Urban Drainage simulation programs are sometimes referred to as time-area methods. These methods are based on rainfall falling on mostly paved catchments and the runoff generated routed through the pipe network. The urban runoff equations used are based on the Wallingford Procedure (or other values may be substituted). These methods have traditionally concentrated on the portion of runoff that is “flash” or fast runoff. This runoff is important on developed sites as it contributes most to the peak flows. The Wallingford Procedure was not intended for use on sites less than 20% paved.

The runoff from undeveloped or rural sites is slower. The method traditionally used to develop runoff hydrographs from these sites has been the unit hydrograph method. It too requires rainfall and a runoff relationship to generate flows and for that reason is called a rainfall-runoff method. There are similarities with the urban time-area methods and it is possible to set the variables of the Wallingford Procedure to give similar results but it relies heavily on the experience of the engineer. However as the unit hydrograph method is available and comprehensive research has been conducted into its use on rural sites Innovyze has implemented the method to allow engineers to use a more appropriate approach to undeveloped catchments (or parts of a catchment that are largely undeveloped).

Whether it be an urban or a rural catchment the response time of the site is very important. The faster the runoff reaches a point the higher the peak flow. In urban drainage these response times are expressed as a Time of Concentration or Time-Area. In the Unit Hydrograph terminology variables such as Time to Peak and Lag Time are used to define a catchments response time. More importantly the Unit Hydrograph method has calibrated equations to determine the response time on undeveloped catchments. These may be predicted from catchment characteristics or if measured data exists the methods of determining Lag are detailed in the FEH manual.

The other variable that is important in all drainage calculations is the percentage runoff. In urban drainage methods the percentage runoff model centres on the percentage paved area as this is critical. However the rural models pay more attention to soil characteristics and the FSR and FEH unit hydrograph methods have more appropriate equations for largely unpaved catchments. Urban drainage engineers may be surprised by the degree of runoff predicted by the FSR and FEH Unit Hydrograph models but they must remember that the runoff is usually over a much longer time period i.e. rural sites have a much longer response time.

### When to use the UH method

The unit hydrograph method may be used on partly urbanised catchments and here there may be an overlap with the urban simulation approach. However in these cases it is a matter of judgement which method is best and no hard and fast rule exists.

The FEH advises that if the variable URBEXT exceeds 0.5 (Volume 4, chapter 9.3.) then the unit hydrograph method should not be used. This is not much help as it implies that the site is very developed and the usual urban drainage approach should be taken. If the site is largely sewered and contains infiltration and storage structures then the normal urban simulation approach is likely to be more accurate.

### How do UH relate to Peak Flow prediction?

Methods for predicting peak flood flows using statistical methods differ in a number of respects from the unit hydrograph method. Firstly they are not rainfall-runoff methods as they are not directly related to rainfall events. They are derived from the statistical analysis of flows from catchments. Of course the flows have been generated from rainfall events but the analysis is based on the resultant flows. Secondly they generate peak flows only, which cannot be used for simulations or volume calculations. However these peaks should relate to the peak flow generated by the unit hydrograph and because of this they may be used to calibrate the unit hydrograph.

The problems associated with rural runoff determination are similar to those of urban runoff. The two principle variables are the runoff factor and the time to peak. It is obvious that the larger the runoff factor (associated with urbanisation and soil) the larger the runoff. Also the shorter the time to peak the greater the flood flow and this is also influenced by urbanisation. If a site has improved drainage or increased urbanisation the time to peak will be shortened and the peak flood flow will also increase. This may not be apparent from the application of the general formulae and the Tp may have to be modified. If gauged data is available the lag time can be measured and this information should be used in preference to the general formula for Tp..

### Which method? - The FSR, FEH, ReFH or ReFH2 Unit Hydrographs

The ReFH2 method is the latest approach and as such may be used if the site can be identified on the FEH Web Service and the ReFH2 software is installed on the same machine as InfoDrainage. The Ciria SuDS Manual (Chapter 24, C753, 2015) recommends the use of this methodology as the preferred unit hydrograph methodology, however it also provides guidance on the suitability of other methods.

InfoDrainage will call out to the ReFH2 software in order to generate and return an appropriate result. Guidance on the calculation method that ReFH2 uses can be found in the ReFH Technical Report at: http://files.hydrosolutions.co.uk/refh2/ReFH2_Technical_Report.pdf.

The triangular instantaneous unit hydrograph of the FSR and FEH methods has been replaced by a kinked triangle. The equation for Tp has been modified and a variable Base Flow introduced. The runoff equation has also been changed and is based on a loss model derived from the Probability Distributed Model (PDM) developed by Moore.

Note that the ReFH2 methodology should now be used in place of ReFH, however this has been left in the software to allow for the analysis of historic results.

The Flood Estimation Handbook Volume 4 may be referred to for a comprehensive discussion of the differences between FSR and FEH.

The FEH method is closely based on the FSR method. The biggest difference is that the FEH rainfall model can produce significantly different results to the FSR rainfall generation. However as is discussed later, the FSR method may be used in the software with any rainfall including rainfall files generated using the FEH rainfall model.

The FSR approach implemented in the software is that modified by the IoH 124 document for small catchments (less than 25km2). It has the advantage that most of the variables are readily understandable and available. If you are new to the unit hydrograph approach it may help your understanding to work through the FSR method and identify the comparable variables in the FEH and ReFH methods.

The ReFH2, ReFH and FEH approaches rely on the digitally derived data available on the FEH CD. It can be difficult to obtain data for a small catchment from the CD and it is important to check the data with a local site survey. If the boundary of a river catchment were a few metres out it would make little difference to a 300km2 catchment but it could be very significant for a 50ha catchment adjacent to that boundary.

The ReFH2 & ReFH methods may be used if the site can be identified on the FEH CD or FEH Web Service. However small catchments can present particular difficulties and the choice of variables may be more important than the choice of methods. The ReFH2 methodology specifically addresses this issue of scale through the use of ‘Plot scale’ equations and these are utilised in the ReFH2 analysis triggered by InfoDrainage when looking at smaller areas.

Local information on existing watercourses and culvert capacity and the frequency of exceedence should be sought to verify the model. Any measured data available on the site or adjacent sites should be sought. Further information on the performance of the rainfall-runoff method is available in FEH, Volume 4, Chapter 7 and R&D Technical Report FD1913/TR.

### Return period of flow and the return period of the rainfall

The return period of a flooding event depends on a number of factors. If a flooding event is caused by a combination of saturated or snow covered ground, with an usually high water level in the receiving water and a moderate rainfall then the return period of the event is significantly greater than that of the rainfall return period alone.

The hydrological rainfall runoff models contained in FSR and FEH typically use a 81 year RP rainfall in combination with other factors to produce a 50 year flood flow for rural catchments. The relationship between return period of the rainfall and the flood flow peak is detailed in the following table:

Flood Peak Return Period (years) | 2.33 | 10 | 30 | 50 | 100 | 1000 |
---|---|---|---|---|---|---|

Rainfall Return Period (years) | 2 | 17 | 50 | 81 | 140 | 1000 |

(Based on FEH Table 4.3.1. Chapter 4, page 44).

However urban drainage models like the Wallingford Procedure assume that the return period of the flow and the rainfall are the same.

The Ciria report on the design of flood storage reservoirs (Book 14, Ciria, page 41, 1996) uses the same assumption in its design example, which utilises an updated FSR method on a partly urbanised catchment.

Further work on partly urbanised catchments was reported in FSSR 5 which suggested that these catchments were less variable in response and the return period of the rainfall may be taken as equal to the return period of the flood. FEH therefore recommends that for catchments more than 25% urbanised (URBAN > 0.25 or URBEXT > 0.125) the rainfall return period is set equal to the design flood return period and the summer rainfall profile is appropriate. On rural catchments with less urbanisation then FEH table 4.3.1 should be used together with the rainfall winter profile. If URBEXT > 0.5 then the catchment is likely to be sewered and it should be modelled

as an urban drainage model.

For consistency, when the model is automatically generating return period analysis across a site (which may contain elements of FEH and Wallingford procedure runoff analysis) the same storm is used throughout the model and, in line with the FEH assumption for partly urbanised catchments, the return period of the rainfall and runoff are assumed to be the same. Rural hydrographs may be generated separately and added into the model if the above assumptions are not to apply to a particular site. Also a different Areal Reduction Factor may be specified for the urban and unit hydrograph (FSR/FEH Input) methods. In this way an 81 year return period storm may be run and adjusted using the ARF for the network to an equivalent 50 year return period and this set-up would effectively allow different return periods to be run together.

There is not a one to one correlation between rainfall return periods and runoff return periods in the FEH and FSR methods. In rural areas (URBEXT<0.125), for example, a 140 year rainfall RP is needed to produce a 100 year runoff. This poses a difficulty when combining the Wallingford procedure with these unit hydrograph methods. This is resolved in ReFH as both the Wallingford Procedure and ReFH produce the same return period runoff as the rainfall event used to generate the flows.

### Other Rainfall Parameters

The FEH method of generating statistical rainfall may produce significantly different results. Therefore, if FEH rainfall data is used for the urban element then the FEH methodology will also be used for unit hydrograph generation and likewise if FSR rainfall is specified it will be used for all runoff. Where rainfall hyetographs are specified then either method may be used to generate the unit hydrograph as the hyetograph is used in lieu of the statistical rainfall for both the urban and rural runoff generation.

The ReFH method modifies the FEH DDF design rainfall by a seasonal correction factor for summer and winter.