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IndicatorsofNecessaryStoragesforFloodandDroughtManagement:Towardsglobalmaps(Theory)
Kuniyoshi Takeuchi andMuhammadMasoodInternationalCentreforWaterHazardandRiskManagement(ICHARM),PublicWorks
ResearchInstitute(PWRI),Tsukuba,Japanand
BangladeshWaterDevelopmentBoard(BWDB),Dhaka,Bangladesh
EricWoodSymposium"ObservationsandModeling AcrossScales"
Princeton,2-3June2016
Vol.102,1988
SpecialIssueonUS-JapanHydrologicalSeminar,Hawaii,January5-9,1987
Necessary storagesl Storage is the only means to smooth out the variation
of the flow and make hazards mitigated and resources useful.
l How much smoothing is necessary depends on• Level of variation of inflow• Level of necessary control
• flood channel capacity• target release for water use
• Allowable rate of failure
Necessary storages
l There are various ways of calculating necessary storages under a given level of control and a rate of failure.
l Mass curve, simulation methodsl The use of FDC and DDC is another.
Flood Duration Curves and
Drought Duration CurvesKikkawa & Takeuchi, JSCE1975, Takeuchi and Kikkawa, JSCE 1980, Takeuchi, WRR1986, Takeuchi, JH1988, Masood and Takeuchi, JDR 2015
http://rpitt.eng.ua.edu/Workshop/WSErorionControl/Module4/Module4.htm
For Precipitation
Inte
nsity
(Inch
es/h
our)
Duration (minutes)
Intensity-Duration-Frequency curves
Longer time scale～years
Drought
Discharge
Instantaneous values
Moving averages
MRI-AGCM3.2S1979-2003
Bias corrected by EU WFD
Simulated by BTOP Model (Takeuchi &
Ao, 1999)daily in 20km mesh
The Brahmaputra dischargeat the outlet Bahadurabad
3 years
1 year
FDC-DDC Flood Duration Curves
Drought Duration Curves
FDC
DDC
Fix a time length and find the necessary storage within it.
Prob max()∈+,-.
1𝑚 1 𝑥( ≥ 𝑓5∗ 𝑚
()789:
(;()
≤ 𝛼
Prob min()∈+,-.
1𝑚 1 𝑥( ≤ 𝑓@ 𝑚
()789:
(;()
≤ 𝛽
FDC
DDC
Annual max/min m-day moving average discharge
Definitions of Flood Duration Curves 𝑓5∗ 𝑚and Drought Duration Curves 𝑓@ 𝑚
m0
The maximum average discharge in the next m days
Long termmean
FDC
DDC
The minimum average discharge in the next m days
Target release
5% exceedancelevel discharge over m days
5% non-exceedancelevel drought
Necessary storage𝑓B.BD∗ 𝑚
𝑓B.BD 𝑚
Vfc
Vdm
days
to maintain the control level
Inte
nsity
Durationmm
Qm3/s
QmeanQTarget
Move the point along the duration curve and find the largest rectangular.That is the necessary storage,
Q
t0
Long termmean
FDC
DDCWater supply target
Flood channel capacity
m3/s
Inte
nsity
Duration
Necessary Storage
QT:flood
QT:drought
If control targets are different from the long term mean,
BahadurabadHardingebridge
Bhairab bazar
MRI-AGCM3.2S1979-2003, 2075-2099
Bias corrected by EU WFD
Simulated by BTOP modeldaily in 20km
mesh
Bahadurabad
Hardingebridge
Bhairab bazar
Flood
Drought
Present(1979-2003)
Return period5 years
km3
km3
400
80
MRI-AGCM3.2S1979-2003, 2075-2099
Bias corrected by EU WFD
Simulated by BTOP modeldaily in 20km
mesh
Fig 5. Necessary storage (km3) and Iso-necessary storage (months) at present with maintaining discharge Q=Qmean
Floods
Droughts
km3
mon
ths
Present
QTarget=Qmean
(1979-2003)
MRI Present (1979-2003)
Floods
Droughts
km3
mon
ths
Present
QT=3Qm & 0.5Qm
(1979-2003)
Q
t0
Long termmean
FDC
DDC
Inte
nsity
Duration
Climate change impact
Reservoir volume necessary to maintain Q=Qmean (base period) with 5 years return period (black line for base period, 1979-2003 and red line for future period, 2075-2099)
Example of the FDC-DDC changes in GBM at their outlets.
MRI-AGCM3.2S1979-2003, 2075-2099
Bias corrected by EU WFD
Simulated by BTOP modeldaily in 20km
mesh
Fig 7. Changes of Iso-necessary storage (future-present) with maintaining discharge Q=3*Qmean during flood and Q=0.5*Qmean during drought
Floods
Droughts
km3
Future - Present
Q=3Qm & 0.5QmQ=Qmean
km3
（2075-2099）-（1979-2003）
Fig 7. Changes of Iso-necessary storage (future-present) with maintaining discharge Q=Qmean
Floods
Droughts
%
mon
ths
Future - Present
Q=Qmean
（2075-2099）-（1979-2003）
Fig 7. Changes of Iso-necessary storage (future-present) with maintaining discharge Q=3*Qmean during flood and Q=0.5*Qmean during drought
Floods
Droughts
%
mon
ths
Future - Present
Q=3Qm & 0.5Qm
（2075-2099）-（1979-2003）
Other uses of FDC & DDC
l Necessary storages• Hydro-climatological assessment of difficulty or ease of
water resources management• Reservoir design
l Reservoir operation• Expected precipitation or inflow under a given rate of failure
l Palm print of basin hydrology• Hydrological characterization
MmRIVP m
m m
,...,11
0
1
0=≤⎟
⎠
⎞⎜⎝
⎛≤+∑ ∑
−
=
−
=++ β
ν νντντ
Chance constraint reservoir operationWRR 22(2) 1986
)(mfk
m1
VR
)(2 mf
)(1 mf
Six reservoirs’ total storage in Fukuoka
WarsawKrynica三面（新潟）
FDC-DDC of river discharge
FDC-DDC of local precipitation
Poznan
Poland
沖浦（青森） 厚東川（山口）
JH 102, 1988
Palm Prints of basin hydrology
Why Global Maps?
l Global distribution of hydro-climatological, land cover, and geological heterogeneities in terms of necessary storages to smooth out variations.
l Global maps of relative difficulty or ease of managing hydrological floods and droughts.
l Examine scale effects such as Vfc/Qm, Vdm/Qmean ~ A (PET/P)
Necessary storage and long memory
l Assuming a constant release of the long term mean, Hurst (1951) found the adjusted range Rn*~nH, H~0.72>0.5 in the Nile• Rn*=maxSt*-minSt*, St*=St-(t/n)Sn
l Feller (1951) H~0.5 (Brownian motion)l Mandelbrot (1982) fractal 1/fl Klemes, Moran, Lloyd, ….
Necessary storage From time to space
l Relation between Vfc, Vdm and Rn*l Hurst (1951) Rn*~nH Time domainl What about Vfc/Qm, Vdm/Qm~AK? Space domain
A
V/Qm
Budyko’s aridity index(months or days)
(km2)
? ?
? ? ?
Different hydro-climatic zones
DDC
FDC
Catchment Area km2
V/Q
mm
onth
s
V/Q
mm
onth
sGanges
Brahmaputra
Catchment Area km2X 105
X 105QT=Qmean
MRI-AGCM3.2S1979-2003, 2075-2099
Bias corrected by EU WFD
Simulated by BTOP modeldaily in 20km
mesh
Let us look into diversity of global hydrology
from a storage domain!
Thank you!
FDC-DDC publicationsl Kikkawa, H. and K. Takeuchi (1975.2): Characteristics of drought
duration curve and its application, Proc. JSCE, 234, 61-71l Takeuchi, K. and H. Kikkawa (1980.11): Drought duration curve method
as compared with mass curve method, Proc. JSCE, 303, 53-63l Takeuchi, K. (1986.4): Chance-constrained model for real-time reservoir
operation using drought duration curve, Water Resour. Res., 22(2), 551-558
l Takeuchi, K. (1988.9): Hydrological persistence characteristics of floods and droughts-Interregional comparisons, J. Hydrology, 102, 49-67
l Masood, M and K. Takeuchi (2015.7) Climate change impact on the manageability of floods and droughts of the Ganges-Brahmaputra-Meghna basins using Flood Duration Curves and Drought Duration Curves, J. Disaster Research, 5(10), 991-1000
l Masood, M and K. Takeuchi (2015.10) Persistence Characteristics of Floods and Droughts of the Ganges-Brahmaputra-Meghna Basins Using Flood Duration Curve and Drought Duration Curve, J. Water Resource and Hydraulic Engineering, 4(4), 413-421
Q
t0
Long termmean
FDC
DDCWater supply target
Flood channel capacity
Increase by climate change
Increase by climate change
Inte
nsity
Duration
Climate change impact
FDC DDC
Target discharge Target discharge
Qmean
km3/month
Q=Qmean
months %
Q=3*Qmean
months %
Q=Qmean
months %
Q=0.5*Qmean
months %
Brahma-
putra
present 49.7 4.0 0.05 3.9 0.7
future 57.1 15 6.2 55 0.6 1200 3.7 -5 0.6 -14
Ganges present 40.1 6.0 1.0 5.5 1.2
future 46.8 15 8.4 40 2.5 150 5.3 -4 1.1 -8
Meghna present 10.4 6.1 0.1 5.1 1.7
future 12.4 20 9.6 58 0.8 700 4.8 -6 1.5 -11
The smaller the smoothing capacity, the larger the climate change impact.For annual smoothing for drought, climate change would work favorably.
Climate change impacts on necessary storages
DDC:渇水持続曲線法
! ∑−+
=∈=
⋅=1
,...,1
1
11
1)(mt
ttt
yearjtNj
thk x
mnmismallestkmf
th
"#"$%
土論 234, 1975吉川秀夫+小沢･林・
0
20
40
60
80
Jan-90 Jan-91
流量
（m
3/s）
富士川 船山橋
年最小15日流量
年最小30日流量
1990 1991
120日
60日
年最大流量15日～120日