# Presentation: 731496

## Model Output Statistics (MOS) - Objective Interpretation of NWPModel Output

**University of Maryland - March 10, 2005**

**Mark S. Antolik**
**Meteorological Development Laboratory**
**Statistical Modeling Branch**
**NOAA/National Weather Service**
**Silver Spring, MD**

- (301) 713-0023  ext. 110
- email: mark.antolik@noaa.gov

## OUTLINE

**1.  Why objective statistical guidance?**
**2.  What is MOS?**
**       ****Definition and characteristics**
**       ****The “traditional” MOS product suite**
**            ****(NGM, eta, GFS) **
**       ****Recent additions to the lineup**
**3.  Simple regression examples / REEP**
**4.  Development strategy -    **
**             ****MOS in the “real world”**
**5.  Verification **
**6.  Where we’re going - The future of MOS**

## 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**

## A SIMPLE STATISTICAL MODEL

- Relative Frequency of Precipitation as a Function of12-24 Hour NGM Model-Forecast Mean RH

**NGM MEAN RELATIVE HUMIDITY (%)**

**OBSERVED REL. FREQUENCY**

**0**

**10**

**20**

**30**

**40**

**50**

**60**

**70**

**80**

**90**

**100**

**0.0**

**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%**

## MOS Max Temp  vs.  Direct Model Output

##  What is MOS?

## MODEL OUTPUT STATISTICS (MOS)

** ****Numerical Weather Prediction (NWP) Model**
**       ****Forecasts               **
**2.  Prior Surface Weather Observations**
**3.  Geoclimatic Information**
**Current Statistical Method: **
**              ****MULTIPLE LINEAR REGRESSION**
**              ****(Forward Selection)**

**Relates observed weather elements ****(PREDICTANDS)**** to appropriate variables ****(PREDICTORS)**** via a**
**statistical approach.**
**Predictors are obtained from:**

## 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**
**      **

## 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**

## 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 obs **

##   RAPIDLY EVOLVING NWP MODELS AND

**  ****RAPIDLY EVOLVING NWP MODELS AND**
**  ****OBSERVATION PLATFORMS**

**  ****RAPIDLY EVOLVING NWP MODELS AND**
**  ****OBSERVATION PLATFORMS**

**2.  DIFFICULT COLLECTION OF APPROPRIATE**
**     ****PREDICTAND DATA**

**2.  DIFFICULT COLLECTION OF APPROPRIATE**
**     ****PREDICTAND DATA**

**1.  SHORT, UNREPRESENTATIVE**
**     ****DATA SAMPLES**

**1.  SHORT, UNREPRESENTATIVE**
**     ****DATA SAMPLES**

- New observing systems:  (ASOS, WSR-88D)
-                                          (Co-Op, Mesonets)
- “Old” predictands:            The elements don’t change!

**Make for:**

## “Traditional” MOStext products

## GFS MOS GUIDANCE MESSAGEFOUS21-26   (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**

## Eta MOS GUIDANCE MESSAGEFOUS44-49   (MET)

**KTHV   ETA 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                    27          52          41          53    27 **
** ****TMP  47 46 36 34 32 30 31 42 50 51 44 44 44 46 45 50 51 48 41 35 33 **
** ****DPT  27 27 29 28 27 27 28 31 32 33 35 36 37 40 40 39 35 31 28 24 25 **
** ****CLD  BK BK OV OV OV BK BK OV OV OV OV OV OV OV OV BK BK CL CL CL SC **
** ****WDR  31 32 00 00 00 00 00 08 16 14 00 14 15 17 21 25 27 28 27 27 25 **
** ****WSP  05 02 00 00 00 00 00 02 03 04 00 04 08 10 10 17 22 18 08 06 03 **
** ****P06         1     2     5     4     3    46    91    51     0  0  0 **
** ****P12                     5           4          91          51     0 **
** ****Q06         0     0     0     0     0     1     3     1     0  0  0 **
** ****Q12                     0           0           4           1     0 **
** ****T06      0/ 0  0/ 0  0/ 1  0/ 0  0/ 0  0/ 0 11/ 2 11/ 5  8/ 9999/99 **
** ****T12            1/ 0        0/ 1        0/ 0       18/ 5   999/99    **
** ****SNW                     0                       0                 0 **
** ****CIG   8  8  7  8  7  8  8  7  8  8  7  7  4  4  3  7  6  8  8  8  8 **

## GFS / Eta MOS  vs.  NGM MOS

**MORE STATIONS:**
**   ****Now at approx. 1550 forecast sites **
**   ****(CONUS, HI, PR)**
**MORE FORECASTS:**
**   ****Available at projections of 12- 84 hours**
**   ****GFS available for 0600 and 1800 UTC cycles**
**BETTER RESOLUTION:**
**   ****GFS predictors on 95.25 km grid;  Eta on 32 km**
**   ****Predictor fields available at 3-h timesteps**
**   ****Predictors available beyond 48-h projection **
** ***** No extrapolative forecasts**** **
**DEPENDENT SAMPLE NOT “IDEAL”:**
**   ****Fewer seasons**
**   ****Non-static underlying NWP model**

## Slide 16

## Slide 17

## GFS / Eta MOS  vs.  NGM MOS

**MORE STATIONS:**
**   ****Now at approx. 1550 forecast sites **
**   ****(CONUS, HI, PR)**
**MORE FORECASTS:**
**   ****Available at projections of 12- 84 hours**
**   ****GFS available for 0600 and 1800 UTC cycles**
**BETTER RESOLUTION:**
**   ****GFS predictors on 95.25 km grid;  Eta on 32 km**
**   ****Predictor fields available at 3-h timesteps**
**   ****Predictors available beyond 48-h projection **
** ***** No extrapolative forecasts**** **
**DEPENDENT SAMPLE NOT “IDEAL”:**
**   ****Fewer seasons**
**   ****Non-static underlying NWP model**

## GFSX MOS GUIDANCE MESSAGEFEUS21-26   (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|       |       |**

## Recent additions to the MOS product lineup

##  44013  GFS MOS GUIDANCE    6/01/2004  1200 UTC                      
 DT  /JUN  1/JUN  2                 /JUN  3                 /JUN  4  
 HR   18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 
 WD   05 07 09 12 12 15 16 18 18 19 23 27 29 32 33 35 36 28 25 28 29 
 WS   14 12 10 07 06 06 07 08 09 09 07 07 06 06 07 07 07 07 07 10 11 
 WS10 15 13 11 08 07 06 07 09 10 10 07 08 07 06 07 08 08 07 07 10 12 

 DT  /JUN  4         /                                               
 HR   09 12 15 18 21 00                                              
 WD   29 29 30 14 14 17                                              
 WS   12 09 03 03 05 07                                              
 WS10 13 10 03 03 06 08 

** ****DT  /JUN  1/JUN  2                 /JUN  3                 /JUN  4  **
** ****HR   18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 **
** ****WD   05 07 09 12 12 15 16 18 18 19 23 27 29 32 33 35 36 28 25 28 29 **
** ****WS   14 12 10 07 06 06 07 08 09 09 07 07 06 06 07 07 07 07 07 10 11 **
** ****WS10 15 13 11 08 07 06 07 09 10 10 07 08 07 06 07 08 08 07 07 10 12 **
**                                                                     **
** ****DT  /JUN  4         /                                               **
** ****HR   09 12 15 18 21 00                                              **
** ****WD   29 29 30 14 14 17                                              **
** ****WS   12 09 03 03 05 07                                              **
** ****WS10 13 10 03 03 06 08 **

**Marine MOS**

**Marine MOS sites**

**Standard MOS sites**

## MOS Snowfall Guidance

- 36-hr forecast
- 12Z 12/05/03 – 12Z 12/06/03

- 6 - <8

- 4 - < 6

- 2 - < 4

- >Trace - 2

- Verification

**Uses Observations from Cooperative Observer Network**

## Max/Min Guidance for Co-op Sites

**         ****WED 02| THU 03| FRI 04**
**ANNM2    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**

## Application of Linear Regressionto MOS Development

## MOS LINEAR REGRESSION

- JANUARY 1 - JANUARY 30,  1994   0000 UTC**KCMH**

**18-H NGM 850-1000 MB THICKNESS (M)**

**TODAY'S MAX (°F)**

**1150**

**1200**

**1250**

**1300**

**1350**

**10**

**20**

**30**

**40**

**50**

**60**

**0**

**-10**

## MOS LINEAR REGRESSION

- JANUARY 1 - JANUARY 30,  1994   0000 UTC**KCMH**

**18-H NGM 850-1000 MB THICKNESS (M)**

**TODAY'S MAX (°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)**

## REDUCTION OF VARIANCE

- A measure of the “goodness” of fit andPredictor / Predictand correlation

**PREDICTOR**

**PREDICTAND**

**MEAN**

**RV**

**RV**

**Variance  -  Standard Error**

**=**

**Variance**

- {

- }

**UNEXPLAINED VARIANCE**

*****

## MOS LINEAR REGRESSION

- JANUARY 1 - JANUARY 30,  1994   0000 UTC**KUIL**

**18-H NGM 850-1000 MB THICKNESS (M)**

**TODAY'S MAX (°F)**

**1250**

**1300**

**1350**

**1400**

**30**

**40**

**50**

**60**

**RV=26.8%**

## MOS LINEAR REGRESSION

- DECEMBER 1 1993 - MARCH 5 1994   0000 UTC**KCMH**

**AVG. 12-24 H NGM ~1000 - 500 MB RH**

**12-24 H PRECIPITATION ≥ .01"**

**10**

**20**

**30**

**40**

**50**

**60**

**70**

**80**

**90**

**100**

**0**

**1**

## MOS LINEAR REGRESSION

- DECEMBER 1 1993 - MARCH 5 1994   0000 UTC**KCMH**

**AVG. 12-24 H NGM ~1000 - 500 MB RH**

**12-24 H PRECIPITATION ≥ .01"**

**10**

**20**

**30**

**40**

**50**

**60**

**70**

**80**

**90**

**100**

**0**

**1**

- RV=36.5%

## MOS LINEAR REGRESSION

- DECEMBER 1 1993 - MARCH 5 1994   0000 UTC**KCMH**

**AVG. 12-24 H NGM ~1000 - 500 MB RH**

**12-24 H PRECIPITATION ≥ .01"**

**10**

**20**

**30**

**40**

**50**

**60**

**70**

**80**

**90**

**100**

**0**

**1**

- RV=36.5%

- RV=42.4%

## MOS LINEAR REGRESSION

- DECEMBER 1 1993 - MARCH 5 1994   0000 UTC**KCMH**

**AVG. 12-24 H NGM ~1000 - 500 MB RH**

**12-24 H PRECIPITATION ≥ .01"**

**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%))**

## EXAMPLE REGRESSION EQUATIONS

**Y = 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)

## If the predictand is BINARY, MOS regression equations produceestimates of event PROBABILITIES...

**KCMH**

**AVG. 12-24 H NGM ~1000 - 500 MB RH**

**12-24 H PRECIPITATION ≥ .01"**

**10**

**20**

**30**

**40**

**50**

**60**

**70**

**80**

**90**

**100**

**0**

**1**

- 3 Events

- 7 Events

**RF= 30%**

**P = 30%**

## Making a PROBABILISTIC statement...

**Quantifies the uncertainty !**

## DEFINITION of PROBABILITY

- (Wilks, 1994)

-    LONG TERM RELATIVE FREQUENCY OF AN EVENT
-    DEGREE OF BELIEF OR QUANTIFIED JUDGMENT
-      ABOUT THE OCCURRENCE OF AN UNCERTAIN EVENT

-   POINT PROBABILITY
-   AREAL PROBABILITY
-   CONDITIONAL PROBABILITY

- Assessment of probability is ***EXTREMELY**** *dependent upon how predictand “event” is defined:

**KEEP IN MIND:**

- - Time period of consideration
- - Area of occurrence
- - Dependent upon another event?

## 3H Eta MOS thunderstorm probability forecasts   valid 0000 UTC  8/27/2002  (21-24h proj)

**AREAL ****PROBABILITIES**

**What if these were 6-h forecasts?**

## 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**

## Designing an Operational MOS System: Putting theory into practice...

## DEVELOPMENTAL CONSIDERATIONS

**Selection (and QC!) of Suitable **
**  ****Observational Datasets**
**  ****ASOS?   Remote sensor?   Which mesonet?**

**MOS in the real world**

## Suitable observations?

**Appropriate Sensor?**

**Good siting?**

**Real or Memorex?**

**Photo Courtesy W. Shaffer**

## DEVELOPMENTAL CONSIDERATIONS

**Selection (and QC!) of Suitable **
**  ****Observational Datasets**
**  ****ASOS?   Remote sensor?   Which mesonet?**
**Predictand Definition**
**   ****Must be precise !!**

**MOS in the real world**

## PREDICTAND  DEFINITION

**Daytime Maximum Temperature**
**   “****Daytime” is 0700 AM - 0700 PM LST**
**Nighttime Minimum Temperature**
**   “****Nighttime” is 0700 PM - 0800 AM LST**
**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**

## PREDICTAND  DEFINITION

**Determined from 13 consecutive hourly   **
**ASOS obervations, 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**

## = thunderstorm

**Creating a Gridded Predictand**

- = 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:

## 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**

## “APPROPRIATE” PREDICTORS

-  DESCRIBE PHYSICAL PROCESSES ASSOCIATED
-     WITH  OCCURRENCE OF PREDICTAND
-    “MIMIC” FORECASTER THOUGHT PROCESS

**(VERTICAL VELOCITY)  X  (MEAN RH)**

**i.e. for POP:**

## POINT BINARY PREDICTOR

**24-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%)**

## GRID BINARY PREDICTOR

**24 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 )**

## Logit Transform Example

**Logit Transform Example**

- KPIA (Peoria, IL)   0000 UTC ; 18-h projection

## DEVELOPMENTAL CONSIDERATIONS

**Terms in Equations; Selection Criteria**

**(cont.)**

## “REAL” REGRESSION EQUATIONS

- MULTIVARIATE

- , of form:

**Y =  a  + a  X  + a  X  + ... + a  X**

-  large:

**FORWARD SELECTION**

-  procedure determines the

**2**

**N**

**N**

**1**

**0**

**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 NGM QPF,  N = 15      For NGM VIS,  N = 20

-     The

-     predictors and the order in which they appear.

***QUITE***

## FORWARD SELECTION

-   METHOD OF PREDICTOR SELECTION
-      ACCORDING TO CORRELATION WITH
-      PREDICTAND
-   “BEST” OR STATISTICALLY MOST IMPORTANT
-       PREDICTORS CHOSEN FIRST

**FIRST**

-  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**

## DEVELOPMENTAL CONSIDERATIONS

**Terms in Equations; Selection Criteria**
**Dependent Data**
**  ****Sample Size, Stability, Representativeness**
**       ****AVOID OVERFIT !!**
**  ****Stratification - Seasons**
**  ****Pooling – Regions**

**(cont.)**

## MOS LINEAR REGRESSION

- OCTOBER 1 1993 - MARCH 31 1994   0000 UTC**KUIL**

**12-24 H NGM PRECIPITATION AMOUNT (IN.)**

**12-24 H PRECIPITATION ≥ 1.0"**

- 0.00

- 0.25

- 0.50

- 0.75

- 1.00

- 0

- 1

- 0

- RV=14.2%

## AVN/GFS  Cool Season PoP/QPF Regions

**With AVN MOS forecast sites (1406)**

## DEVELOPMENTAL CONSIDERATIONS

**Terms in Equations; Selection Criteria**
**Dependent Data**
**  ****Sample Size, Stability, Representativeness**
**       ****AVOID OVERFIT !!**
**  ****Stratification - Seasons**
**  ****Pooling – Regions**
**Categorical Forecasts?**

**(cont.)**

## MOS BEST CATEGORY SELECTION

**MOS BEST CATEGORY SELECTION**

**           ****KDCA 12-Hour QPF Probabilities**                         48-Hour Projection valid 1200 UTC 10/31/93

- NO

**PROBABILITY (%)**

- NO

- NO

- NO

- 4

- 1

- 6

- 3

- 2

- 5

- 0

- YES

- YES

**THRESHOLD**

**EXCEEDED?**

**TO MOS GUIDANCE MESSAGES**

## How well do we do?MOS Verification

## 1. Improved model realism

**       ****better model = better statistical system**
**2. Coarse, consistent archive grid**
**       ****smoothing of fine-scale detail**
**       ****constant grid 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)**

**Performance of Current MOS Systems**

**To ensure that model changes and small sample size have minimal impact, we rely upon...**

## Degrees (F)

**Degrees (F)**

## Temperature Verification - 0000 UTCCool Season 2002 -2003

## Temperature Verification - 0000 UTCCool Season 2002 -2003

- Temperature Verification - 0000 UTCCool Season 2002 -2003

## QPF Verification - 0000 UTCCool Season  2002 - 2003

- QPF Verification - 0000 UTCCool Season  2002 - 2003

## Max T

- GFSX 12-h Forecast Skill - 0000 UTCMax Temperatures and PoP

**Brier Score % Improvement over Climate **
**Cool Season 1997**** ****- 2003**

**Max T**

**PoP**

## Max Temperature Verification

- LFM

- NGM

- EDAS

- AVN

- Day/Nite

**Max Temperature Verification**

- Cool Season; 1966 - 2003

- Perf. Pg. /
- PE MOS

**24-h**

**48-h**

## MOS:  Today and Beyond

## The Future of MOS

**Complete current centralized suite**
**   ****GFSX MOS:  add 1200 UTC cycle; **
**                         ****some predictand changes**
**   ****Eta MOS:      add visibility forecasts**
**Additional stations**
**   ****New sites in the western Pacific, CONUS**
**Digital / graphic formats**
**   ****http://www.nws.noaa.gov/mdl/synop/**

**Updated “Traditional”  Products**

##  GFSX MOS Day 7 Maximum Temperature 

## Eta MOS  6-hr Probability of Precipitation (PoP)

**Eta MOS  6-hr Probability of Precipitation (PoP)**

**Yeah, we do that!**

**http://www.nws.noaa.gov/mdl/synop**

**PROBABILITIES?**

## The Future of MOS

**“****Enhanced-Resolution” MOS Systems**

**“****MOS at any point”**
**   ****Support new NWS digital forecast database**
**       ****2.5 km - 5 km**** ****resolution**
**   ****Emphasis on high-density surface networks**
**       ****Co-Op, buoy, mesonet**
**   ****Equations valid away from observing sites**
**   ****Use high-resolution geophysical data **

## Gridded MOS Domains

## Slide 73

## Slide 74

## Slide 75

## Slide 76

## Gridded MOS – Central CA

## Gridded MOS Concept - Step 1

**Gridded MOS Concept - Step 1**

**“****Blending” first guess and high-density station forecasts**

**First guess field from**
** ****Generalized Operator Equation**

**First guess + guidance**
**at all available sites**

**Day 1 Max Temp 00 UTC  03/03/05**

**Day 1 Max Temp**
**00 UTC  03/03/05**

## Gridded MOS Concept - Step 2

**Gridded MOS Concept - Step 2**

**First guess + station forecasts +**
** ****terrain **

**First guess + guidance**
**at all available sites**

**Add further detail to analysis with high-resolution geophysical data and “smart” interpolation**

**Day 1 Max Temp**
**00 UTC  03/03/05**

**Day 1 Max Temp**
**00 UTC  03/03/05**

## The Future of MOS

**“****Enhanced-Resolution” MOS Systems**

**“****MOS at any point”**
**   ****Support new NWS digital forecast database**
**       ****2.5 km - 5 km**** ****resolution**
**   ****Emphasis on high-density surface networks**
**       ****Co-Op, buoy, mesonet**
**   ****Equations valid away from observing sites**
**   ****Use high-resolution geophysical data **
**“****True” gridded MOS **
**   ****Observations and forecasts valid on fine grid**
**   ****Use remotely-sensed predictand data**
**   ****PoP/QPF “Demonstration” System**
**       **** ****4-km HRAP grid; WSR-88D **

## Remotely-sensed precipitation data

**Remotely-sensed precipitation data**

## REFERENCES

**Wilks,D.:  Statistical Methods in the                       Atmospheric Sciences, Chap. 6, p. 159 - 210.**
**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, **_**Wx. &**_**    **_**Forecasting**_**, p. 401 - 412.**