model output statistics (mos) - objective interpretation of nwp model output
DESCRIPTION
Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output. University of Maryland – April 4, 2012. Mark S. Antolik Meteorological Development Laboratory Statistical Modeling Branch NOAA/National Weather Service Silver Spring, MD. (301) 713-0023 ext. 110 - PowerPoint PPT PresentationTRANSCRIPT
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Model Output Statistics (MOS) - Objective Interpretation of
NWPModel OutputUniversity of Maryland – April 4, 2012
Mark S. AntolikMeteorological Development Laboratory
Statistical Modeling BranchNOAA/National Weather Service
Silver Spring, MD
(301) 713-0023 ext. 110email: [email protected]
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MOS Operational System “Fun Facts”With apologies to David
Letterman, of course!
●9 million regression equations●75 million forecasts per day●1200 products sent daily
●400,000 lines of code – mostly FORTRAN
●180 min. supercomputer time daily
●All developed and maintained by
~ 12 MDL / SMB meteorologists!
X8
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OUTLINE 1. Why objective statistical guidance?
2. What is MOS? Definition and characteristics The “traditional” MOS product suite (GFS, NAM) Other additions to the lineup
3. Simple regression examples / REEP
4. Development strategy - MOS in the “real world”
5. Verification
6. Dealing with NWP model changes
7. Where we’re going – GMOS and the future
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WHY STATISTICAL GUIDANCE?
●Add value to direct NWP model output
Objectively interpret model - remove systematic biases - quantify uncertainty Predict what the model does not Produce site-specific forecasts (i.e. a “downscaling” technique)
●Assist forecasters “First Guess” for expected local conditions “Built-in” model/climo memory for new staff
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A SIMPLE STATISTICAL MODELRelative Frequency of Precipitation as a Function of
12-24 Hour NGM Model-Forecast Mean RH
NGM MEAN RELATIVE HUMIDITY (%)
OB
SER
VED
REL.
FR
EQ
UEN
CY
0 10 20 30 40 50 60 70 80 90 1000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
3-YR SAMPLE; 200 STATIONS
1987-1990 COOL SEASON
47%
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MOS Max Temp vs. Direct Model Output
2
3
4
5
6
7
8
MA
E (
deg
F)
24 48 72 96 120 144 168 192Projection (hours)
NEW MOS CLIMO DMO
MRF MOS Max Temp1999 Warm Season - CONUS/AK
MOS
DMO
CLIMO
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What is MOS?What is MOS?
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MODEL OUTPUT STATISTICS (MOS)
1. Numerical Weather Prediction (NWP) Model Forecasts 2. Prior Surface Weather Observations3. Geoclimatic Information
Current Statistical Method: MULTIPLE LINEAR REGRESSION (Forward Selection)
Relates observed weather elements (PREDICTANDS) to appropriate variables (PREDICTORS) via astatistical approach.
Predictors are obtained from:
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MODEL OUTPUT STATISTICS (MOS)
Properties
●Mathematically simple, yet powerful
●Need historical record of observations
at forecast points (Hopefully a long, stable one!)
●Equations are applied to future run of
similar forecast model
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MODEL OUTPUT STATISTICS (MOS)
Properties (cont.)
●Non-linearity can be modeled by using
NWP variables and transformations
●Probability forecasts possible from a
single run of NWP model
●Other statistical methods can be used
e.g. Polynomial or logistic regression; Neural networks
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MODEL OUTPUT STATISTICS (MOS)
●ADVANTAGES Recognition of model predictability Removal of some systematic model bias Optimal predictor selection Reliable probabilities Specific element and site forecasts ●DISADVANTAGES Short samples Changing NWP models Availability & quality of observations
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MAJOR CHALLENGE TO MOS DEVELOPMENT:
RAPIDLY EVOLVING NWP MODELS AND
OBSERVATION PLATFORMS
RAPIDLY EVOLVING NWP MODELS AND
OBSERVATION PLATFORMS
2. DIFFICULT COLLECTION OF APPROPRIATE PREDICTAND DATA
1. SHORT, UNREPRESENTATIVE DATA SAMPLES
MODELS
NCEP
OBS
Mesonets
MOS
New observing systems: (ASOS, WSR-88D, Satellite) (Co-Op, Mesonets)“Old” predictands: The elements don’t change!
Can make for:
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““Traditional” MOSTraditional” MOStext productstext products
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GFS MOS GUIDANCE MESSAGEFOUS21-26 (MAV)
KLNS GFS MOS GUIDANCE 11/29/2004 1200 UTC DT /NOV 29/NOV 30 /DEC 1 /DEC 2 HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12 N/X 28 48 35 49 33 TMP 43 44 39 36 33 32 31 39 46 45 41 38 37 39 41 44 45 44 40 40 35 DPT 27 27 28 29 29 29 29 33 35 35 36 35 36 39 41 42 37 34 30 30 28 CLD CL BK BK BK OV OV OV OV OV OV OV OV OV OV OV OV OV BK CL CL CL WDR 34 36 00 00 00 00 00 00 00 14 12 12 10 11 12 19 28 29 29 29 28 WSP 06 02 00 00 00 00 00 00 00 01 02 04 04 06 07 08 15 17 18 09 05 P06 0 0 4 3 11 65 94 96 7 0 0 P12 6 19 94 96 0 Q06 0 0 0 0 0 3 4 4 0 0 0 Q12 0 0 4 2 0 T06 0/ 0 0/18 0/ 3 0/ 0 0/ 0 0/18 2/ 1 10/ 4 0/ 3 1/ 0 T12 0/26 0/17 0/27 10/25 1/38 POZ 2 0 0 1 2 4 4 0 1 1 2 3 3 1 1 0 2 1 2 3 1 POS 13 2 1 2 1 0 0 0 0 0 0 0 0 2 0 0 0 3 0 9 28 TYP R R R R R R R R R R R R R R R R R R R R R SNW 0 0 0 CIG 8 8 8 8 7 7 7 8 8 7 7 7 4 2 3 3 6 7 8 8 8 VIS 7 7 7 7 7 7 7 7 7 7 7 7 5 5 4 2 6 7 7 7 7 OBV N N N N N N N N N N N N BR BR BR BR N N N N N
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NAM MOS GUIDANCE MESSAGEFOUS44-49 (MET)
KBWI NAM MOS GUIDANCE 2/27/2009 1200 UTC DT /FEB 27/FEB 28 /MAR 1 /MAR 2 HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12 N/X 38 46 32 41 24 TMP 59 58 55 54 49 43 38 38 43 45 40 38 37 35 33 34 37 38 33 29 25 DPT 46 47 48 46 37 30 24 22 22 22 24 27 28 26 25 24 24 21 17 12 10 CLD OV OV OV OV OV SC SC SC CL BK OV OV OV OV OV OV OV OV OV OV BK WDR 21 20 22 25 31 32 34 36 01 03 05 04 01 36 35 35 35 34 35 33 34 WSP 15 09 08 06 10 11 10 12 10 09 08 10 12 13 14 16 11 13 15 16 17 P06 89 10 3 2 2 76 73 13 17 27 19 P12 10 3 81 17 30 Q06 1 0 0 0 0 4 1 0 0 0 0 Q12 0 0 4 0 0 T06 2/ 9 0/ 5 0 /0 0/ 5 3/ 1 5/ 3 0/ 0 0/ 2 2/ 5 0/ 0 T12 2/ 9 0/ 5 5/ 3 1/ 2 7/ 5 SNW 0 0 0 CIG 6 6 4 5 7 8 8 8 8 8 7 6 4 3 4 3 4 4 7 6 7 VIS 7 7 6 7 7 7 7 7 7 7 7 7 3 6 5 7 7 7 7 7 7 OBV N N N N N N N N N N N N BR N BR N N N N N N
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Short-range (GFS / NAM) MOS
●STATIONS: Now at approx. 1990 Forecast Sites (CONUS, AK, HI, PR, Canada)
●FORECASTS: Available at projections of 6-84 hours GFS available for 0600 and 1800 UTC cycles
●RESOLUTION: GFS predictors on 95.25 km grid; NAM on 32
km Predictor fields available at 3-h timesteps
●DEPENDENT SAMPLE NOT “IDEAL”: Fewer seasons than older MOS systems Non-static underlying NWP model
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Approx. 1990 sites
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Short-range (GFS / NAM) MOS
●STATIONS: Now at approx. 1990 Forecast Sites (CONUS, AK, HI, PR)
●FORECASTS: Available at projections of 6-84 hours GFS available for 0600 and 1800 UTC cycles
●RESOLUTION: GFS predictors on 95.25 km grid; NAM on 32
km Predictor fields available at 3-h timesteps
●DEPENDENT SAMPLE NOT “IDEAL”: Fewer seasons than older MOS systems Non-static underlying NWP model
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GFSX MOS GUIDANCE MESSAGEFEUS21-26 (MEX)
KCXY GFSX MOS GUIDANCE 11/26/2004 0000 UTC FHR 24| 36 48| 60 72| 84 96|108 120|132 144|156 168|180 192 FRI 26| SAT 27| SUN 28| MON 29| TUE 30| WED 01| THU 02| FRI 03 CLIMO X/N 43| 29 47| 40 55| 35 51| 29 45| 32 40| 36 42| 30 45 31 46 TMP 37| 32 43| 43 46| 37 41| 32 39| 35 36| 38 37| 33 37 DPT 24| 27 37| 40 32| 28 28| 26 31| 32 30| 32 27| 24 25 CLD PC| OV OV| OV PC| CL PC| PC OV| OV OV| PC CL| CL CL WND 10| 5 11| 11 16| 10 10| 5 9| 6 10| 12 14| 12 12 P12 0| 5 13| 91 13| 3 9| 14 24| 52 54| 48 21| 12 25 20 18 P24 | 16| 100| 9| 26| 62| 72| 25 29 Q12 0| 0 0| 3 0| 0 0| 0 0| 2 2| 2 | Q24 | 0| 3| 0| 0| 4| | T12 0| 0 0| 3 0| 0 0| 0 4| 6 4| 3 1| 1 1 T24 | 0 | 3 | 0 | 0 | 6 | 4 | 1 PZP 12| 9 12| 4 3| 5 6| 10 8| 8 3| 16 10| 12 8 PSN 62| 15 3| 0 0| 10 9| 15 24| 1 0| 9 32| 27 18 PRS 26| 24 7| 0 17| 18 20| 13 15| 1 2| 18 9| 11 11 TYP S| RS R| R R| R R| R RS| R R| R RS| RS R SNW | 0| 0| 0| 0| | |
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MOS station-oriented products:MOS station-oriented products: Other additions Other additions
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44004 GFS MOS GUIDANCE 11/22/2005 1200 UTC DT /NOV 22/NOV 23 /NOV 24 /NOV 25 HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 TMP 58 53 49 49 50 48 46 44 44 45 47 48 51 54 56 60 62 61 59 51 47 WD 23 25 27 28 28 29 29 28 28 27 27 25 22 22 22 23 23 23 24 27 28 WS 33 31 29 25 23 22 24 25 23 18 14 12 14 19 26 29 30 29 29 28 24 WS10 36 34 31 26 25 24 26 27 25 19 15 13 15 21 28 31 32 31 31 30 26
DT /NOV 25 / HR 09 12 15 18 21 00 TMP 45 45 45 47 47 47 WD 29 29 28 30 29 34 WS 18 15 10 10 13 12 WS10 20 16 11 11 14 13
Marine MOS
Marine MOS sites
Standard MOS sites
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GFS-BASED MOS COOP MAX/MIN GUIDANCE 3/01/05 1800 UTC WED 02| THU 03| FRI 04ANNM2 26 46| 24 45| 25 46 BERM2 28 41| 25 39| 25 43 BTVM2 23 39| 21 38| 20 43 CBLM2 20 40| 18 39| 20 46 CHEM2 25 42| 21 39| 21 44 CNWM2 21 42| 21 40| 20 45 DMAM2 20 37| 18 37| 20 42 ELCM2 25 41| 21 41| 18 45 EMMM2 23 42| 20 41| 20 43 FREM2 23 46| 21 42| 23 44 FRSM2 17 27| 13 27| 13 36 GLDM2 21 37| 18 39| 18 43 HAGM2 23 43| 18 43| 19 45 KAPG 27 41| 23 37| 22 43 LRLM2 23 44| 21 42| 22 46 MECM2 24 47| 20 42| 20 45 MILM2 25 48| 22 41| 20 39 MLLM2 22 39| 18 37| 18 41 OLDM2 18 31| 13 28| 12 35 OXNM2 23 42| 22 40| 23 48 PRAM2 22 49| 22 45| 18 45
Max/Min Guidance for Co-op Sites
Glenn Dale, MD
Laurel 3 W
Beltsville, MD
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Wake, USMidway, US
Saipan, ROM
Western Pacific MOS Guidance
NSTU GFS MOS GUIDANCE 11/07/2008 1200 UTC DT /NOV 7/NOV 8 /NOV 9 /NOV 10HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12TMP 84 85 85 85 82 82 81 79 80 83 84 83 81 81 80 79 81 84 86 82 80DPT 77 77 78 77 76 77 76 75 77 78 77 77 76 77 76 75 77 78 77 77 76WDR 08 08 08 09 08 07 05 04 06 07 08 07 05 02 35 01 02 07 07 08 10 WSP 17 17 15 13 11 08 07 07 07 08 09 08 07 05 04 04 04 08 09 06 06P06 36 37 47 46 50 43 25 35 43 30 31P12 60 66 60 59 47
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Application of Linear RegressionApplication of Linear Regressionto MOS Developmentto MOS Development
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MOS LINEAR REGRESSIONJANUARY 1 - JANUARY 30, 1994 0000 UTC
KCMH
18-H NGM 850-1000 MB THICKNESS (M)
TO
DA
Y'S
MA
X (
°F)
1150 1200 1250 1300 1350
10
20
30
40
50
60
0
-10
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MOS LINEAR REGRESSIONJANUARY 1 - JANUARY 30, 1994 0000 UTC
KCMH
18-H NGM 850-1000 MB THICKNESS (M)
TO
DA
Y'S
MA
X (
°F)
1150 1200 1250 1300 1350
10
20
30
40
50
60
0
-10
RV=93.1%
MAX T = -352 + (0.3 x 850-1000 mb THK)
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REDUCTION OF VARIANCEA measure of the “goodness” of fit and
Predictor / Predictand correlation
PREDICTOR
PR
ED
ICTA
ND
MEAN
RV
RV
Variance - Standard Error=
Variance
{} UNEXPLAINED VARIANCE
*
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MOS LINEAR REGRESSIONJANUARY 1 - JANUARY 30, 1994 0000 UTC
KUIL
18-H NGM 850-1000 MB THICKNESS (M)
TO
DA
Y'S
MA
X (
°F)
1250 1300 1350 140030
40
50
60
RV=26.8%
Different site,Different relationship!
Same predictor,
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MOS LINEAR REGRESSIONDECEMBER 1 1993 - MARCH 5 1994 0000 UTC
KCMH
AVG. 12-24 H NGM ~1000 - 500 MB RH
12-2
4 H
PR
EC
IPIT
AT
ION
≥ .0
1"
10 20 30 40 50 60 70 80 90 100
0
1
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MOS LINEAR REGRESSIONDECEMBER 1 1993 - MARCH 5 1994 0000 UTC
KCMH
AVG. 12-24 H NGM ~1000 - 500 MB RH
12-2
4 H
PR
EC
IPIT
AT
ION
≥ .0
1"
10 20 30 40 50 60 70 80 90 100
0
1
RV=36.5%
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MOS LINEAR REGRESSIONDECEMBER 1 1993 - MARCH 5 1994 0000 UTC
KCMH
AVG. 12-24 H NGM ~1000 - 500 MB RH
12-2
4 H
PR
EC
IPIT
AT
ION
≥ .0
1"
10 20 30 40 50 60 70 80 90 100
0
1
RV=36.5%
RV=42.4%
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MOS LINEAR REGRESSIONDECEMBER 1 1993 - MARCH 5 1994 0000 UTC
KCMH
AVG. 12-24 H NGM ~1000 - 500 MB RH
12-2
4 H
PR
EC
IPIT
AT
ION
≥ .0
1"
10 20 30 40 50 60 70 80 90 100
0
1
RV=36.5%
RV=42.4%
RV=44.9%
POP = -0.234 + (0.007 X MRH) +
(0.478 X BINARY MRH (70%))
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EXAMPLE REGRESSION EQUATIONSY = a + bX
CMH MAX TEMPERATURE EQUATION
CMH PROBABILITY OF PRECIPITATION EQUATION
MAX T = -352 + (0.3 x 850 -1000 mb THICKNESS)
POP = -0.234 + (0.007 x MEAN RH)
+ (0.478 x BINARY MEAN RH CUTOFF AT 70%)*
*(IF MRH ≥ 70% BINARY MRH = 1; else BINARY MRH = 0)
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If the predictand is BINARY, MOS regression equations produce
estimates of event PROBABILITIES...KCMH
AVG. 12-24 H NGM ~1000 - 500 MB RH
12-2
4 H
PR
EC
IPIT
AT
ION
≥ .0
1"
10 20 30 40 50 60 70 80 90 100
0
1
3 Events
7 Events
RF= 30%P = 30%
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Making a PROBABILISTIC statement...
Quantifies the uncertainty !
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DEFINITION of PROBABILITY
(Wilks, 2006)
● The degree of belief, or quantified judgment, about the occurrence of an uncertain event.
OR
● The long-term relative frequency of an event.
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PROBABILITY FORECASTS
● POINT PROBABILITIES● AREAL PROBABILITIES● CONDITIONAL
PROBABILITIES
Assessment of probability is EXTREMELY dependent upon how predictand “event” is defined:
Some things to keep in mind
-Time period of consideration-Area of occurrence-Dependent upon another event?
MOS forecasts can be:
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3H Eta MOS thunderstorm probability forecasts valid 0000 UTC 8/27/2002 (21-24h proj)
40-km gridbox10% contour interval
20-km gridbox10% contour interval
AREAL PROBABILITIES
What if these were 6-h forecasts?
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PROPERTIES OF
MOS PROBABILITY FORECASTS
●Unbiased Average forecast probability equals long-term relative frequency of event●Reliable Conditionally or “Piecewise” unbiased over entire range of forecast probabilities●Reflect predictability of event Range narrows and approaches event RF as NWP model skill declines - extreme forecast projection - rare events
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Reliable Probabilities…
Reliabilty of 12-h PQPF > 0.25", 48h ForecastsCool Seasons 05-06 and 06-07, 335 sites
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Forecast
Rel
ativ
e Fr
eque
ncy
65
182
400
638
800
1159
1437
2108
3467
8611
6192933811
0
10000
20000
30000
40000
50000
60000
70000
Mean: 4.7%
Even for rare events
12-h Precip > 0.25”
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Designing an Designing an Operational MOS System:Operational MOS System:
Putting theory into practice… Putting theory into practice…
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DEVELOPMENTAL CONSIDERATIONS
●Selection (and QC!) of Suitable Observational Datasets ASOS? Remote sensor? Which
mesonet?
MOS in the real world
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Suitable observations?
Appropriate Sensor?Good siting?
Real or Memorex?
Photo Courtesy W. Shaffer
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MOS Snowfall Guidance
36-hr forecast 12Z 12/05/03 – 12Z 12/06/03
6 - <8
4 - < 62 - < 4
>Trace - 2
Verification
Uses Observations from Cooperative Observer Network
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DEVELOPMENTAL CONSIDERATIONS
●Selection (and QC!) of Suitable Observational Datasets ASOS? Remote sensor? Which
mesonet?
●Predictand Definition Must be precise !!
MOS in the real world
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PREDICTAND DEFINITION
Daytime Maximum Temperature “Daytime” is 0700 AM - 0700 PM LST *
Nighttime Minimum Temperature “Nighttime” is 0700 PM - 0800 AM LST * * CONUS – differs in AK
Probability of Precipitation Precipitation occurrence is accumulation of ≥ 0.01 inches of liquid-equivalent at a gauge location within a specified period
Max/Min and PoP
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PREDICTAND DEFINITION
●Determined from 13 consecutive hourly
ASOS observations, satellite augmented
●Assign value to each METAR report:
CLR; FEW; SCT; BKN; OVC 0 ; 0.15; 0.38; 0.69; 1
●Take weighted average of above
●Categorize: CL < .3125 ≤ PC ≤ .6875 < OV
GFSX 12-h Average Cloud Amount
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Creating a Gridded Predictand
××××××
××××××
××××××××××
××××××××
××××××
××××××
××××××××××
××××××××
= thunderstorm = no thunderstorm
Lightning strikes are summed over the “appropriate” time period and assigned to the center of “appropriate” grid boxes
A thunderstorm is deemed to have occurred when one or more lightning strikes are observed within a given gridbox:
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DEVELOPMENTAL CONSIDERATIONS
●Selection (and QC!) of Suitable Observational Datasets ASOS? Remote sensor? Which
mesonet?
●Predictand Definition Must be precise !!
●Choice of Predictors “Appropriate” formulation Binary or other transform?
MOS in the real world
![Page 50: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/50.jpg)
“APPROPRIATE” PREDICTORS
● DESCRIBE PHYSICAL PROCESSES ASSOCIATED
WITH OCCURRENCE OF PREDICTAND
● “MIMIC” FORECASTER THOUGHT PROCESS
(VERTICAL VELOCITY) X (MEAN RH)
PRECIPITABLE WATERVERTICAL VELOCITYMOISTURE DIVERGENCEMODEL PRECIPITATION
1000-500 MB THKTROPOPAUSE HGT
Xi.e. for POP:
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POINT BINARY PREDICTOR24-H MEAN RH CUTOFF = 70%
INTERPOLATE ; STATION RH ≥ 70% , BINARY = 1 BINARY = 0 OTHERWISE
96 86 89 94
87 73 76 90
76 60 69 92
64 54 68 93
RH ≥70% ; BINARY AT KCMH = 1
•KCMH
(71%)
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GRID BINARY PREDICTOR24 H MEAN RH CUTOFF = 70%
WHERE RH ≥ 70% ; GRIDPOINT = 1 ; INTERPOLATE
1 1 1 1
1 1 1 1
1 0 0 1
0 0 0 1
0 ≤ VALUE AT KCMH ≤ 1
•KCMH
(.21 )
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-0.2
0
0.2
0.4
0.6
0.8
1
1.2
250 255 260 265 270 275 280 285 290
850 MB TEMP
PR
OB
. o
f F
RO
ZE
N (
PO
Z)
Logit Transform Example
POZ = - 0.01 + 0.9444 (LOGIT TRAN (850 T))RV = 0.7209
1 + e- (a + bx)
________1
POZ = 12.5 - 0.0446 (850 T)
RV = 0.6136
KPIA (Peoria, IL) 0000 UTC ; 18-h projection
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DEVELOPMENTAL CONSIDERATIONS
●Terms in Equations; Selection Criteria
(cont.)
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“REAL” REGRESSION EQUATIONS
MULTIVARIATE, of form:
Y = a + a X + a X + ... + a X
large:
FORWARD SELECTION procedure determines the
2 NN10 1 2
MOS regression equations are
Where, the "a's" represent COEFFICIENTS
the "X's" represent PREDICTOR variables
The maximum number of terms, N, can be
For GFS QPF, N = 15 For GFS VIS, N = 20
The predictors and the order in which they appear.
QUITE
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FORWARD SELECTION
● METHOD OF PREDICTOR SELECTION ACCORDING TO CORRELATION WITH PREDICTAND
● “BEST” OR STATISTICALLY MOST IMPORTANT
PREDICTORS CHOSEN FIRSTFIRST predictor selected accounts for greatest reduction of variance (RV)
Subsequent predictors chosen that give greatest RV in conjunction with predictors already selected
selection when desired maximum number of terms is reached or new predictors provide less than a user-specified minimum RV
●
●
● STOP
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DEVELOPMENTAL CONSIDERATIONS
●Terms in Equations; Selection Criteria
●Dependent Data Sample Size, Stability, Representativeness AVOID OVERFIT !! Stratification - Seasons Pooling – Regions
(cont.)
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MOS LINEAR REGRESSIONOCTOBER 1 1993 - MARCH 31 1994 0000 UTC
KUIL
12-24 H NGM PRECIPITATION AMOUNT (IN.)
12-2
4 H
PR
EC
IPIT
AT
ION
≥ 1
.0"
0.00 0.25 0.50 0.75 1.00
0
1
0
RV=14.2%
Few observed cases,Limited skill!
Short sample,
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GFS MOS Cool Season PoP/QPF Regions
With GFS MOS forecast sites (1720) + PRISM
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DEVELOPMENTAL CONSIDERATIONS
●Terms in Equations; Selection Criteria
●Dependent Data Sample Size, Stability, Representativeness AVOID OVERFIT !! Stratification - Seasons Pooling – Regions
●Categorical Forecasts?
(cont.)
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0
20
40
60
80
0.01" 0.10" 0.25" 0.50" 1.00" 2.00"PRECIPITATION AMOUNT EQUAL TO OR EXCEEDING
FORECAST
THRESHOLD
MOS BEST CATEGORY SELECTION KDCA 12-Hour QPF Probabilities
48-Hour Projection valid 1200 UTC 10/31/93
PR
OB
AB
ILIT
Y (
%)
THRESHOLD
EXCEEDED?
TO MOS GUIDANCE MESSAGES
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How well do we do?How well do we do?
MOS VerificationMOS Verification
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2-M TEMPERATURE MAE at 1591 STATIONS
1
2
3
4
5
6
7
8
6 18 30 42 54 66 78 90 102 114 126 138 150 162 174 190
PROJECTION (HOURS)
MA
E (D
EG
RE
ES
F)
GFS DMO
GFS MOS
Temperature Verification - 0000 UTCGFS MOS vs. GFS DMO (4/2004 - 5/2006)
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Temperature Verification - 0000 UTC Warm Season: April – September, 2010
Mean Absolute Error - 00Z TemperaturesCONUS (300 stations)
April 1 - September 30, 2010
1.5
2
2.5
3
3.5
4
6 12 18 24 30 36 42 48 54 60 66 72 78 84
Projection (hours)
MA
E (d
eg
rees F
)
NAM GFS
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Temperature Bias - 0000 UTC Warm Season: April – September, 2010
Bias - 00Z TemperatureCONUS (300 stations)
April 1 - September 30, 2010
-2
-1
0
1
2
6 12 18 24 30 36 42 48 54 60 66 72 78 84Projection (hours)
Mea
n A
lg. E
rror
(F)
NAM GFS
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Temperature Bias - 0000 UTC 10/06; 01/07; 03/08
Bias - 00z TemperatureCONUS - 300 Stations
Oct. 1 - 31, 2006, Jan. 1 - 31 2007, Mar. 1 - 31 2008
-2
-1
0
1
2
6 12 18 24 30 36 42 48 54 60 66 72 78 84
Projection (hrs)
Mea
n A
lg. E
rror
(F)
NAM GFS
Projection (Hours)
Having a representative
verification sample is important, too!
![Page 67: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/67.jpg)
PoP Verification - 0000 UTC 10/06; 01/07; 03/08
6-h PoP Verif; Oct 2006, Jan 2007, Mar 2008
0.04
0.05
0.06
0.07
0.08
0.09
0.1
12 18 24 30 36 42 48 54 60 66 72 78 84
Forecast Projection (Hrs)
Bri
er
Sc
ore
NAM GFS
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0%
10%
20%
30%
40%
50%
97-98 98-99 99-00 00-01 01-02 02-03 03-04
F48 F96
F144 F192
GFSX 12-h Forecast Skill - 0000 UTCMax Temperatures and PoP
0%
10%
20%
30%
40%
50%
60%
70%
97-98 98-99 99-00 00-01 01-02 02-03 03-04
Day 2 Day 4
Day 6 Day 8
% Improvement over Climate Cool Season 1997 - 2003
Max T PoP
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45-yr Max Temperature VerificationGuidance / WFO; Cool Season 1966 - 2010
NAM
LFMNGM
EDASAVN
Day/NitePerf. Pg. / PE MOS
24-h
48-h
20101970 1980 1990 2000GFS
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Dealing withDealing withNWP model changesNWP model changes
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1. Improved model realism better model = better statistical system
2. Coarse, consistent archive grid smoothing of fine-scale detail constant mesh length for grid-sensitive calculations
3. Enlarged geographic regions larger data pools help to stabilize equations
4. Use of “robust” predictor variables fewer boundary layer variables variables likely immune to known model changes; (e.g. combinations of state variables only)
Mitigating the effects on development
To help reduce the impact of model changes and small sample size, we rely upon... MODEL
S
NCEP
OBS
Mesonets
MOS
![Page 72: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/72.jpg)
• Parallel evaluation Run MOS…new vs. old NWP model Assess impacts on MOS skill
Responding to NWP Model Changes
![Page 73: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/73.jpg)
6h PoP Verification335 Stations, 00Z runs, March-April 2006
0.06
0.07
0.08
0.09
0.10
12 18 24 30 36 42 48 54 60 66 72 78 84
PROJECTION (h)
BR
IER
SC
OR
E ETAMOS
ETA-NMM
GFSMOS
Responding to NWP Model Changes
Eta MOS PoP: Eta vs. NMM output
![Page 74: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/74.jpg)
• Parallel evaluation Run MOS…new vs. old NWP model Assess impacts on MOS skill
• Do nothing? OK if impacts are minimal But, often they aren’t! (GFS wind / temps)
Responding to NWP Model Changes
![Page 75: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/75.jpg)
2009 - 2011 GFS MOS Wind Bias
2009
2010May-Jul
2011
Jan-Apr
2011
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GFSMOS”fix”
GFSMOSold
Bia
s (k
no
ts)
Forecast Projection
0
![Page 77: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/77.jpg)
• Parallel evaluation Run MOS…new vs. old NWP model Assess impacts on MOS skill
• Do nothing? OK if impacts are minimal But, often they aren’t! (GFS wind / temps)
• OK, now what? • Model changes may be recent
i.e. limited sample available from new model version• Error characteristics significantly different• Undesirable effects on MOS performance
Responding to NWP Model Changes
![Page 78: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/78.jpg)
• Bias Correction for MOS?
Responding to NWP Model Changes
![Page 79: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/79.jpg)
Daily Bias Correction based on past N (7, 10, 20 or 30)- day forecast errors
Bias correction: F' = F (t) – Bias
N
1t
O(t)][F(t)N1
Bias
Daily biases can be treated equally or weighted to favor most recent days, etc.
Today
P1
Future
P2
Past
Past N days
t = N 1
F = Forecasts ; O = Observations N = Days in training sample
(typically, N = 7, 10, 20, or 30)
![Page 80: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/80.jpg)
Raw / Corrected GFS MOS Wind MAE
KABQ – 00UTC, 96-h Projection
![Page 81: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/81.jpg)
Raw / Corrected GFS MOS Temp MAE
Southwest U.S. – 00UTC, 48-h Projection
![Page 82: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/82.jpg)
• Bias Correction for MOS? Apply to Temps? Winds? Run continuously in background? Satisfactory in rapidly-varying conditions?
• Redevelop? Short sample from new model or “mixed”? Full System, selected elements? Biggest impacts on single-station equations (Temp, Wind)
Responding to NWP Model Changes
![Page 83: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/83.jpg)
MOS DEWPOINT BIASOVERALL
-0.500.000.501.001.502.002.503.003.50
6 12 18 24 30 36 42 48 54 60 66 72 78 84
PROJECTION (h)
BIA
S (
deg
F)
NMM
ETAonNMM
ETA
0.00 0.00
350 Stations; CONUS + AK
NAM
NAM
NAM / Eta MOS Dewpoint Comparison Jul 15-31, 2006 and May 1-15, 2007
Using even just a little data from the new NWP model
version can be helpful!
![Page 84: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/84.jpg)
KORD ETA MOS GUIDANCE 9/27/2007 1200 UTCDT /SEPT 27/SEPT 28 /SEPT 29 /SEPT 30HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12N/X 50 72 50 78 57TMP 67 69 64 60 56 53 52 64 70 70 65 58 55 53 53 65 74 77 71 61 58DPT 54 52 51 50 48 46 46 48 45 44 44 47 47 47 48 50 49 49 51 55 53CLD OV BK SC SC CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL FWWDR 23 27 30 30 29 28 30 32 33 34 06 11 16 17 17 18 18 19 17 19 20WSP 09 10 08 06 05 05 04 07 08 07 06 02 02 02 04 08 09 10 08 08 08P06 19 3 6 1 0 0 1 3 3 8 10P12 6 1 1 6 12Q06 0 0 0 0 0 0 0 0 0 0 0Q12 0 0 0 0 0T06 1/ 0 9/ 7 0/ 0 0/ 7 0/ 0 0/ 1 0/ 0 0/ 8 2/ 0999/99T12 9/ 7 0/ 7 0/ 1 0/ 8 999/99SNW 0 0 0CIG 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8VIS 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7OBV N N N N N N N N N N N N N N N N N N N N N
““Classic” Eta MOSClassic” Eta MOS Hybrid “NAM MOS”Hybrid “NAM MOS”KORD NMM MOS GUIDANCE 9/27/2007 1200 UTCDT /SEPT 27/SEPT 28 /SEPT 29 /SEPT
30HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06
12N/X 51 74 49 76
58TMP 68 65 62 60 57 52 52 63 71 73 69 59 53 51 50 63 72 76 73 60
58DPT 54 53 53 51 49 48 48 48 47 45 45 47 47 47 48 50 50 50 51 52
55CLD OV OV SC FW CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL FW
FWWDR 23 27 30 30 29 28 30 32 33 34 04 10 16 16 17 18 18 19 17 19
20WSP 08 10 08 06 05 05 05 07 08 07 05 03 02 03 04 08 09 10 08 08
08P06 21 3 2 1 1 0 0 3 5 10
12P12 3 1 0 7
16Q06 0 0 0 0 0 0 0 0 0 0
0Q12 0 0 0 0
0T06 1/ 0 6/ 1 0/ 0 0/ 3 0/ 0 0/ 0 0/ 0 0/ 1 4/
0999/99T12 6/ 1 0/ 3 0/ 0 0/ 1 999/99SNW 0 0
0CIG 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
8VIS 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7OBV N N N N N N N N N N N N N N N N N N N N
N
• All Eta model inputAll Eta model input• All elements used eta-basedAll elements used eta-based equationsequations
• All NMM model inputAll NMM model input• Redeveloped elements use new Redeveloped elements use new NMM-based equationsNMM-based equations• Other elements use older Eta-Other elements use older Eta- based equations applied to based equations applied to NMMNMM
Eta MOS Replacement
December 9, 2008
![Page 85: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/85.jpg)
• Bias Correction for MOS? Apply to Temps? Winds? Run continuously in background? Satisfactory in rapidly-varying conditions?
• Redevelop? Short sample from new model or “mixed”? Full System, selected elements? Biggest impacts on single-station equations (Temp, Wind)
• Reforecasts? 1-2 year sample probably sufficient for T, Wind Rare elements need longer or “mixed” sample? Requires additional supercomputer resources
Responding to NWP Model Changes
![Page 86: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/86.jpg)
MOS: Today and BeyondMOS: Today and Beyond
![Page 87: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/87.jpg)
●GFS / GFSX MOS: Update GFSX Sky Cover equations (Completes 1200 UTC text message) Expand GFSX to Day 10 for some elements Update climate normals (1981-2010 NCDC) Bias-corrected T, Td, Max/Min, windspeed
●NAM MOS (Eta MOS replacement): Add precipitation type suite (TYP, POZ, POS) Add 0600 and 1800 UTC cycles? Update remaining eta-based elements Update temperature suite with NMM-b data
The Future of MOS“Traditional” Station-oriented Products
![Page 88: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/88.jpg)
The Future of MOS
●Western Pacific MOS: Add new elements (Sky Cover, CIG)
●General: Evaluate impacts of NWP model
changes Periodic addition of new CONUS sites Gradual phaseout of station-oriented
graphics
“Traditional” Station-oriented Products (contd.)
![Page 89: Model Output Statistics (MOS) - Objective Interpretation of NWP Model Output](https://reader036.vdocuments.mx/reader036/viewer/2022070407/5681438d550346895db00bae/html5/thumbnails/89.jpg)
GFS MOS 24-hr Conditional Probability of Precipitation ≥
0.25”
http://www.nws.noaa.gov/mdl/synop
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End of an era?End of an era?KDCA GFS MOS GUIDANCE 11/27/2006 1200 UTCDT /NOV 27/NOV 28 /NOV 29 /NOV 30 HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12 N/X 44 66 47 63 51 TMP 61 60 54 49 47 45 45 54 62 63 57 51 49 48 49 54 61 61 57 55 53 DPT 39 39 41 44 43 42 42 44 43 44 45 45 46 46 47 49 50 51 52 52 52CLD OV BK BK FW CL CL SC SC SC SC BK BK BK OV OV OV OV OV OV OV OVWDR 22 22 23 23 22 24 18 17 17 15 15 16 17 17 15 16 19 19 20 20 21 WSP 03 04 03 02 01 01 01 02 03 03 03 03 01 01 02 02 04 04 04 05 04 P06 0 0 1 1 0 1 4 3 5 8 12 P12 2 4 7 8 16 Q06 0 0 0 0 0 0 0 0 0 0 0 Q12 0 0 0 0 0 T06 0/24 0/ 1 0/ 0 0/ 0 0/16 0/ 0 0/ 0 0/ 0 0/20 0/ 0 T12 0/24 0/ 0 0/16 0/ 0 0/20POZ 0 0 1 1 1 1 0 0 0 1 2 1 2 1 0 0 1 1 2 2 0 POS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 TYP R R R R R R R R R R R R R R R R R R R R R SNW 0 0 0 CIG 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 3 4 4 1 2 1 VIS 7 7 7 7 7 7 7 7 7 7 7 7 6 3 1 5 7 7 6 5 1 OBV N N N N N N N N N N N N BR FG FG BR N N HZ BR FG
WANTED! High-resolution, gridded guidance for NDFD
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Gridded MOSGFS-based CONUS-wide @ 5km
http://www.weather.gov/mdl/synop/gridded/sectors/index.php
Max / Min
Temp / Td
Winds
RH
Tstm
PoP
Gusts
QPF
Snowfall
Sky Cover
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Wait…Stop the Presses!!2.5-km CONUS GMOS - “live” on Feb. 27, 2012
Max Temperature15 UTC 02/13/12
Max Temperature15 UTC 02/13/12
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Alaska Gridded MOSAK GMOS: GFS-based, 3-km grid
All elements complete January, 2010
3-km grid
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Hawaii Gridded MOSHawaii GMOS: GFS-based, 2.5-km grid
ImplementedNovember, 2010
Max / Min
Temp / Td
Winds
RH
PoP
Gusts
2.5-km grid
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The Future of MOS“Enhanced-Resolution” Gridded MOS Systems
●“MOS at any point” (e.g. GMOS) Support NWS digital forecast database 2.5 km - 5 km resolution Equations valid away from observing sites Emphasis on high-density surface networks Use high-resolution geophysical data
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• METAR
• Buoys/C-MAN
• Mesonet (RAWS/SNOTEL/Other)
• NOAA cooperative observer network
• RFC-supplied sites
Surface observation systems used in GMOS
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Approx. 1990 sites
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Approx. 11,000 sites!
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Gridded MOS – Central CA
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Geophysical Datasets
5-km Terrain 5-km Land Cover
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Gridded MOS Concept - Step 1“Blending” first guess and high-density station forecasts
First guess field from Generalized Operator Equation
or other source
First guess + guidanceat all available sites
Day 1 Max Temp 00 UTC 03/03/05
Day 1 Max Temp00 UTC 03/03/05
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Developing the “First Guess” Field
• Generalized operator equation (GOE) Pool observations regionally Develop equations for all elements, projections Apply equations at all grid points within region
• Use average field value at all stations
• Use other user-specified constant
• Use NWP model forecast
Some options
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Gridded MOS Concept - Step 2
First guess + station forecasts + terrain
First guess + guidanceat all available sites
Add further detail to analysis with high-resolution geophysical data and “smart” interpolation
Day 1 Max Temp00 UTC 03/03/05
Day 1 Max Temp00 UTC 03/03/05
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GMOS Analysis
• Method of successive corrections (“BCDG”) Bergthorssen and Doos (1955); Cressman (1959); Glahn (1985, LAMP vertical adjustment)
• Elevation (“lapse rate”) adjustment Inferred from forecasts at different elevations Calculations done “on the fly” from station data Can vary by specific element, synoptic situation
• Land/water gridpoints treated differently
Basic Methodology (Glahn, et al. 2009, WaF)
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GMOS Analysis
• Special, terrain-following smoother
• ROI can be adjusted to account for variations in density of observed data
• Nudging can be performed to help preserve nearby station data
• Parameters can be adjusted individually for each weather element
Other Features
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GMOS Analysis
• Not optimized for all weather elements and synoptic situations Need situation specific, dynamic models?
• May not capture localized variations in vertical structure Vertical adjustment uses several station “neighbors”
• May have problems in data-sparse regions over flat terrain Defaults to pure Cressman analysis with small ROI Can result in some “bulls-eye” features
Some Issues
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NDGD vs. NDFD
NDFD Max TNDGD Max T
Which is “better”?
Max Temperature00 UTC 03/11/06
Max Temperature00 UTC 03/11/06
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NDGD vs. NDFD
NDFD RHNDGD RH
Which is “better”?
Relative Humidity21 UTC 03/10/06
Relative Humidity21 UTC 03/10/06
Forecasters adding detail: Which is “better”? More accurate?
Fewer obs available to analysis = less detail in GMOS
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AK GMOS Temps & Observing Sites
3-km grid
Even fewer obs available – Yikes!
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The Future of MOS“Enhanced-Resolution”, Gridded MOS Systems
●“MOS at any point” (e.g. GMOS) Support NWS digital forecast database 2.5 km - 5 km resolution Equations valid away from observing sites Emphasis on high-density surface networks Use high-resolution geophysical data
●“True” gridded MOS Observations and forecasts valid on fine grid Use remotely-sensed predictand data e.g. WSR-88D QPE, Satellite clouds, NLDN
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Remotely-sensed precipitation data
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Gridded MOS: Where do we go from here?
• Additions to current CONUS GMOS system Present weather grid NAM-based companion system (short-range) Probabilistic and/or ensemble-based products
The Future of MOS
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Sample Forecast as Quantile Function (CDF)
25
30
35
40
45
50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
Te
mp
era
ture
(72-h Temp KBWI 12/14/2004)
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Ensemble MOS [5%, 95%] Quantile Temps.
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Gridded MOS: Where do we go from here?
• Additions to current CONUS GMOS system “Predominant” weather grid NAM-based companion system (short-range) Probabilistic and/or ensemble-based products
• Increase CONUS resolution from 5-km to 2.5-km NCEP jobstream Feb. 2012; awaits comms upgrade
• Update land / water mask based on WFO input
• Improve GMOS interpolation procedures
The Future of MOS
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• Increase utilization of mesonet data Investigate MADIS archive (NCO/TOC/ESRL) ~20,000 additional sites?
• Incorporate remotely-sensed data where possible SCP augmented clouds (already in use) WSR-88D QPF: March 13, 2012 NSSL MRMS (Multi-radar, Multi-sensor) dataset?
• Expand GMOS for AK; add other OCONUS areas AK: Increase grid extent; improve marine winds Hawaii: add QPF, Sky Cover Puerto Rico
Gridded MOS: Where do we go from here?
The Future of MOS
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REFERENCES…the “classics”
Wilks, D.: Statistical Methods in the Atmospheric Sciences, 2nd Ed., Chap. 6,p. 179 - 254.
Draper, N.R., and H. Smith: Applied Regression Analysis, Chap. 6, p. 307 - 308.
Glahn, H.R., and D. Lowry, 1972: The use of model output statistics in objective weather forecasting, JAM, 11, 1203 - 1211.
Carter, G.M., et al., 1989: Statistical forecasts based on the NMC’s NWP System, Wea. & Forecasting, 4, 401 - 412.
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REFERENCES (GMOS)
Glahn, H.R., et al., 2009: The Gridding of MOS., Wea. & Forecasting, 24, 520 – 529.