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

Third National Dam Safety Conference 16-17 February 2017, Roorkee EVALUATION OF EFFECT OF PMP ESTIMATION ON PMF ESTIMATES Sagar Rohidas Chavan and V. V. Srinivas Department of Civil Engineering Indian Institute of Science

Introduction M ajor Hydrologic Structures (e.g., dams which are located upstream of thickly populated areas and/or nuclear facilities) Limiting case DESIGN PROBABLE M AXIM UM FLOOD FLOOD (PM F) DESIGN PROBABLE M AXIM UM PRECIPITATION RAINF ALL (PM P) PM P: greatest depth of precipitation for a given duration that is meteorologically possible for a watershed (WM O 1986, 2009) Source: Electronic media 2

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

Hershfield M ethod [Hershfield 1961, 1965]  Frequency analysis of annual maximum precipitation records         t     i i  env     X X  t   t  i   M n 1 PMP t X k  k i 1, , N   n m n m  i t -target location  n 1 12 Frequency Factor (K m ) 10 (or) 8 6 4 2 0 4 6 8 10 12 14 16 18 Mean annual maximum 1-day precipitation (cm) 4

Chavan, S. R., and Srinivas, V. V. (2017), Regionalization based envelope curves for PM P estimation by Hershfield method. International Journal of Climatology, Wiley & Royal M eteorological Society, doi: 10.1002/ joc.4951 A is introduced to increase proximity of the envelope curve to points depicting sites having ‘low M AMP and high FF’ as well as ‘high M AMP and low FF’ U L R +L +L +L ICWRCOE 2015 5

M ultifractal Approach (M A) (Douglas and Barros (2003)  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) Scale ratio Pr � � > � � ∼ � �� � �    L ���� = 10 � � � � � � � � : codimension function                 1 c ln p ln ln T ln e e 6

Test for presence of fractality in observed precipitation Figure: Empirical PDF of � � showing hyperbolic falloff, indicating large influence of extreme events on tail probabilities 7

Design Probable M aximum Precipitation (DPM P) ���� = 10 � � � � � Intercept=B M axima of accumulated rainfall 1,000 � � � : codimension function A λ (mm  10)                 1 c ln p ln ln T ln e e Scale ratio    L 100 1 10 Duration, τ (days) Figure: Verification of scaling relationship 8

Modeling hydrological response of catchments using geomorphological concepts     t    m 1      k t e    1  GIUH t ( ) (hour )    Ω  Case S n T R a R b R l   k k m  (km 2 ) (km)  where  1 0.9 5 756 2172 4.99 5.00 2.73  0.78   R 2 4.5 4 152 988 5.77 5.02 2.82   0.07   b m 3.29 R (adimensional) l  3 9 4 74 694 4.85 4.18 2.15   R a  4 22.5 3 29 432 6.68 5.39 3.45 0.48    R L    a  k 0.70 (hours)    R R v  b l

Time (hour) 0.07 GIUH (1/hour) 0.035 0 0 20 40 60 80 100 Time (hour) 10

Self-similarity properties of channel networks Moussa (1996) derived the following formulations for n (number of sources) and T (total length of stream network)   A typical channel     n S S network for S = S A 0 1        2 S          T OE S S 0 0   S A burnt_ASTER burnt_SRTM SRTM ASTER 7 10 3 10 T (km) n 2 10 6 10 -4 -3 -2 -4 -3 -2 10 10 10 10 10 10 S/S 0 S/S 0 11

Equivalent GIUH 1 1          2 2 2  Equivalent H-Sratios: 2        R R R   le ae      be    t    0.78   m 1     k t e R   0.07    be  E-GIUH ; where m 3.29 R      le   k k m R ae   0.5      0.48   R R S R L     0.5    1  be le ae e L OE S   k 0.70     e 0 2 S R   R R v     0 be le le  Scaling properties: � , � � � : Equivalent length of highest order stream (km) � : Representative peak flow velocity in the catchment (km/ h)

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 Time (hour) Time (hour) 0.07 0.05 E-GIUH (1/hour) GIUH (1/hour) 0.035 0.025 0 0 0 20 40 60 80 0 20 40 60 80 100 Time (hour) Time (hour) Figure: GIUHs and E-GIUHs constructed for stream networks 13

Case study on Hemavathy dam Catchment area : 2810 km 2 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 14

Description of data and methodology 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) 15

Results

Flow velocity corresponding to PM P 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) 17

PM P estimates obtained based on HM and M A (mm) 1000 2-day PM P 800 600 400 200 0 y y y HM M A-100 M A-500 M A-1000 (mm) 1000 3-day PM P 800 600 400 200 0 y y y HM M A-100 M A-500 M A-1000 18

PM F hydrographs obtained based on HM and M A 1.2E+4 1.8E+4 1.6E+4 1.0E+4 1.4E+4 PMP duration = 3 days PM P duration = 2 days 8.0E+3 1.2E+4 PM F (m 3 / s) PM F (m 3 / s) 1.0E+4 6.0E+3 8.0E+3 4.0E+3 6.0E+3 4.0E+3 2.0E+3 2.0E+3 0.0E+0 0.0E+0 0 50 100 150 0 50 100 150 Time (hours) Time (hours) Existing spillway capacity of the dam: 3,624.5 m 3 /s PM P(HM )>> PM P(CWC)  10,000 m 3 / s >> PM P (M A) 19

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 1050.6 M m 3 Pool volume at failure 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 20

Average Breach Width V w : 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 m 3 ) 21

Breach Formation time H b : Height of water above the breach bottom at the time of failure (Height of the dam=44.81 m) ICWRCOE 2015 22

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Inundation map corresponding to 2-day duration PM P HM M ultifractal

DBA_hema_Hersh_2day Plan: Plan_25km_Hersh2day 2/17/2017 Hema_25 1 950 Legend EG Max WS WS Max WS 900 Crit Max WS Ground Elevation (m) 850 800 DBA_hema_MA_1000 Plan: Plan_25km_MA1000_2day 2/17/2017 Hema_25 1 900 Legend 750 0 20000 40000 60000 80000 100000 EG Max WS 880 Main Channel Distance (m) WS Max WS 860 Crit Max WS Ground 840 Elevation (m) maximum height/ depth of 820 water reached during the 800 flood event based on HM 780 760 740 0 20000 40000 60000 80000 100000 ICWRCOE 2015 25 Main Channel Distance (m)

Conclusion  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 Acknowledgements  Directorate of Economics and statistics, Bangalore  Water Resources Development Organization (WRDO), Karnataka  Central Water Commission (CWC) 26

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