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