EVALUATION OF EFFECT OF PMPESTIMATION ON PMF ESTIMATES

Sagar Rohidas Chavan and V. V. SrinivasDepartment of Civil EngineeringIndian Institute of Science

Third National Dam Safety Conference 16-17

February 2017, Roorkee

Major Hydrologic Structures(e.g., dams which are located upstreamof thickly populated areas and/or nuclearfacilities)

2Source: Electronic media

DESIGNFLOOD

PROBABLE MAXIMUM FLOOD(PMF)

DESIGNRAINFALL

PROBABLE MAXIMUM PRECIPITATION(PMP)

Limiting case

PMP: greatest depth of precipitation for agiven duration that is meteorologically possiblefor a watershed (WMO 1986, 2009)

Introduction

PMP Estimation: HERSHFIELD METHOD; MULTIFRACTALAPPROACH

Rainfall-runoff relation: EQUIVALENT GEOMORPHOLOGICALINSTANTANEOUS UNIT HYDROGRAPH (E-GIUH)

Dam break Analysis & Inundation map : HEC-RAS & HEC-Geo RAS

3

Paper Title: EVALUATION OF EFFECT OF PMP ESTIMATION ON PMF ESTIMATES

Frequency analysis of annual maximum precipitation records

4

Hershfield Method [Hershfield 1961, 1965]

4 6 8 10 12 14 16 180

2

4

6

8

10

12

Mean annual maximum 1-day precipitation (cm)

Freq

uenc

y Fa

ctor

(Km

)

tenvt t

n m nPMP t X k t-target location

1

1

1, ,i i

i M nm i

n

X Xk i N

(or)

ICWRCOE 2015 5

Chavan, S. R., and Srinivas, V. V.(2017), Regionalization basedenvelope curves for PMPestimation by Hershfield method.International Journal ofClimatology, Wiley & RoyalMeteorological Society, doi:10.1002/joc.4951

R

A is introduced to increaseproximity of the envelopecurve to points depicting siteshaving ‘low MAMP and highFF’ as well as ‘high MAMP andlow FF’

+L

+L+L

L U

Multifractal field : Precipitation intensity,휀

Properties at different temporal scales described using scale-invariant Multiplicative Cascade Model

Design Probable Maximum Precipitation (DPMP)Pr 휀 > 휆 ∼ 휆

퐷푃푀푃 = 10 휏

푐 훾 : codimension function

6

Multifractal Approach (MA)

1e ec ln p ln ln T ln

L Scale ratio

(Douglas and Barros (2003)

7

Figure:Empirical PDF of 휀 showing hyperbolic falloff, indicating large influence of extreme events on tail probabilities

Test for presence of fractality in observed precipitation

8

100

1,000

1 10

Aλ

(mm

10)

Duration, τ (days)

Figure: Verification of scaling relationship

퐷푃푀푃 = 10 휏

1e ec ln p ln ln T ln

Intercept=B

Max

ima

of a

ccum

ulat

ed ra

infa

ll

L Scale ratio

푐 훾 : codimension function

Design Probable Maximum Precipitation (DPMP)

Case S(km2)

Ω n T(km)

Ra Rb Rl

1 0.9 5 756 2172 4.99 5.00 2.732 4.5 4 152 988 5.77 5.02 2.823 9 4 74 694 4.85 4.18 2.154 22.5 3 29 432 6.68 5.39 3.45

11

0.780.07

0.48

( ) (hour )

where

3.29 (adimensional)

0.70 (hours)

tm k

bl

a

a

b l

t eGIUH tk k m

Rm RR

R LkR R v

Modeling hydrological response of catchments using geomorphological concepts

10

Time (hour)

0 20 40 60 80 1000

0.035

0.07

Time (hour)

GIU

H (1

/hou

r)

11

Moussa (1996) derived the followingformulations for n (number of sources)and T (total length of stream network)

Self-similarity properties of channel networks

0n S S

10-4 10-3 10-2

102

103

S/S0

n

10-4 10-3 10-2106

107

S/S0

T (k

m)

12

0 0A

ST OE S SS

A typical channel network for S = SA

burnt_ASTER burnt_SRTM SRTM ASTER

Equivalent H-S ratios:

Scaling properties: 훼 , 휆퐿 : Equivalent length of highest order stream (km)푣: Representative peak flow velocity in the catchment (km/h)

1

2aeR

122

leR

2beR

Equivalent GIUH

0.7810.07

0.48 0.50.5 1

00

E-GIUH ; where 3.29

0.70 2

tm k

bele

ae

ae e

be le

be lee

le

t e Rm Rk k m R

R LkR R v

R RSL OE SS R

13

Time (hour) Time (hour)

0 20 40 60 80 1000

0.035

0.07

Time (hour)

GIU

H (1

/hou

r)

0 20 40 60 800

0.025

0.05

Time (hour)

E-G

IUH

(1/h

our)

Figure: GIUHs and E-GIUHs constructed for stream networks

ASTER DEM based GIUHASTER DEM based GIUH SRTM DEM based GIUH

SRTM DEM based E-GIUH ASTER DEM based E-GIUH

burnt _SRTM DEM based E-GIUH burnt _ASTER DEM based E-GIUH

Catchment area : 2810 km2

Location: Gorur (near Hassan) in Cauvery river basin, Karnataka Dam features: Height: 58 m; Length: 4692 m Gross storage capacity: 964 MCM Spillway capacity: 3624.5 cumecs

Case study on Hemavathy dam

14

SRTM DEM

Daily Streamflow(1977 to 2011)

Daily rainfall : 49 rain gauges (1970-2011)

Nine major flood events forcalibration of velocity

휙-index technique to determineeffective rainfall hyetographs(ERHs)

Areal average PMP estimation(Thiessen polygon; Kriging)

15

Description of data and methodology

Results

Flow velocity corresponding to PMP

17

Range-1(i 35mm/day) Range-2 (i >35 mm/day)

Representative velocity v corresponding to each of the 9 major floodevents in the catchment was estimated through calibration bygenetic algorithm (GA)

18

PMP estimates obtained based on HM and MA

0

200

400

600

800

1000

HM MA-100 MA-500 MA-1000

2-da

y PM

P

y y y

(mm

)

0

200

400

600

800

1000

HM MA-100 MA-500 MA-1000

3-da

y PM

P

y y y

(mm

)

19

PMF hydrographs obtained based on HM and MA

Existing spillway capacity of the dam: 3,624.5 m3/s

0.0E+0

2.0E+3

4.0E+3

6.0E+3

8.0E+3

1.0E+4

1.2E+4

1.4E+4

1.6E+4

1.8E+4

0 50 100 150

PMF

(m3 /

s)

Time (hours)

PMP duration = 2 days

0.0E+0

2.0E+3

4.0E+3

6.0E+3

8.0E+3

1.0E+4

1.2E+4

0 50 100 150

PMF

(m3 /

s)

Time (hours)

PMP duration = 3 days

PMP(HM)>> PMP(CWC)10,000 m3/s >> PMP (MA)

20

Table 2. Dam breach Data

Breach method Froehlich (2008)

Top of dam elevation 894.81 m

Breach bottom elevation 850 m

Pool elevation at failure 894.1 m

Pool volume at failure 1050.6 Mm3

Failure mode Overtopping

Dam Crest Width 2.44 m

Slope of U/S Dam face Z1 (H:V) 3:1

Slope of D/S Dam face Z2 (H:V) 2:1

Water surface elevation that triggers failure 894.81 m

Breach formation time (h) 4.05

Breach section side slopes (H:V) 1:1

Final bottom width of breach 270 m

Final bottom elevation of breach 850 m

Breach weir coefficient 2.6

21

Average Breach Width

Vw : water volume above the breach bottom at the time of failure which can be considered as volume of water in the reservoir at the time of failure (1050.6 Mm3)

ICWRCOE 2015 22

Breach Formation time

Hb : Height of water above the breach bottom at the time of failure (Height of the dam=44.81 m)

23

HM Multifractal

Inundation map corresponding to 2-day duration PMP

ICWRCOE 2015 25

0 20000 40000 60000 80000 100000750

800

850

900

950

DBA_hema_Hersh_2day Plan: Plan_25km_Hersh2day 2/17/2017

Main Channel Distance (m)

Elev

atio

n (m

)Le gend

EG Max WS

WS Max WS

Crit Max WS

Ground

Hema_25 1

maximum height/depth of water reached during the flood event based on HM

0 20000 40000 60000 80000 100000740

760

780

800

820

840

860

880

900

DBA_hema_MA_1000 Plan: Plan_25km_MA1000_2day 2/17/2017

Main Channel Distance (m)

Elev

atio

n (m

)

Le ge nd

EG Max WS

WS Max WS

Crit Max WS

Ground

Hema_25 1

Uncertainty in PMP & PMF estimates cannot be ignored in dam break analysis studies.

Implications of the uncertainty on area inundated downstream of dams is worth investigation

Conclusion

26

Acknowledgements Directorate of Economics and statistics, Bangalore Water Resources Development Organization (WRDO), Karnataka Central Water Commission (CWC)

Thank you

Bernardara P., Schertzer D., Sauquet E., Tchiguirinskaia I, Lang M. (2008). The flood probability distributiontail: how heavy is it? Stochastic Environmental Research and Risk Assessment, 22(1): 107-122.

Chavan, S. R., and Srinivas, V. V. (2015) Effect of DEM Source on Equivalent Horton-Strahler Ratio basedGIUH for Catchments in Two Indian River Basins. Journal of Hydrology, Elsevier, Netherlands, 528(1-4): 463-489.

Chavan, S. R., and, Srinivas, V. V. (2016) An approach to assess impact of climate change on estimates ofPMP and PMF, Proceedings of Second National Dam Safety Conference, IISc Bangalore, 12-13January, 2016, pp.55-63.

Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology. Mc-Graw Hill, New York.Douglas, E. M., and Barros, A. P. (2003) Probable Maximum Precipitation Estimation Using Multifractals:

Application in the Eastern United States. Journal of Hydrometeorology, 4: 1012–1024.Gupta, V. K., Waymire, E., and Wang, C.T. (1980) A representation of an instantaneous unit hydrograph

from geomorphology. Water Resources Research. 16(5): 855–862.Hubert, P., Tessier, Y., Lovejoy, S., Schertzer, D., Schmitt, F., Ladoy, P., Carbonnel, J.P., Violette, S., and

Desurosne, I. (1993) Multifractals and extreme rainfall events. Geophysical Research Letters, 20(10):931-934.

Moussa, R. (2009) Definition of new equivalent indices of Horton-Strahler ratios for the derivation of theGeomorphological Instantaneous Unit Hydrograph. Water Resources Research, 45, W09406. DOI:10.1029/2008WR007330.

Rodríguez-Iturbe, I., and Valdés, J. B. (1979) The geomorphologic structure of hydrologic response. WaterResources Research, 15(6): 1409 – 1420.

Rosso, R. (1984) Nash model relation to Horton order ratios. Water Resources Research, 20(7): 914 – 921.Swain, R. E., England, J. F., Bullard, K. L., and Raff, D. A. (2004) Hydrologic hazard curve estimating

procedures. Research report DSO-04-08, U.S. Department of Interior, Bureau of Reclamation.World Meteorological Organization (2009) Manual on Estimation of Probable Maximum Precipitation

(PMP). World Meterological Organization, WMO-No. 1045, Geneva, Switzerland.

References

28

29

Event No.

Effective Rainfall Hyetograph (ERH)

(mm)

Direct Runoff Hydrograph (DRH) (m3/s)

1 10.23, 9.87 159.20, 366.96, 93.65, 14.22, 7.98 2 8.52, 18.52 243.48, 351.70, 81.16, 50.99, 12.48, 11.78 3 5.51, 38.02, 16.45, 3.93 349.96, 697.85, 501.88, 300.37, 201.51, 70.41, 36.41 4 7.73, 29.89 232.38, 693.69, 88.44, 55.84

5 3.49, 62.28, 67.74, 51.03

375.29, 1275.01, 1644.40, 339.17, 269.85, 190.42, 172.73, 97.12, 81.17, 78.39, 78.04

6 9.78, 21.63 324.30, 458.53, 65.90, 5.20

7 36.19, 102.59 767.91, 2382.13, 567.09, 302.10, 121.40, 105.79, 40.93, 8.09

8 4.48, 13.14, 27.05, 8.52 202.90, 366.27, 730.46, 382.92, 72.15, 34.34, 8.33 9 17.19, 35.38, 27.10 366.27, 826.54, 805.02, 298.29, 174.47, 94.34, 57.93, 39.54

Table 2. Effective rainfall hyetograph (ERH) and direct runoff hydrograph(DRH) at 1-day

interval for the selected 9 major historical flood events occurred in the catchment of

Hemavathy dam.

30

Figure 2. Self-similarity properties of the channel network

10-2

101

102

S/S0

n

10-2

105.3

105.5

105.7

105.9

S/S0

T (k

m)

31