Resolution
c Time Integration Procedure
3 Boundary Conditions
a Horizontal
b Vertical
4 Terrain
5 Physical Processes
Source: Fred Carr
Given all these assumptions and
limitations, we have no right to
do as well in forecasting the
weather as we do!
• What other disciplines forecast the future
with as much success as meteorology?
NWP in Finland
• Currently, NWP models are run by FMI (limited domain
over Europe) and by the European Centre for MediumRange Weather Forecasts (global)
• Currently the FMI model is run at about 9 & 22 km and
the ECMWF model is run at 25 km grid spacing,
meaning that these models can resolve features about 6
times those grid spacings.
• The new AROME experimental model is running at 2.5
km grid spacing.
22 km HIRLAM
9 km HIRLAM
2.5 km AROME
9 km HIRLAM
2.5 km AROME
observed radar reflectivity
9 km HIRLAM
2.5 km AROME
The Hopes of the Testbed
• Higher-resolution observations will provide higherresolution initial conditions, which could be put into a
higher-resolution NWP model, producing higherresolution forecasts.
• The hope is that precise forecasts of convection, the sea
breeze, rain/snow forecasting, and winds could be made
up to a few hours in advance.
• BUT…
Difficulties Lie Ahead…
• The reality is often that you end up with a higherresolution, less-accurate forecast.
• Results from forecasting/research experiments
at the NOAA/Storm Prediction Center show
value can be added sometimes with highresolution forecasts.
• When that value can be added is a very
important forecasting/research question!!!
Difficulties Lie Ahead…
• Producing the initial conditions from sparse resolution (in
space and time) and incomplete observations is not
easy.
• Creating a gridded 3-D/4-D dataset suitable for
initializing a NWP model is called data assimilation.
• How it is proposed to be done in the Helsinki Testbed is
described next…
Erik Gregow
Project Manager LAPS
• Numerical weather prediction model that adequately
represents the physical laws of the atmosphere over the
whole globe
• Initial conditions that adequately represent the state of
the atmosphere (three-dimensional wind, temperature,
pressure, moisture and cloud parameters)
Good Numerical Forecasts
Require…
• Numerical weather prediction model that adequately
represents the physical laws of the atmosphere over the
whole globe
• Initial conditions that adequately represent the state of
the atmosphere (three-dimensional wind, temperature,
pressure, moisture and cloud parameters)
Monitoring
Current
Conditions
September 6
20GMT
A
D
A
S
Potential Discussion Points
• Why are analyses needed?
– Application driven: data assimilation for NWP (forecasting) vs.
objective analysis (specifying the present, or past)
• What are the goals of the analysis?
– Define microclimates?
• Requires attention to details of geospatial information (e.g., limit
terrain smoothing)
– Resolve mesoscale/synoptic-scale weather features?
• Requires good prediction from previous analysis
• What’s the current state-of-the-art and what’s likely to be
available in the future?
– Deterministic analyses relative to ensembles of analyses
(“ensemble synoptic analysis”–Greg Hakim)
• How is analysis quality determined? What is truth?
– Why not rely on observations alone to verify model guidance?
Observations vs. Truth
• “Truth? You can’t handle the truth!”
• Truth is unknown and depends on
application: “expected value for 5 x 5
km2 area”
• Assumption: average of many
unbiased observations should be
same as expected value of truth
• However, accurate observations may
be biased or unrepresentative due to
siting or other factors
What’s an appropriate analysis given the
inequitable distribution of observations?
Case 1
?
x
= observation
Case 2
Case 3
?
x
?
x
x
= grid cell
What’s an appropriate analysis given
the variety of weather phenomena?
Elevated Valley
Inversions
Front
?
O
?
O
O
O
O
z
T
?
O
Analyses vs. Truth
Analysis value = Background value + observation Correction
- An analysis is more than spatial interpolation
- A good analysis requires:
- a good background field supplied by a model forecast
- observations with sufficient density to resolve critical weather
and climate features
- information on the error characteristics of the observations and
background field
- good techniques (forward observation operators) to transform
the background gridded values into pseudo observations
- Analysis error relative to unknown truth should be smaller than
errors of observations and background field
- Ensemble average of analyses should be closer to truth than single
deterministic approach IF the analyses are unbiased
Truth: Continuum vs. Discrete
Truth is unknown
Truth depends on application
Temperature
Truth
Truth = H (Truth)
West
Truth
East
Discrete Analysis Error
Temperature
Goal of objective analysis: minimize error
relative to Truth not Truth!
Analysis
Error
Analysis
West
Truth
Truth
East
ADAS
•Near-real time surface
analysis of T, RH, V
(Lazarus et al. 2002 WAF;
Myrick et al. 2005 WAF;
Myrick & Horel 2006 WAF)
•Analyses on NWS GFE
grid at 5 km spacing
•Background field: RUC
•Horizontal, vertical &
anisotropic weighting
Description:
In the following slides, temperature results from LAPS/MM5 analysis
are shown.
The objective is to compare a normal MM5 analysis with LAPS/MM5
analysis, also verify against some observations that are not included
into the LAPS analysis
Input to LAPS analysis is here:
- MM5 9-km resolution (input to MM5 is ECMWF 0.35 deg)
- 52 surface observations from HTB area
MM5 analysis: Temperature at 9 m height, with 1 km resolution
The analysis is based on 0.35 degree boundary fields from ECMWF operational analysis.
09 Aug 2005,15 UTC
MM5 analysis: Temperature at 9 m height, with 1 km resolution
Verification: The figures, within the plot, are measurements from certain stations not included in
the LAPS analysis
*23.7
*
* 23.4
23.6
24.3
*
*
26.0
*
23.0
*
22.1
25.4
*
25.4
23.5
*
*
*20.5
*
*
20.7
20.2
22.0
*
20.9
*
*
20.4
09 Aug 2005,15 UTC
LAPS/MM5 analysis: Temperature at 9 m height, with 3 km resolution
Verification: The figures, within the plot, are measurements from certain stations not included in
the LAPS analysis
*23.7
*
* 23.4
23.6
24.3
*
*
26.0
*
23.0
*
22.1
25.4
*
25.4
23.5
*
*
*20.5
*
*
20.7
20.2
22.0
*
20.9
*
*
20.4
09 Aug 2005,15 UTC
LAPS/MM5 analysis: Temperature at 9 m height, with 1 km resolution
Verification: The figures, within the plot, are measurements from certain stations not included in
the LAPS analysis
*23.7
*
* 23.4
23.6
24.3
*
*
26.0
*
23.0
*
22.1
25.4
*
25.4
23.5
*
*
*20.5
*
*
20.7
20.2
22.0
*
20.9
*
*
20.4
09 Aug 2005,15 UTC
WHAT IS TRUTH?
LAPS/MM5 analysis: Temperature at 9 m height, with 1 km resolution
Verification: The figures, within the plot, are measurements from certain stations
which are not included in the LAPS analysis
*23.7
*
* 23.4
23.6
24.3
*
*
26.0
*
23.0
*
22.1
25.4
*
25.4
23.5
*
*
*20.5
*
*
20.7
20.2
22.0
*
20.9
*
*
20.4
09 Aug 2005,15 UTC
Data Assimilation Surprises
•
Torn and Hakim (unpublished) have applied an ensemble Kalman filter for several hurricanes to
determine the most sensitive regions for forecasts in the western Pacific Ocean. The largest
sensitivities are associated with upper-level troughs upstream of the tropical cyclone. Observation
impact calculations indicate that assimilating ~40 key observations can have nearly the same
impact on the forecast as assimilating all 12,000 available observations.
•
Sensitivity of the 48 hour forecast of tropical cyclone minimum central pressure to the analysis of
500 hPa geopotential height (colors) for the forecast initialized 12 UTC 19 October 2004. Regions
of warm (cold) colors indicate that increasing the analysis of 500 hPa height at that point will
increase (decrease) the 48 hour forecast of minimum central pressure. The contours are the
ensemble mean analysis of 500 hPa height.
More Data Assimilation Woes
• Adaptive observations: collecting data where the
forecast is most sensitive
• Sometimes assimilating more data produces a
worse forecast (Morss and Emanuel)
• Heretical thought: What if none of the hundreds
of observations from the Helsinki Testbed made
any difference to the forecast?
Challenges Ahead for Testbed/LAPS
• The Testbed only samples the lower troposphere at best,
not the mid and upper troposphere.
• Weather phenomena, even adequately sampled by the
Testbed data, will move out of the Testbed domain within
an hour or two.
• Weather phenomena inadequately sampled by the
Testbed data will move into the domain and screw up
your forecast.
• Predictability of mesoscale weather features is unknown.
• All of this assumes a perfect model.
Challenges Ahead for Forecasters
• Determinism is dead—long live probabilistic forecasting!
• High-resolution model output cannot be interpreted the
same way as a coarser-resolution model output.
• Forecasters need to be retrained.
• Communication of high-resolution forecasts to end users
is not simple (i.e., you cannot just send raw model output
to users and expect them to use it).
• This ensures jobs for good forecasters in the future.

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