THA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

Change of the Probability Distribution of Annual Maximum River
Discharge Derived from the d4PDF datasets at the Indochinese
Peninsula
Patinya HANITTINAN1 *, Yasuto TACHIKAWA2, Yutaka ICHIKAWA3and KazuakiYOROZU4

Abstract This study investigates the differences in theprobability distribution function of the future annual
maximum river discharges (2051-2110) at the
Indochinese Peninsula derived from the new climate
datasets – database for Policy Decision making for
future climate change (d4PDF). First, daily riverdischarge of the future period was simulated using thekinematic wave flow routing model, 1K-FRM. Based on
this analysis, we combined fifteen 60-member
ensembles separately for six different sea surface
temperature (SST) patterns, which allows us to examine
the statistical significant of the difference between theprobability distribution. Then, we applied a nonparametric, two-sample Kolmogorov-Smirnov (K-S) test
to the annual maximum river discharge produced by
SST patterns in 15 groups. Finally, the results of eachcase indicate that the differences in probability
distribution of the annual maximum discharges are
statistically significant for the majority of the
Indochinese Peninsula, except parts of the Mekong delta
and southern Peninsulain Thailand. The implication ofthis finding should help underpin the case to merge thedatasets from different SST patterns and fully utilize itin frequency analysis of extremely large datasets for amore credible hydrologic impact assessment.
Keywords Climate change, Indochinese Peninsula,
d4PDF, Kolmogorov-Smirnov test, 1K-FRM, Annual
maximum daily discharge
1Patinya Hanittinan
Graduate School of Engineering, Kyoto University
Kyoto, Japan
Hanittinan.patinya.77a@st.kyoto-u.ac.jp
Authors Name/s per 2nd Affiliation (Author)
2
Yasuto Tachikawa
Graduate School of Engineering, Kyoto University
Kyoto, Japantachikawa@hywr.kuciv.kyoto-u.ac.jp
3
Yutaka Ichikawa
Graduate School of Engineering, Kyoto University
Kyoto, Japan
Ichikawa@hywr.kuciv.kyoto-u.ac.jp
4
Kazuaki Yorozu
Graduate School of Engineering, Kyoto University
Kyoto, Japan
Yorozu@hywr.kuciv.kyoto-u.ac.jp

Introduction
It is widely acknowledged thatwarming of climatechange will have impacts on global hydrological cycle(Kundzewicz et al., 2007), with implications for thedrainage basin that vary in scale from small to medium
sized catchments (Chun et al., 2009; Thompson, 2012),
major to regional river basins (Conway and Hulme,
1996; Arnell, 1999), and global scales (Nohara et al.,2006; Gosling et al., 2010; Nakaegawa et al., 2013;
Hirabayashi et al., 2013).
To understand the effect of changing climate to those
sectors, General Circulation Models (GCMs) are served
as fundamental tools in future projections with
continuing improvements in recent years. However,there are a range of uncertainties that are introduced
throughout
thesehydro-meteorologicalimpactassessments. First, uncertainty is related to the definitionof the greenhouse gases emission scenarios used to force
the GCMs. Secondly, uncertaintyis associated with theinternal variability, which representsthe naturalfluctuation of climate at daily to multi-decadal timescale (Karoly and Wu, 2005).Structural model
uncertainty caused by difference use of the GCMs andleads to various projections presents a third source of
uncertainty.
In general, quantification of all aspect of climate
projection uncertainty ideally requires multi-model
ensembles in complement with the exploration of singlemodel uncertainty using perturbed physics ensemble(PPEs) experiments. In practice, however, single
projection of climate response to increasing GHGs
emissions, are far more useful to practitioners andpolicymakers when they accompanied by some measureof the associated uncertainty. There have been studies
that utilize the latter method, which are sets ofsimulation within single GCM but different choices forvarious parameters perturbation, with aim toanalyze
uncertainty in projections of surface air temperatures,aerosol forcing, greenhousegases concentrations, andprecipitation(Murphy et al., 2004; Endo et al., 2012;
Mizuta et al., 2014)by using large and diverse sets ofrealizations to generate probability density function(PDFs) of extreme events at regional scale. Naturally,
impact of climate change on surface water distribution
cascades from the onset of changes in precipitation andits variability to a total runoff, and finally becomes a

THA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

river discharge. Therefore, analysis of its implication toa hydrological cycle will yield significant values to theprocess of developing adaptation strategies.
To increase reliability of the probabilistic analysis of
the future hydrological variables, one way to address
this challenge is to combinemultiple projections given
by PPEs. Unfortunately,relying only on large number ofsamples could give misleading results because the datafrom different perturbed ensemble might not originate
from an identical source of population and could also
have different prior distribution functions. For theformer question, several studies were conducted andfound that uncertainty in the tropical cyclone activity,
precipitation, total runoff, and annual maximum daily
dischargesin mainland Southeast Asia and South Asia
are derived mainly from differences in the cumulus
schemes rather than the different sea surface
temperature (SST) patterns (Endo et al., 2012;
Murakami et al., 2012; Hanittinan et al., 2015).
Here we focus on the latter part of the question;
therefore, we proceed to analyze the change of theprobability distribution function of annual maximum
daily discharge projections, derived from the latest 60km-mesh extremely large multi-SST ensembles of MRIAGCM 3.2H under the same cumulus parameterization
scheme (Yoshimura et al., 2011) – d4PDF, to examine
the statistical difference of its prior empirical
distribution function. The two-sample KolmogorovSmirnov test (K-S test) was conducted with the
projected discharges in the Indochinese Peninsula (seeFig.1).
Characteristics of the d4PDF forcing data
The GCM outputs utilized in this study were generated
by the atmospheric general circulation model MRIAGCM 3.2H developed by the Meteorological ResearchInstitute, Japan and archived in the d4PDF database.
The dataset has two major sets of experiments: thepresent climate (1951-2010) with 100 perturbed
ensembles and the future 4K warming experiment(2051-2110) with 90 perturb ensembles from six
different SST patterns, e.g., CCSM4 (CC), GFDL-CM3(GF), Had-GEM2-AO (HA), MIROC5 (MI), MPI-ESMMR (MP) and MRI-CGCM3 (MR), under the
Yoshimura cumulus convection scheme.
Modeling Approach: River flow routing modelRiver discharge in the Indochinese Peninsula region
was projected using flow routing model 1K-FRM. 1KFRM is a physically-based, distributed flow routing
model
with
kinematic
wave
approximation(Hunukumbura et al., 2012). 1K-FRM was based on awatershed topography model. The topographic
information used for 1K-FRM in this study was
generated from processing scale-free global streamflow
network datasetswith a spatial resolution of 5 arc
minute.

Fig. 1 The Indochinese Peninsula and its major river basins(Masutani et al., 2006). The flow direction is definedusing the 8-direction method which assumes the flow
direction to the steepest downward slope to an
immediate neighboring cell. The total runoff from thed4PDF is then routed by the kinematic wave equations
at each flow element in accordance with the flow
direction information.
Two-sample Kolmogorov-Smirnov test
The non-parametric, two-sample KolmogorovSmirnov test statistics (Dn) was used to determine thechange in distributions of the future annual maximum
daily from each possible groups of the 15-cluster 6-SST
patterns 60-member (6x60x15 = 900) ensembles of thed4PDF.This measure is defined as the maximum
difference between two cumulative distributionfunctions, ranged between 0 and 1. Therefore, in thiscase, the Kolmogorov-Smirnov statistics is:

Dn ,n' = Sup F1,n ( x) − F2,n' ( x)(1)xWhere F1,n and F2,n are the empirical distributionfunctions of the first and the second sample respectively,
and sup is the supremum function.
The null hypothesis H0 for the statistical testing of priordistribution function difference of the river discharge
was assumed that there is no significance difference
between the annual maximum daily discharges derived
from the pairs of the d4PDF SST patterns. The null
hypothesis is rejected at level α if

Dn ,n' > c(α )n + n'nn '(2)

Where n and n’ are the sizes of first and second sample of
the annual maximum daily discharge from two SST
patterns of future climate. The value of c(α) is equal toTHA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

(1) CC-GF(2) CC-HA(3) CC-MI(4) CC-MP(5) CC-MR(6) GF-HA(8) GF-MP(7) GF-MI(9) GF-MR
Fig. 2 Geographical distribution of the Kolmogorov-Smirnov test statistics of annual maximum daily discharge foreach pair of the d4PDF SST patterns
1.36 at 95% confidence level. According to the equation distribution for each group were calculated at each grid2, KS statistics exceeding 0.0641 indicates rejection of the point. On the entire Indochinese Peninsula standpoint,null hypothesis.
there are only two cases where most of the river basins
signal rejection of the null hypothesis. However, On thebasins scale, the very clear rejections of the null
Results and discussions
hypothesis were found at the Irrawaddy, Chao Phraya,(1) Two-sample Kolmogorov-Smirnov test statistics
and the Mekong River Basin with remarkably similar
Figure 2 and 3 present geographical distribution of the patterns in12 of 15 groups of SST patterns. Meanwhile,
Kolmogorov-Smirnov statistics (Dn) from 15 groups of The KS statistics is also high at the Salween River basin,
the 900-members annual maximum daily discharge of but only reject the null hypothesis in 8 of 15 cases, with
the Indochinese Peninsula of each SST patterns.
Statistically significant changes in the probability

THA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

(10) HA-MI(11) HA-MP(12) HA-MR(13) MI-MP(14) MI-MR(15) MP-MR
Fig. 3Same as Figure 2 but for the remaining groups of annual maximum daily discharge from d4PDF SST patterns(a)(b)
Fig. 4 KS statistics evaluation consistency (a) the case of KS statistics null hypothesis acceptance and (b) the case of
KS statistics null hypothesis rejection
the other 4 cases indicated the acceptance of the null
hypothesis. For parts of Mekong Delta and thesouthernIndochinese Peninsula, the changes in theprobability distribution are found not to be statisticallysignificantin most of the group of d4PDF SST patterns(13-14 cases). The characteristics of change in theprobability distributionat the Red River Basin in
Vietnam was found having unique pattern, whichchange of the probability distribution is statisticallysignificant in 7 out of 15 cases. Figure 4a and 4b
summarize K-S statistical evaluation consistency of thechange in probability distribution of SST-derived annual
maximum daily discharge of the Indochinese Peninsula.
For the case of hypothesis acceptance, most of theregion, except the middle part of Mekong Delta and theSouthern Indochina (parts of Phetchaburi River Basin ofThailand), are predicting the significant difference in
only 3 to 7 cases of total 15. In contrast, the case of
hypothesis rejection,is broadly consistent across the
Irrawaddy Basin, the middle part of Mekong Basin, andChao Phraya River Basin.
The implication of hydrologic analysis for the resultsin Figure 2,3 and 4 can be summarized as follows:
1) In the region where null hypothesis is rejected
imply that the difference in the priorprobability distribution function between the
two SST-derived annual maximum daily
discharge are significant.Combination of thetwo rejected datasets could increase the river

THA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

discharge projection uncertainty for eachparticular grid points.
2) In the region where null hypothesis is not
rejected imply the opposite outcome, whichmeans that the difference in the priorprobability distribution between the two SSTderived annual maximum daily discharge are
not statistically significant. Therefore, thecombined ensemble in the non-rejected region
should bring more reliable probabilistic
projection of the changes in probability density
function (PDF) of the annual maximum daily
discharge of the Indochinese Peninsula.
This study could potentially be served as acomplementary to the past studies (Nakaegawa et al.,2006; Endo et al., 2012; Murakami et al., 2015;
Hanittinan et al., 2015), which indicated that theuncertainty of hydro-meteorological data, e.g.,precipitation, runoff, and river discharge in terms of
total variance due to non-uniform mother population andshould underpin the case to combine the datasets that
met the criteria set by the aforementioned articles andthe one proposed in this study.In addition to the regionwide analysis, results of the KS test to examine
statistical difference of the changes in the probability

distribution at two selected locations, were also
analyzed.
(2) Two-sample Kolmogorov-Smirnov analysis atselected gauging stations
Table 1presents an outcomes of the K-S test atselected locations 1) C.2 station of Chao Phraya Basinand 2) Kampong Chhnang station of Mekong Delta. The
results at C.2 station showed that there are4cases of the
SST patterns groups that the annual maximum daily
discharge projection difference are not statisticallysignificant (CC-MP, CC-MR, GF-MI, HA-MR).
Meanwhile, there are 11 possible combinations of the
SST patterns that the null hypothesis was rejected (CCHA, CC-MI, CC-MR, GF-MP, GF-MR,HA-MI, HAMP, HA-MR, MI-MP, MI-MR, MP-MR). Thereby, thecombination of 1800-member ensembles(900 + 900
samples) from the combination between the two SST–
derived annual maximum daily discharge at C.2 station
could potentially utilized to better construct theprobability density function of the annual maximum
daily discharge. Meanwhile, much larger numberof
samplesup to 3,600-member ensemble of the annual
maximum daily discharge (CC-HA-MI-MR) could be
used for the same purpose at Kampong Chhnang station.

Table 1K-S statistics evaluation of the null hypothesis at two selected gauging stations (C.2 and Monywa stations)
SST patterns

KS test statistics (Dn) null hypothesis evaluation
GF
HA
MI
MP
C.21
K2
C.21
K2
C.21
K2
C.21
K2
✘
✘
✘
✔
✘
✔
✔
✘
✘
✘
✔
✘
✘
✔
✘
✘
✘
✔
✘
✔
✔
✘
✘
✔
✘
✔
✘
✔
✘
✔
✘
✔
✘
✔
✔
✔
✘
✔
✘
✔

CC
C.21
✘
✘
✘
✔
✔

CC
GF
HA
MI
MP
MR

K2
✘
✔
✔
✘
✔

MR
C.21
K2
✔
✔
✘
✔
✔
✔
✘
✔
✘
✔
-

1

C.2 = C.2 river gauging station in the Chao Phraya River Basin
K = Kampong Chhnang gauging station in the Mekong Delta2✔=

acceptance

of

the

null

hypothesis,

Conclusions
In this study, difference between the two probability
distribution function of the annual maximum daily
dischargeforced by the total runoff from 15 groups ofsea surface temperature patterns, was investigated using
the non-parametric, two-sample Kolmogorov-Smirnov
test. The Indochinese Peninsula was chosen as thestudied area. Application of the two-sample K-S test to
the studied area showed that there is significant
difference between cumulative probability distributionof the annual maximum daily discharge in most of the
SST combinations (12 cases out of 15) at the Irrawaddy
River Basin, Chao Phraya River Basin, the middle partof Mekong River Basin, and 8 out of 15 combinations at
the Salween Basin. The finding also showed that thedifference of the probability distribution at the Mekong
Delta and the southern Indochinese Peninsula in✘=rejection
of
the
null
hypothesis
Thailand are not statistically significant in most of the
SST combination, with only 1-3 cases that the null
hypothesis has been rejected.
These findings help clarified that it is possible toincrease a number of sample in the future annual
extreme river discharge datasets in the Indochinese
Peninsula up to multi thousands, which should better
derive probability density function and could be useful
the hydrological analysis of extreme floods. Future
research must also focus on investigating the otherhydro-meteorological variables such as precipitation andtotal runoff to help confirms and explains thecharacteristics of the detected changes of annual
maximum daily discharge of the Indochinese Peninsula.

THA 2017 International Conference on“Water Management and Climate Change Towards Asia's Water-Energy-Food Nexus”
25 - 27January 2017, Bangkok, Thailand.

Acknowledgements

This study utilized the database for Policy Decision
making for Future climate change (d4PDF), which
was produced under the SOUSEI program.
References
Arnell, N.W., Osborn, T., 2006. Interfacing Climate andImpacts Models in Integrated Assessment Modelling,
Tyndall Centre for Climate Change ResearchTechnical Report 52. Tyndall Centre for Climate
Change Research, Southampton and Norwich.
Conway, D., Hulme, M., 1996. The impacts of climate
variability and future climate change in the Nile Basinon water resources in Egypt. Int. J. Water Resour.
Dev. 12, 277–296.
Endo, H., Kitoh, A., Ose, T., Mizuta, R., and Kusunoki,S.: Future changes and uncertainties in Asian
precipitation simulated by multiphysics and multi–sea
surface temperature ensemble experiments with highresolution
MeteorologicalResearch
Instituteatmospheric general circulation models (MRIAGCMs), J. Geophys. Res., 117, D16118, 2012.
Gosling, S.N., Bretherton, D., Haines, K., Arnell, N.W.,
2010. Global hydrology modelling and uncertainty:
running multiple ensembles with a campus grid.
Philos. Trans. Roy. Soc. A 368, 1–17.
Hanittinan P, Tachikawa Y, Ichikawa Y, Yorozu K.
2016. Evaluation of Future River Discharge
Uncertainties In the Indochina Peninsula Simulated byMulti-Physics Ensemble Experiments Using Two-way
ANOVA. Journal of Japan Society of Civil Engineers,
Ser. B1 (Hydraulic Engineering)72(4): I_13-I_18.
Hirabayashi, Y., Mahendran, R., Koirala, S.,
Konoshima, L., Yamazaki, D., Watanabe, S., Kim, H.,
and Kanae S., 2013. Global flood risk under climatechange Nat. Clim. Change 3, 816–21.
Hunukumbura, P.B., Tachikawa, Y., Shiiba, M., 2012,
Distributed hydrological model transferability acrossbasins with different physio-climatic characteristics.
Hydrological Processes, 26 (6), 793- 808.
Karoly, D.J., Wu, Q., 2005. Detection of regionalsurface temperature trends. J. Clim. 18, 4337–4343.
Kundzewicz, Z.W., Mata, L.J., Arnell, N.W., Döll, P.,
Kabat, P., Jiménez, B., Miller, K.A., Oki, T., Sen, Z.,
Shiklomanov, I.A., 2007. Freshwater resources andtheir management. In: Parry, M.L., Canziani, O.F.,
Palutikof, J.P., van der Linden, P.J., Hanson, C.E.
(Eds.), Climate Change 2007: Impacts, Adaptation and
Vulnerability. Contribution of Working Group II tothe
FourthAssessment
ReportoftheIntergovernmental Panel on Climate Change.
Cambridge University Press, Cambridge, pp. 173–210.
Masutani, K., Akai, K., Magome, J. (2006) A new
scaling algorithm of gridded river networks, Japan
Society of Hydrology and Water Resources, 19 (2),139 – 150 (in Japanese)
Mizuta, R., Arakawa, O, Ose, T, Kusunoki, S., Endo,
H., and Kitoh, A.: Classification of CMIP5 futureclimate responses by the tropical sea surface
temperature changes. SOLA, 10, 167-171, 2014,
doi:10.2151/sola.2014-035.
Murakami H, Wang Y, Yoshimura H, Mizuta R, Sugi
M, Shindo E, Adachi Y, Yukimoto S, Hosaka M,
Kusunoki S, Ose T, Kitoh A. 2012. Future Changes inTropical Cyclone Activity Projected by the New HighResolution MRI-AGCM. J.Climate. 25: 3237-3260.
DOI: 10.1175/JCLI-D-11-00415.1.
Murphy, J. M., Sexton, D. M. H., Barnett, D. N., Jones,
G. S., Webb, M. J., Collins, M. & Stainforth, D. A.
2004 Quantification of modelling uncertainties in alarge ensemble of climate change simulations. Nature
429, 768–772. (doi:10.1038/nature02771)
Nakaegawa, T., Nakamitsu, M. 2006. Change in the
Probability Density Function of 500-hPa Geopotential
Heights during the El Niño and La Niña events.
Papers in Meteorology and Geophysics, 56, 25-33.
Nakaegawa, T., Kitoh, A., Hosaka, M. 2013: Dischargeof major global rivers in the late 21st century climate
projected with the high horizontal resolution MRIAGCMs -overview-. Hydrological Processes, 27,
3301-3318. /doi:10.1002/hyp.9831
Nohara, D., A. Kitoh, M. Hosaka, and T. Oki. 2006,
Impact of climate change on river discharge projectedby multimodel ensemble, J. Hydrometeorol., 7(5),1076–1089.
Thompson, J.R., 2012. Modelling the impacts of climatechange on upland catchments in southwest Scotlandusing MIKE SHE and the UKCP09 probabilistic
projections. Hydrol. Res. 43, 507–530.
Yoshimura H, Mizuta R, Murakami H. 2015. A Spectral
Cumulus Parameterization Scheme Interpolating
between Two Convective Updrafts with SemiLagrangian
CalculationofTransport
byCompensatory Subsidence. Mon. Wea. Rev. 143: 597621. DOI: 10.1175/MWR-D-14-00068.1