 15 Aug 2022
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FSSR16 Method
 Updated on 15 Aug 2022
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Data
Field in Data Entry Form  Description  Name in Datafile 

ARF  Areal reduction factor to calculate event rainfall. If set to zero then the areal reduction factor is calculated by Flood Modeller. Range 0.0 to 1.0.  arf 
Baseflow Value  Userdefined baseflow (m^{3}/s)  BF 
Minimum Flow  Adjusted baseflow (m^{3}/s). Usually zero. Sets a minimum flow to be generated by the unit. This may be required for program stability  BFADJS 
Baseflow Calculation Method  Baseflow flag FSSR16 (bfflag='F16BF'): use FSSR 16 calculation method for baseflow, or Observed (bfflag='OBSBF'): use userdefined baseflow value.  BFFLAG 
Simulation Type  Flow values to use during simulation, can be one of:
For example, if 'base flow' is selected then the baseflow contribution is used for the boundary flow value for the simulation.  bfonly 
Tp Coefficent  Calibration factor for T_{p}. Default value is 1.0  CALIB 
Catchment Area  Contributing catchment area (km^{2})  CAREA 
Country  Country (`ENGLAND', `WALES', `SCOTLAND' or `IRELAND')  COUNTRY 
Catchment Wetness Index Flag  Catchment wetness index calculation flag FSR (cwflag='FSRCW'):use FSR method or Observed (cwflag='OBSCW'): use userinput value  CWFLAG 
Observed CWI  (Userdefined) catchment wetness index (mm)  CWI 
Event Rainfall Flag  Event rainfall flag FSR (erflag=`FSRER'):use FSR method to calculate rainfall depth or Observed (erflag='OBSER'): use userinput rainfall depth  ERFLAG 
Use Equal Return Periods  When this flag is set to (force='FORCE'), the program stops if T_{f} is not equal to T_{s} for the SUMMER rainfall profile option.  FORCE 
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 REBDYtype unit, applying the Rainfall profile to a RainfallOnly boundary (the latter must be used in conjunction with a lateral inflow node)  hymode 
M52D  5 year return period 2 day duration rainfall (mm) (Figure II.3.2 in FSR)  M52D 
M525D  5 year return period 25 day duration rainfall (mm) (Figure II.3.4 in FSR)  M525D 
Main Stream Length  Main stream length (km)  MSL 
n/a  Number of rainfall profile values  nrp 
n/a  Number of unit hydrograph values  nuh 
Rainfall depth  Event rainfall precipitation (mm)  P 
PR  Percentage runoff (range 0  100)  PR 
Runoff Flag  Percentage runoff calculation flag: FSSR16 (prflag='FSRPR'): use FSSR16 method and SPR to caluclate percent runoff: or Observed (prflag=`OBSPR'):use userinput PR value.  PRFLAG 
Percent Runoff Flag  FIXED (or blank) for fixed percentage runoff, VARIABLE for PR varying through the storm  PRVAR 
Jenkinson’s r  Ratio of 60 minute M5 rainfall to 2 day M5 rainfall (M560min/M52D) (Jenkinson's r)  r 
Storm Profile: Rainfall  Observed rainfall profile values, starting at tstart with data interval t (mm)  rp 
Storm Profile Flag  Rainfall profile flag: FSR 50% Summer (rpflag=`SUMRP'):use standard FSR 50% Summer profile; FSR 75% Winter (rpflag='WINRP'):use standard FSR 75% Winter profile: or Observed (rpflag='OBSRP'): use observed rainfall [profile].  RPFLAG 
Use refined rainfall profile  If checked (refine rp=1), uses a finer discretisation of the standard FSR rainfall profiles  can prevent 'blocky' rainfall profiles for long storm/short data interval events.  refine_rp 
SMD  Residual soil moisture deficit (mm). Not used for FSSR16 computations  RSMD 
Stream Slope (S1085)  Stream slope over 10 to 85% of mainstream length (m/km)  S1085 
SAAR  Standard annual average rainfall (mm)  SAAR 
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.  SCALING 
Method  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.  SCFLAG 
  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)  scfact 
n/a  Soil index; a weighted sum of soil fractions SOIL1,..., SOIL5 (not used in this unit but a value between 0 and 1 inclusive must be entered; retained for historical purposes)  SOIL 
Snow Melt Rate  Rate of snowmelt (mm/day)  SNRATE 
SPR  Standard percentage runoff (range 0  100)  SPR 
Storm Area  Storm area (km^{2}). When STAREA is entered as zero then STAREA is set to CAREA  STAREA 
Storm Duration  Storm duration (hrs)  STDUR 
Data Interval  Time interval used for rainfall profile and unit hydrograph (hrs)  t 
Time Delay  Optional delay time (hrs), eg if tdelay=2hrs then the hydrograph will start 2hrs after the start time of the simulation  tdelay 
Rainfall Return Period  Return period of rainfall event (years)  Ts 
Flood Return Period  Flood return period (years)  Tf 
Tp Value  Userdefined time to peak of thour unit hydrograph (hrs)  Tp 
Tp Calculation Method  Unit hydrograph T_{p} flag. FSSR16 (tpflag='F16P'): use FSSR16 method to calculate unit hydrograph timetopeak; R124 (tpflag='R124TP'): use IoH report 124, or Observed (tpflag=`OBSTP'): use userdefined value.  TPFLAG 
UH Ordinate  Unit hydrograph ordinates with data interval t (units: uhunit, default: m^{3}/s/mm)  uh 
UH Time  Unit hydrograph time (hrs) 

Units  Units of unit hydrograph ordinates: Default is Cumecs/mm (uhunit='MMAREA')  uhunit 
TB Scale Factor  Unit hydrograph time base (T_{B}) adjustment factor. New time base is uhbadj multiplied by the calculated TB value. The UH peak is adjusted accordingly to preserve its unit property.  uhbadj 
Unit Hydrograph Flag  Unit hydrograph flag. FSR (uhflag='FSRUH'): use standard FSR triangular hydrograph, or Observed (uhflag='OBSUH'): use userdefined unit hydrograph  UHFLAG 
Urban Fraction  Fraction of catchment in urban development (range 0.0  1.0)  URBAN 
n/a  Elevation (mAD). Not used in FSSR16 computations  z 
Theory and Guidance
The FSSR16 Boundary Method (FSSR16BDY) derives an inflow hydrograph from a catchment or subcatchment. The hydrograph then becomes a boundary condition equivalent to a Flow Time Boundary.
The FSSR16 Boundary is a rainfallrunoff model based on procedures set out in the Flood Studies Report (1975) and includes revisions contained in subsequent supplementary reports.
The FSSR16 Boundary will either generate flow hydrographs for design return period events, or will simulate runoff during historic events using recorded rainfall and other input data.
The rainfallrunoff model is based on unit hydrograph theory. For the required location effective rainfall is transformed into a runoff hydrograph by convolution with the unit hydrograph.
The Flood Studies Supplementary Reports (19771988) Number 16 (FSSR16) of 1985 derived new regression equations based on a larger data set than those in the original FSR. This data set included a wider range of catchment types, with a greater number smaller and more highly urbanised catchments than had been available previously. The report recommended that these regression equations be used for design in preference to the original FSR set.
The flowtime curve produced by this unit can be checked prior to a full computational run using the Calculated Hydrograph tab or running a Boundary Mode simulation. A summary of the data is output as an ASCII file with the extension '.zzb' and the hydrograph is tabulated in an ASCII file with the extension 'zzh'. If the boundary run extends over the length of the event then the resultant hydrograph can be graphed using the Time Series option. You can generate a datafile with only one node (which is a Hydrological Boundary) and run Boundary Mode in order to generate the hydrograph.
When used in a Steadystate simulation you may wish to set the boundary flow to be at the peak flow rate from the hydrograph  to do this toggle the Simulation Type field to display: Peak flow. Alternatively you may wish to toggle the field to display: Full hydrograph  this will enable you to run a steady simulation at a specific time in the event.
To apply the FSR method, parameter values can be estimated by regression based on data obtained from maps if observed values are not available. Where such data are available, or can be derived from analysis of recorded events, this data should be used in preference to the regression equations; this facility is included within the FSSR16BDY unit.
The user should also be aware that design flow hydrographs produced by all standard methods can be highly inaccurate if not calibrated. Specialised hydrological advice may be required to supplement the predictions made by the software.
The concept of 'flags' is used to describe data control. These flags are typically specified via radio buttons (e.g. Runoff: FSSR16 (SPR) or Observed (PR)) and referred to below in the form xxFLAG (e.g. PRFLAG, UHFLAG etc.), equivalent to those written to the data file, and are used to select from a number of different options. Data which are not required by the option selected need not be specified.
Equations
The FSSR16 Boundary calculates total runoff according to:

for m = 1, M where: Q_{m}_{ }= total runoff at time m P_{mn} = precipitation at time (m  n); either calculated (ERFLAG = `FSRER') or observed (ERFLAG = `OBSER'). This value will use rainfall profile data which can either be based on winter data (RPFLAG = `WINRP'), summer data (RPFLAG = `SUMRP'), or observed values (RPFLAG = `OBSRP'). UH_{n} = unit hydrograph ordinate n; either calculated (UHFLAG = `FSRUH') or observed (UHFLAG = `OBSUH') PR = percentage runoff; either calculated (PRFLAG =`F16PR') or observed (PRFLAG = `OBSPR') M = total time period for the flood hydrograph N = total time period for the rainfall event 
Regression Equations
The observed value of any of these processes can be entered directly. They could also be calculated by setting appropriate flags so that the unit will use one or more of the following regression equations:
Baseflow
If BFFLAG = F16BF':


Total Percentage Runoff
If PRFLAG = F16PR':

where: PRRURAL = SPR + DPR_{CWI} + DPR_{RAIN} DPRCWI = 0.25 (CWI  125) DPRRAIN = 0.45 (P  40)^{0.7} (P > 40mm) = 0 (P £ 40mm) P = precipitation (mm) DPR = dynamic Percentage Runoff CWI may be entered directly (CWFLAG = `OBSCW') or the program can calculate it using a method based on Figure I.6.62 in the Flood Studies Report of 1975 (CWFLAG = `FSRCW'). PT is calculated as the sum of the rainfall and the snowmelt. SPR may be treated as a calibration parameter or calculated from the equation:
where: S1, S2 and so on are the proportions of the soil fractions in the catchment. The equation is from FSSR16 and the soil fractions are from FSR Figure I.4.18. 
Unit Hydrograph parameters
If TPFLAG = F16TP then use the FSSR16 equation:


If TPFLAG = R124TP then use the equation recommended in IH Report 124:

where: Tp(0)_{rural}_{ }= 283*S1085^{0.33}SAAR0.54MSL^{0.23} and B = 1  3 exp([T_{p}(0)rural/7]^{2}) Tp(t) = T_{p}_{ }(0) + t/2 Qp = 0.22 CAREA / T_{p}(t) where: Tp (0) = time to peak of the instantaneous unit hydrograph (hrs) Tp (t) = time to peak of thour unit hydrograph (hrs) Q_{p}_{ }= peak flow of thour unit hydrograph (m^{3}/s) 
For the regression equations used when calculating rainfall refer to the Flood Studies Report (1975), Volume I, Chapter 6.
General
The user is referred to the Flood Studies Report (1975) and Flood Studies Supplementary Reports (19771988) Report No. 16 for fuller details of the methodology and derivation of the synthetic equations.
The data used to derive the FSR synthetic equations were gathered from catchments under 500 Km2 in the United Kingdom and were mostly from events less than twice the mean annual flood. Application to larger catchments (especially those larger than 1000 km2), to overseas catchments, or to the prediction of floods with higher return periods must be made with caution.
It is further recommended that where possible, the model parameter values obtained from the regression equations are replaced with, or revised using, values from observed data. General recommendations on parameter estimation are given below.
If a direct estimate of the lag time is available, the FSR recommends calculating T_{p} as:

where: LAG is the time between the centroid of rainfall and centroid of hydrograph peak. 
The data interval, t (hours), is chosen by the modeller by using the equation recommended by the FSR given below:


This should then be rounded off to a convenient number of hours or a fraction of an hour.
Furthermore, it is usually important to find the critical values of parameters such as CWI, D, storm profile and P 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 FSR and the conclusions are:
 Simulated flows are largely insensitive to rainfall profiles except in responsive catchments. The FSR recommends use of the 75% winter profile or 50% summer profile. These two profiles are included as options in the FSSR16BDY unit and can be accessed by setting the Storm Profile flag.
 Simulated peak flows can be sensitive to D, the storm duration. If this parameter is not treated as a calibration parameter, it should be chosen according to:
with D taken as the nearest odd integer multiple of t. 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. The value of Tp used is the time to peak of the thour unit hydrograph.(9)
 Simulated peak flows are sensitive to CWI, the catchment wetness index. If it is not treated as a calibration parameter, the FSSR16BDY unit will calculate it using FSR Figure I.6.62. The relevant flag is CWFLAG.
In the FSR procedure the flow return period is not necessarily equal to the storm (rainfall) return period.
 For summer rain profiles the FSR recommends that the storm return period is set equal to the flow return period. If this is not done the simulation will stop unless the 'force' flag has been set.
 For winter profiles, however, the FSR procedure provides a relationship between the storm and flow return periods (e.g. a 140 year storm return period for a 75% winter storm profile is said to produce a 100 year return period flow). In FSSR16BDY the program will use these relationships if the storm return period is set to zero.
General guidance for estimating the values of AREA, MSL, S1085, RSM, URBAN and SOIL are presented in the Flood Studies Report, Volume I, Chapter 4.
Areal reduction factors are based on the storm area (STAREA) unless the storm area is set to zero in which case the areal reduction factor is based on the catchment area. An areal reduction factor can be specified in the data file.
For further information on the FSR method, see:
 Sutcliffe J.V. (1978)
 Flood Studies Supplementary Reports (19771988) numbers 5, 13 and 16.
 Marshall D.C.W. and Bayliss A.C. (1994)
 Boorman D.B. et al (1990)
Datafile Format
Line 1  Keyword `FSSR16BDY'
Line 2  Label
Line 3  z
Line 4  tdelay, t, bfonly
Line 5  COUNTRY
Line 6  CAREA, S1085, MSL, SOIL, URBAN
Line 7  STAREA, STDUR, RSMD, SNRATE
Line 8  SAAR, M52D, r, M525D, FORCE
Line 9  ERFLAG
Line 10  P (if ERFLAG = `OBSER')
Line 10  Tf , Ts , arf (if ERFLAG = `FSRER')
Line 11  CWFLAG
Line 12  CWI (if CWFLAG = `OBSCW')
Line 12  Any Value (if CWFLAG = `FSRCW')
Line 13  PRFLAG, [PRVAR]
Line 14  PR (if PRFLAG = `OBSPR')
Line 14  SPR (if PRFLAG = `F16PR')
Line 15  TPFLAG
Line 16  CALIB, Tp (if TPFLAG = `OBSTP')
Line 16  CALIB (if TPFLAG = F16TP' or `R124TP')
Line 17  BFFLAG
Line 18  BFADJS, BF (if BFFLAG = `OBSBF')
Line 18  BFADJS (if BFFLAG = `F16BF')
Line 19  UHFLAG
Line 20  0 (if UHFLAG = `FSRUH')
Line 20  nuh (if UHFLAG = `OBSUH')
Line 21 to Line 20 + nuh  uh (if UHFLAG = `OBSUH')
Line 21 + nuh  RPFLAG
Line 22 + nuh  0 (if RPFLAG = `WINRP')
Line 22 + nuh  0 (if RPFLAG = `SUMRP')
Line 22 + nuh  nrp (if RPFLAG = `OBSRP')
Line 23 + nuh to Line 22 + nuh + nrp  rp (if RPFLAG = `OBSRP')