Dealing with uncertanties in hydrologic studies, Ferdinand Diermanse

1. Dealing with uncertanties in hydrologic studies
Ferdinand Diermanse, Deltares

2. Topics
 Risk analysis
 Uncertainties
 Statistical methods
 Joint probability methods
 Brisbane River catchment flood studies

3. flood risk (management)
RISK
HAZARD
PROBABILITY FLOODED AREA
EXPOSURE VULNERABILITYXX

4. Flood prone areas in The Netherlands

5. Dikes, dunes and barriers

6. Costs versus benefit
Investment costs
Expected damages
Total costs
Costs
Level of protection
6
Optimal protection when marginal benefits
equal marginal costs

7. Local Individual Risk (LIR)
Probability per year for a single
inhabitant of becoming a flood
casualty

8. Resulting safety standards
standar
ds
standards
6-yearly safety assessment

9. Uncertainties
Various sources:
1.Natural variability
2.Measurement errors
3.Modelling errors
4.Lack of data

10. Histogram
Basic Statistics
Frequency Cumulative Relative Frequency
Value
11,00010,0009,0008,0007,0006,0005,0004,0003,0002,0001,000
Frequency
1,900
1,850
1,800
1,750
1,700
1,650
1,600
1,550
1,500
1,450
1,400
1,350
1,300
1,250
1,200
1,150
1,100
1,050
1,000
950
900
850
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
50
0

11. Derive distribution function from histogram

12. Game of two dice
6 7 8 9 10 11 12
5 6 7 8 9 10 11
4 5 6 7 8 9 10
3 4 5 6 7 8 9
2 3 4 5 6 7 8
1 2 3 4 5 6 7
1 2 3 4 5 6

13. Example of two dice: histogram

14. Histogram from 1000 throws

15. Histogram from 50 throws

16. Extreme value statistics for flood risk analysis
0
0.04
0.08
0.12
0.16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
?

17. Flood Frequency Analysis (FFA) approach
Ranking 100 years of peak discharges
nr. year discharge
1 1926 3175
2 1993 3039
3 1995 2746
4 2003 2548
5 2002 2327
… … …

18. Estimating probabilities for the Meuse river
Intial estimate
nr. year discharge prob.
1 1926 3175 1/100
2 1993 3039 2/100
3 1995 2746 3/100
4 2003 2548 4/100
5 2002 2327 5/100
… … … …

19. Estimating probabilities for the Meuse river
Intial estimate
nr. year discharge prob. ARI
1 1926 3175 1/100 100
2 1993 3039 2/100 50
3 1995 2746 3/100 33
4 2003 2548 4/100 25
5 2002 2327 5/100 20
… … … … …

20. Plotting annual maxima
1000
1500
2000
2500
3000
3500
1 10 100
return period (years)
discharge(m3/s)
1926
1993
1995
Average Return Interval (ARI)

21. Fitting a distribution function (Gumbel)
1000
1500
2000
2500
3000
3500
1 10 100
return period (years)
discharge(m3/s)
data
function
Average Return Interval (ARI)

22. Extrapolation for larger return periods
1000
1500
2000
2500
3000
3500
4000
4500
5000
1 10 100 1000 10000
return period (years)
discharge(m3/s)
data
function

23. 1000
1500
2000
2500
3000
3500
4000
4500
5000
1 10 100 1000 10000
return period (years)
discharge(m3/s)
data
function
Extrapolation for larger return periods
1000 years
Average Return Interval (ARI)

24. Homogeneity of measurement series
Nile discharge
Aswan Dam

25. Model based approaches
0
200
400
600
800
1000
1200
01/01/1975
15/01/1975
29/01/1975
12/02/1975
26/02/1975
12/03/1975
26/03/1975
09/04/1975
23/04/1975
07/05/1975
21/05/1975
04/06/1975
18/06/1975
02/07/1975
16/07/1975
30/07/1975
13/08/1975
27/08/1975
10/09/1975
24/09/1975
08/10/1975
22/10/1975
05/11/1975
19/11/1975
03/12/1975
17/12/1975
31/12/1975
Rainfall
+
models
discharges
Design Event Approach (DEA)

26. Joint probability methods
River system
Takes into account that there are multiple factors may contribute to flood
levels:
Rainfall depth
Spatio-temporal rainfall patterns
Initial soil conditions
Initial reservoir conditions
Ocean water levels
…

27. Example: tidal river
Sea
River discharge
local water level influenced
by river discharge and sea
water level
2.75 3
3
3.25
3.25
3.5
3.5
3.5
3.75
3.75
3.75
3.75
4
4
4
4
4.25
4.25
4.25
4.5
4.5
4.5
4.75
4.75
5
discharge [1000 m
3
/s]
seawaterlevel[m+NAP]
local water level [m+NAP]
1 2 3 4 5 6 7 8 9 10
1
1.5
2
2.5
3
3.5
4

28. example tidal river
Sea
River
2.75 3
3
3.25
3.25
3.5
3.5
3.5
3.75
3.75
3.75
3.75
4
4
4
4
4.25
4.25
4.25
4.5
4.5
4.5
4.75
4.75
5
discharge [1000 m
3
/s]
seawaterlevel[m+NAP]
local water level [m+NAP]
1 2 3 4 5 6 7 8 9 10
1
1.5
2
2.5
3
3.5
4
example: flooding occurs
if h>4.5 m+NAP

29. example tidal river
Sea
River
Flood events
1. identify all events for
which h>4.5 m+ref
2.determine the probability for
each of these events and take the
sum

30. Analogy: game of two dice
opponent has to throw 10 or more to win the game
6 7 8 9 10 11 12
5 6 7 8 9 10 11
4 5 6 7 8 9 10
3 4 5 6 7 8 9
2 3 4 5 6 7 8
1 2 3 4 5 6 7
1 2 3 4 5 6

31. Analogy: game of two dice
opponent has to throw 10 or more to win the game
6 7 8 9 10 11 12
5 6 7 8 9 10 11
4 5 6 7 8 9 10
3 4 5 6 7 8 9
2 3 4 5 6 7 8
1 2 3 4 5 6 7
1 2 3 4 5 6
Six undesired “events”
Each with probability 1/36
Total probability: 6/36 = 1/6

32. Flood risk complexer than dice
 number of variables may be larger than 2
 variables can be correlated
 continuous values instead of discrete values
 complex hydrodynamic processes
⇒ no analytical solution available
⇒ estimation techniques required

33. Joint probability methods
Numerical integration Monte Carlo
FORM Directional sampling

34. Crude Monte Carlo
-4 -2 0 2 4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
x1
f(x
1
)
-4 -3 -2 -1 0 1 2 3 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x2
f(x
2
)

35. Simple example Crude Monte Carlo
( ) ( )Uniform 0,1f x =
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x1
x2
4
π
1
4
π
−
Compute the surface of a quarter circle with radius = 1
2
rπFull circle:
πFull circle, r=1:
4
π
Quarter circle, r=1:

36. Uniform samples
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x1
x2
inside
outside

37. Monte Carlo estimate
10
0
10
1
10
2
10
3
10
4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
number of samples
MCestimate
1-π/4

38. Brisbane River
Catchment Flood
Study
Hydrology Phase

39. Brisbane River Catchment Flood Study – phase 2
Estimate probabilities of flood discharges and volumes at 23 locations for
‘no dam’ and ‘with dam’ conditions, using the following methods:
1.Flood frequency analysis
2.Design event approach
3.Joint probability (Monte Carlo) approach

40. Essence of Monte Carlo Simulation
1. Generate a large number of synthetic events
2. Simulate each event with a hydrological/hydraulic model
3. At each location, quantify how often flood levels are exceeded
Main challenges:
oSynthetic events have to be realistic and representative
oComputation times

41. Correlations
1. Extreme rainfall likely to co-incide with
increased ocean water levels
2. Reservoir volumes at the beginning of an
event are related (if one reservoir is full,
the other reservoirs are more likeley to be
full as well)
3. Initial soil conditions in the various
subcatchments are related

42. Correlation model for initial losses
Gaussian Copula

43. Monte Carlo sampling: CRC-CH method

44. Importance sampling
10
0
10
2
10
4
10
6
10
8
0
200
400
600
800
1000
1200
1400
1600
1800
2000
ARI (years)
discharge(m3/s) crude Monte Carlo
importance sampling

45. Spatio-temporal rainfall patterns (STEPS)
128-256-512 km 64-128-256 km 32-64-128 km
16-32-64 km 8-16-32 km 2-4-8 km4-8-16 km
Break up the rainfall map into a set of maps for different scales
Parameterize time evolution of each scale, large scales evolve slowly, small scales fast
Multiply maps to get the rainfall forecast.
From: Seed (2013)

46. Results are realistic rainfall patterns
From: Seed (2013)

47. URBS hydrological model

48. Reservoir modelling in RTC tools
From: Seed (2013)
Loss-of-communications strategy

49. Flow diagram as implemented in Delft-FEWS

50. Current status of BRCFS – phase 2
 Finalising draft computation results of the three methods for ‘no
dam’ and ‘with dam’ conditions
 Start of the reconciliation proces
 Sept 11: workshop with client, IPE and various stakeholders