International Workshop on Climate Downscaling studies

Maeng-Ki Kim1, Seonae Kim1, Jinuk Kim2, Jin Heo3, Jeong-Soo Park3,
Won-Tae Kwon4, and Myoung-Seok Suh1
1 Department of Atmospheric Science, Kongju National University, Gongju, Korea
2 National Institute of Meteorological Sciences, Jeju, Korea

3 Department of Statistics, Chonnam National University, Gwangju, Korea
4 The Korean Society of Climate Change Research, Seoul, Korea`

Kim Maeng-Ki., S. Kim, J. Heo, and J-S. Park, 2016: Statistical downscaling for daily precipitation in Korea using combined PRISM, RCM,
and quantile mapping: Part 1, Methodology and evaluation in historical simulation, Asia-Pacific Journal of Atmospheric Sciences152(2),79-89.

INDEX
01 Introduction
02 Data and GIS Information
03 Results
04 Summary
05 Reference2

01 Introduction

Global climate models (GCM) and regional climate
models (RCM) provide climate change data at global
and regional scales, respectively, for practical use,such as climate change adaptation policy-making.
However, dynamic models struggle to provide climatechange data with a horizontal resolution of less than 5
km, mainly due to systematic bias (Giorgi and Mearns,
1991; Chen et al., 1999; Hellström et al., 2001; Kim et al., 2004; Oh
et al., 2004; Varis et al., 2004; Christensen et al., 2008; Hong and
Kanamitsu, 2014) and the computational costs of long-term simulations of various scenario.
In this study, to downscale the climate variables of the RCM to a finer spatial resolution
than the observational station scale, we developed the PRISM-based Dynamic
downscaling Error correction (PRIDE) model, which is suitable for complex
topographies.
3

01 Introduction
Schematic diagram

PRIDE MODEL

Statistical downscaling model for High resolution
Climate Change scenario data

PRISM based Dynamic downscaling Error correction ModelRCM
PRISM based Seasonal Cycle

RCM based Anomaly
Systematic bias

•
•
•
•

Model Seasonal Cycle

DEM Elevation
Topographic facet
Coastal proximity
Distance

Adjustment

Weighting Factors

Quantile mapping

RCP Scenario(IPCC AR5)
HadGEM3-RA (NIMR)

MK-PRISMHigh resolution data (1km)Model Bias Corrected Climate Change Scenario Model4

02 Data and GIS Information
DATA – Observed data
Figure 1 Location of observation stations (circle) and DEM elevation(shading) with 1-km resolution in Korea. Red and blue circles
indicate ASOS and AWS, respectively.

The total number of observation sites : 537
from the Korea Meteorological Agency(KMA)* Automated Synoptic Observation System (ASOS) : 75
* Automated Weather System (AWS) : 462


Variable : daily precipitation data

Period : From 2000 to 2010 (11 years).

DATA – Regional Climate Model
HadGEM3-RA ( derived by the boundary conditions of the historical run of the HadGEM2-AO(CMIP5), which is a contributionof the National Institute of meteorological Sciences, Korea, ( NIMS ))NIMR is participating in the CORDEX with a regional climate model, HadGEM3-RA which is based on the global atmospheric
HadGEM3 of the Met Office Hadley Centre (MOHC) Grid : the horizontal resolution is selected to 0.11°, about 12.5km
 Historical period : 2000 - 2010 (11years)
2000 - 2005 (historical data from RCM)
2006 – 2010 (scenario data of RCP 8.5 from RCM )5

02 Data and GIS Information
GIS Information

Fig. 2. (a) Topographic facet and (b) coastal proximity for a horizontal resolution of 1 km in Korea. The two values listed in the legend of (b)indicate the distance from the coastal line and altitude from sea level, respectively.

Topographic facets, DEM elevation, and coastal proximity are important parameters with significant influence on
climate and weather and thus must be considered in the interpolation to high resolution.
The effect of these parameters is already included in the observation value, especially at monthly or seasonal
timescales rather than daily timescales.

603 Resultsa. MK-PRISM module

a. MK-PRISM module
Y = β1 X + β0(1)

W = [ Fd W(d)2 + Fz W(z)2 ]0.5 W(f) W(p)(2)[[ Eq. (1) ]]Y is the estimated precipitation at the target grid cell.
X is the DEM height at the target grid cell.
β1 and β0 are the regression coefficients.
[[ Eq. (2) ]]W is the total weighting function for the weighted linear regression.
W(d) : Weighting factor of distanceW(z) : Weighting factor of elevation
W(f) : Weighting factor of topographic facetW(p) : Weighting factor of ocean proximity
Fd : the coefficient of the relative importance for the distance (0.8)
Fz : the coefficient of the relative importance for the elevation (0.2)[ we used 0.8(Fd) and 0.2(Fz)based on Daly (2006). ]The MK-PRISM module is Modified Korea- PRISM which was changed beta critical value and applied nonprecipitation zone.
Please refer to Daly (2006), Daly et al. (2008), Kim et al. (2012) and Kim et al. (2013) for details. Below, a brief
7
summary of the module is presented.

03 Resultsa. MK-PRISM module
observation

MK-PRISM

SummerAnnualFig. 4. Spatial distribution of precipitation obtained from observation (left panel) and MK-PRISM (right panel) for
11 years from 2000 to 2010. Upper and lower panels indicate summer and annual precipitation, respectively.

8

03 Resultsa. MK-PRISM module

Observation

MK-PRISM

Fig. 5. Time series of 5-d moving average (red line) of daily precipitation (black line) obtained from (a)observation and (b) MKPRISM for 11 years from 2000 to 2010. The two vertical lines represent the starting
date (19 June) and ending date (24 July), respectively, of the Changma period defined by KMA (2011).



The mean bias for daily precipitation showed the range from minimum value of 0.14 mm/day in
November to maximum value of 0.67mm/day in August.
 The RMSE showed the range from 0.64mm/day in December to 3.68mm/day in August.
9

03 Resultsb. RCM and systematic bias

b. RCM and systematic bias
Although the RCM is the best dynamic downscaling tool for climate change data at a regional scale,it faces some limitations when simulating climatology on a daily timescale and climate variability,
indicating that systematic bias cannot be avoidable in the current state of the art.
In pure scientific studies, anomalies may be more important than climatology because the response
induced by forcing(e.g., greenhouse gas and aerosol forcing) can be evaluated by climate anomalies.
[ RCM minus MK-PRISM ]Fig. 6. Time series of 5-d moving average precipitation anomaly (shading) for RCM compared to the climatological annual cycle (solid line).
Solid lines indicate the precipitation time series estimated by MK-PRISM. Blue and red shading areas represent overestimation andunderestimation, respectively, compared to observation. The two vertical lines represent the starting date (19 June) and ending date (24 July),
respectively, of the Changma period defined by KMA.

The seasonal cycle itself is one of the important components of systematic bias in the RCM.

10

03 Resultsb. RCM and systematic bias

We assumed that the daily precipitation (Pd) about RCM and observation consists of a daily
seasonal cycle component and an anomaly component.
12.5km

12.5kmex) Precipitation on July 10, 2000
m : model, o : observationd : specific day , s : seasonal cycle , a : anomaly

Barnesinterpolation
Method1 km

RCM Daily PRCP
(July 10, 2000)

1 km

RCM Anomaly(July 10, 2000)

pmd

pms  pma

(10)

p od

p os  p oa

(11)

pid

pos  pma

(12)

p id

p os

PRIDv2.0 Daily PRCP
(7.10.2000)

MK-PRISM Climatology(July 10)p ma

RCM Anomaly(July 10, 2000)

11

03 Resultsb. RCM and systematic bias

The RCM significantly underestimates the no precipitation class compared to observation and MK-PRISM
but significantly overestimates light precipitation (0 < P ≤10 mm/day).
The PRIDE v2.0 partially removes the bias in the two peaks and one lull, which indicates the improvementof climate change data comparing with RCM.
[ RCM minus MK-PRISM ][ PRIDE minus MK-PRISM ]Fig. 7. Histogram of daily precipitation (P) for five classes (P = 0, 0 < P ≤10 mm d−1, 10 < P ≤ 80 mm d−1, 80 mm d−1 < P). Red, gray, blue, andblack bar indicate RCM, PRIDE v2.0, MK-PRISM, and observation(OBS), respectively, for 11 years from 2000 to 2010.
12

03 Resultsc. Quantile mapping module and verificationc. Quantile mapping(QM) module and verification
The QM is a popular method for correcting the difference in climate variables between theobservation and model using a Probability Density Function (PDF) or Cumulative Density Function(CDF) framework (Piani et al., 2010a; Gudmundsson et al., 2012; Teutschbein and Seibert, 2012).
We have used CDF fitting as the final step to correct systematic bias.
In QM, the first step is to find a transfer function (TF) between observation data and intermediate
data for the following training period (Piani et al., 2010a, 2010b) based on the gamma distribution
for both the observed and modeled precipitation intensity.

Six Transfer functions (TF)

• Linear TF

CDFobs(f(Pm)) = CDFmodel (Pm)P0 =f (Pm)

(13)
(14)

∶
∶

• Multiple TF:∶• Exponential TF∶:
Piani et al. (2010b).

13

Fig 1(b). Piani et al. (2010b).

03 Resultsc. Quantile mapping module and verification

The transfer functions are estimated at each grid point and each month.
To avoid discontinuity between two neighboring months, the daily TF is determined by the linear
weighting of two TFs based on Piani et al. (2010b) as follows.

Timeinterpolation()

TF-JANex) 11 FEB

Six TFs
TF-FEBex) 23 FEB

PRIDE v2.0
data
Minimum

MAPE•••

MK-PRISM
data

TF-MAR

TF-DECMAPE : Mean Absolute Prediction Errord : day∶m : from the middle day of month.
14

03 Resultsc. Quantile mapping module and verification

Fig. 8. Scatter-diagram of the square root of precipitation (P) from observation (y axis) and PRIDEv2.0 model (x axis) at the sample target grid during (a) January and (b) July for 11 years from 2000 to2010. ECDF for daily precipitation (mm d−1) during (c) January and (d) July.

15

03 Resultsc. Quantile mapping module and verification

The six transfer functions were independently tested for each grid point to obtain the best transfer
function for a given grid point.
We have obtained the spatial distributions from the best transfer function selected for each grid in Jeju
(Fig. 9) and the percentage of the transfer function selected (Table 1).

Table 1 Six transfer function types used in this study andthe percentage of the transfer function selected for Jeju
for the period 2000-2010. Po and Pm represent theobservation and model, respectively. a, b, c, x0, and τ
are the free parameters that are subject to calibration.
Transfer function
:

13.6

:
:
:

Fig. 9. Spatial distribution of the selected transfer function in Jeju. Numerical values
represent the best transfer function for each grid point. See Table 1 for the transfer
function.

2.0
0.7

:

:

Percentage (%)

0.0
21.4
62.3

16

03 Resultsc. Quantile mapping module and verification

Result of K-fold cross-validation

Table 2 Relative mean absolute error (MAE) of daily
precipitation for PRIDE v2.0 and 3.0 in Jeju. The relative
MAE is calculated by ∑where yi and yi
represent the observed and estimated values, respectively.
Month

220.0
155.6

147.1
94.1
77.6

Fig. 10. Histogram verification of daily precipitation (P) for fiveclasses (P = 0, 0 < P ≤ 10 mm/d, 10 < P ≤ 80 mm/d, 80 mm /d < P)
in Jeju for 11 years form 2000 to 2010. Gray, green and blue bars
indicate PRIDE v2.0, v3.0 and MK-PRISM, respectively.`

Relative MAE
PRIDE v2.0

PRIDE v3.0

JAN

0.838

0.620

FEB

1.023

1.113

MAR

1.891

1.183

APR

1.555

1.570

MAY

1.944

1.640

JUN

1.158

1.186

JUL

3.479

2.842

AUG

3.115

1.008

SEP

5.500

2.703

OCT

2.090

1.211

NOV

1.121

0.804

DEC

1.097

1.365

AVERAGE

2.068

1.437
17

04 Summary
In this study, we present the Parameter-elevation Relationships on Independent Slopes
Model (PRISM)-based Dynamic downscaling Error correction (PRIDE) model, which issuitable for complex topographies, such as the Korean peninsula.
The PRIDE model is constructed by combining the PRISM module, the Regional Climate
Model (RCM) anomaly, and quantile mapping (QM) to produce high-resolution (1 km)
grid data at a daily time scale.
The results show that the systematic bias of the RCM was significantly reduced by simply
substituting the climatological observational seasonal cycle at a daily timescale for eachgrid point obtained from the PRISM.
QM was then applied to correct additional systematic bias by constructing the transfer
functions under the cumulative density function framework between the model andobservation using six types of transfer functions.
K-fold cross-validation of the PRIDE model shows that the number of precipitation days
modeled is approximately 90 ~ 121% of the number observed for the five daily
precipitation classes, indicating that the PRIDE model reasonably estimates theobservational frequency of daily precipitation under a quantile framework.
The relative Mean Absolute Error (MAE) is also discussed in the framework of theintensity of daily precipitation.
18

04 Summary

Future ..
• We are applying by Using Multi RCM (Ensemble) and are
producing Future period scenario.
• We are trying to test other QM method (EDCDF, QDM ,DQM..)
for comparing with PRIDE Model.
RCM

PRDv2

PRDv3

EDCDF

QDM

300

4

250

2

200
Days

OBS

0

150
100
50
0

P=0

0<p≤1010<p≤20

20<p≤80p>80

19

05 Reference
Baek, H.-J., J. Lee, H.-S. Lee, Y.-K. Hyun, C. Cho, W.-T. Kwon, C. Marzin, S.-Y. Gan, M.-J. Kim, D.-H. Choi, J. Lee, J. Lee, K.-O. Boo, H.-S.
Kang, and Y.-H. Byun, 2013: Climate change in the 21st century simulated by HadGEM2-AO under representative concentration
pathways. Asia-Pacific J. Atmos. Sci., 49, 603-618. doi:10.1007/s13143-013-0053-7.
Chen, S., J. O. Roads, H. H. Juang, and M. Kanamitsu, 1999: Global to regional simulations of California wintertime precipitation. J. Geophys.
Res., 104, 31517-31532.
Christensen, J. H., F. Boberg, O. B. Christensen, and P. Lucas-Picher, 2008: On the need for bias correction of regional climate change
projections of temperature and precipitation. Geophys. Res. Lett., 35, L20709.
Daly, C., W. Gibson, G. Taylor, G. Johnson, and P. Pasteris, 2002: A knowledge-based approach to the statistical mapping of climate. Clim. Res.,22, 99-113.
Daly, C., E. H. Helmer, and M. Quinones, 2003: Mapping the climate of Puerto Rico, Vieques and Culebra. Int. J. Climatol., 23, 1359-1381.
Daly, C., M. Halbleib, J. I. Smith, W. P. Gibson, M. K. Doggett, G. H. Taylor, J. Curtis, and P. P. Pasteris, 2008: Physiographically sensitive
mapping of climatological temperature and precipitation across the conterminous United States. Int. J. Climatol., 28, 2031-2064.
Giorgi, F., and L. O. Mearns, 1991: Approaches to the simulation of regional climate change: a review. Rev. Geophys., 29, 191-216.
Gudmundsson, L., J. B. Bremnes, J. E. Haugen, and T. Engen-Skaugen, 2012: Technical Note: downscaling RCM precipitation to the station
scale using statistical transformations – a comparison of methods. Hydrol. Earth Syst. Sci., 16, 3383–3390. doi:10.5194/hess-16-3383-2012.
Hellström, C., D. Chen, C. Achberger, and J. Räisänen, 2001: Comparison of climate change scenarios for Sweden based on statistical anddynamical downscaling of monthly precipitation. Clim. Res., 19, 45-55.
Hong, K.-O., M. S. Suh, D.-K. Rha, D.-H. Chang, C. Kim, and M.-K. Kim, 2007: Estimation of high resolution gridded temperature using GIS
and PRISM. Atmosphere, 17, 255-268.(In Korean)Hong, S.-Y. and M. Kanamitsu, 2014: Dynamical downscaling: fundamental issues from an NWP point of view and recommendations. Asia-Pac
J. Atmos Sci, 50(1), 83-104. doi:10.1007/s13143-014-0029-2.
Kim, M.-K., M.-S. Han, D.-H. Jang, S.-G. Baek, W.-S. Lee, Y.-H. Kim, and S. Kim, 2012: Production technique of observation Grid data of 1km
resolution. J. Clim. Research, 7(1), 55-68.(In Korean)Kim, M.-K., D.-H. Lee, and J. Kim, 2013: Production and validation of daily grid data with 1km resolution in South Korea.. J. Clim. Research,
8(1), 13-25.(In Korean)
Oh, J.-H., T. Kim, M.-K. Kim, S.-H. Lee, S.-K. Min, and W.-T. Kwon, 2004: Regional climate simulation for Korea using dynamic downscaling
and statistical adjustment. JMSJ, 82, 1629-1643. doi:10.2151/jmsj.82.1629.
Piani, C., J. O. Haerter, and E. Coppola, 2010a: Statistical bias correction for daily precipitation in regional climate models over Europe. Theor.
Appl. Climatol., 99, 187–192. doi: 10.1007/s00704-009-0134-9.
Piani, C., G. P. Weedon, M. Best, S. M. Gomes, P. Viterbo, S. Hagemann, and J. O. Haerter, 2010b: Statistical bias correction of global simulated
daily precipitation and temperature for the application of hydrological models. J. Hydrol., 395, 199–215. doi:10.1016/j.jhydro.2010.10.024.
Shin, S.-C., M.-K. Kim, M.-S. Suh, D.-H. Jang, C.-S. Kim, W.-S. Lee, and Y.-H. Kim, 2008: Estimation of high resolution gridded precipitation
using GIS and PRISM. Atmosphere, 18, 71-81.(In Korean)
Teutschbein, C., and J. Seibert, 2012: Bias correction of regional climate model simulations for hydrological climate-change impact studies:
review and evaluation of different methods. J. Hydrol., 456–457, 12-29.
Varis, O., T. Kajander, and R. Lemmelä, 2004: Climate and water: from climate models to water resources management and vice versa. Climatic20
Change, 66, 321-344.

THE

END
THANK

YOU

21

03 Resultsa. MK-PRISM module

Distance weighting function in the MK-PRISM is defined as follows.
W d

1 for d
1km
for d 1

(3)

Where d means the distance between grid point and observation distance weighting exponent a of 2 isused.
Elevation weighting are different for three categories as follows.
W z

1 for ∆z∆∆

0 for ∆z∆z
for ∆z

(4)
∆

∆z

∆z

Here ∆z represents the difference in distance between target grid cell and station point.
∆z and ∆z represent the critical value of ∆z for elevation weight of 1 and 0, respectively.
We have used 100m for ∆z and 1000m for ∆z .
Elevation weighting exponent b of 1 is used in this study.
22

03 Resultsa. MK-PRISM module

Facet weighting was defined for two categories in equation (5).
W f
1 for ∆f
1 and B 0
1
for ∆f
1
∆f
B

(5)
0

Where ∆f indicates the difference in topographic facet between target grid cell and station point and B
represents the number of obstacles (between target grid cell and observation point where have different
topographic facet.

Coastal proximity weighting is defined in equation (6).
W p
1 for ∆p00 for ∆p p
1
for 0
∆
∆p

(6)
p

Where ∆p represents the difference in ocean proximity between target grid cell and observation point andp represents critical value of ∆p for coastal proximity weighting of 0.
The coastal proximity exponent (v) of 1.0 is used from sensitivity study in this study.

23

03 Resultsa. MK-PRISM module

Y = β1 X + β0(1)

W = [ Fd W(d)2 + Fz W(z)2 ]0.5 W(f) W(p)(2)
The regression coefficients are estimated by equation (8) and (9) as follows.
̅

∑
∑

∑
∑

,

∑
̅
∑

̅

̅

̅ and

(7)
(8)
(9)

represent the means of variables X and Y, respectively, at the target grid in equation (1).

The subscript i indicates a specific station inside the search range around the target grid.

24

03 Resultsc. Comparing Quantile mapping methods

RCM

PRDv2

PRDv3

EDCDF

QDM

OBS

300
4

250

2

Days

200

0

150
100
50
0

P=0

0<p≤1010<p≤20

20<p≤80

p>80

03 Resultsc. Quantile mapping module and verification

REF. Intelligent Sensor Systems
Ricardo Gutierrez-Osuna
Wright State University 26