ReFH Method (ReFH Rainfall Runoff Method)
    • 21 Sep 2022
    • 19 Minutes to read
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    ReFH Method (ReFH Rainfall Runoff Method)

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    Article Summary




    Default value



    Time interval used in unit hydrograph and rainfall profile (hrs).




    aT calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the aT value is calculated by Flood Modeller by interpolating for the given return period from a lookup table of aT values against return periods for the given season. Note that the season is obtained from the value set by SEASONFLAG.

    If set to 'USER', the input value of aT is used.



    ALPHA (aT)

    Initial soil moisture correction factor. (only used if ALPHAFLAG is set to 'USER').  


    0 < aT ≤ 1 if ALPHAFLAG='USER'


    Areal reduction factor to relate point rainfall to areal rainfall. Range 0.0 to 1.0. The input value of arf is ignored and calculated internally if ARFFLAG is set to 'DESIGN'.


    0 < arf ≤ 1 if ARFFLAG='USER'


    ARF calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' 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.

    If set to 'USER', the input value of arf is used.




    Initial Baseflow (m3/s). The input value of BF0 is ignored and calculated internally if BF0FLAG is set to 'DESIGN'.


    >0 if BF0FLAG='USER'


    Baseflow calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the initial baseflow is calculated by Flood Modeller as a function of CINI, SAAR and [catchment] AREA.

    If set to 'USER', the input value of BF0 is used.




    Baseflow index catchment descriptor




    Flow values to use during simulation, can be one of: 'BFONLY' (base flow only), 'PFONLY' (peak flow only) or blank (full hydrograph).

    For example, if 'BFONLY' is selected then the baseflow contribution is used for the boundary flow value for the whole simulation.




    Baseflow lag (hrs, only used if BLFLAG is set to 'USER').


    >0 if BLFLAG='USER'


    Baseflow lag donor correction [multiplicative] factor.




    Baseflow lag (BL) calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the BL is calculated by Flood Modeller as a function BFIHOST, PROPWET, URBEXT and DPLBAR.

    If set to 'USER', the input value of BL is used.

    A donor correction factor may also be applied to the calculated value of BL.




    Baseflow recharge (only used if BRFLAG is set to 'USER').


    >0 if BRFLAG='USER'


    Baseflow recharge donor correction [multiplicative] factor.




    Baseflow recharge (BR) calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the BR is calculated by Flood Modeller as a function BFIHOST and PROPWET.

    If set to 'USER', the input value of BR is used.

    A donor correction factor may also be applied to the calculated value of BR.




    Catchment descriptor - DDF model parameter c.




    Contributing catchment area (km2)


    >0; warning if area < 0.038 or  area > 9868


    Initial soil moisture content (mm, only used if CINIFLAG is set to 'USER').


    >0 if CINIFLAG='USER'


    CINI calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the CINI value is calculated by Flood Modeller as a function CMAX, BFIHOST and PROPWET for the current season (defined by SEASONFLAG).

    If set to 'USER', the input value of CINI is used.




    Maximum soil moisture capacity (mm, only used if CMAXFLAG is set to 'USER').


    >0 if CMAXFLAG='USER'


    CMAX calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the CMAX  value is calculated by Flood Modeller as a function BFIHOST and PROPWET.

    If set to 'USER', the input value of CMAX is used.

    A donor correction factor may also be applied to the calculated value of CMAX 





    CMAX  donor correction [multiplicative] factor.




    Catchment descriptor - DDF model parameter d1.




    Catchment descriptor - DDF model parameter d2.




    Catchment descriptor - DDF model parameter d3.




    Mean drainage path length catchment descriptor (km)




    Mean drainage path slope catchment descriptor (m/km)




    Catchment descriptor - DDF model parameter e.




    Easting coordinate of catchment outflow (not used in calculations)




    Event rainfall calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the DDF model, SCF and ARF are combined to give a rainfall depth.

    If set to 'USER', the input value of precipitation is used.


    For METHOD='DLL', only 'DESIGN' is possible



    Catchment descriptor - DDF model parameter f.




    Boundary mode flag: 'HYDROGRAPH' 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 lateral inflow unit)




    Node label identifier




    Calculation method - determines whether the WHS dll ('DLL') or the 'hardcoded' method from the published report ('REPORT') is used for calculations.


    'DLL' or 'REPORT'


    Minimum flow (m3/s). Usually zero. Forces the resultant hydrograph to be not less than the specified flow. This may be required for program stability




    Northing coordinate of catchment outflow (not used in calculations)




    Number of rainfall profile values


    >0 if RPFLAG='USER'


    Number of unit hydrograph ordinates.


    >0 if UHFLAG='USER'


    Event rainfall precipitation (mm). This is deemed to include any seasonal or areal correction factors.

    Only used if ERFLAG is set to 'USER'.


    >0 if ERFLAG='USER'


    Catchment descriptor - proportion of time catchment soil moisture deficit (SMD) was below 6mm during the period 1961-1990. (range 0.0 - 1.0)


    0 ≤ PROPWET≤ 1


    Rainfall profile starting at tstart with data interval t (mm)


    ≥ 0 if RPFLAG='USER';



    Rainfall profile option ('DESIGN' or 'USER').

    If set to 'DESIGN', then the standard rainfall profile for the current season (50% summer or 75% winter) is used.

    If set to 'USER', the input values of the rainfall profiles are used.


    For METHOD='DLL', only 'DESIGN' is possible


    Season flag - 'SUMMER', 'WINTER' or 'DEFAULT'. If set to 'DEFAULT', then WINTER applies if URBEXT<0.125; SUMMER otherwise.

    Uses the design rainfall profile (50% summer or 75% winter), SCF, CINI, aT and BF0 values for the season, where appropriate.

    75% winter and 50% summer profiles are taken from Figure 3.5 in FEH Volume 4




    Standard annual average rainfall (mm) - catchment descriptor.




    Hydrograph scaling method ('FULL' or 'RUNOFF'). 'FULL' scales the whole hydrograph; 'RUNOFF' scales only the quick runoff component of the hydrograph.

    Used in conjunction with SCFLAG and scfact.




    Seasonal correction factor applied to the DDF rainfall (along with ARF) to derive the design rainfall (only used if SCFFLAG is set to 'USER').


    >0 if SCFFLAG='USER'


    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.

    Used in conjunction with SCFLAG and SCALING.




    SCF calculation option ('DESIGN' or 'USER').

    If set to 'DESIGN' then the SCF is calculated by Flood Modeller as a function SAAR and the storm duration for the current season (as given by SEASONFLAG).

    If set to 'USER', the input value of SCF is used.




    Hydrograph scaling option ('PEAK' or 'SCALE'). 'PEAK' scales the hydrograph to fit a peak; 'SCALE' scales the hydrograph by a given factor, scfact.

    Used in conjunction with SCALING and scfact.




    Rate of snowmelt (mm/day). Not used (yet) in ReFH.




    Storm area (km2). This is used only in calculating ARF (and has no effect on the rainfall volume); if STAREA is entered as zero or negative then STAREA is set to CAREA


    For METHOD='DLL', this is not active


    Storm duration (hrs). Should be the nearest odd integer multiple of ∆t.




    Return period (years)


    >1; warning if T>150


    Optional delay time (hrs), e.g. if tdelay=2hrs then the hydrograph will start 2hrs after the start time of the simulation.




    Time to peak of instantaneous unit hydrograph (hrs)


    >0 if TPFLAG='USER'


    TP donor correction [multiplicative] factor.




    Unit hydrograph Tp option ('DESIGN' or 'USER'). If set to 'DESIGN', Tp is calculated using catchment descriptors; if set to 'USER', the user input value of Tp is used.




    Time to peak of t-hour unit hydrograph (hrs) - not currently used




    Unit hydrograph ordinates with data interval Dt (see units); only used if UHFLAG is set to 'USER'.


    ≥0 if UHFLAG='USER'


    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 option ('DESIGN' or 'USER'). If set to 'DESIGN' then the ReFH design 'kinked-triangle' unit hydrograph is used, using TP, Uc and UP.

    If set to 'USER', the input values of the unit hydrograph are used.




    Dimensionless instantaneous unit hydrograph 'kink' facto the multiplier applied to UC, the triangular UH ordinate at time 2TP. NB If Uk = 1, then a triangular unit hydrograph results.

    Only used if UKFLAG is set to 'USER'.


    >0 if UKFLAG='USER'; also cannot allow UH time base to be < 2Tp


    Uk calculation option ('DESIGN' or 'USER'). If set to 'DESIGN' then the standard factor of 0.8 is used.

    If set to 'USER', the user input values of Uk is used.




    Units of the unit hydrograph ordinates. Keyword can be one of:

    • 'cm100k': 1cm depth over 100km2 (units = m3/s/cm/100km2)

    • 'cmarea': 1cm depth over catchment area (units = m3/s/cm)

    • 'mm100k': 1mm depth over 100km2 (units = m3/s/mm/100km2)

    • 'mmarea': 1mm depth over catchment area (units = m3/s/mm)

    NB The conventional units often used are m3/s/cm/100km2




    Dimensionless instantaneous unit hydrograph ordinate at time to peak. Only used if UPFLAG is set to 'USER'.


    <2 if UPFLAG='USER'


    UP calculation option ('DESIGN' or 'USER'). If set to 'DESIGN' then the standard value of 0.65 is used.

    If set to 'USER', the user input values of UP is used.




    Extent of urban/suburban land cover (range 0.0 - 1.0) - catchment descriptor.

    NB The value of URBEXT affects the default season, i.e. if SEASONFLAG is set to 'DEFAULT', i.e. summer applies if URBEXT ≥ 0.125; winter otherwise.


    0 ≤ URBEXT ≤ 1


    Elevation (mAD). Not used in ReFH calculations.



    Theory and Guidance


    The [ReFH*](Revitalised Flood Hydrograph) Method Boundary (ReFHBDY) derives an inflow hydrograph for a catchment or sub-catchment. The hydrograph then becomes a boundary condition, equivalent to a Flow Time Boundary, and can therefore form inputs to a hydrodynamic or routing model. This inflow can be applied at the upstream end of a reach or may be distributed over a reach in conjunction with the Lateral Inflow unit. When run in boundary mode, the resultant hydrograph may be viewed using the Graphical or Tabular postprocessors; furthermore, summary hydrograph (.zzh) and data input (*.zzb) files may be viewed prior to running a full simulation; this preview functionality is also available within the Flood Modeller interface.

    Alternatively, the rainfall component of the ReFH Boundary can be used as a direct rainfall boundary (equivalent to an REBDY), when used in conjunction with a Lateral Inflow unit, by selecting the Hyetograph Boundary type option.

    The ReFH Boundary is a rainfall-runoff model using procedures developed by CEH to update the FSR/FEH Rainfall Runoff Method, in response to concerns that the FSR/FEH design model tended to overestimate design floods. ReFH improves the way that design events are modelled and has a number of advantages over the FSR/FEH unit hydrograph and losses model. The key improvements are:

    • a new baseflow model which provides a more objective method of separating total runoff into baseflow and direct runoff;
    • a loss model based on the uniform PDM model of Moore (1985);
    • improved handling of antecedent soil moisture conditions;
    • a more flexible unit hydrograph shape,
    • explicit reconciliation to statistical estimates of peak flow.

    Users should note that in order to use local data with the ReFH Method, it is strongly recommended that model parameters are estimated using the full ReFH software developed by CEH and Wallingford Hydrosolutions ( The FEH supplementary Report No. 1 ('The Revitalised FSR/FEH Rainfall-Runoff Method') provides further guidance on the method and use of local data. In all cases users are advised to check the latest guidance on the use of local data.

    Where the catchment is ungauged and there is no opportunity to use local data, then the ReFH Method Boundary should be used in preference to the FEH Method Boundary. This is because the catchment descriptor equations have undergone further calibration and improvement as part of the development of the ReFH method.

    The ReFH hydrograph peak can be reconciled to a statistical estimate of the design peak and is now achieved by adjusting parameters in the loss model (Cini and aT). The reconciliation procedure is described further below.

    It is strongly recommended that users of the ReFH Boundary read the Technical Report, produced by CEH and available from The user should also be conversant with the methods described in the Flood Estimation Handbook and must be aware that design flow hydrographs produced by the ReFH method can still be highly inaccurate if the model parameters are based solely on catchment descriptors.

    When using the ReFH Method users should also note that the use of this method for Scottish catchments has not been verified and as of July 2008 SEPA will not accept a design flood estimate based solely on the ReFH method, but will continue to accept the FSR/FEH rainfall-runoff method as an appropriate method for rivers in Scotland.

    The Revitalised Method

    As mentioned above, the ReFH model is composed of three sub-models, a loss model, a routing model and a baseflow model.

    The loss model is based on the Probability Distributed Model (PDM). Effective rainfall is now evaluated sequentially during a storm and if soil storage is filled, runoff will equal 100%. The new model requires an estimate of the initial soil moisture content (Cini) at time zero. Cini is estimated on a seasonal basis (summer or winter) by the new model (i.e. using catchment descriptors - see equations below) or alternatively, the user can define a value (within the ReFH software Cini can also be modelled from antecedent conditions). The model also requires an estimate for Cmax which can also be obtained from catchment descriptors or defined by the user. A more complete description of the loss model can be found in section 3 of the Technical Report.

    The routing model still uses an instantaneous unit hydrograph (IUH) and scales this to each catchment by area and time to peak (Tp). However, in ReFH the shape of the IUH has been changed by adding a kink at 2Tp along the descending limb. This gives the formerly triangular IUH a slightly more realistic profile, and introduces two new terms Up and Uk (see equations for further details). Importantly, the ReFH model estimate of Tp is not equivalent to the FEH estimate of Tp, and users should be careful as to not confuse the two. The new ReFH model has led to a revision in the catchment descriptor predictor equation used to calculate (Tp). The new formula makes use of the same four catchment descriptors but the coefficients have changed (see equations for further details). A more complete description of the routing model can also be found in section 3 of the Technical Report.

    The baseflow model in the FSR/FEH rainfall runoff model was a constant value, independent of direct runoff. The new ReFH baseflow model works on the assumption that the input to the baseflow reservoir is related to the rate of surface runoff. Model parameters are Baseflow Recharge (BR), Baseflow Lag (BL) and Initial Baseflow (BF0). All three baseflow parameters can be estimated from catchment descriptors or the user can specify their own, using local data and the additional software from CEH.

    FSR/FEH storm profiles continue to be used in the new ReFH model and the equations for calculating the Areal Reduction Factor (ARF) and Critical Storm Duration (D) remain unchanged (see equations). However, because the equation for estimating Tp from catchment descriptors has changed, the ReFH recommended storm duration (D) will be different from the value returned by using the FEHBDY.

    The user should note that unlike the FEH method, there is always equivalence between the rainfall return period and the flood return period in ReFH. This has been achieved through introduction of a seasonal correction factor, where annual maximum rainfall statistics are converted to seasonal statistics (winter or summer) depending upon location, season (determined from catchment descriptors or specified by the user), duration and flood return period.

    Peak Flow Reconciliation

    The ReFH design (or catchment descriptor) method has been calibrated to ensure that flood frequency curves derived from the method correspond to the flood frequency curves derived through a pooled statistical analysis of AMAX events. For any given catchment at any given return period T, the difference between the peak flow estimate generated from the ReFH model (using T-year design rainfall) and the corresponding T-year estimate obtained from the pooled analysis was minimised by adjusting a free variable. In this case the free variable is termed a and the term will vary with return period. The ReFH method assumes that the a coefficient is equal to one for a 5-year return period (a5 = 1).

    Note that the method has been calibrated using URBEXT1990 values, and it is these that will be imported using the Flood Modeller "Import Catchment Descriptors" facility, rather than URBEXT2000 values.

    Calibration of the ReFH design method proved problematic as the gradients of the flood frequency curves generated by the pooled statistical method and the ReFH model were quite different and so different correcting ratios would need to be applied to the 5 year flood from say the 100 year flood. This effectively meant that the ReFH model must lose increasingly more water at higher return periods than at lower return periods. The decision was taken to impose these extra losses on the design method by modifying the ReFH loss model. A catchment specific value of the initial soil moisture condition (Cini) would be calculated when T = 5 year (and so a = 1), such that the 5 year estimate of peak flow from the ReFH method was reconciled with the 5 year estimate from the statistical pooled method. With Cini fixed, the free variable a will then vary as the return period is increased. The ReFH method was calibrated up to the 150 year event and users should also note that only seven urban catchments were used in the calibration procedure. Thus there are a number of limitations associated with the method and the user is referred to section 6 of the Technical Report for further information.

    The procedure adopted by CEH to calibrate the ReFH model is important to understand, and it is recommended that the user reconciles their ReFH design peak flow estimates to statistical pooled estimates using a similar method. Through trial and error, the user should first adjust Cini for the 5 year return period until the ReFH peak flow corresponds to the statistical estimate of the 5 year flow. Once the 5 year peak flows have been reconciled by adjusting Cini, the user can then reconcile peak flows at other return periods by adjusting the a factor (leaving Cini at the value derived for the 5 year return period).

    Using the ReFHBDY unit within the Flood Modeller interface

    On opening an ReFHBDY unit within the Flood Modeller interface, the user is presented with five tabs: Catchment, Rainfall, Models, Options and Results. The first three tabs form the components of ReFH; the Options tab allows for some model adjustment and the Results tab displays the values for the generated hydrograph and its intermediate constituent components.

    Prior to viewing the Results tab or running a simulation, the minimum input requirements are the Catchment Descriptors (Catchment Tab), Storm Duration, Data Interval and Return Period (Rainfall Tab). Although a recommended timestep range and storm duration are provided on the Results Tab, an estimate of these must still be provided initially.

    Catchment descriptors may be imported from a csv file produced by the FEH CD-ROM (using the Import Catchment Descriptors button), or may be input manually. Note that only those descriptors used in the calculations are imported, in addition to the Easting and Northing grid reference, which are provided for information only (although may be used by postprocessing tools, e.g. TabularCSV, to extract coordinates).

    All parameters have the option to use the 'ReFH design standard' or from 'Catchment Descriptors' as appropriate, and may be overridden by a user input ('User Defined'). By default, all options are initially set to 'ReFH design standard' or 'Catchment Descriptors'. Similarly, the season (Rainfall Tab) is initially set to 'DEFAULT', which will apply a summer or winter design, depending on the degree of urbanisation of the catchment (URBEXT > 0.125 indicates a Summer storm is recommended). The season can also be overridden explicitly. The "Reset all options" button will reset all of these options to 'ReFH design standard' or 'Catchment Descriptors' (or 'DEFAULT' in the case of season).

    Donor correction factors (DCF), will be applied to all parameters whose method is set to 'Catchment Descriptors'. Thus, for a design standard calculation [uncorrected], the DCF should be set to 1 (the default).

    Optimised model parameters may be imported from a CSV file produced by the ReFH software by using the "import parameters" button. The parameters that may be imported thus are: Cmax, Tp, Up, Uk, BL and BR. If using this facility, the appropriate methods will automatically be set to 'User Defined'.

    The Options Tab allows the user to select the calculation method using the CEH-approved dynamic link library (DLL) calculation engine or the equations obtained from the Published Report. The 'Published Report' option uses equations and methods interpreted literally from the Published Report and is provided to allow greater felxibility, e.g. the Urban enhancements, a larger storm area to influence the calculated ARF value and to facilitate a user-input storm to be used.Furthermore, the dll is only available in 32-bit format and will not work with 64-bit versions of Flood Modeller. NB The storm area (if different from the catchment area) only affects the ARF calculation in 'Published Report' mode and has no effect on total rainfall volume.

    The ReFH calculation engine DLL (FEHRRModel.dll) is produced by Wallingford HydroSolutions Ltd.

    By clicking on the Results tab, the user is effectively launching a boundary mode simulation of Flood Modeller of a model containing the single ReFHBDY unit. This produces the output hydrograph and its constituents in tabulated form, and many of the intermediate calculated parameters. Recommended values for design storm duration and timestep are given, which can be subsequently checked against those originally entered. N.B. if subsequently adjusting the storm duration or time interval, these should be rounded so that the duration divided by the interval is an odd integer. The hydrographs and hyetographs may also be viewed graphically via the Plot button. The hydrograph (.zzh) and summary data (.zzb) output files are also produced and are able to be viewed via the appropriate button on the tab. Occasionally, the simulation may fail, e.g. due to bad input data or an inappropriate licence, and like any Flood Modeller simulation, will generate a run error and produce diagnostic output in such instances. The user is advised to check this output (N.B. The error dialogue box may appear partially hidden behind the "Please Wait..." dialogue box).


    The following equations are those published in the Technical Report. These are the equations used when selecting the 'Published Report' calculation method.

    CMAX = 596.7 BFIHOST 0.95 PROPWET -0.24

    CINI,winter = 0.5 CMAX ( 1.2 - 1.7 BFIHOST + 0.82 PROPWET )

    CINI,summer = 0.5 CMAX ( 0.9 - 0.82BFIHOST - 0.43 PROPWET )

    T= 1.563 PROPWET -1.09 DPLBAR 0.6 (1 + URBEXT) -3.34 DPSBAR -0.28

    Up = 0.65

    Uk = 0.8

    BL = 25.47 BFIHOST0.47 PROPWET-0.53 (1 + URBEXT)-3.01 DPLBAR0.21

    BR = 3.751 BFIHOST1.08 PROPWET0.36

    BF0,winter = AREA (63.79 (CINI - 120.79) + 5.54 SAAR) × 10-5

    BF0,summer = AREA (33.94 (CINI - 85.42) + 3.14 SAAR) × 10-5

    Recommended D = Tp(1 + SAAR/1000)

    Recommended timestep is 10-20% of the time to peak, Tp.

    Datafile Format

    Line 1 - Keyword 'ReFHBDY' (case insensitive) #REVISION#1

    Line 2 - Label

    Line 3 - z, easting, northing

    Line 4 - tdelay, ∆t, bfonly, SCFLAG, scfact, hymode, SCALING, minflow


    Line 6 - STAREA, STDUR, SNRATE (SNRATE not currently used in ReFH)

    Line 7 - ERFLAG, ARFFLAG, comment

    Line 8 - P, T, arf, c, d1 ,d2 ,d3 ,e, f (P only used if ERFLAG = /'USER/'; the remainder only if ERFLAG = 'DESIGN')


    Line 10 - nrp

    Line 10.1 to Line 17.nrp - rp

    Line 11 - CMAXFLAG, CINIFLAG, ALPHAFLAG, comment



    Line 14 - TPDCF, Tp0, TpT, DPLBAR, DPSBAR, PROPWET, Up, Uk (Tp only used if TPFLAG = 'USER')

    Line 15 - nuh, units, uhfctr (nuh may equal zero if UHFLAG = 'DESIGN')

    Line 15.1 to Line 15.nuh - uh


    Line 17 - BLDCF, BL, BRDCF, BR, BF0

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