EFFECT OF EXTREME STORMS ON TREATY OBLIGATIONS IN THE RIO CONCHOS

Samuel Sandoval-Solis | CE 397 | Statistics in Water Resources

RIO GRANDE/RIO BRAVO BASIN

RULES OF THE GAME:TREATY OF 1944 – RIO GRANDE / BRAVO

• For Mexico:- 2/3 of 6 Mexican

Tributaries (Including the Conchos)

- ½ of Gains – Losses- All waters from San Juan

And Alamos River• For the U.S.:- All water from US

tributaries- 1/3 of 6 Mexican

Tributaries, this 1/3 shall not be less than 431 MCM/year on 5 year cycles.

- ½ Gains Losses• Re-set of treaty cycles• Every 5 years or- If the U.S. active storage in

both international dams is filled with U.S. water

Amistad Dam

Falcon Dam

2 – Las Vacas3 – San Diego4 – San Rodrigo5 – Escondido

6 – Salado

1 – Rio Conchos

OBJECTIVES

1. Obtain a PDF and CDF for the Rio Conchos2. Evaluate how the occurrence of extreme storms

are related with wet conditions .3. Evaluate how extreme storms have influenced

the re-start of treaty cycles4. Evaluate how a change in the occurrence

frequency of extreme storms will affect the re-start of treaty cycles.

PDF AND CDF FOR THE RIO CONCHOS BASIN

DistributionStatistic Original Log10 Square Root Cube RootMean (MCM/year) 740 2.739 25.431 8.501Standard Error 73 0.051 1.328 0.306Median 623 2.794 24.946 8.537Mode #N/A #N/A #N/A #N/AStandard Deviation 536 0.376 9.757 2.248Sample Variance 287709 0.141 95.207 5.054Kurtosis 2.054 0.028 -0.111 -0.306Skewness 1.260 -0.709 0.280 -0.053Range 2591 1.585 43.258 9.750Minimum 69 1.840 8.322 4.107Maximum 2661 3.425 51.580 13.857Sum 39971 147.883 1373.295 459.034Count 54 54 54 54Confidence Level(95.0%) 146 0.103 2.663 0.614

Annual Dataset: 1955 - 2008

PDF AND CDF FOR THE RIO CONCHOS BASIN

64 125 216 343 512 729 1000 1331 1728 2197 27440.00

0.05

0.10

0.15

0.20

0.25

fs(x)p(x)

Rio Conchos Outflow (MCM/year)

f(x)

Chi-Square test for goodness of fit.Theoretical =15.5 > Calculated 14.4

PDF AND CDF FOR THE RIO CONCHOS BASIN

0 500 1000 1500 2000 2500 30000.000.100.200.300.400.500.600.700.800.901.00

Normal Distribution Observed Data

Outflow (Million m3/year)

F(x)

2482.2

5.8

)(3/1

Q

xF

PDF AND CDF FOR THE RIO CONCHOS BASIN

2482.2

5.8

)(3/1

Q

xF

-3 -2 -1 0 1 2 30

500

1000

1500

2000

2500

3000

Cubic root Flow Observed FlowZ

Q (MCM/year)

EXTREME STORMS AND WET CONDITIONS IN THE RIO CONCHOS BASIN

Storms from the Gulf

National Hurricane Center <http://www.nhc.noaa.gov/index.shtml>

Storms from the Pacific

EXTREME STORMS AND WET CONDITIONS IN THE RIO CONCHOS BASIN

National Hurricane Center <http://www.nhc.noaa.gov/index.shtml>

Storms from the PacificYear Date Name Category1957 6-Oct Notname TD1957 22-Oct Notname L1962 4-Oct Doreen TS1966 17-Sep Helga TD1968 13-Sep Naomi TS1969 12-Oct Jennifer TD1973 26-Sep Irah TD1973 27-Sep Jennifer TD1974 24-Sep Orlene TD1978 26-Sep Paul TD1986 2-Oct Paine H1990 2-Oct Rachel TS1993 13-Sep Lidia TS1994 14-Oct Rosa TS1996 14-Sep Fausto TS2008 12-Oct Norbert TS

16 Extreme Storms

EXTREME STORMS AND WET CONDITIONS IN THE RIO CONCHOS BASIN

EXTREME STORMS AND WET CONDITIONS IN THE RIO CONCHOS BASIN

0 500 1000 1500 2000 2500 30000.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Outflow (Million m3/year)

F(x)

Wet Conditions p>0.75

Dryp<0.25

Normal Conditions0.25<p<0.75

Q = 1005 M

CM/Year

Q = 340 M

CMC/Year

Condition # of Storms Rel. Frequency

Dry 3 19%

Normal 7 44%

Wet 6 38%

2482.2

5.8

)(3/1

Q

xF

7 Storms30 years

6 Storms13 years

3 Storms11 Years

EXTREME STORMS AND WET CONDITIONS IN THE RIO CONCHOS BASIN

0 500 1000 1500 2000 2500 30000.00

0.20

0.40

0.60

0.80

1.00

F(x)

Wet

Dry

Normal

2482.2

5.8

)(3/1

Q

xF

Cond. # of Storms # of years λ

Dry 3 11 0.27

Normal 7 30 0.23

Wet 6 13 0.46

All 16 54 0.30

Condition λ (Storms/year) P(# of Storm≥1)Dry 0.27 0.24

Normal 0.23 0.21Wet 0.46 0.37

Whole Period* 0.275 0.240

Poisson Distribution

*Period Considered before 1968 when both international dams were built. # of Hurricanes = 11;, # of years = 40

EXTREME STORMS AND RE-SET IN TREATY CYCLES

3 out of 11 Extreme Storms influenced the re-set of treaty cycles: Orlene (24/Sep/1974) Cycle 6Paul (26/Sep/1978) Cycle 8 Norbert (8/Oct/2008) Cycle 28

Only 3 cycles out of 21 were re-set due to Extreme Storms

P(Re-Set|Storm)=3/11=0.2727

Event CycleDate

DurationExtreme Storm

Beginning EndingName Date

Difference (years) (days)

1 4 01-Oct-1968 21-Aug-1972 3.89 2 5 22-Aug-1972 15-Feb-1973 0.485 3 6 16-Feb-1973 16-Oct-1974 1.666 Orlene 24-Sep-1974 224 7 17-Oct-1974 08-Dec-1976 2.145 5 8 09-Dec-1976 06-Nov-1978 1.91 Paul 26-Sep-1978 416 9 07-Nov-1978 16-Nov-1978 0.0277 10 17-Nov-1978 07-Sep-1979 0.808 8 11 08-Sep-1979 11-Jun-1981 1.756 9 12 12-Jun-1981 03-Sep-1981 0.23

10 13 04-Sep-1981 11-Oct-1981 0.104 11 14 12-Oct-1981 26-Oct-1981 0.041 12 15 27-Oct-1981 01-Jun-1982 0.597 13 17 02-Jun-1987 23-Jun-1987 0.0614 18 24-Jun-1987 02-Aug-1987 0.11 15 19 03-Aug-1987 31-Aug-1987 0.079 16 20 01-Sep-1987 29-Sep-1988 1.079 17 21 30-Sep-1988 02-Nov-1991 3.093 18 22 03-Nov-1991 17-Dec-1991 0.123 19 23 18-Dec-1991 23-Jul-1992 0.597 20 24 24-Jul-1992 26-Sep-1992 0.178 21 28 01-Oct-2007 08-Oct-2008 1.019 Norbert 12-Oct-2008 4

EXTREME STORMS AND RE-START IN TREATY CYCLES

P(Re-Set)

0.301

P(Storm)

0.240 P(No Re-set)

0.699Status Quo

P(Re-Set)

0.563

P(No storm)0.760

P(No Re-set)0.437

%50%8.42%2.7)(Re;49996.042771.007226.0)(Re

)|(Re*)()|(Re*)()(Re

SetPSetP

NoStormSetPNoStormPStormSetPStormPSetP

%50%2.33%8.16)(Re;50004.033186.016817.0)Re(

)|Re(*)()|Re(*)()Re(

SetPsetNoP

NoStormsetNoPNoStormPStormsetNoPStormPsetNoP

EXTREME STORMS AND RE-START IN TREATY CYCLES

0848.0)lim.|Re(

0722.0)|Re(

ateCAlterCyclesTratysetsStormP

QuoStatusCyclesTratysetsStormP

P ( Re-Set) = 0.0785 = 7.85%

Increase the occurrence of Extreme storms by a 20% (Arbitrary)

P(Re-Set)

0.301

P(Storm)

0.240 P(No Re-set)

0.699Status Quo

0.500

P(Re-Set)

0.563

P(No storm)0.760

P(No Re-set)0.437

P(Reset)

0.306

P(Storm)

0.277 P(No reset)

0.694Alter. Climate

0.500

P(Re-Set)

0.575

P(No storm)0.723

P(No Re-set)0.425

)lim|(Re)lim(

)|(Re*)()(Re

ateCAlterSetPateCAlterP

QuoStausSetPQuoStausPSetP

CONCLUSIONS• The PDF and CDF for the Rio Conchos was estimated• Extreme Storms from the Pacific has more influence in the Rio Conchos

Basin.• The occurrence of stream storms is not a liability of wet periods in the

basin• A Poisson distribution was used to determine the PDF and CDF for

extreme storms in the Conchos basin P(Ex. St. ≥1) =0.240.• The occurrence of extremes storms is not a definitive factor to Re-Start

the treaty cycles• Combining the occurrence of extreme storms and the re-start of treaty

cycles due to extreme storms, there is a 0.0722 probability that the treaty cycles are re-set at the begging of each year.

• Increasing by 20% the occurrence of extreme storms does not significantly increase the probability to re-start the treaty cycles (0.0785)

PROCEDUREOutflow Hist.

Data : 1955-2008

Goodness of fit Chi-Square Test

1) PDF and CDF for the Rio Conchos

Hurricanes Hist. Data :

1957-2008

Influence: Pacific or Gulf?

Frequency of Occurrence

CDF and IQR = Define Dry, Normal

and Wet Cond

2) Conditions + Frequency Storms = Influence of Storms

in Wet Periods

Treaty Cycles Records : 1957-2008

PDF and CDF (Poisson Distribution) for extreme

Storms

Frequency of Occurrence of

Extreme Storms

3) Influence of Extreme Storms in Re-Start of Treaty Cycles P(Re-Start|

Storm)

4)Change the PDF for Extreme Storms + P (Re-start|Storm) = Evaluate how a change in the Storm Occurrence will affectthe

Re-start of Treaty Cycles