EVALUATION OF EFFECT OF PMP ESTIMATION ON PMF ESTIMATES Sagar - - PowerPoint PPT Presentation

EVALUATION OF EFFECT OF PMP ESTIMATION ON PMF ESTIMATES

Sagar Rohidas Chavan and V. V. Srinivas

Department of Civil Engineering Indian Institute of Science

Third National Dam Safety Conference 16-17 February 2017, Roorkee

M ajor Hydrologic Structures (e.g., dams which are located upstream

• f thickly populated areas and/or nuclear

facilities)

2

Source: Electronic media

DESIGN FLOOD

PROBABLE M AXIM UM FLOOD (PM F)

DESIGN RAINF ALL

PROBABLE M AXIM UM PRECIPITATION (PM P)

Limiting case

PM P: greatest depth of precipitation for a given duration that is meteorologically possible for a watershed (WM O 1986, 2009)

Introduction

PM P Estimation: HERSHFIELD M ETHOD; M UL TIFRACTAL APPROACH Rainfall-runoff relation: EQUIVALENT GEOM ORPHOLOGICAL INSTANTANEOUSUNIT HYDROGRAPH (E-GIUH) Dam break Analysis & Inundation map : HEC-RAS& HEC-Geo RAS

3

Paper Title: EVALUATION OF EFFECT OF PM P ESTIM ATION ON PM F ESTIM ATES

 Frequency analysis of annual maximum precipitation records

4

Hershfield M ethod [Hershfield 1961, 1965]

4 6 8 10 12 14 16 18 2 4 6 8 10 12

Mean annual maximum 1-day precipitation (cm) Frequency Factor (Km)

 

 

 

 

 

t

env t t n m n

PMP t X k   

t-target location

       

1 1

1, ,

i i i M n m i n

X X k i N 

 

   

(or)

ICWRCOE 2015 5

Chavan, S. R., and Srinivas, V. V. (2017), Regionalization based envelope curves for PM P estimation by Hershfield method. International Journal

• f

Climatology, Wiley & Royal M eteorological Society, doi: 10.1002/ joc.4951

R

A is introduced to increase proximity

• f

the envelope curve to points depicting sites having ‘low M AMP and high FF’ as well as ‘high M AMP and low FF’

+L +L +L L U

 M ultifractal field : Precipitation intensity,  Properties at different temporal scales described using scale-

invariant M ultiplicative Cascade M odel

 Design Probable M aximum Precipitation (DPM P)

Pr > ∼

= 10 : codimension function

6

M ultifractal Approach (M A)

 

 

     

1 e e

c ln p ln ln T ln   



  L   

Scale ratio (Douglas and Barros (2003)

7

Figure:Empirical PDF of 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

= 10

 

 

     

1 e e

c ln p ln ln T ln   



 

Intercept=B M axima of accumulated rainfall

L   

Scale ratio

: codimension function

Design Probable M aximum Precipitation (DPM P)

Case S (km2) Ω n T (km) Ra Rb Rl 1 0.9 5 756 2172 4.99 5.00 2.73 2 4.5 4 152 988 5.77 5.02 2.82 3 9 4 74 694 4.85 4.18 2.15 4 22.5 3 29 432 6.68 5.39 3.45

 

1 1 0.78 0.07 0.48

( ) (hour ) where 3.29 (adimensional) 0.70 (hours)

t m k b l a a b l

t e GIUH t k k m R m R R R L k R R v

         

                                  

Modeling hydrological response of catchments using geomorphological concepts

10

Time (hour)

20 40 60 80 100 0.035 0.07

Time (hour) GIUH (1/hour)

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

Self-similarity properties of channel networks

 

n S S









10

• 4

10

• 3

10

• 2

10

10

S/S0 n

10

• 4

10

• 3

10

• 2

10

10

S/S0 T (km)

 

1 2 A

S T OE S S S



 

 

          

A typical channel network for S = SA

burnt_ASTER burnt_SRTM SRTM ASTER

 Equivalent H-Sratios:  Scaling properties: , : Equivalent length of highest order stream (km) : Representative peak flow velocity in the catchment (km/ h)

1

2

ae

R

 

       

1 2

2

le

R

 

       

2

be

R



 

Equivalent GIUH  

0.78 1 0.07 0.48

0.5 0.5 1

E-GIUH ; where 3.29 0.70

2

t m k be le ae ae e be le

be le e le

t e R m R k k m R R L k R R v

R R S L OE S S R





       



                                     

  

13 Time (hour) Time (hour)

20 40 60 80 100 0.035 0.07

Time (hour) GIUH (1/hour)

20 40 60 80 0.025 0.05

Time (hour) E-GIUH (1/hour) Figure: GIUHs and E-GIUHs constructed for stream networks

ASTER DEM based GIUH H 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 M CM Spillway capacity: 3624.5 cumecs

Case study on Hemavathy dam

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SRTM DEM Daily Streamflow(1977 to 2011) Daily rainfall : 49 rain gauges (1970-2011)

• Nine

major flood events for calibration of velocity

• -index technique to determine

effective rainfall hyetographs (ERHs)

• Areal

average PM P estimation (Thiessen polygon; Kriging)

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Description of data and methodology

Results

Flow velocity corresponding to PM P

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

Representative velocity v corresponding to each of the 9 major flood events in the catchment was estimated through calibration by genetic algorithm (GA)

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PM P estimates obtained based on HM and M A

200 400 600 800 1000

HM M A-100 M A-500 M A-1000

2-day PM P

y y y (mm)

200 400 600 800 1000

HM M A-100 M A-500 M A-1000

3-day PM P

y y y (mm)

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PM F hydrographs obtained based on HM and M A

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 50 100 150 PM F (m3/ s) Time (hours)

PM P duration = 2 days

0.0E+0 2.0E+3 4.0E+3 6.0E+3 8.0E+3 1.0E+4 1.2E+4 50 100 150 PM F (m 3/ s) Time (hours)

PMP duration = 3 days

PM P(HM )>> PM P(CWC)10,000 m3/ s >> PM P (M A)

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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 M m3 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

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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 M m3)

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 M ultifractal

Inundation map corresponding to 2-day duration PM P

ICWRCOE 2015 25

20000 40000 60000 80000 100000 750 800 850 900 950

DBA_hema_Hersh_2day Plan: Plan_25km_Hersh2day 2/17/2017

Main Channel Distance (m) Elevation (m) Legend 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

20000 40000 60000 80000 100000 740 760 780 800 820 840 860 880 900

DBA_hema_MA_1000 Plan: Plan_25km_MA1000_2day 2/17/2017

Main Channel Distance (m) Elevation (m) Legend EG Max WS WS Max WS Crit Max WS Ground Hema_25 1

• Uncertainty in PM P & PM F estimates cannot be ignored in dam

break analysis studies.

• Implications of the uncertainty on area inundated downstream of

dams is worth investigation

Conclusion

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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 distribution tail: 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 based GIUH 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 of PMP and PMF, Proceedings of Second National Dam Safety Conference, IISc Bangalore, 12-13 January, 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 the Geomorphological 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. Water Resources 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

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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.

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Figure 2. Self-similarity properties of the channel network

10

• 2

10

1

10

2

S/S0 n

10

• 2

10

5.3

10

5.5

10

5.7

10

5.9

S/S0 T (km)

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