initial conditions of the uw s hort r ange e nsemble f orecast system
DESCRIPTION
Initial Conditions Of the UW S hort R ange E nsemble F orecast System Tony Eckel, UW Atmos. Grad. Student Advisor: Prof. Cliff Mass. From our point of view, truth is random sample from the pdf. - Let all ICs evolve to build PDF at future time (i.e., a forecast pdf) - PowerPoint PPT PresentationTRANSCRIPT
Initial ConditionsOf the UW
Short Range Ensemble ForecastSystem
Tony Eckel, UW Atmos. Grad. Student
Advisor: Prof. Cliff Mass
- Construct the initial state of the atmosphere with multiple, equally likely analyses, or initial conditions (ICs)
Ensemble Forecasting Theory
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1 3 5 7 9 11 13 15 17 19
Fre
quen
cy
Initial State0 5 10 15 20
0.2
0.4
.5
7.6946e-023
dnorm ( ),,x 10 1
200 x
- From our point of view, truth is random sample from the pdf
0 5 10 15 20
0.2
0.4
.5
0.000514093
dnorm ( ),,x 10 3
200 x
0 5 10 15 20
0.2
0.4
.5
7.4336e-007
dnorm ( ),,x 10 2
200 x
0
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1 3 5 7 9 11 13 15 17 19
0
1
2
3
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1 3 5 7 9 11 13 15 17 19
24hr Forecast State 48hr Forecast State
- Let all ICs evolve to build PDF at future time (i.e., a forecast pdf)
- Error growth spreads out PDF as forecast lead time increases
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1 3 5 7 9 11 13 15 17 190
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1 3 5 7 9 11 13 15 17 190
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1 3 5 7 9 11 13 15 17 19
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 don’t always perform the way they should. (especially a problem for SREF)
Limitations of EFF
requ
ency
Initial State0 5 10 15 20
0.2
0.4
.5
0.000514093
dnorm ( ),,x 10 3
200 x
0 5 10 15 20
0.2
0.4
.5
7.4336e-007
dnorm ( ),,x 10 2
200 x24hr Forecast State 48hr Forecast State0 5 10 15 20
0.2
0.4
.5
7.6946e-023
dnorm ( ),,x 10 1
200 x
truth’s pdf
ensemble
phasespace
eta
mrf
cmc
avn
ngpT
UW SREF Methodology OverviewAnalysis pdf :
Forecast pdf :
5 “independent” atmospheric analyses
Analysis pdf
Forecast pdf
48hr forecast state (core)
48hr true state
5 divergent, “equally likely” solutions using the same primitive equation model, mm5
phasespace
eta
mrf
cmc
T
48hr forecast state (core)
48hr true state
Analysis pdf :
Forecast pdf :
5-1+3=7 “independent” atmospheric analyses, plus the Centroid (C)8 divergent, “equally likely” solutions using the same primitive equation model, mm5
Forecast pdf
uk
gsp
Analysis pdf
cwb
ngp
C
UW SREF Methodology Overview
avn
ngp
phasespace
eta
cmc
T
48hr forecast state (core)
48hr true state
Analysis pdf :
Forecast pdf :
7 “independent” atmospheric analyses, Centroid, plus 7 “mirrored” ICs15 divergent, “equally likely” solutions using the same primitive equation model, mm5
avn
uk
gsp
cwbuk
eta
cmc
gsp
ngp
avnuk
gsp
cwb
Analysis pdfcwb
C
48hr forecast state (perturbation)
UW SREF Methodology Overview
Forecast pdf
phasespace
T
48hr forecast state (core)
48hr true state
Analysis pdf :
Forecast pdf :
7 “independent” atmospheric analyses, Centroid, plus 7 “mirrored” ICs15 divergent, “equally likely” solutions using the same primitive equation model, mm5
Forecast pdf
48hr forecast state (perturbation)
ngp
uk
eta
cmc
gsp
avn
Analysis pdfcwb
Cngp
eta
cmc
avn
gsp
cwb
uk
UW SREF Methodology Overview
Generating New Initial ConditionsSTEP 1: Find vector in model phase space between an analysisand 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
C cmc
cmcC
Sea
Lev
el P
ress
ure
(mb)
~1000 km cmc newcent
Generating New Initial ConditionsSTEP 1: Find vector in model phase space between an analysisand 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
C cmc
cmcC
-1.0 < pf < 1.0• Over samples center of analysis pdf• Perturbations don’t diverge• Non-unique solutions
–0.5
Sea
Lev
el P
ress
ure
(mb)
~1000 km cmc newcent
Generating New Initial ConditionsSTEP 1: Find vector in model phase space between an analysisand 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
C cmc
cmcC
pf > 1.0 or pf < –1.0 • Samples “out of bounds” of analysis error• Less likely solutions (greater error)• Overspread forecast pdf
–1.5
Sea
Lev
el P
ress
ure
(mb)
~1000 km cmc newcent
Generating New Initial ConditionsSTEP 1: Find vector in model phase space between an analysisand 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
C cmc
cmcC
pf = 1.0• Within analysis error with unique, realistic structure• “Equally likely” solution, with similar or reduced error• Divergent forecast
1.0
Sea
Lev
el P
ress
ure
(mb)
~1000 km cmc newcent
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
CASE STUDY: Annual UW Atmos Department Hike Scheduled Hike:28 Sep 17z 29 Sep 00z
C
Forecast Initialization: 27 Sep 00z
Case study: thirteen 36km mm5 runs.Begin by examining just three…
48h eta 29 Sep 00z
Blanca Lake
Blanca Lake
1.0cmc
00h cmc 27 Sep 00z 00h 1.0cmc 27 Sep 00z
00h cent 27 Sep 00z
24h cmc 28 Sep 00z 24h 1.0cmc 28 Sep 00z
24h cent 28 Sep 00z 00h eta 28 Sep 00z
48h cmc 29 Sep 00z 48h 1.0cmc 29 Sep 00z
48h cent 29 Sep 00z 00h eta 29 Sep 00z
eta
All 13, 48h Forecastsfor slp and 6hr precipValid 29 Sep 00z
ukmo
tcwb
cent
ngps
cmc 1.0cmc
avn 1.0avn
1.0eta
1.0ukmo
1.0ngps
Probability of Precip
> 0 mm: 6/13 = 46.2%> 2 mm: 4/13 = 30.8%> 4 mm: 1/13 = 7.7%
BlancaLake
1.0tcwb
EXTRA SLIDES
00h 1.0cmc – cent00h cent – cmc
Linear vs. Nonlinear Dispersion
C new
pf = 1.0cmc
What is gained by running all those perturbations?
24h 1.0cmc – cent24h cent – cmc
12h cent – cmc 12h 1.0cmc – cent
48h 1.0cmc – cent48h cent – cmc
36h cent – cmc 36h 1.0cmc – cent
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
N Analyses(equally likely)
N 48hr Forecasts(equally likely)
OBS
Ensemble Forecasting Process
Products
ModelConfidence
DataRange
Consensus
Probability
MODEL
MODEL
MODEL
MODEL
500mb Hght/Vort
Increase Spread in Decreased Less confidence the different forecasts Predictability in forecast
Model Confidence ProductsSpaghetti Diagram Variance (Spread) Chart
A visualization
of predictability
- 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
Consensus Products
1000/500 Hpa Geopotential Thickness [m] at YokosukaInitial DTG 00Z 28 JAN 1999
0 1 2 3 4 5 6 7 8 9 10Forecast Day
5520
5460
5400
5340
5280
5220
5160
5100
5040
4980
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
FNMOC EFS Probability of 19.5 m Gale Force WindsEFS Mean SLP Contours 00Z20NOV1998 tau 72
65N
60N
55N
50N
45N
40N
35N
30N
25N
20N
15N
10N
5N
EQ120E 130E 140E 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W
Probability Products
- Shows the probability of occurrence of critical event (i.e., surface winds > 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
Probability of 24 hr Precip >
Initial Time: 00Z, 27 Mar 00 FCST Lead Time: 48 hrs
0 10 20 30 40 50 60 70 80 90 100 Probability Scale
0.10”
Probability of Quantitative Precipitation Forecast (PQPF)
0.25”0.50”1.00”
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
Probability of Warning Criteria at McGuire AFB Bas e d o n 1 5 /0 6 Z MM5 En s e m b le
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100
Date/T ime
Pro
ba
bili
ty (
%)
T S torm
W inds> 35k t
W inds> 50k t
S now> .5"/hr
Fzg Rain
15/06 12 18 16/00 06 12 18 17/00 06