u.s. department of commerce national …€¦ · u.s. department of commerce national oceanic and...

0U.S. DEPARTMENT OF COMMERCE

NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATIONNATIONAL WEATHER SERVICE

NATIONAL METEOROLOGICAL CENTER

* h i,

OFFICE NOTE 364

Skill of Medium Range Forecasts

Francis D. HughesPrediction Branch, Climate Analysis Center

February 1990

This is an unreviewed manuscript, primarily intended for informal exchangeof information among NMC staff members.

_W~~~~~~ ~~~PURPOSE

This paper depicts in a graphical manner the skill of the Medium Range (3-

10 day) man and machine (numerical model guidance) forecasts. It will be

updated each February in order to present the latest scores for each of the

several forecast categories in the medium range forecast program (MRFP). Only

scores with at least a 5-year period of record are presented. This paper

contains the standardized and unstandardized mean sea level pressure and 500mb

correlation; the Gilman, Hughes and experimental precipitation skill; the

minimum/maximum average absolute temperature error; and the 5-day mean

normalized 500mb correlation, temperature, and precipitation skill scores.

2

Numerical Model Guidance (Past to Present)

1. Acronyms

a. Baro - Reed Baratropic Advection Model Hemisphericb. 6L PE - 6-layer Primitive Equation Model Hemisphericc. CM - Course Mesh 380km FM - Fine Mesh 190kmd. SMG26 - Spectral Model Global 24 modes 6-layerse. SMG2C - Spectral Model Hemispheric 24 modes 12-layersf. SMG3C - Spectral Model Global 30 modes 12-layersg. SMG4C - Spectral Model Global 40 modes 12-layersh. SMG4H - Spectral Model Global 40 modes 18-layersi. SMG8H - Spectral Model Global 80 modes 18-layers

2. 00Z Guidance

a. To 84-hours

(1) From 1970 through 1977: 6L PE CM(2) From 1978 through 1979: 7L PE FM(3) From January 1980 to August 15, 1980: 7L PE FM to

60-hours then 7L PE CM with Fourth Order Differencingto 84-hours.

(4) From August 15, 1980 to April 15, 1981: SMG3C to 48-hours

then SMH2C to 84-hours.(5) From April 15, 1981 through October 19, 1983: SMG3C to

48-hours then SMG2C to 84-hours.(6) From October 19, 1983 through December 1984: SMG4C(7) From January 01, 1985 through December 1986: SMG4H(8) From August 13, 1987 through December 1989: SMG8H

b. Greater then 84-hours to 144-hours

(1) From 1970 through 1979: Baro (Mesh 1977-1979)(2) From January 1980 to August 15, 1980: 7L PE CM with

Fourth Order Differencing.(3) From August 15, 1980 to April 15, 1981: SMH2C

(4) From April 15, 1981 through April 1982: SMG26(5) From May 1982 through October 19, 1983: SMG2C(6) From October 19, 1983 through December 1984: SMG4C(7) From January 01, 1985 through December 1986: SMG4H(8) From August 13, 1987 through December 1989: SMG8H

c. Greater the 144-hours to 240-hours

(1) From November 1977 through April 1981: Baro Mesh(2) From December 1977 through April 15, 1981: 3L PE CM(3) From April 15, 1981 through October 19, 1983: SMG26

to 192-hours then SMG26 to 240 hours.(4) From October 19, 1983 through December 1984: SMG4C to

- 1 : , i . . I - - ,

3

240-hours.(5) From January 01, 1985 through August 12, 1987: SMG4H to

240-hours.(6) From August 13, 1987 through December 1989: SMG8H to

240-hours.

3. 12Z Guidance

a. To 60-hours

(1) From 1970 through 1977: 6L PE CM

b. Greater than 60-hours to 96-hours (500 mb only)

(1) From 1970 through 1977: Baro (mesh in 1977)

c. To 48-hours

(1) From October 1971 through August 1977: 7L PE FM (old LFM)(2) From September 1977 through 1987: 7L PE LFM (127km)

d. Greater than 48-hours to 120-hours (500mb only)

(1) From 1978 through 1989: Baro run from the 48-hour LFMinserted into the 60-hour SMG8H from OOZ.

Forecast Day

12Z

12hrs 00Z 00Z

Day 1

12Z

36hrs

Day 2

12Z

60hrs00Z 0

Day 3 Day 4 Day 5

12Z 12Z 12Z

84hrs 108hrs 132hrs0Z 00Z 00Z 00Z

c<~~~ ~~SMG8H

< 48hr LFM - BARO >

Day 6 Day 7 Day 8 Day 9 Day 10

12Z 12Z 12Z 12Z 12Z

156hrs 180hrs 204hrs 228hrs 252hrs00Z 00Z 000z00Z 00Z 00Z

- -

*Note I analysis replaced the IUF in late July 1984.

*Note OI analysis replaced the HUF in late July 1984.

r

I _

4

Figure 1 depicts the North American (NOAM, 130 grid points) mean sea level

pressure (MSLP) and 500mb correlation score verification area.

Figures 2-13 are plots of the calendar year 1989 monthly mean correlation scores

for the man and NMC/NWP/MRF model NOAM area MSLP progs verifying on days 1-9

after forecast day.

Figures 14-25 are plots of the calendar year 1989 monthly mean standardized

correlation scores for the man and NMC/NWP/MRF model NOAM area MSLP progs

verifying on days 1-9 after forecast day. (See Appendix A for an explanation of

! · this score).


correlation scores for the NMC/NWP/MRF model NOAM area 500mb progs verifying on

days 1-9 after forecast day.


correlation scores for the NMC/NWP/(AVN, NGM, LFM) models NOAM area MSLP progs

verifying on days 1-(3,2,2) after forecast day.


correlation scores for the NMC/NWP/(AVN, NGM, LFM) model NOAM area 500mb progs

verifying on days 1-(3,2,2) after forecast day.

Figure 62 is a plot of the 1968/70-1989 calendar year standardized correlation

scores for the man and NMC/NWP model NOAM area MSLP progs verifying on days 3, 4

and 5 after forecast day.

Figure 63 is a plot of the 1970-89 calendar year standardized correlation scores

for the NMC/NWP model NOAM area 500mb progs verifying on days 3, 4 and 5 after

forecast day.

Figure 64 is a plot of the 1979-89 calendar year normalized correlation scores

for the man, NMC/NWP model, and ECMWF model (82-89) NOAM area 500mb mean progs

verifying 6-10 days after forecast day.

Figure 65 depicts the 41 stations in the United States where the temperature

forecasts are verified.

Figures 66-77 are plots of the calendar year 1989 monthly mean absolute error

minimum/maximum temperature scores for the man, Klein-Lewis (KL) Perfect Prog,

MOS, linear regression corrected Perfect Prog, and climatology U.S. area

temperature forecasts verifying on days 1-9 after forecast day.

Figure 78 is a plot of the 1971-89 calendar year average absolute error minimum

temperature scores for the man and KL Perfect Prog U.S. area temperature forecast

verifying on days 3 and 5 after forecast day.

Figure 79 is a plot of the 1971-89 calendar year average absolute error maximum

temperature scores for the man and KL Perfect Prog U.S. area temperature forecasts

verifying on days 3 and 5 after forecast day.

5

Figure 80 is a plot of the 1971-89 calendar year average absolute error(minimum + maximum) - 2 temperature scores for the man, KL Perfect Prog, andclimatology U.S. area temperature forecasts verifying on days (3+4+5) - 3after forecast day.

Figure 81 is a plot of the 1978-89 5-class and 3-class temperature skillscores for the man U.S. area categorical temperature forecasts verifying 6-10days after forecast day. (See Appendix B for an explanation of this score.)

Figure 82 depicts the 100 stations in the United States where the precipitationforecasts are verified.

Figure 83 is an example of a day 3, 4 or 5 precipitation forecast. The dashedlines are the 24-hour departure from normal probability of precipitation (DN POP)forecast for January 3. The solid lines are the 24-hour climatological (normal)probability of precipitation (NPOP) for the first 15 days of January. A total of(DN POP + NPOP) > 30 is considered "yes" forecast of precipitation (> 0.01 inch).

All stations with an (NPOP) > 30 are considered as a "yes" climatological forecast

of precipitation.

Figures 84-95 are plots of the calendar year 1989 monthly mean Gilman, Hughes, andProbability precipitation skill scores for the man and climatology U.S. areaprecipitation forecasts verifying on days 1-9 after forecast day. (See AppendixesC, D and E for an explanation of these scores.)

Figure 96 is a plot of the 1970-89 Gilman precipitation skill scores for theman and climatology U.S. area precipitation forecasts verifying on days 3, 4 and5 after forecast day.

Figure 97 is a plot of the 1978-89 3-class precipitation skill scores for theman and NMC/NWP model U.S. area categorical precipitation forecasts verifying 1-5days after forecast day. (For an explanation of this score see Appendix F.)

Figure 98 is a plot of theman and NMC/NWP model U.S.days after forecast day.

1978-89 3-class precipitation skill scores for thearea categorical precipitation forecasts verifying 6-10

6

SECTION 1

Man and Machine (NMC/NWP Model Guidance)

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101 Fig. 94

DAYS 1 THRU 9 100 STATION UNITED S TATES AREA PRECIPITATIONS KILL S C ORES FOR NOV 1989

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32

OFFICIAL CALENDAR YEAR AVERAGE30 PRECIPITATION GILMAN SKILL SCORES

FOR DAYS 3, 4, AND 5 PROGS

28_ -

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24A

DAY 322

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CLIMATOLOGY - 10.4

08 I I I

1965 1970 1975 1980 1985 1990YEAR

Fig. 97

OFFICIAL AND NMC/NWP MODEL CALENDAR YEAR

AVERAGE 3-CLASS PRECIPITATION SKILL SCORES

FOR 1-5 DAY PROGS

OFFICIAL

MODEL

10 I I

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CLIMATOLOGY - 4.5

I , I I I i t I

85 90YEAR

35

30

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105 Fig. 98

OFFICIAL AND NMC/NWP MODEL CALENDAR YEARAVERAGE 3-CLASS PRECIPITATION SKILL SCORESFOR 6-10 DAY PROGS (APPROXIMATELY 13 PER MONTH)

OFFICIAL\.

CLIMATOLOGY -4. 5

00o-75 80 85

YEAR

15

M

To

10

5I

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90 95

106

Vw~~~~~~ ~~~COMMENTS

SECTION 1 MAN AND MACHINE (NMC/NWP MODEL GUIDANCE)

MSLP & 500MB CORRELATION SCORES PAGES 6 TO 69

The pattern correlation score (Appendix A) has been the basic score used to

verify the MSLP and 500mb progs since the start of the MRFP. The correlation

score was chosen since it is more sensitive to the phasing of troughs and ridges

(considered to be more important) than to the depth or heighth of these systems.

The MSLP and 500mb operational analyses (HUF) were used to verify the forecast

through 1976 and the LFM since 1977.

The NOAM standardized correlation score is the oldest score of record. It

was assumed from the start that a MSLP standardized (anomaly divided by the

standard deviation at each grid point) score of greater than 0.0 (climatology)

would result in the derived forecasts of temperatures and precipitation having

more skill than climatology (as a forecast). However, experience has indicated

that a NOAM score of 0.17 or better is required to accomplish this.

Most of the forecasters complained from the beginning about verifying a

forecast of the standardized MSLP field (which they could not "see") instead of

the one they produced (the actual field). In order to appease the forecaster

and to obtain a score for the normal (climatology) as a forecast the

unstandardized (actual MSLP field) score was introduced in 1977 and has been

used successfully ever since.

A glance at Figures 62-64 indicates that both the man (official) and

NMC/NWP model guidance scores were records for 1989. No comment is made

concerning the "betterment" of the man (official) progs over the guidance except

that it appears to be significant. Since the scores for the circulation

forecasts were records one might expect the derived forecasts of temperature and

.* precipitation also to be at or near record levels.

1 07

SECTION II - MAN AND MACHINE (KLEIN-LEWIS PERFECT PROG) AVERAGEABSOLUTE ERROR/SKILL TEMPERATURE SCORES PAGES 70 TO 87

Despite the record scores for the circulation forecasts only the day 3 KL

average absolute error and the 3-class 6-10 day skill scores (Figures 78-81)

showed any improvement over 1988 but even these were not record scores. Perhaps

this can be understood in part by the fact that climatology scored the third

highest average absolute error since 1971.

SECTION III - MAN AND MACHINE (NMC/NWP MODEL)PRECIPITATION SKILL SCORES PAGES 88 TO 105

Perhaps the most dramatic response to the improvement in the circulation

forecasts can be seen in the 3-class skill score for the 1-5 day progs (Fig.

97). Also both the Gilman and 3-class skill scores for the days 3, 4 an 5 and

6-10 days progs respectively were at record levels (Figs. 96, 98).

CONCLUSION

1989 turned out to be a record year for the circulation progs and to a

lesser extent for the precipitation forecasts but was a somewhat disappointing

year with regard to the temperature forecasts..

-i

108

Appendix A

The standardized mean sea level pressure correlation score is used to

determine the skill of the man and machine days 3, 4 and 5 mean sea level pressure

forecasts. The correlation score is employed because the phasing instead of the

intensity of systems primarily determines how well the various weather parameters

can be forecast. The standardizing procedure prevents the contribution of the

high variability (higher latitude) grid points from overwhelming the low variability

grid points (lower latitude).

f = forecast mean sea level pressure at a grid point

o = observed mean sea level pressure at a grid point

~-= standard deviation at a grid point

n = normal mean sea level pressure at a grid point

I.t~ F= f-n 0= o

= average standardized forecast across n grid points

0 = average standardized observedast across n grid points

0 = average standardized observed across n grid points

RMS F =F RMS 0=

IRMS Error = F-O 0)'

Average Absolute Error =

Correlation = F ( - F 0) X100

Since the normal mean sea level pressure is subtracted from the forecast/

observed pressure at each grid point, it is assumed that the correlation of the

normal to the observed is always zero. Therefore, any positive score is considered

:I

109

APPENDIX A (cont'd)

co have skill over the normal. Some doubts have been raised about this assumption,

however, and for the past 5 years the unstandardized correlation score also has

been calculated. This procedure allows a correlation score to be computed for the

normal. This score then is simply the correlation of the forecast to the observed

mean sea-level pressure.

110

APPENDIX B

The 5 day mean temperature skill score is a generalization of the

iHeidke skill score where the expected values are derived from the observed

temperature

Heidke Skill = C-E C = total correct (hits)

N-E N = total number of forecasts (61)

E = expected number of hits

The expected value is calculated as follows from the number of

stations in each of the observed temperature categories:

E = 1/8 x Much Below + 1/8 x Much Above +

1/4 x Below + 1/4 x Above + 1/4 x Normal

The 5-day mean 3-class temperature skill score simply "lumps" together

the much below with the below and the much above with the above. The expected

(E) then is equal to 1/4 X Below + 1/4 X Normal + 1/4 Above.

I- .-- :, . ;- . .

111

Appendix C

The Gilman skill score is a generalization of the Heidke skill score where the

xpected values are derived from a randomized version of the precipitation forecast.

C-EHeidke Skill = N-E C = total correct (hits)

N = total number of forecasts (100)


flowever, for a randomized forecast allowance must be made for stations having far

different precipitation climate (N POP) across the United States. Therefore, to

compute and score an expected chance forecast, climatology must be considered.

The procedure for this is as follows:

First, the actual number of forecasts of precipitation are distributed

randomly taking into account station climatology. The expected number of

chance hits is then given by:

E = (Pi ri + (1 - Pi )(1 - ri)) or

E = 2 Pi ri + N - Pi -_ ri (a)

where ri = 1 for precipitation (Z.01 inch) and 0 for no precipitaiton (4.01 inch).

Now an expression for Pi, which is the probability that after the forecast

precipitation events are redistributed randomly a forecast precipitation event

will fall at point "i" is given approximately by p±CF ,(b). Here F = total

number of forecasted precipitation events and ai = climatic precipitation

probability (N POP). This approximate value for Pi is most valid for small

values of F and (ai /ai ) and is unstable at times. Because of this instability

the less sophisticated but more stable Hughes skill score was developed.

Substituting the expression (b) into (a) gives E 2'2A" + N-F-R, where

E = the approximate expected value of a randomized forecast, R = total precipi-

tation cases, and N = total number of stations. If the climatic probabilities

are uniform (ai =aj =a), then the approximate value of E reduces to the standard

Heidke value given by: E (N-F)(N-R)+FRN

112

Appendix D

The Hughes skill score is a generalization of the Heidke skill score where

the expected values are derived from the observed precipitation:

Heidke Skill C-EN-E

C= total correct (hits)

N = total number of forecasts (100)

E= expected number of hits

If the average precipitation climate (NPOP) of 12 stations having

precipitation is 25, then the expected (precipitation) is simply 12 x .25 or 3

stations. If the average NPOP of the (100-12) stations not having precipitation

is also 25 then the expected (E) then is 69 stations. If the forecast his (C)

75 stations correctly, his skill score then is (75-69)/(100-69) x 100 or 19._O

113

APPENDIX E

The (Hughes) probability score is not a skill score yet it is quite

simple to understand. A rough score (RS) is calculated for each station

(N=1 to 100) as follows:

Forecast Observed RS

(DN POP + NPOP) ~30 P=1 +(1 - NPOP)

(DN POP + NPOP) .30 P=O and NPOP _-50 -(NPOP)

(DN POP + NPOP) -30 P=1 and NPOP --50 -(NPOP)

(DN POP + NPOP) 230 P=0 and NPOP 50 -(1 - NPOP)

(DN POP + NPOP) -30 P=1 and NPOP -450 -(1 - NPOP)

(DN POP + NPOP) <30 P=O +(NPOP)

Since the total rough score (TRS) for the 100 stations does not equal

100 points, a simple iterative technique is employed which uses the RS as

a f(NPOP) for each station to bring the total number of points up to 100.

The FORTRAN language routine is:

TTY = 0

70 DO 69 I = 1, 100

TRS = (100.0 - TRS) * ABS(RS(I)) * .01IF(RS(I)) 73, 74, 74

73 RS(I) = RS(I) - TRSGO TO 69

74 RS(I) = RS(I) + TRS69 TTY = TTY + ABS(RS(I))

TRS = TTYTTY = 0.0IF (TRS - 99.8) 70, 71, 71

71 CONTINUE

, >j

114

APPENDIX F

The 5-Day mean precipitation skill score is a generalization of the

Heidke skill score where the expected values are derived from the observed

precipitation:

Heidke Skill = C-E C = total correct (hits)

N-E N = total number of forecasts (100)


For example, in January the number of stations in the area covered by

the (NP/P), (NP/M/H) and (L/M/H) categories is 21, 28 and 51 respectively.

The average value of the probability of NP for the stations in the (NP/P)

area is 70% and 40% in the (NP/M/H) area. Now if (NP/L) is coded as 1, M as

2 and (P/H) as 3, then the number of stations expected to have coded value

1 thru 3 is as follows:

33% of (L/M/H) = 51 x .33 = 17 stations coded 1, 2, 3

40% of (NP/M/H) = 28 x .40 = 11 stations coded as 1 and 8.5 coded as 2,3

70% of (NP/P) = 21 x .70 = 14. 7 stations coded as 1 and 6. 3 coded as 3

Thus, code 1 = 17 + 11 + 14. 7 = 42 7 stationscode 2 = 17 + 8.5 =25 5'stations

code 3 = 17 + 8.5 +6.3 = 31. 8 stations

100. 0 statioeis

Therefore, the expected value =. 427a + . 255b + . 318c

where a, b and c are the number of coded values 1, 2 and 3 observed.

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