1 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

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 [ P f (week1) – Po (week1) ] = Bias1 1/N Σ [ P f (week2) – Po (week2) ] = Bias2 P f : 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 ?

13 Skill 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 [ P f (week1) – Po (week1) ] = Bias1 1/N Σ [ P f (week2) – Po (week2) ] = Bias2 P f : GFS ensemble week1 & week2 precip forecast Po: Observed week1 & week2 precip from CPC daily global Unified Precip N = ( 30, 7..….)

15 1) 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 1Week 2 Bias Correction No Bias Correction Bias Correction No Bias Correction North America South America Asia Australia Africa Table 2. Averaged (May 1, 2008 – June 7, 2009) RMSE over different monsoon regions (unit: mm/week) Week 1Week 2 Bias Correction No Bias Correction Bias Correction No Bias Correction North America South America Asia Australia Africa The effectiveness of bias correction is mainly space dependent. Bias correction can correct spatial distribution of P f & reduce its error. Similarity of P f & P o Distance of P f & P o 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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (week2) – Po (week2) ] = Bias2

23 Annual Mean Bias or Raw Forecast Error Week-1 mean Bias Week-2 mean Bias

24 Mean Bias of Daily R2 & Observed Precip ( )

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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (week2) – Po (week2) ] = Bias2 P f (week1) – Po (week1) = Error1 P f (week2) – Po (week2) = Error2 No bias correction applied

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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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (week2) – Po (week2) ] = Bias2 P f (week1) – Po (week1) = Error1 P f (week2) – Po (week2) = Error2 No bias correction applied Raw forecast errors are dominated by the 1 st, 2 nd or 3 rd 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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (week2) – Po (week2) ] = Bias2 P f (week1) – Po (week1) = Error1 P f (week2) – Po (week2) = Error2 Bias correction: Error1 = Error1 – Bias1 Error2 = Error2 – Bias2

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

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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 [ P f (week1) – Po (week1) ] = Bias1 1/30 Σ [ P f (week2) – Po (week2) ] = Bias2 P f (week1) – Po (week1) = Error1 P f (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.

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).

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42 30-day running mean P1=0.9511, C1= PR1=16.27, FR1=18.02 P2=0.9015, C2= PR2=23.67, FR2=26.56

43 30-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