Initial Conditions

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Initial Conditions Of the UW Short Range Ensemble
Forecast System Tony Eckel, UW Atmos. Grad.
Student Advisor Prof. Cliff Mass
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Ensemble Forecasting Theory
- Construct the initial state of the atmosphere
with multiple, equally likely analyses, or
initial conditions (ICs)
Frequency
Initial State
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Limitations of EF
Difficult to consistently construct the correct
analysis/forecast pdf. Errors in mean and spread
result from 1) Model error 2) Choice of
ICs 3) Under sampling due to limits of
computer processing Result EF products dont
always perform the way they should.
(especially a problem for SREF)
ensemble pdf
Frequency
Initial State
24hr Forecast State
48hr Forecast State
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UW SREF Methodology Overview
Analysis pdf Forecast pdf
5 divergent, equally likely solutions using the
same primitive equation model, mm5
phase space
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UW SREF Methodology Overview
Analysis pdf Forecast pdf
5-137 independent atmospheric analyses, plus
the Centroid (C)
8 divergent, equally likely solutions using the
same primitive equation model, mm5
phase space
48hr true state
48hr forecast state (core)
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UW SREF Methodology Overview
Analysis pdf
Analysis pdf Forecast pdf
7 independent atmospheric analyses, Centroid,
plus 7 mirrored ICs
15 divergent, equally likely solutions using
the same primitive equation model, mm5
phase space
48hr true state
48hr forecast state (core)
48hr forecast state (perturbation)
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UW SREF Methodology Overview
Analysis pdf Forecast pdf
7 independent atmospheric analyses, Centroid,
plus 7 mirrored ICs
15 divergent, equally likely solutions using
the same primitive equation model, mm5
phase space
48hr true state
48hr forecast state (core)
48hr forecast state (perturbation)
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Generating New Initial Conditions
STEP 1 Find vector in model phase space between
an analysis and centroid by differencing all
state variables over all grid points. STEP 2
Make a perturbation by vector multiplying
analysis error by a perturbation factor (pf)
(I.e., actual error could be smaller or larger,
but in the same direction.) P
pf (C cmc) STEP 3 Make a new IC by
adding/subtracting the perturbation to the
centroid. new C P
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Generating New Initial Conditions
STEP 1 Find vector in model phase space between
an analysis and centroid by differencing all
state variables over all grid points. STEP 2
Make a perturbation by vector multiplying
analysis error by a perturbation factor (pf)
(I.e., actual error could be smaller or larger,
but in the same direction.) P
pf (C cmc) STEP 3 Make a new IC by
adding/subtracting the perturbation to the
centroid. new C P
0.5

• -1.0 lt pf lt 1.0
• Over samples center of analysis pdf
• Perturbations dont diverge
• Non-unique solutions

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Generating New Initial Conditions
STEP 1 Find vector in model phase space between
an analysis and centroid by differencing all
state variables over all grid points. STEP 2
Make a perturbation by vector multiplying
analysis error by a perturbation factor (pf)
(I.e., actual error could be smaller or larger,
but in the same direction.) P
pf (C cmc) STEP 3 Make a new IC by
adding/subtracting the perturbation to the
centroid. new C P

• pf gt 1.0 or pf lt 1.0
• Samples out of bounds of analysis error
• Less likely solutions (greater error)
• Overspread forecast pdf

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Generating New Initial Conditions
STEP 1 Find vector in model phase space between
an analysis and centroid by differencing all
state variables over all grid points. STEP 2
Make a perturbation by vector multiplying
analysis error by a perturbation factor (pf)
(I.e., actual error could be smaller or larger,
but in the same direction.) P
pf (C cmc) STEP 3 Make a new IC by
adding/subtracting the perturbation to the
centroid. new C P

• pf 1.0
• Within analysis error with unique, realistic
  structure
• Equally likely solution, with similar or
  reduced error
• Divergent forecast

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ICs Analyses, Centroid, and Mirrors

• Strengths
• Good representation of analysis error
• Perturbations to synoptic scale disturbances
• Reasonable sample of PDF?
• Magnitude of perturbation(s) set by spread among
  analyses
• Bigger spread ? Bigger perturbations
• Dynamically conditioned ICs
• Weaknesses
• Limited by number and quality of available
  analyses
• May miss key features of analysis error
• Analyses must be independent (i.e., dissimilar
  biases)
• Calibration difficult no stability since
  analyses may change techniques

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CASE STUDY Annual UW Atmos Department Hike
Scheduled Hike 28 Sep 17z ? 29 Sep 00z
Forecast Initialization 27 Sep 00z
Blanca Lake
48h eta 29 Sep 00z
Case study thirteen 36km mm5 runs. Begin by
examining just three
1.0
Blanca Lake
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00h cmc 27 Sep 00z
00h 1.0cmc 27 Sep 00z
00h cent 27 Sep 00z
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24h cmc 28 Sep 00z
24h 1.0cmc 28 Sep 00z
24h cent 28 Sep 00z
00h eta 28 Sep 00z
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48h cmc 29 Sep 00z
48h 1.0cmc 29 Sep 00z
48h cent 29 Sep 00z
00h eta 29 Sep 00z
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Blanca Lake
All 13, 48h Forecasts for slp and 6hr
precip Valid 29 Sep 00z
Probability of Precip gt 0 mm 6/13 46.2 gt 2
mm 4/13 30.8 gt 4 mm 1/13 7.7
cent
eta
ngps
1.0eta
1.0ngps
ukmo
cmc
1.0cmc
1.0ukmo
tcwb
1.0avn
1.0tcwb
avn
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EXTRA SLIDES
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Linear vs. Nonlinear Dispersion
What is gained by running all those perturbations?
pf 1.0
00h 1.0cmc cent
00h cent cmc
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12h cent cmc
12h 1.0cmc cent
24h 1.0cmc cent
24h cent cmc
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36h cent cmc
36h 1.0cmc cent
48h 1.0cmc cent
48h cent cmc
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Bulk Error Stats

• Used eta analysis as the verification
• Variable geopotential height
• Sample Size
• 150 x 126 x 11
• 207900

Case Study Init Date 18 Sep 00z
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(No Transcript)
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Ensemble Forecasting Process
N Analyses (equally likely)
N 48hr Forecasts (equally likely)
Products
500mb Hght/Vort
O B S
M O D E L
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Model Confidence Products
Variance (Spread) Chart
Spaghetti Diagram
A visualization of predictability
Increase Spread in
Decreased Less confidence the
different forecasts
Predictability in forecast
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Consensus Products

• Assuming a big enough sample and a near normal
  distribution, the average yields the expected
  value or the best guess forecast
• Averaging washes out the important small scale
  features

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Data Range Products

• Shows the range of possibilities (spread of the
  PDF) for any weather element at a given location
• Value is in defining the possible extremes for a
  forecast situation

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Probability Products

• Shows the probability of occurrence of critical
  event (i.e., surface winds gt 35 kts)
• Calculation P(event) ( exceeding threshold)
  / (total ) , or 1 p value of PDF
• Can be tailored for ANY weather element and
  threshold of interest

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Probability of Quantitative Precipitation
Forecast (PQPF)
Initial Time 00Z, 27 Mar 00
FCST Lead Time 48 hrs
Probability of 24 hr Precip gt
0.10
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Future Products ?
For DoD operations, products tailored to a
specific location or mission could be produced
from a fine scale model ensemble. These products
could be similar to the previous examples, or
something like this