Streamflow Based Methods
Table of Contents
1. Chapter 2 of 3 Streamflow Based Methods
1.1 Flood Frequency Analysis
Flood frequency analysis is a method of analysing the statistics of recorded flood data with the objective of defining the probability of distribution of the data for subsequent use in flood estimation. The most common application of flood frequency analysis is with observed flow data although analysis of flood depth can often be equally appropriate. The reader is referred to Australian Rainfall and Runoff for a complete description of flood frequency methods.These methods compute peak flow magnitudes of different average recurrence intervals and are only suitable for instantaneous flow and steady flow analysis. Flood frequency analysis is carried out using either the annual series or partial series approach. As a general rule, the annual series is used when estimating flows less frequent than the 10 year ARI while the partial series is used for estimating more frequent events.
A major advantage of streamflowbased methods is its ease of use. Implicit in using this approach, however, is the assumption that catchment characteristics remain unchanged throughout the period for which data was available.
1.1.1 Annual Flood Series
In the annual series approach, observed peak flows for each year (either calendar or water year) are fitted to a probability distribution. Australian Rainfall and Runoff recommends the use of the LogPearson Type III probability distribution. The probability distribution involves three parameters representing the statistical properties of the logarithmic values of the peak flows. These are the mean, standard deviation and the coefficient of skewness. When the coefficient of skewness is zero, the LogPearson Type III distribution becomes the twoparameter Log Normal distribution. Fitting the LogPearson Type III distribution to the logarithmic values of the observed peak flows involves deriving the three parameters for the peak flow data. Once fitted, the flood frequency curve can then be used to predict probabilistic flows of any Annual Exceedence Probability (AEP) or Average Recurrence Interval (ARI).1.1.2 Partial Flood Series
The partial series approach adopts a "threshold discharge" value as the criterion in selecting flood events for statistical analysis compared to the calendar year or water year criterion of the annual series analysis. The use of a "threshold discharge" as the selection criterion is used in recognition of the fact that the annual flood series can be deficient in accounting for frequent flood events. It is important to ensure that all events selected are independent of each other.Flood magnitudes for frequent events tend to be underestimated by the annual flood series owing to the fact that the method requires only one event per year to be included in the statistical analysis regardless of (i) the magnitude of this event (could have been a drought year) and (ii) the number of other events of similar magnitude (as would occur in a wet year). In selecting all peak flows larger than a threshold value, a better estimation of the average recurrence interval of peak flows, especially for events of high frequency of occurrence, can be realised.
The partial series frequency curve allows peak discharges of average recurrence intervals of less than a year to be determined owing to the fact the number of flood events included in the analysis can exceed the number of years of record available. For any given site, the flow estimates for any given ARI by a partial series analysis will always be higher or equal to a corresponding estimate using an annual series analysis. A theoretical expression relating the ARIs of a given peak flow from a partial series analysis and an annual series analysis was derived by Langbein as follows:
where: Y_{A} is the average recurrence interval derived from an annual series analysis.
Y_{P} is the average recurrence interval derived from a partial series analysis.
A graphical representation of the Langbein relationship is provided in ARR Volume 1.
For AEP less than 10% (or average recurrence interval greater than 10 years) both approaches are expected to give similar design flows. Apart from requiring a higher degree of effort in carrying out a partial series analysis, this type of analysis also has the disadvantage of having no known probability distribution which can be fitted to the data. It is necessary to draw a line of best fit of the data plotted on a semilog scale with the discharge in natural scale and the average recurrence interval plotted on logarithmic scale.
1.1.3 Plotting Flood Data
Plotting of the observed flow data is often helpful in understanding the statistical characteristics of the flow data. For annual series analysis, the logarithmic normal probability graph paper is often used while this together with a semilogarithmic graph paper are used for partial series analysis.To enable the observed flow data to be plotted, it is first necessary for their plotting positions to be evaluated. Their plotting portions may be viewed as estimates of their probability for exceeding and are evaluated by first ranking the flow data in descending order. The plotting position of each individual flow data is computed as follows:
If the plotting position is expressed in the form of an average recurrence interval (YP ), YP is given as;
The parameters m and N in equations 2.2 and 2.3 relate to the ranking of the individual flow and the number of years of available data respectively.
When applying the annual series, the highest rank value will equal the number of years of available data and the plotting position as computed in equation (2.2) will always be less than unity. With partial series, equation (2.3) is used to allow determination of average recurrence intervals of less than one year for flow data with rankings exceeding the number of years of available data.
It should be noted that the plotting positions derived from an annual series analysis and a partial series analysis have different interpretations. The average recurrence interval based on annual flood series data reflects the average interval between years in which a given discharge is exceeded, whether once or more than once while the ARI from a partial series analysis reflects the average interval between exceeding of the given discharge (Laurensen,1987).
1.1.4 Fitting the Log Pearson III distribution
In the annual flood series analysis, the LogPearson Type III probability distribution is often used to describe the flood frequency. The distribution can be fitted to the data by computation of the mean, standard deviation and coefficient of skewness of the logarithmic values of the flow data. These parameters, together with standard probability tables, can then be used to determine probabilistic flows for any AEPs.The reader is referred to Australian Rainfall and Runoff for a detailed description of the procedure. The reader should also pay particular attention to the procedure recommended in identifying and dealing with data uncertainties and in the computation of confidence limits in the derived flood frequency curve.
1.2 Index Flood Method
A regional procedure based on regression analysis of flood frequency curves derived for many locations within Western Australia was developed by the Main Roads for estimation of peak flows up to the 2% AEP in small to medium rural catchments. The procedure is referred to as the Index Flood Method and is based on multivariate statistical regression analysis of representative flood peaks to catchment physical and meteorological characteristics. This method is described in detail in Australian Rainfall and Runoff.In the regional analysis, Western Australia was divided into the four regions of the South West, the Wheatbelt, the North West and the Kimberley. Reliable streamflow data from stream gauging stations within each of these regions were used to derive flood frequency curves. In some regions, the areas are further subdivided to reflect different soil types and vegetation. For each area, multivariate regression analysis was carried out to relate the index peak discharge to such catchment characteristics as the catchment area, the mainstream length, stream slope, mean annual rainfall, degree of forest clearing etc. In most locations the 50% AEP or 2 year ARI peak discharge is used as the index flood except for the Wheatbelt and North West regions where the 5 year ARI peak discharge was used. The shape of the flood frequency curves derived for each location were also analysed and normalised to the index flood. The frequency factors so derived express the magnitudes of probabilistic peak discharges for a range of ARI as ratios of the index flood magnitude.
Tables 2.1 and 2.2 list the formulae for the index floods and corresponding frequency factors respectively for the various regions in Western Australia.
Table 2.1 Index Flood Method Formulae
Regions  Catchment Type  Index Flood Magnitude (Q_{2} or Q_{5})  Standard Error of Estimate 
South West  Jarrah Forest
Low Jarrah Forest 
Q_{2} = 8.22 x 10^{9} A^{0.73} P^{2.22} (LSe)^{0.28}10^{0.0064CL}  +35.3% to 26.1% 
Jarrah Forest with Loamy Soil
Karri Forest (>15% cleared) with Loamy Soil 
Q_{2} = 3.68 x 10^{8} A^{0.68} P^{2.29} 10^{0.0081CL}  +50.1% to 33.4%  
Karri Forest  Q_{2} = 6.01 x 10^{9} A^{0.87} P^{2.41}  +4.7% to  4.5%  
Wheatbelt  Loamy Soil Catchments (75%100% cleared)  Q_{5} = 2.77 x 10^{6} A^{0.52} P^{2.12}  +107% to 51.1% 
Loamy Soil Catchments
Lateritic Soil Catchments Sandy Soil Catchments 
Q_{5} = 0.304 A^{0.60} 10^{0.0052CL}  +113% to 53.1%  
North West  Pilbara  Loamy Soil Catchments  Q_{5} = 6.73 x 10^{4} A^{0.72} P^{1.51}  +41.1% to 29.3% 
Kimberley  Average Rainfall between 450mm and 850mm  Q_{2} = 9.34 A^{0.56}  +39.5% to 28.3% 
Notation
A  Catchment Area (km^{2})
CL  clearing measured as a percentage of the catchment area
P  average annual rainfall (mm) over the catchment area
L  mainstream length (km) measured from the catchment outlet to the most remote point on the catchment boundary
Se  equal area stream slope (m/km)
Table 2.2 Frequency Factors for the Index Flood Method
Regions  Catchment Type  Conditions 
Average Recurrence Interval 

2 
5 
10 
20 
50 

South West  Jarrah Forest with Lateritic Soil  0% clearing 
1.00 
1.60 
2.20 
3.00 
4.25 
Low Jarrah Forest with Sandy Soil  50% clearing 
1.00 
1.45 
1.85 
2.30 
3.00 

100% clearing 
1.00 
1.28 
1.50 
1.75 
2.05 

Jarrah Forest with Loamy Soil
Karri Forest (>15% cleared) with Loamy Soil 
1.00 
1.75 
2.55 
3.50 
5.10 

Karri Forest 
1.00 
1.51 
1.94 
2.40 
3.05 

Wheatbelt  Loamy Soil Catchments (75%100% cleared) 
0.48 
1.00 
1.84 
3.23 
6.10 

Loamy Soil Catchments
Lateritic Soil Catchments Sandy Soil Catchments 
0.50 
1.00 
1.76 
3.05 
5.65 

North West  Pilbara  Loamy Soil Catchments  Catchment Area = 1 km^{2} 
0.55 
1.00 
1.58 
2.40 
3.90 
Catchment Area = 10 km^{2} 
0.52 
1.00 
1.70 
2.77 
4.90 

Catchment Area = 100 km^{2} 
0.50 
1.00 
1.81 
3.20 
6.30 

Catchment Area = 1000 km^{2} 
0.48 
1.00 
1.94 
3.70 
7.90 

Catchment Area = 10000 km^{2} 
0.46 
1.00 
2.08 
4.25 
9.90 

Kimberley  Average Rainfall between 450mm  Catchment Area = 1 km^{2} 
1.00 
1.37 
1.63 
1.90 
2.25 
and 850mm  Catchment Area = 10 km^{2} 
1.00 
1.47 
1.87 
2.31 
2.95 

Catchment Area = 100 km^{2} 
1.00 
1.58 
2.15 
2.85 
3.88 

Catchment Area = 1000 km^{2} 
1.00 
1.69 
2.47 
3.50 
5.20 

Catchment Area = 10000 km^{2} 
1.00 
1.81 
2.84 
4.27 
6.85 
1.3 Worked Example
 Flood Frequency Analysis: The reader is referred to Section 10.9 of ARR Volume 1 for detailed worked examples.
 Index Flood Method: The reader is referred to Section 5.4.7 of ARR Volume 1 for detailed worked examples.
Reference
Australian Rainfall And Runoff;(1987), A Guide to Flood Estimation, Volume I & II.