MOS

• What does acronym stand for ?– MODEL OUTPUT STATISTICS

• What is the difference between the GFS and GFS MOS ?

GFS MOS• KUNV GFS MOS GUIDANCE 2/26/2008 1200 UTC• DT /FEB 26/FEB 27 /FEB 28 /FEB 29• HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12• N/X 25 27 15 24 16• TMP 36 35 34 33 32 29 26 25 26 25 21 19 18 17 17 19 23 24 21 19 17• DPT 31 31 29 29 26 22 18 16 13 11 9 7 6 6 5 4 4 4 3 8 10• CLD OV OV OV OV OV OV OV OV OV OV OV OV OV SC BK BK BK SC CL SC OV• WDR 05 36 30 29 29 29 29 29 29 29 29 29 28 28 28 28 28 28 28 23 15• WSP 03 04 06 11 14 15 13 13 14 14 12 11 11 10 09 13 14 13 06 02 03• P06 100 51 35 24 26 11 10 2 0 0 0• P12 65 41 11 6 1• Q06 3 1 0 0 0 0 0 0 0 0 0• Q12 1 1 0 0 0• T06 1/ 0 2/ 1 0/ 1 0/ 0 0/ 0 0/ 0 0/ 0 0/ 0 0/ 3 0/ 0• T12 3/ 1 0/ 1 0/ 0 0/ 0 0/ 3• POZ 7 0 2 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1• POS 41 33 55 65 96100100100100100100100100100 99100100100100100 99• TYP S R S S S S S S S S S S S S S S S S S S S• SNW 4 1 0• CIG 3 3 3 4 4 6 6 5 6 6 6 6 6 6 6 6 6 6 8 8 7• VIS 3 3 4 3 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7• OBV BR BR BR BR N N N N N N N N N N N N N N N N N

GFS MODEL• Station: UNV Lat: 40.85 Lon: -77.83 Elev: 378 Closest grid pt: 29.6

km.• Initialization Time: 08-02-26 1200 UTC• HOUR VALID PMSL THCK 6HRPCN 2m_TMP 850TMP 850REL 700REL 10m_WD 850WND• ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------• 000 26/12 1006 540 29 -1 91 98 14/003 20/026• 006 26/18 997 543 0.38 33 1 99 100 12/005 20/037• 012 27/00 993 540 0.13 34 0 97 79 30/005 26/018• 018 27/06 997 530 0.02 28 -8 100 92 31/014 34/028• 024 27/12 1002 522 0.01 20 -10 89 91 31/014 33/034• 030 27/18 1006 517 0.01 23 -13 90 99 30/014 31/027• 036 28/00 1010 511 0.01 16 -16 89 75 31/013 31/032• 042 28/06 1014 507 0.01 12 -18 91 44 30/011 31/031• 048 28/12 1018 504 0.01 11 -19 98 44 29/010 30/032• 054 28/18 1022 506 0.01 19 -17 98 17 29/013 30/025• 060 29/00 1027 513 0.02 18 -16 98 11 29/008 30/027• 066 29/06 1031 519 0.00 12 -14 45 9 26/003 28/019• 072 29/12 1030 524 0.00 13 -9 52 90 16/007 24/023

MOS

• AVN = Dynamical Model

–Seven fundamental equations !

• Seven Fundamental Equations:– Temperature equation (dT/dt=)

• ADVECTION/DIABATIC/ADIABATIC

– Three equations of motion (dV/dt=)• HORIZONTAL MOTIONS: PGF/COR/FR• VERTICAL MOTIONS

– Hydrostatic Equation (dp/dz= -g)– Continuity equation (du/dx + dv/dy + dw/dz=0)– Water vapor equation (dq/dt=)

MOS

• AVN = Dynamical Model

–Seven fundamental equations !

• AVN MOS = Statistical Model

–No seven fundamental equations !

–Equations are statistical, not dynamical !

MOS

• Why even have MOS ?– Predicts unique parameters

• Visibility• Cloud ceilings

– Predicts better than dynamic models (averaged over all cases)

• Surface weather-> temp., dew pt., winds

MOS

• How does MOS make its predictions?– Uses technique of association– Objectively relates (associates) model output

to observed weather using statistical technique of linear regression

Glahn and Lowry (1972)

MOS

• Two steps to MOS ……….– Equation Development

– Equation Application

MOS

• Equation Development ->>– PREDICTOR

• Variable that is doing the PREDICTING

– PREDICTAND• Variable that is getting PREDICTED

• (Multiple) Linear Regression– Relates PREDICTOR to PREDICTAND

MOS: Equation Development

Y1 = mx1 + b1

850mb Model Temp VS. Observed Surface Temperature

-20

-15

-10

-5

0

5

10

15

20

25

30

-10 0 10 20 30 40

Observed Surface temperature (C)"THE PREDICTAND"

Model Predicted 850mb temp (C)

(30 hr. fcst, valid 18z):"THE PREDICTOR"

MOS: Temperature

• Predictors– Model low level temps (i.e. 850mb/2m)

– Model relative humidity• Accounts for clouds

– Model wind direction /speed– Climatology– Previous day’s min (max)

• Single site development

Glahn and Lowry (1972)

MOS: Precipitation

• Predictors– Model mean relative humidity (i.e. 1000-

500mb layer average)

– Precipitation output of model– Model vertical velocity (i.e. 700, 500, 850mb)

– Model low level wind direction (i.e. 10m)

• Regional development

MOS: Wind

• Predictors– Low-level wind direction/speed output of

model (i.e. 10m, 850mb wind)

• Single site development

MOS Characteristics

• Requires large sample size–Several years of model output

–Increases statistical significance

MOS

• Partially removes systematic model errors (i.e. biases)– If model has a cool bias at 850mb, MOS

will account for/remove model bias

• Works best when models are not tweaked (i.e. no change to physics)

MOS: Equation Application

NAM

NAM

NAM

GFS MOS• KUNV GFS MOS GUIDANCE 2/26/2008 1200 UTC• DT /FEB 26/FEB 27 /FEB 28 /FEB 29• HR 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12• N/X 25 27 15 24 16• TMP 36 35 34 33 32 29 26 25 26 25 21 19 18 17 17 19 23 24 21 19 17• DPT 31 31 29 29 26 22 18 16 13 11 9 7 6 6 5 4 4 4 3 8 10• CLD OV OV OV OV OV OV OV OV OV OV OV OV OV SC BK BK BK SC CL SC OV• WDR 05 36 30 29 29 29 29 29 29 29 29 29 28 28 28 28 28 28 28 23 15• WSP 03 04 06 11 14 15 13 13 14 14 12 11 11 10 09 13 14 13 06 02 03• P06 100 51 35 24 26 11 10 2 0 0 0• P12 65 41 11 6 1• Q06 3 1 0 0 0 0 0 0 0 0 0• Q12 1 1 0 0 0• T06 1/ 0 2/ 1 0/ 1 0/ 0 0/ 0 0/ 0 0/ 0 0/ 0 0/ 3 0/ 0• T12 3/ 1 0/ 1 0/ 0 0/ 0 0/ 3• POZ 7 0 2 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1• POS 41 33 55 65 96100100100100100100100100100 99100100100100100 99• TYP S R S S S S S S S S S S S S S S S S S S S• SNW 4 1 0• CIG 3 3 3 4 4 6 6 5 6 6 6 6 6 6 6 6 6 6 8 8 7• VIS 3 3 4 3 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7• OBV BR BR BR BR N N N N N N N N N N N N N N N N N

GFS MODEL• Station: UNV Lat: 40.85 Lon: -77.83 Elev: 378 Closest grid pt: 29.6

km.• Initialization Time: 08-02-26 1200 UTC• HOUR VALID PMSL THCK 6HRPCN 2m_TMP 850TMP 850REL 700REL 10m_WD 850WND• ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------• 000 26/12 1006 540 29 -1 91 98 14/003 20/026• 006 26/18 997 543 0.38 33 1 99 100 12/005 20/037• 012 27/00 993 540 0.13 34 0 97 79 30/005 26/018• 018 27/06 997 530 0.02 28 -8 100 92 31/014 34/028• 024 27/12 1002 522 0.01 20 -10 89 91 31/014 33/034• 030 27/18 1006 517 0.01 23 -13 90 99 30/014 31/027• 036 28/00 1010 511 0.01 16 -16 89 75 31/013 31/032• 042 28/06 1014 507 0.01 12 -18 91 44 30/011 31/031• 048 28/12 1018 504 0.01 11 -19 98 44 29/010 30/032• 054 28/18 1022 506 0.01 19 -17 98 17 29/013 30/025• 060 29/00 1027 513 0.02 18 -16 98 11 29/008 30/027• 066 29/06 1031 519 0.00 12 -14 45 9 26/003 28/019• 072 29/12 1030 524 0.00 13 -9 52 90 16/007 24/023

MOS ERRORS: Who’s at fault?

• Dynamic model (gfs model)– Garbage In = Garbage Out

• Statistical model (gfs mos)– Imperfect statistical relationships

(i.e. lines of best fit are not line of perfect fit!)

• Forecasting MOS error (utilizing association method)

HOW TO BEAT MOS

• Know how it works

• MOS tends to do well:– Weather near climatology

(equations lean toward modal case)

• MOS tends to do poor:– Weather departs from climatology

( the “outliers” of the scatter plot)– Bad model data used as input (GI=GO)

HOW TO BEAT MOS

• Which city is more likely to have the bigger bust in the following situation?– Clear skies, light winds, snow cover

• ST. LOUIS vs. INTERNATIONAL FALLS