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Climate Test Bed Seminar Series 24 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
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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
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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
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The quality of soil moisture prediction largely or almost
entirely depends on the quality of precipitation prediction
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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..….)
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North America
Seasonal cycle with
Large day to day fluctuation
On 0.5x0.5 obs grid
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South America
On 0.5x0.5 obs grid
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Asia-Australia
On 0.5x0.5 obs grid
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Africa
On 0.5x0.5 obs grid
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How good is GFS?
On 0.5x0.5 obs grid Seasonal cycle with Large day to day fluctuation
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On 0.5x0.5 obs grid
How good is GFS?
Seasonal cycle with Large day to day fluctuation
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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 ?
Skill does not depend 13
much on the grid
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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..….)
1) Skill depends on the definition of bias 15
2) 30-day bias correction better than 7-day bias correction
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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 ?
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Bias correction is time &
location dependent
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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 23.58
South
America 29.55 41.06 32.27 41.72
Asia
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%
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CONUS
30-day running mean
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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?
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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
Mm
m m
t EOF s PC
Mean t
s Bias
1
) ( )
( )
,
(
2
,
1
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Annual Mean Bias or Raw Forecast Error
Week-1 mean Bias
Week-2 mean Bias
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Mean Bias of Daily R2 & Observed Precip (1979-2006)
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summer
winter
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winter summer
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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?)
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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
Mm
m m
t EOF s PC
Mean t
s Error
1
) ( )
( )
,
(
2
,
1
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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 1
st,2
ndor 3
rdEOFs 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
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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 – Bias1 Error2 = Error2 – Bias2
Mm
m m
t EOF s PC
Mean t
s Error
1
) ( )
( )
,
(
2
,
1
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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
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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 – Bias1 Error2 = 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.
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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
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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).
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42 30-day running mean
P1=0.9511, C1=0.9512 PR1=16.27,
FR1=18.02
P2=0.9015, C2=0.8957 PR2=23.67,
FR2=26.56
30-day running mean 43 Precip
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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
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• 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
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