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