1

Climate Test Bed Seminar Series24 June 2009

Bias Correction & Forecast Skill of NCEP GFS Ensemble Week 1 & Week 2

Precipitation & Soil Moisture Forecasts

Yun Fan & Huug van den Dool

Acknowledgement: Jae Schemm, John Janowiak, Doug Lecomte, Jin Huang, Pingping Xie,

Viviane Silva, Peitao Peng, Vern Kousky, Wayne Higgins

2

Outline

• Motivation• Methodology • Performance of NCEP GFS Week1 & Week2

Ensemble Precipitation Forecasts• Analysis of Week1 & Week2 Biases & Errors• Application: land model forced with bias

corrected week1 week2 P & T2m forecast• Future Work

3

History of Soil Moisture “Dynamical” Outlook CPC Leaky Bucket Hydrological Model

Forced With Week 1 & Week 2 GFS Forecasts

Single member HR MRF (started around 1997 & CONUS)

Ensemble GFS (started late 2001 & CONUS)

Bias corrected Ensemble GFS (started late 2003 & CONUS)

Bias corrected Ensemble GFS (started late 2007 & global land)

:

The prediction skill of soil moisture crucially depends on our ability to predict precipitation Early stage (both good and bad comments)

Recent years (more & more good comments)

So its time to verify & quantify:daily GFS ensemble week 1 & week 2 precip forecast skills & statistics

4

The quality of soil moisture prediction largely or almost entirely depends on the quality of precipitation prediction

5

Daily bias correction based on

last 30 (or 7) day forecast errors

Week1

Future

Week2

Today

Past

Last 30 day

1/N Σ [ Pf (week1) – Po (week1) ] = Bias1

1/N Σ [ Pf (week2) – Po (week2) ] = Bias2

Pf : GFS ensemble week1 & week2 precip forecast

Po: Observed week1 & week2 precip from CPC daily global Unified Precip

N = ( 30, 7..….)

6

North America

Seasonal cycle with

Large day to day fluctuation

On 0.5x0.5 obs grid

7

South America

On 0.5x0.5 obs grid

8

Asia-Australia

On 0.5x0.5 obs grid

9

Africa

On 0.5x0.5 obs grid

10

How good is GFS?

On 0.5x0.5 obs grid

Seasonal cycle with

Large day to day fluctuation

11

On 0.5x0.5 obs grid

How good is GFS?

Seasonal cycle with

Large day to day fluctuation

12

Comparison (based on last 30-day forecast errors) Obs grids (regrid model grids to 0.5x0.5 obs grids) Model grids (regrid obs grids to 2.5x2.5 model grids)

Question: Does grid matter for skills assessment?

13Skill does not depend much on the grid

14

Comparison

bias corrected skills (based on last 30-day forecast errors) bias corrected skills (based on last 7-day forecast errors)

Question: Does the bias estimate influence skill?

Week1

Future

Week2

Today

Past

Last 30 day

1/N Σ [ Pf (week1) – Po (week1) ] = Bias1

1/N Σ [ Pf (week2) – Po (week2) ] = Bias2

Pf : GFS ensemble week1 & week2 precip forecast

Po: Observed week1 & week2 precip from CPC daily global Unified Precip

N = ( 30, 7..….)

151) Skill depends on the definition of bias

2) 30-day bias correction better than 7-day bias correction

16

Comparison

bias corrected skills (based on last 30-day forecast errors) raw forecast skills (no bias correction applied)

Question: Does bias correction improve skill

in terms of Spatial Correlation and RMSE?

17

Bias correction is time &

location dependent

18

Bias correction helps everywhere

19

Table 1. Averaged (May 1, 2008 – June 7, 2009) spatial correlations over different monsoon regions

Week 1 Week 2

Bias Correction

No Bias Correction

Bias Correction

No Bias Correction

North America 0.49 0.48 0.24 0.26

South America 0.45 0.25 0.31 0.18

Asia Australia 0.47 0.40 0.29 0.26

Africa 0.40 0.24 0.25 0.13

Table 2. Averaged (May 1, 2008 – June 7, 2009) RMSE over different monsoon regions (unit: mm/week)

Week 1 Week 2

Bias Correction

No Bias Correction

Bias Correction

No Bias Correction

North America 19.18 22.82 21.61 23.58South

America 29.55 41.06 32.27 41.72Asia

Australia 22.65 27.62 25.24 29.15

Africa 17.06 19.47 17.66 19.33

The effectiveness of bias correction is mainly space dependent.

Bias correction can correct spatial

distribution of Pf & reduce its error.

Similarity of Pf & Po

Distance of Pf & Po

Reduced by 28%

Reduced by 23%

Increased by 80%

Increased by 67%

20

CONUS

30-day running mean

21

In terms of Spatial Anomaly Correlation, bias correction helps:1) very little over North America

2) considerably over South America & Africa

3) a little over Asia-Australia

In terms of RMSE:Bias correction helps everywhere

Questions: Why bias correction works but varies in space and time?

What biases look like?

Are biases removable & to what extent are they removable?

22

Temporal-spatial structures of last 30-day biases:

Daily Bias1 & Bias2 used to correct GFS ensemble week1 & week2 forecasts

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2

M

mmm sEOFtPCMeantsBias

1

)()(),(2,1

23

Annual Mean Bias or Raw Forecast Error

Week-1 mean Bias

Week-2 mean Bias

24

Mean Bias of Daily R2 & Observed Precip (1979-2006)

25

summer

winter

26

winter

summer

27

Temporal-spatial structures of last 30-day biases:

Daily Bias1 & Bias2 used to correct GFS ensemble week1 & week2 forecasts

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2

Large-scale & low-frequency (annual or semi-annual cycles) are prominent

First two EOF modes of Bias1 & Bias2 explain about 60% total variances

GFS has prominent annual cycle errors (lesson for model development?)

28

Temporal-spatial structures of real time raw forecast errors:

Daily GFS week1 & week2 forecast errors without bias correction

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2Pf (week1) – Po (week1) = Error1

Pf (week2) – Po (week2) = Error2

No bias correction applied

M

mmm sEOFtPCMeantsError

1

)()(),(2,1

29

30

31

Temporal-spatial structures of real time raw forecast errors:

Daily GFS week1 & week2 forecast errors without bias correction

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2

Pf (week1) – Po (week1) = Error1

Pf (week2) – Po (week2) = Error2

No bias correction applied

Raw forecast errors are dominated by the 1st, 2nd or 3rd EOFs in Bias1 & Bias2

First two EOF modes of Error1 & Error2 explain about 23~35% total variances

At least this amount of error is removable. But so far bias correction was not done by EOF analysis

32

Temporal-spatial structures of real time forecast errors:

GFS week1 & week2 forecast errors with last 30-day bias correction

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2

Pf (week1) – Po (week1) = Error1

Pf (week2) – Po (week2) = Error2

Bias correction:

Error1 = Error1 – Bias1Error2 = Error2 – Bias2

M

mmm sEOFtPCMeantsError

1

)()(),(2,1

33

Annual Mean Forecast Error after bias correction

5 times smaller than mean bias or raw forecast error

Week-1 mean forecast error

Week-2 mean forecast error

34

35

36

Temporal-spatial structures of real time forecast errors:

GFS week1 & week2 forecast errors with last 30-day bias correction

Week1

Future

Week2

Today

Past

Last 30 day

1/30 Σ [ Pf (week1) – Po (week1) ] = Bias1

1/30 Σ [ Pf (week2) – Po (week2) ] = Bias2

Pf (week1) – Po (week1) = Error1

Pf (week2) – Po (week2) = Error2

Bias correction:

Error1 = Error1 – Bias1Error2 = Error2 – Bias2

Bias Corrected Forecast Errors are much more random (in time mainly, EOFs more “white”).

Leading EOF modes of Bias1, Bias2, & Error1, Error2 Show that GFS has prominent large-scale & low-frequency errors or GFS has difficulty to reproduce those observed Precip patterns & their evolution. However, to some extent they can be corrected through bias correction, especially in winter season.

37

Application

Soil Moisture “Dynamical” Outlook CPC Leaky Bucket Hydrological Model

Forced With Week-1 & Week-2 GFS Ensemble Forecasts

(Daily data from 01Nov2003 to present)

All initial conditions & verification datasets are from leaky bucket model forced with daily observed P & T2m

38

Some Thoughts:

• Once this (SST, w) was the lower boundary….• Both SST and w have (high) persistence• Old ‘standard’ in meteorology: If you cannot beat

persistence …..• For instance: dw/dt = P – E - R = F

or w(t+1)=w(t) + F

• Clearly if we do not know F with sufficient skill, the forecast loses against persistence (F=0).

39

40

41

42

30-day running mean

P1=0.9511, C1=0.9512PR1=16.27, FR1=18.02

P2=0.9015, C2=0.8957PR2=23.67, FR2=26.56

4330-day running mean

Precip

44

Even moderate forecast skill at right time still help a lot

45

30-day running mean for week-2

Hybrid persistence = week-1 forecast persists to week-2

46

• Moderate week-1 & week-2 GFS P forecast skills• Last 30-d biases dominated by low-frequency &

large-scale errors• Bias corrections are time & location dependent• Soil moisture forecast skill hardly beats its

persistence over CONUS• The inability to outperform persistence relates

to the skill of precipitation not being above a threshold (AC>0.5 is required)

Summary

47

• Is PDF bias correction better?

• GFS Week3 & Week4 Precip Assessment

• GFS hindcasts?

• How about New CFSRR?

Future Work