Expansion of information

Question 1

Possible problems with estimation of design floods:

Answer 1

1. Observed data are not consistent. Especially the rating curve (W-Q-relationship) is erroneous, because of missing measurements in the flood range.
2. The selection of the probability distribution (PD) is affecting strongly the derived design floods for large return periods. There is a risk of applying a PD not suitable for the population.
3. The observed series is too short. Using this sample for PD selection is not robust.
4. The sample is not homogeneous. There are trends, breaks, etc. in the series caused by natural or anthropogenic changes.

Question 2

Possibilities for expansion of information to reduce flood estimation uncertainty:

Answer 2

1. Causal information expansion
   a) External: considering additional information from precipitation and retention in the catchment
   b) Internal: separating the sample with flood events into genetically more homogeneous sub-samples
2. Temporal information expansion
   a) External: considering historical floods
   b) Internal: using partial duration series (PDS), also called peak over threshold series (POT), instead of annual series
3. Spatial information expansion:
   Application of regional samples for more robust estimation and regionalisation methods to transfer information from gauged to ungauged basins

Question 3

1a. External causal information expansion

Answer 3

• Assumption: probability distributions of flood peak HQ and rainfall PD for duration D are parallel if T > 10 yr given saturation of the catchment
• Selection of relevant rainfall duration D according to time of concentration
• Fitting probability distribution F(PD)
• Extrapolation of F(HQ) by parallel shifting of F(PD) at T=10yr of F(HQ)
• For catchments outside France the return period T at which saturation is assumed may be different

Question 4

1b. Internal causal information expansion

Answer 4

• Separation of floods into e.g. summer floods (convective rain) and winter floods (snow, frontal rain)
• Fitting probability distributions individually
• Non-exceedance probability for annual HQ is yielded according to multiplication law for probabilities of independent events:

Question 5

2a. External temporal information expansion

Answer 5

• Using information about historical floods in frequency analysis
• High water marks at buildings  transformation W in Q  large uncertainty since change in cross section geometry
• All flood values HQ will be associated the non-exceedance probabilities Pne according to the historical period:

Question 6

2b. Internal temporal information extension

Answer 6

• A discharge series from n years may contains more than n floods
• Especially for short series using floods above a threshold (partial duration series, PDS) X=HQ>s instead of using one flood per year (annual maximum series, AMS) Y=HQ(yr) might be better

Question 7

Notes on partial duration series statistics

Answer 7

 Partial Duration Series (PDS) are also called Peak Over Threshold Series (POT)

 Selection of HQ > s, such that flood events are independent! → can be reached by defining a minimum separation time between events

 Selection of the flow threshold s, is often such that nx ≈ 2…3*ny

 For the extreme value statistics with POT data it can be shown that the General Pareto Distribution (GPD) is preferred to the
General Extreme Value (GEV) distribution

Question 8

Spatial information extension

Answer 8

I. Improvement of flood quantile estimation using additional information from similar or neighbouring sites

II. Estimations for unobserved cross sections/ basins

Question 9

Spatial information extension

Index-flood-method:

Answer 9

• Assumption: Probability distributions of floods at different gauges in a region are equal except for a scale parameter (“index-flood”)
• Often, as scale parameter the mean annual flood can be used μ=MHQ
• Theregional probability distribution F(HQ/μ) can be estimated using average parameters weighted by the sample size of the gauges :

Question 10

Summary procedure after Hosking & Wallis (1999):

Answer 10

1. Date plausibility checks
2. Identification of flood homogeneous regions
3. Scaling of floods Hq=HQ/MHQ
4. Estimation of local L-moments (Eq. 6.6 and Eq. 6.8)
5. Selection of a suitable unique probability distribution F
6. Estimation of regional L-moments/ distribution F(Hq) (Eq. 6.26)
7. Regionalisation of the index-flood MHQ=f(basin) (Eq. 6.27)
8. Estimation of quantiles HQ(F)=MHQ*Hq(F), validation