Water Resources Planning and Management
Daene C. McKinney
River Basin Modeling
Water Resources• Water at:
– Wrong place, wrong quantity, wrong time • What to do?• Manipulate the hydrologic cycle
– Build facilities? Remove facilities? Reoperate facilities?
• Reservoirs• Canals• Levees• Other infrastructure
ScalesTime Scales• Water management plans
– Consider average conditions within discrete time periods
• Weekly, monthly or seasonal– Over a long time horizon
• Year, decade, century– Shortest time period
• No less than travel time from the upper basin to mouth
• For shorter time periods some kind of flow routing required
• Flood management– Conditions over much shorter
periods• Hours, Days, Week
Processes
• Processes we need to describe:– Precipitation– Runoff– Infiltration– Percolation– Evapotranspiration – Chemical concentration– Groundwater
Data
• Measurement• Data sources• Flow conditions
– Natural– Present– Unregulated– Regulated– Future
• Reservoir losses• Missing data
– Precipitation-runoff models– Stochastic streamflow
models– Extending and filling in
historic records
Yield
• Yield - amount of water that can be supplied during some time interval
• Firm yield - amount of water that can be supplied in a critical period – Without storage: firm yield is lowest streamflow on record,– With storage: firm yield can be increased to approximately
the mean annual flow of stream
Regulation and Storage
• Critical period - period of lowest flow on record – “having observed an event in past, it is possible to
experience it again in future”
• Storage must be provided to deliver additional water over total streamflow record
• Given target yield, required capacity depends on risk that yield will not be delivered, i.e., the reliability of the system
Hydrologic Frequency Analysis
• Flow duration curves– Percent of time during which specified flow rates
are equaled or exceeded at a given location
Pr{ Q > q }
Central Asia
Naryn River
Syr Darya
Naryn River Annual Flows
Glacier meltMin. flow
Median flow
Naryn River Annual Flows
Quantiles• X is a continuous RV
• p-th quantile is xp
• Median: x50 – equally likely to be above as below that value
• Examples– Floodplain management - the 100-year flood x0.99 – Water quality management
• minimum 7-day-average low flow expected once in 10 years• 10th percentile of the distribution of the annual minima of the 7-day
average flows
p
xp X
FX(x)
Quantiles
• Observed values, sample of size n
largestsmallest
...
)()1(
)()2()1(
n
n
xx
xxx
}Pr{ pxXp
},...,,{ 21 nxxx
• Order statistics (observations ordered by magnitude
• Sample estimates of quantiles can be obtained by using
1
n
ip pi xx )(
},...,,{ 21 nxxx
Flow Duration Curve
P(X>x)= Ranked
Year Flow Rank 1-i/(n+1)= Flow
x i 1-p x(i)
1911 10817 1 0.99 6525
1912 11126 2 0.98 7478
1913 11503 3 0.97 8014
1914 11428 4 0.96 8161
1915 10233 5 0.95 8378
…
1997 10343 87 0.06 15062
1998 14511 88 0.05 15242
1999 14557 89 0.04 16504
2000 12614 90 0.03 16675
2001 12615 91 0.02 18754
2002 16675 92=n 0.01 20725
11}Pr{1
n
ixXp p
Flow Duration Curve
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
0 10 20 30 40 50 60 70 80 90 100
% time equal or exceeded
Flo
w (
mln
m3
)
Firm yield = 6500 mln m3
Secondary yield = 8700 mln m3
Flow duration curve - Discharge vs % of time flow is equaled or exceeded.
Firm yield is flow that is equaled or exceeded 100% of the time
Increase Firm Yield - Add storage
• To increase the firm yield of a stream, impoundments are built. Need to develop the storage-yield relationship for a river
• Simplified methods– Mass curve (Rippl) method– Sequent peak method
• More complex methods– Optimization– Simulation
Simplified Methods
• Mass curve (Rippl) method– Graphical estimate of storage required to supply given
yield– Constructed by summing inflows over period of record and
plotting these versus time and comparing to demands
• Time interval includes “critical period”– Time over which flows reached a minimum– Causes the greatest drawdown of reservoir
Rippl method
Tjiwhere
QRMaximumKj
tttd
211
Rippl Method Qt Rt
t Q(t) Q(t) R(t) R(t)
t Q(t) Q(t) R(t) R(t)
Oct 18 18 9.3 9.3 Apr 1 169 9.3 175.8
Nov 22 40 9.3 18.5 May 0 169 9.3 185.0
Dec 17 57 9.3 27.8 Jun 0 169 9.3 194.3
Jan 26 83 9.3 37.0 Jul 0 169 9.3 203.5
Feb 15 98 9.3 46.3 Aug 0 169 9.3 212.8
Mar 32 130 9.3 55.5 Sep 7 176 9.3 222.0
Apr 8 138 9.3 64.8 Oct 15 191 9.3 231.3
May 3 141 9.3 74.0 Nov 17 208 9.3 240.5
Jun 0 141 9.3 83.3 Dec 25 233 9.3 249.8
Jul 0 141 9.3 92.5 Jan 47 280 9.3 259.0
Aug 0 141 9.3 101.8 Feb 16 296 9.3 268.3
Sep 0 141 9.3 111.0 Mar 18 314 9.3 277.5
Oct 5 146 9.3 120.3 Apr 7 321 9.3 286.8
Nov 6 152 9.3 129.5 May 4 325 9.3 296.0
Dec 6 158 9.3 138.8 Jun 0 325 9.3 305.3
Jan 5 163 9.3 148.0 Jul 1 326 9.3 314.5
Feb 3 166 9.3 157.3 Aug 3 329 9.3 323.8
Mar 2 168 9.3 166.5 Sep 4 333 9.3 333.0
0
50
100
150
200
250
300
350
400
450
500
Oct Apr Oct Apr Oct Apr Oct Apr
Time
tQt
demand
Capacity K
Accumulated Releases, R
Accumulated Inflows, Q
Sequent Peak Method
00
0
1
11
ttt
ttttttt KQRIf
KQRIfKQRK
0
20
40
60
80
100
120
140
October April October April October April October
Time
Infl
ow
, R
elea
se,
Cap
acit
y Rt
Qt
Kt K =120.5
t Rt Qt Kt-1 Kt October 9.25 18 0.0 0.0 November 9.25 22 0.0 0.0 December 9.25 17 0.0 0.0 January 9.25 26 0.0 0.0 February 9.25 15 0.0 0.0 March 9.25 32 0.0 0.0 April 9.25 8 0.0 1.3 May 9.25 3 1.3 7.5 … … … … … May 9.25 0 81.3 90.5 June 9.25 0 90.5 99.8 July 9.25 0 99.8 109.0 August 9.25 0 109.0 118.3 September 9.25 7 118.3 120.5 October 9.25 15 120.5 114.8 November 9.25 17 114.8 107.0 December 9.25 25 107.0 91.3 … … … … … January 9.25 26 45.3 28.5 February 9.25 15 28.5 22.8 March 9.25 32 22.8 0.0