- 24 Oct 2022
- 25 Minutes to read
FEH Method (FEH Rainfall Runoff Method)
- Updated on 24 Oct 2022
- 25 Minutes to read
The FEH Rainfall Runoff Method Boundary (FEHBDY) derives an inflow hydrograph from a catchment or sub-catchment. The hydrograph then becomes a boundary condition equivalent to a Flow Time Boundary. Alternatively, the rainfall component of the FEH Boundary can be used as a direct rainfall boundary (equivalent to a REBDY), when used in conjunction with a Lateral Inflow unit, by selecting the 'Hyetograph' Boundary Type Option.
Theory and Guidance
The FEH Boundary is a rainfall-runoff model based on procedures described in the Flood Estimation Handbook (1999). It is essential that users of the FEH Boundary are fully conversant with the appropriate parts of the Flood Estimation Handbook - neither the software nor this documentation fully reproduce the guidance or definition of the methods presented in the Handbook. In particular, Volumes 1 and 4 of the Handbook include important guidance on the choice of methods for flood frequency estimates and on restrictions in the applicability of the methods. For example, design flow hydrographs produced by the FEH rainfall-runoff method can be highly inaccurate if parameter estimation is based solely on catchment descriptors.
For up-to-date information on the Flood Estimation Handbook please visit the Centre for Ecology and Hydrology website.
The FEH Boundary is designed to be flexible so that the components of the rainfall-runoff model (such as baseflow, percentage runoff, unit hydrograph) can either be estimated from the catchment descriptors or can be directly provided based on event data (usually the preferred option). In addition, the generated flow hydrographs can be scaled to match the flood peak obtained by the FEH statistical methods.
The rainfall-runoff model is based on unit hydrograph (UH) theory. For the required location, effective rainfall is transformed into a runoff hydrograph by convolution with the unit hydrograph. Please refer to Volume 4 of the FEH or standard hydrology texts for general details of unit hydrograph theory.
In the absence of flood event data, the parameters of the FEH rainfall-runoff model can be estimated from catchment descriptors. These catchment descriptors and the parameters of the rainfall frequency model can be obtained from the Centre for Ecology and Hydrology website and/or the FEH CD-ROM (if appropriate). A facility exists within Flood Modeller to import all relevant catchment descriptors and rainfall parameters from the standard FEH CD-ROM CSV (comma separated variable) output file.
The hydrograph produced by the FEH Boundary can be checked prior to use by either clicking on the 'Calculated hydrograph' tab in the FEHBDY properties dialog in the Flood Modeller interface, or by running a 'Boundary mode' simulation. A summary of the input data and rainfall-runoff component values is written to an ASCII file with the extension '.zzb'. The hydrograph and mass balance is tabulated in an ASCII file with the extension 'zzh'. When a boundary mode run has been undertaken, the hydrographs at all hydrological boundaries can be viewed (and compared) using the Flood Modeller Interface time series feature.
You can generate a datafile with:
- only one FEHBDY node
- many FEHBDY nodes each representing versions of the same catchment (eg different return periods or model component options)
- many FEHBDY nodes each representing different sub-catchments, optionally linked to additional Flood Modeller units such as Muskingum-Cunge routing units, hydrodynamic river sections, reservoirs/ponds, structures, junctions etc.
The FEHBDY unit contains a number of options to control the method of calculation. Within the Flood Modeller ASCII data file, these options are referred to in the form xxFLAG (e.g. PRFLAG, UHFLAG etc). This format is also used below to describe the options (the Flood Modeller Interface does not require knowledge of these 'flags').
The FEH Boundary calculates total runoff as a function of the following components:
P = precipitation; either calculated for a specific return period (ERFLAG = 'FEHER') or 'observed' (ERFLAG = 'OBSER'). This rainfall depth will use a rainfall profile either based on winter data (RPFLAG = 'WINRP'), summer data (RPFLAG = 'SUMRP'), or observed/derived values (RPFLAG = 'OBSRP').
UH = unit hydrograph; either calculated (UHFLAG = 'FSRUH') or observed/derived (UHFLAG = 'OBSUH')
PR = percentage runoff; either calculated (PRFLAG ='FEHPR') or observed/derived (PRFLAG = 'OBSPR')
BF = baseflow, either calculated (BFFLAG= 'F16BF') or observed/derived (BFFLAG='OBSBF')
Where the above components are 'calculated' then the following equations are used (new terms are either defined after introduction or are listed in the subsequent Data section).
If using the standard FEH rainfall profile (ERFLAG=FEHER):
The design rainfall depth is calculated from the depth-duration-frequency (DDF) relationships defined in FEH Volume 2 Section 2.3. The rainfall depth is multiplied by the areal reduction factor to produce areal rainfall.
Unit Hydrograph parameters
The unit hydrograph can either be derived from local data and specified as a time series of UH ordinates (usually preferred), or the standard FEH triangular UH can be used. Where the standard FEH UH is used (UHFLAG=FSRUH) then Tp can either be specified (TPFLAG=OBSTP) or calculated (TPFLAG = FEHTP) from:
and DPSBAR, DPLBAR, PROPWET, URBEXT and CAREA are defined in the Data section and are usually obtained from the Centre for Ecology and Hydrology website and/or the FEH CD-ROM (if appropriate).
Total Percentage Runoff
If using the FEH method and SPR to calculate percent runoff (PRFLAG = FEHPR):
and SPR and CWI are as defined in the Data section, with SPR best obtained through analysis of local event data, but in the absence of records can be obtained from the Centre for Ecology and Hydrology website and/or the FEH CD-ROM (if appropriate), and CWI may be entered directly (CWFLAG = 'OBSCW') or, for the design case, the program can calculate it from a digitised version of Figure 3.7 in FEH Volume 4.
If using the standard FSSR16/FEH calculation method for baseflow (BFFLAG = F16BF):
CAREA, CWI and SAAR are as defined in the Data section.
Note that several fields within the datafile are left blank (or contain zeros). This is to facilitate easier portability between the FSRBDY and FEHBDY units, i.e. fields describing FSRBDY parameters which are not used by FEHBDY or have no FEHBDY equivalent are ignored and therefore do not need to be overwritten when converting FSRBDY boundary units to FEHBDY boundaries.
Probable Maximum Flood (PMF)
The FEH Rainfall Runoff Method Boundary allows you to obtain a PMF (Probable Maximum Flood) estimation for the catchment using the FEH guidelines. This involves the introduction of the Probable Maximum Precipitation (PMP) design storm hyetograph, including modifications to the CWI and snowmelt contributions, in addition to further modifications to other constituent factors, namely the unit hydrograph and percentage runoff. These modifications are relative to those for the T-year flood estimation. The design storm period remains unchanged. A choice of summer and winter PMPs are available. For further reading and a detailed description of the method, see the FEH Vol. IV, Chapter 4 and Hough and Hollis (2006).
Design PMP - EMP
Values for EMP2h and EMP24h, the all-year point estimated maximum precipitations (EMPs) of 2-hour and 24-hour duration for the catchment, must be supplied (in mm). Additionally, the 25-day EMP (EMP25d) is required for design storms of long duration (D > 19.1hrs). Examples of appropriate values can be found in the FEH Vol. IV, Figures 4.1-4.3.
The hyetograph is then derived from the supplied EMPs, the EM rainfall and seasonal variation factors as given in the FEH, and the areal reduction factor (ARF) at each time interval Dt, 3Dt, ... D.
For time intervals of more than 0.5hr, the ARF is calculated by Flood Modeller as a function of STAREA and STDUR from a digitised form of Figure 3.4 in the FEH Volume 4. For time intervals between 0.25hr and 0.5hr, the ARF is interpolated from values in this table. For time intervals of less than 15 minutes, the ARF is extrapolated from this table and may be inaccurate.
Design PMP - Snowmelt
For Winter PMPs, storm event and antecedent period snowmelt contributions may be added, which also may affect the CWI. Snowmelt is invoked by supplying positive values for the snowmelt rates (in mm/day). Alternatively, snowmelt rates can be calculated automatically as:
- Melt rate (storm) = 100-yr melt rate + melt rate due to storm rain energy
- Antecedent melt rate = 100-yr melt rate + melt rate due to antecedent rain energy
The 100-year melt rate and melt rate energy are determined based on the following:
Melt rate energy =
and the 5-year melt rate and M100:M5 growth rate are obtained by a regression equation based on Northing and Altitude (ALTBAR), and using extreme value analysis based on the nearest available weather station, respectively.
When using snowmelt, a value for S100 (100-year snow depth water equivalent, in mm) must also be set. The snowmelt contribution to the precipitation at during each time interval Dt is therefore
Dt * melt rate
subject to enough snow from the total S100 being available.
For Summer PMPs, no snowmelt contribution will be added, irrespective of whether a snowmelt rate is supplied.
Design PMP - CWI
For the Catchment Wetness Index (CWI) for a PMP, the equation used is:
with the estimated antecedent rainfall given by
For a Winter PMP, if a snowmelt option is chosen, the CWI is the summation of the CWI due to antecedent rainfall and the CWI due to antecedent melt, and is further incremented by:
If the amount of snow remaining from S100 after the contribution from the storm period has been removed is insufficient, then the necessary adjustments are made according to FEH Vol IV, Section 4.3.4.
The calculation for baseflow is dependent on CWI, therefore this value will also be different from that for the T-year flood estimation.
Frozen Ground SPR
The calculated percentage runoff method remains the same as that for the FEH T-year flood estimation FEH with the exception that a Winter PMF is assumed to contain the frozen ground adjustment that the SPR cannot be lower than 53%. If this frozen ground adjustment is not required for a Winter PMF, then the user should manually calculate a percentage runoff and select an Observed PR.
Unit hydrograph time-to-peak
The calculated time-to-peak of the PMF instantaneous unit hydrograph is adjusted by a factor of 0.67 from that of the standard FSR unit hydrograph, thus:
If an Observed time-to-peak is selected, it is assumed that this factor is contained within the value and no adjustment is made.
The user is referred to the Flood Estimation Handbook, for full details of the derivation, application and limitations of the rainfall-runoff method.
The FEH recommends that where possible, certain of the rainfall-runoff model parameter values obtained from catchment descriptors are replaced with, or revised using, values from observed data. General recommendations on parameter estimation are:
- If suitable event data are available then the FEH recommends calculating Tpfrom such data, for example
- The data interval, t, should be small enough that the flood hydrograph is well defined. A data interval of 10%-20% of the Tp(0) is usually suitable. This should then be rounded off to a convenient value such as 0.25, 0.5, 1 or 2 hours.
It is usually important to find the critical values of parameters such as storm duration and storm profile which give the largest flood peak (or largest flood volume in some cases). The sensitivity of the model results to these parameters is described in the FEH and some conclusions are:
- For deriving design events the FEH recommends use of the 75% winter profile or 50% summer profiles. On predominantly rural catchments (URBEXT < 0.125) the 75% winter profile is recommended. On more urban catchments (0.125 ≤ URBEXT ≤ 0.5) the 50% summer profile is recommended. These two profiles are included as options in the FEHBDY unit and can be accessed by setting the options RPFLAG to 'WINRP' or 'SUMRP' respectively.
- Simulated peak flows can be sensitive to D, the storm duration. For the design case, the recommended storm duration for critical flood peak is:
With D taken as the nearest odd integer multiple of t. Note that with reservoired catchments or semi-distributed catchment modelling it will be necessary to consider a range of durations. The raw value of D, i.e. not adjusted for t, is output under "Critical Storm Duration" in the *.zzb (data summary) file after an unsteady or boundary mode simulation. NB The value of Tp used is the time to peak of the t-hour unit hydrograph.
In the FEH procedure the flow return period is not necessarily equal to the storm (rainfall) return period.
- In rural or only moderately urbanised catchments (URBEXT < 0.125) the FEH procedure provides a relationship between the storm and flow return periods (e.g. a 140-year storm return period is said to produce a 100-year return period flow).
- For urban catchments (0.125 ≤ URBEXT ≤ 0.5), the storm and flow return periods are assumed to be equal.
The FEHBDY unit will use this relationship to calculate storm return period if the storm return period in the datafile is set to zero. For highly urbanised catchments (URBEXT > 0.5), FEH procedures are not recommended, and, in such cases, a non-fatal warning message will be displayed.
The point rainfall calculation (ERFLAG='FEHER') is derived from a Depth-Duration-Frequency (DDF) model (FEH, Volume 2, Chapter 2). For a valid DDF model, the storm return period must be greater than one year, whereas one greater than 10000 years is not recommended. Furthermore, the parameters were based on observations of return periods of no greater than 1000 years. When importing the parameters for the DDF method from the FEH CD-ROM output, the values used are c,¼,f, rather than c(1km),¼,f(1km). The Flood Modeller implementation of the DDF model is based on a sliding duration rainfall (FEH Volume 2 Section 2.5), rather than a fixed duration.
For user-input unit hydrograph ordinates, the user may specify the units of these values from a selection of four commonly used units. These are any combination of 1cm or 1mm of effective rainfall depth covering either the whole catchment area or per 100km2. These units will also be used in the various unit hydrograph output options, either textually (*.zzb and *.zzh files) and graphically, via the user interface. The units specified also apply for output when deriving the unit hydrograph by the FEH (FSR) method.
Whilst the FEHBDY is essentially a UK-specific lumped single event rainfall-runoff model, the underlying unit hydrograph approach is applicable to other countries if the various components of the model are defined using local data.
Field in Data Entry Form
Name in Datafile
Mean catchment altitude (m). Only used in derivation of event and antecedent period snowmelt rates. Range 0.0 to 9968.0
Antecedent Melt Rate
Rate of snowmelt (mm/day) during the antecedent period. Used in CWI calculations. This is converted to the appropriate units and added to the runoff hydrograph. The facility to include snowmelt is not part of the standard rainfall frequency method.
Areal reduction factor to relate point rainfall to areal rainfall. If set to zero then the areal reduction factor is calculated by Flood Modeller as a function of STAREA and STDUR from a digitised form of Figure 3.4 in the FEH Volume 4. If STAREA is set to zero then CAREA is used. Range 0.0 to 1.0
User-defined baseflow (m3/s)
Adjusted baseflow (m3/s). Usually zero. Forces the resultant hydrograph to be not less than the specified flow. This may be required for program stability
Baseflow Calculation Method
Baseflow flag. FEH (bfflag='F16BF'): use FSSR16/FEH calculation method for baseflow, or Observed (bfflag='OBSBF'): use user-defined baseflow value.
Flow values to use during simulation, can be one of:
'base flow' (bfonly)
'peak flow' (pfonly)
'full hydrograph' (<blank>; default)
For example, if 'base flow' is selected then the baseflow contribution is used for the boundary flow value for the whole simulation.
DDF model parameter c
Override of snowmelt rates provided with calculated values. Override on (CALCRATES = 'CALCTRUE'): snowmelt rates during the storm event (SMRATE) and antecedent period (AMRATE) are recalculated from catchment parameters at simulation runtime. Override off (CALCRATES = 'CALCFALSE'): use user-input values. A blank value is equivalent to CALCFALSE.
Calibration factor for Tp (eg CALIB=1.1 increases Tp by 10%). Default value is 1.0
Contributing catchment area (km2)
Catchment Wetness Index Flag
Catchment wetness index calculation flag. FEH (cwflag='FSRCW'): use user-input value. For a PMF calculation, selecting FEH uses the PMF CWI calculation (cwflag='PMFCW')
Catchment wetness index (mm)
Country location flag. GB for Great Britain or NI for Northern Ireland.
Storm duration (hrs)
DDF model parameter d1
DDF model parameter d2
DDF model parameter d3
Mean drainage path length (km)
Mean drainage path slope (m/km)
DDF model parameter e
Easting coordinate of catchment outflow (Only used in derivation of event and antecedent period snowmelt rates.)
Estimated maximum 2-hour rainfall (mm). Used in PMP calculation only.
Estimated maximum 24-hour rainfall (mm). Used in PMP calculation only.
Estimated maximum 25-day rainfall (mm). Used in PMP calculation only.
Event Rainfall Flag
Event rainfall flag. FEH (erflag='FEHER'): use FEH method to calculate rainfall depth: PMF (erflag='PMFER'): use the FEH method to calculate a PMP depth or Observed(erflag='OBSER'): use user-input rainfall depth
DDF model parameter
Use Equal Return Periods
When this field is set to (force= 'FORCE'), the program stops if Tf is not equal to Ts for the SUMMER rainfall profile option.
Boundary Type Flag
Boundary mode flag: 'HYDROGRAPH' (the default if blank) denotes a generated hydrograph (i.e. the unit behaves as a QTBDY); 'HYETOGRAPH' indicates that it behaves as a REBDY-type unit, applying the Rainfall profile to a Rainfall-Only boundary (the latter must be used in conjunction with a lateral inflow node)
Node label identifier
Northing coordinate of catchment outflow (Only used in derivation of event and antecedent period snowmelt rates.)
Number of rainfall profile values (maximum of 4600)
Number of unit hydrograph values (maximum of 400)
Event rainfall precipitation (mm)
Percentage runoff (range 0 - 100)
Percentage runoff calculation flag: FEH (prflag='FEHPR'): use FEH method and SPR to calculate percent runoff; or Observed (prflag='OBSPR'): use user-input PR value.
Percentage Runoff Option
Option for variable or fixed percentage run-off. Keyword either 'FIXED' or 'VARIABLE'. If VARIABLE then the method used is to scale the specified PR value (or that calculated from a specified SPR) during the storm based on the method described in FEH Volume 4 Section A.5.2
Proportion of time catchment soil moisture deficit (SMD) was below 6mm during the period 1961-1990. (Range 0.0 - 1.0)
Storm Profile: Rainfall
User-defined rainfall profile starting at tstart with data interval t (mm)
Storm Profile Flag
Rainfall profile option:
75% winter and 50% summer profiles are taken from Figure 3.5 in FEH Volume 4
PMP profiles are used if a PMF event is selected, and are derived using Section 4.3.2 in FEH Volume 4
Use refined rainfall profile
If checked (refine rp=1), uses a finer discretisation of the standard FSR/FEH rainfall profiles - can prevent 'blocky'rainfall profiles for long storm/short data interval events
Standard annual average rainfall (mm)
Hydrograph Scaling Method:Scale
Hydrograph scaling method: 'FULL' (scaling ='FULL'; default) scales the whole hydrograph; Quick Runoff (scaling='RUNOFF'): scaling only applies to the quick runoff component of the hydrograph.
Used in conjunction with SCFLAG and scfact.
Hydrograph scaling option. By a factor of ('scflag='SCALE' [default]) - applies the specified factor; To fit peak of (scflag='PEAK') - fits the hydrograph peak to the specified value.
Hydrograph Scaling Option
If SCFLAG=PEAK then all hydrograph ordinates are scaled (by a constant value) to achieve a peak flow of scfact
If SCFLAG=SCALE then all hydrograph ordinates are multiplied by scfact (default is 1.0)
100-year snow depth water equivalent (used in PMP calculations only)
Snow Melt Rate (Storm)
Rate of snowmelt (mm/day) during the storm event period. This is converted to the appropriate units and added to the runoff hydrograph. The facility to include snowmelt is not part of the standard rainfall frequency method.
Standard percentage runoff (range 0 - 100)
Storm area (km2) when STAREA is entered as zero then STAREA is set to CAREA
Storm duration (hrs). Should be the nearest odd integer multiple of t
Time interval used for rainfall profile and unit hydrograph (hrs)
Average temperature (oC). Default value 10, minimum 0. Only used in derivation of event and antecedent period snowmelt rates.
Optional delay time (hrs), e.g. if tdelay=2hrs then the hydrograph will start 2hrs after the start time of the simulation
Rainfall Return Period
Storm return period (years). If set to 0.0 then calculated from Figure 3.2 of FEH Volume 4. Must be > 1 year
Flood Return Period
Flood return period (years)
User-defined time to peak of t-hour unit hydrograph (hrs)
Tp Calculation Method
Unit hydrograph Tp flag. FEH (tpflag='FEH16P'): use FEH method to calculate unit hydrograph time-to-peak, or Observed (tpflag='OBSTP'): use user-defined value.
Storm Return Period
Storm return period (years). If set to 0.0 then calculated from Figure 3.2 of FEH Volume 4. Must be > 1 year
Unit hydrograph ordinates with data interval t (see units)
unit hydrograph time (hrs)
TB Scale Factor
Unit hydrograph time base (TB) adjustment factor. New time base is uhbadj multiplied by the calculated TB value. The UH peak is adjusted accordingly to preserve its unit property.
Scaling factor for the unit hydrograph ordinates. Only used if the 'units' keyword is not recognised. If zero or blank then units of m3/s/mm are used. (Not accessible from the user interface.)
Unit Hydrograph Flag
Unit hydrograph flag. FEH (uhflag='FSRUH'): use standard FSR/FEH triangular hydrograph, or Observed (uhflag='OBSUH'): use user-defined unit hydrograph.
Units of the unit hydrograph ordinates. Keyword can be one of:
Extent of urban/suburban land cover (range 0.0 - 1.0)
Elevation (m AD). Not used in FEHBDY computations
Line 1 : Keyword 'FEHBDY' [comment]
Line 2 : Label
Line 3 : z, easting, northing
Line 4 : tdelay, t, bfonly, SCFLAG, scfact, hymode
Line 5 : CYFLAG
Line 6 : CAREA, <blank>, <blank>, <blank>, URBEXT, ALTBAR
Line 7 : STAREA, STDUR, <blank>, SNRATE, SN100, TEMP, AMRATE, CALCRATES
Line 8 : SAAR, <blank>, <blank>, <blank>, FORCE
Line 9 : ERFLAG
Line 10 : P (if ERFLAG = 'OBSER')
Line 10 : Tf, Ts, arf, c, d1, d2, d3, e, f (if ERFLAG = 'FEHER')
Line 10 : <blank>, <blank>, arf (if ERFLAG = 'PMFER')
Line 11 : CWFLAG
Line 12 : CWI (if CWFLAG = 'OBSCW')
Line 12 : <blank> (if CWFLAG = 'FSRCW' or 'PMFCW')
Line 13 : PRFLAG, PRVAR
Line 14 : PR (if PRFLAG = 'OBSPR')
Line 14 : SPR (if PRFLAG = 'FEHPR')
Line 15 : TPFLAG
Line 16 : CALIB, Tp (if TPFLAG = 'OBSTP')
Line 16 : CALIB, DPLBAR, DPSBAR, PROPWET (if TPFLAG = 'FEHTP')
Line 17 : BFFLAG
Line 18 : BFADJS, BF (if BFFLAG = 'OBSBF')
Line 18 : BFADJS (if BFFLAG = 'F16BF')
Line 19 : UHFLAG
Line 20 : 0, units, uhfctr (if UHFLAG = 'FSRUH')
Line 20 : nuh, units, uhfctr (if UHFLAG = 'OBSUH')
Line 21 to Line 20+nuh : uh (if UHFLAG = 'OBSUH')
Line 21+nuh : RPFLAG
Line 22+nuh : 0, em2h, em24h, em25d (if ERFLAG = 'PMFER')
Line 22+nuh : 0 (if RPFLAG = 'WINRP', ERFLAG¹ 'PMFER')
Line 22+nuh : 0 (if RPFLAG = 'SUMRP', ERFLAG¹ 'PMFER')
Line 22+nuh : nrp (if RPFLAG = 'OBSRP')
Line 23+nuh to Line 22+nuh+nrp : rp (if RPFLAG = 'OBSRP')
where items in square brackets are optional, and other parameters are as defined in the data section.
FEHBDY M029 0.000 385115 242872 0.000 0.250 SCALEFACT 1.000HYDROGRAPH 1.000 FULL OVERRIDE GB 16.1700 0.000 0.000 0.000 0.005 400 0.000 5.250 0.000 168.471 200.000 10 96.011 CALCTRUE 1175.000 0.000 0.000 0.000 PMFER 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 FSRCW 0.000 FEHPR FIXED 42.760 FEHTP 1.000 5.170 178.100 0.520 F16BF 0.000 FSRUH 0 mmarea WINPMP 1 0 158.000 290.000 500.000