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Quantile Based Bias Correction
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Transcript of Quantile Based Bias Correction
Quantile-based bias correction for
global climate model precipitation
data in Bagmati river basin, Nepal
B.K. Mishra, S. Herath
United Nations University - Institute for Sustainability and Peace
January 7, 2011
1
Introduction
One of the greatest challenges facing modern society in a
changing climate is the management of risk (R)
associated with hydrological extremes, namely floods and
droughts.
N
TR )
11(1
2
• Global Climate Models (GCM) output are used to force
hydrological simulations for risk assessment of climate
change impacts on the extreme events.
• However, GCM outputs are often characterized by
biases and coarse resolution that limit their application
for basin level hydrological modeling.
Introduction
3
GCM output should be utilized in climate change impact
studies only after due consideration on its coarse
resolution and biasness i.e., by
Downscaling
Bias correction
Introduction
4
Recently, many GCMs are available with high spatial and
temporal resolution output data.
e.g., MRI-GCM output available at 20-km daily/hourly
resolution
Introduction
5
SST Ocean
CMIP3 CGCM
Multi-model
Atmosphere
110-180km mesh 20km mesh
SST
5km & 1km mesh
High-resolution
global atmospheric
model
Regional cloud
resolving model
by nesting
2075-2099 1979-2003 Year
SST
Present
Future
High resolution climate models ( Souce: Akio KITOH (MRI) ppt)
50-100km mesh
Boundary condition
Predicted
SST
Atmosphere
Boundary condition
Near Future
2015-2039
SST=Sea Surface Temperature
MRI / JMA / AESTO
6
• Here, the MRI-GCM daily precipitation data will be
used in Bagmati river basin of Nepal for climate change
impact studies.
• This daily GCM precipitation data can be considered
acceptable from spatial/temporal resolution point of
view for the present study basin.
Objective
However, gap exists in term of biases. This research
intends to develop an innovative technique to minimize
the biases in the GCM output.
7
Bagmati river basin, Nepal
Study area
8
Study area
• Catchment area = 2750 km2
• Capital city is situated in this basin
• Annual rainfall is 1900 mm
• About 80% rainfall takes place during July-Sept.
• Daily precipitation data is available of past 40 years at seven
stations from Department of Hydrology and Meteorology,
Nepal
9
Study area
7 grid boxes of the MRI-GCM covers most of the study area.
10
11
Rainfall
Type
Annual
rainfall, mm
No. of wet days
per year
Maximum
rainfall, mm
Observed 1523 133 (4.37 months) 177
GCM 1593 244 (8.02 months) 88.1
12
13
Month Relative
error (%)
Jan 27
Feb 87.8
Mar 25.7
Apr 5.6
May 39.5
Jun 21.6
Jul -17.2
Aug -19.1
Sep 8.5
Oct 66.9
Nov 172.7
Dec -9.8
14
15
Limitations with GCM precipitation output
• Too many wet days (i.e. rainfall frequency)
• Smaller rainfall values (i.e. rainfall intensity)
16
Quantile-based bias correction
In this approach, bias correction of daily rainfall is based on
following two considerations:
• Rainfall frequency is corrected by truncating the distribution of
the GCM daily rainfall based on the non-exceedance probability,
F(x_historical=0.0),
• Rainfall intensity is corrected by adjusting cumulative
distribution functions (CDFs) of the truncated non-zero rainfall
days (i.e. CDF_gcm→CDF_historical)
17
1
F(xGCM=0.0)
F(xhist=0.0)
0 0
GCM
Historical
Correcting Bias in Daily GCM Output:
Rainfall Frequency
calibrated threshold
Daily rainfall (x) mm
18
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 25 50 75 100 125 150 175 200
No
n-e
xce
edan
ce p
rob
abil
ity,
F
Rainfall, mm
GCM8503
Observed
GCM1539
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 25 50 75 100 125 150 175 200
No
n-e
xce
edan
ce p
rob
abil
ity,
F
Rainfall, mm
GCM8503
Observed
GCM1539
Before correction
After correction
19
Before correction After correction Before correction After correction
132.9 243.63 132.79 237.6 133.2
GCM20 GCM21
No. of wet days per year
Observed
20
Correcting Bias in Daily GCM Output:
Rainfall Intensity
GCM
Historical
0
Daily rainfall (x), mm
1
0 0
F(x)
x'i
F(xi)
xi
))((1'
iGCMobsi xFFx
21
It is widely recognized that the distribution of daily
precipitation can be approximated by the gamma distribution.
With the shape (α) and scale (β) parameters, gamma distribution can
be expressed by the following probability density function (PDF)
and cumulative distribution function (CDF):
)exp()(
1)( 1
xxxf
x
xTrunc
dttfxF )()(
Using gamma distribution
For bias correction, the CDF of the daily GCM rainfall FGCM(x) is compared with the CDF
of the daily observation rainfall Fobs (x). The bias corrected GCM rainfall (x’GCM) can then
be calculated as: ))((1 xFFx GCMobsGCM
22
1. Split the observation and truncated GCM values into extreme values and other values
2. Fit a gamma distribution for observed daily precipitation series– Fobs(xobs)
3. Fit a gamma distribution for GCM precipitation of the same period – FGCM20(xGCM20)
4. Fit a gamma distribution for 21st century GCM precipitation – FGCM21(xGCM21)
5. Map the GCM distributions onto observed distribution
Major steps for rainfall intensity correction:
))(( 2020
1
20 GCMGCMobsGCM xFFxcorrected
6. Correct the future GCM output with the scale of corrected/raw GCM results
))((
))((
2121
1
20
2121
1
2121
GCMGCMGCM
GCMGCMobsGCMGCM
xFF
xFFxx
corrected
23
Pro
bab
ility
of
no
n-e
xcee
dan
ce
All of the daily precipitation
Top 0.1%
Daily Precipitation
GCM20
Observation
GCM21 GCM21
GCM21corrected
Daily precipitation
Pro
bab
ility
of
no
n-e
xcee
dan
ce
GCM20
Observation
Extreme (top 0.1%) values correction
In this study, extreme values corresponds to top 0.1% probability
of non-exceedance.
Extreme values correction
24
1. Samples except top 0.1% of observation,
GCM present and future truncated data
series are divided into each month.
Pro
bab
ility
of
no
n-x
ceed
ance
GCM20
Observation
Daily Precipitation
GCM21 Except top 0.1%
2. The ratio between observation and
GCM20 is estimated for each month and
each quantile is regarded as correction
coefficient and multiplied to GCM21 of
same month and same quantile and
corrected value is obtained.
Pro
ba
bili
ty o
f N
on
Exce
eda
nce
Daily Precipitation Pro
ba
bili
ty o
f N
on
Exce
eda
nce
Daily Precipitation
Pro
ba
bili
ty o
f N
on
Exce
eda
nce
Daily Precipitation
January February
December
Samples except top
0.1% is divided into
each month.
Other values correction
25
26
GCM GCMcorr
Jan 27 47.2
Feb 87.8 16.9
Mar 25.7 20.2
Apr 5.6 24.9
May 39.5 25.3
Jun 21.6 -13.5
Jul -17.2 -10.8
Aug -19.1 -11.4
Sep 8.5 -7.6
Oct 66.9 41.7
Nov 172.7 -8
Dec -9.8 -2.1
Relative error (%)Month
27
28
29
Conclusive remarks
• Comparison of GCM data series with observation data
series pointed to correct rainfall frequency and
intensity.
• Truncation of GCM data series based on the non-
exceedance probability, F(x_historical=0.0) noticeably
improved the rainfall frequency bias.
• The quantile-based bias correction considerably
improved rainfall intensity for monsoon months (May -
October).
30
Future works
• Testing other probable frequency distributions to the
precipitation data series for better bias correction
• Application of bias-corrected data-series in
hydrological modeling to investigate impact of climate
change on streamflow
31
Thank you!
32