ReFH()
functionThis quick guide provides an overview of how to generate a design hydrograph using the ReFH method. It is assumed that the reader has knowledge of the theory of the ReFH method; this guide is intended to demonstrate how to use the UKFE package rather than to explain the method.
The ReFH()
function is designed for flexibility and each
parameter of the model, along with the inputs and initial conditions,
can be user-defined. By default, when catchment descriptors are
provided, the ReFH function uses these descriptors to estimate the
parameters of the ReFH model, and an estimate of the two-year rainfall
for the critical duration. When catchment descriptors are applied,
individual parameters and settings can still be adjusted by the user and
these adjustments override the estimates from the catchment descriptors.
Further details can be found in the function’s help file.
This function applies the ReFH model as specified by Kjeldsen (2007). The ReFH model has since been updated to address some of the limitations. The updated version(s), known as ReFH2, was developed by Wallingford Hydro Solutions (2019) and is available for a licence fee. Henceforth, the original model is denoted ReFH1, and the term ‘ReFH’ is used when the comment applies to the original and updated versions.
The ReFH outputs are commonly used only to derive a reasonable hydrograph shape. This shape is then scaled to match the peak flow estimate derived using other methods (usually FEH statistical methods). An example of doing this with the function is provided below. There is no automated way of doing so within the function but ReFH parameters can be calibrated using observed rainfall and data to replicate storm events.
Assumptions and limitations of the ReFH1 model are provided at the bottom after the example of how to derive a design hydrograph.
In the following example, the ReFH() function is used to derive a design hydrograph, i.e., a hydrograph shape scaled to our design flood estimate (assuming the site to be ungauged). The default use of ReFH() with the catchment descriptors provides the rainfall-runoff outputs for an estimate of the two-year design rainfall event:
# Obtain catchment descriptors for NRFA gauge 55002
CDs.55002 <- GetCDs(55002)
# Obtain outputs of the ReFH model from catchment descriptors for a default 2-year
# rainfall event
ReFH(CDs.55002)
#> [[1]]
#> AREA TP D BR BL Cmax Cini BFini
#> 1 1894.257 12.90487 28.77787 1.14785 63.50554 309.7927 138.5238 150.4984
#>
#> [[2]]
#> Rain NetRain Runoff Baseflow TotalFlow
#> 1 0.28 0.13 0.00 150.50 150.50
#> 2 0.34 0.15 0.13 148.15 148.28
#> 3 0.41 0.19 0.55 145.84 146.39
#> 4 0.50 0.23 1.31 143.58 144.89
#> 5 0.61 0.28 2.50 141.37 143.87
#> 6 0.74 0.34 4.21 139.22 143.43
#> 7 0.90 0.41 6.55 137.14 143.69
#> 8 1.09 0.50 9.66 135.14 144.80
#> 9 1.32 0.61 13.71 133.24 146.96
#> 10 1.60 0.75 18.92 131.45 150.37
#> 11 1.93 0.92 25.52 129.80 155.32
#> 12 2.32 1.12 33.84 128.30 162.15
#> 13 2.78 1.36 44.26 127.00 171.26
#> 14 3.29 1.64 57.21 125.93 183.14
#> 15 3.61 1.84 73.01 125.13 198.13
#> 16 3.29 1.71 91.92 124.65 216.57
#> 17 2.78 1.48 113.92 124.55 238.47
#> 18 2.32 1.25 138.51 124.87 263.37
#> 19 1.93 1.06 165.05 125.64 290.69
#> 20 1.60 0.88 192.95 126.89 319.83
#> 21 1.32 0.74 221.58 128.62 350.21
#> 22 1.09 0.61 250.36 130.84 381.21
#> 23 0.90 0.51 278.67 133.54 412.21
#> 24 0.74 0.42 305.86 136.70 442.56
#> 25 0.61 0.35 331.23 140.28 471.51
#> 26 0.50 0.29 354.02 144.23 498.26
#> 27 0.41 0.24 373.36 148.50 521.86
#> 28 0.34 0.20 388.31 153.01 541.32
#> 29 0.28 0.16 398.07 157.67 555.74
#> 30 NA NA 402.57 162.39 564.96
#> 31 NA NA 402.26 167.07 569.33
#> 32 NA NA 397.76 171.63 569.39
#> 33 NA NA 389.79 176.01 565.80
#> 34 NA NA 378.97 180.15 559.12
#> 35 NA NA 365.88 184.02 549.90
#> 36 NA NA 351.02 187.57 538.59
#> 37 NA NA 334.84 190.79 525.63
#> 38 NA NA 317.75 193.66 511.41
#> 39 NA NA 300.13 196.17 496.31
#> 40 NA NA 282.36 198.33 480.69
#> 41 NA NA 264.79 200.14 464.93
#> 42 NA NA 247.72 201.61 449.32
#> 43 NA NA 231.24 202.75 433.99
#> 44 NA NA 215.59 203.59 419.18
#> 45 NA NA 200.83 204.14 404.97
#> 46 NA NA 186.81 204.43 391.23
#> 47 NA NA 173.41 204.46 377.87
#> 48 NA NA 160.54 204.26 364.81
#> 49 NA NA 148.18 203.84 352.02
#> 50 NA NA 136.26 203.21 339.47
#> 51 NA NA 124.75 202.37 327.12
#> 52 NA NA 113.61 201.35 314.95
#> 53 NA NA 102.82 200.14 302.96
#> 54 NA NA 92.39 198.76 291.15
#> 55 NA NA 82.32 197.23 279.54
#> 56 NA NA 72.64 195.53 268.17
#> 57 NA NA 63.33 193.70 257.03
#> 58 NA NA 54.43 191.73 246.16
#> 59 NA NA 46.03 189.63 235.66
#> 60 NA NA 38.24 187.42 225.67
#> 61 NA NA 31.19 185.12 216.31
#> 62 NA NA 25.03 182.73 207.76
#> 63 NA NA 19.85 180.28 200.13
#> 64 NA NA 15.57 177.78 193.35
#> 65 NA NA 12.06 175.25 187.31
#> 66 NA NA 9.21 172.70 181.91
#> 67 NA NA 6.91 170.15 177.06
#> 68 NA NA 5.08 167.60 172.68
#> 69 NA NA 3.63 165.06 168.69
#> 70 NA NA 2.51 162.53 165.04
#> 71 NA NA 1.65 160.03 161.68
#> 72 NA NA 1.01 157.56 158.57
#> 73 NA NA 0.56 155.11 155.67
#> 74 NA NA 0.26 152.69 152.95
#> 75 NA NA 0.08 150.31 150.39
The output that is printed to the console is a list with two elements. The first element is a data frame of parameters, initial conditions and the catchment area. The second is a data frame with the following columns: Rain, NetRain, Runoff, Baseflow and TotalFlow. A runoff hydrograph plot is also produced.
To scale the hydrograph to the design flow estimate, the results from the ungauged pooling can be used (assuming this is for the ungauged case). We can use the estimate from the FEH statistical analysis vignette:
# Create an ungauged pooling group for site 55002
PoolUG.55002 <- Pool(CDs.55002, exclude = 55002)
# Estimate QMED for site 55002 using catchment descriptors and two donor gauges
CDsQmed.55002 <- QMED(CDs.55002, Don2 = c(55007, 55016))$QMEDs.adj
# Estimate design flows using the above pooling group and QMED
Results55002 <- PoolEst(PoolUG.55002, QMED = CDsQmed.55002)
The results are in the form of a list. The first element provides the return levels, and the 100-year flow estimate is in the seventh row in the second column. We’ll make it an object and use it to scale the hydrograph:
# Extract the 100-year flow estimate
Q100.55002 <- Results55002[[1]][7, 2]
# Obtain outputs of the ReFH model from catchment descriptors for a default 2-year
# rainfall, scaling to the 100-year peak flow estimate
ReFH(CDs.55002, scaled = Q100.55002)
#> [[1]]
#> AREA TP D BR BL Cmax Cini BFini
#> 1 1894.257 12.90487 28.77787 1.14785 63.50554 309.7927 138.5238 150.4984
#>
#> [[2]]
#> [1] 336.539 331.574 327.342 323.992 321.711 320.725 321.310 323.803
#> [9] 328.616 336.253 347.327 362.590 382.955 409.522 443.056 484.283
#> [17] 533.253 588.944 650.036 715.201 783.115 852.437 921.772 989.630
#> [25] 1054.377 1114.180 1166.956 1210.475 1242.724 1263.332 1273.110 1273.253
#> [33] 1265.210 1250.287 1229.656 1204.369 1175.383 1143.587 1109.823 1074.910
#> [41] 1039.660 1004.759 970.482 937.362 905.577 874.862 844.986 815.768
#> [49] 787.178 759.111 731.495 704.286 677.469 651.061 625.105 599.674
#> [57] 574.751 550.444 526.978 504.625 483.710 464.596 447.520 432.355
#> [65] 418.854 406.784 395.938 386.134 377.219 369.060 361.546 354.585
#> [73] 348.096 342.015 336.287
In this case, the second element of the output list in the console is a numeric vector containing the scaled hydrograph, instead of the results data frame.
For use outside of ‘R’, these outputs can be saved as objects and then written to CSV files:
# Save the ReFH design hydrograph to an object called 'DesignHydro.55002.unscaled'
DesignHydro.55002.unscaled <- ReFH(CDs.55002)
# Write to csv
write.csv(DesignHydro.55002.unscaled, "my/file/path/DesHydro55002_unscaled.csv", row.names = FALSE)
# Save the ReFH design hydrograph to an object called 'DesignHydro.55002.scaled'
DesignHydro.55002.scaled <- ReFH(CDs.55002, scaled = Q100.55002)
# Write to csv
write.csv(DesignHydro.55002.scaled, "my/file/path/DesHydro55002_scaled.csv", row.names = FALSE)
Note in these examples that row.names = FALSE
in the
write.csv()
function: our data has no row names, so this
prevents an index column being added to the CSV.
The ReFH model has three components that conceptualise the catchment process.
Model structure:
The loss model quantifies, for each timestep of rainfall, the proportion of the rain that is effective (the rain that forms the runoff hydrograph). It does so by assuming a maximum catchment soil moisture capacity in mm (Cmax) and an initial catchment soil moisture content in mm (Cini). The original ReFH report (Kjeldsen, 2007) suggests that the Cini / Cmax (Cini divided by Cmax) can be conceptualised as the initial proportion of the catchment that is saturated, and the initial rainfall on this saturated area will form the storm hydrograph. It is assumed that the proportion of rain becoming effective is the same as this saturated proportion.
As rainfall is added, catchment soil moisture increases and Cini / Cmax becomes Ct / Cmax, i.e. the soil moisture for the given timestep divided by the Cmax is the proportion of rain for each timestep which becomes effective.
The unit hydrograph (UH) model is a well-established method for routing effective rainfall to the catchment outlet (Sherman, 1932). There are a number of assumptions:
The baseflow model assumes that the saturated area of the catchment that produces surface runoff is the same area that also produces the baseflow recharge. The assumption is that the ratio of recharge to runoff is fixed (the BR parameter). A further parameter, baseflow lag (BL), ensures that the resulting baseflow hydrograph is lagged behind that of the runoff hydrograph (effectively providing a slow flow component). However, this baseflow model does not consider the volume of rainfall directly in the same way the unit hydrograph component does. The resulting baseflow hydrograph is in addition to the runoff hydrograph volume and is calculated as a proportion of it. This means that the volume of the total hydrograph minus initial baseflow is greater than the net/effective rainfall. For the most part, this is not a significant problem because it is assumed that some of the remaining volume of the rainfall makes up the difference. However, if the proportion of effective rainfall is closer to one, the volume of the hydrograph can be greater than the gross/total input of rainfall. This will almost certainly not happen unless the event duration is considerably longer than recommended and only in catchments with a high initial proportion of saturation (due to low BFIHOST and high PROPWET). Note that ReFH2 addresses this issue but is not available via UKFE.
ReFH()
functionThere are three primary use cases: