24. Alternative Runoff Methods (ARM)

A SWMM subcatchment makes its runoff with a nonlinear reservoir: rain on the surface, infiltration off it, and Manning's equation across a width. Many design standards ask for something else — an NRCS unit hydrograph, a Clark or Snyder hydrograph, the Modified Rational method — and PCSWMM calls the subcatchments that use one Alternative Runoff Method (ARM) subcatchments. AquaSWMM offers the same idea.

• What stays the same: an ARM subcatchment is still an ordinary subcatchment. It keeps its polygon, area, outlet and rain gage, and it draws, selects, renames, copies and deletes like any other.
• What changes: only where its runoff comes from. AquaSWMM computes its hydrograph and the EPA engine routes it through the network. Any mix of SWMM5 and ARM subcatchments, and of ARM methods, can share a model.

24.1 Turning a subcatchment into ARM

Select the subcatchment. Its property sheet ends with a Runoff Method block, which reads Runoff Method: SWMM5 until you change it. Pick an Alternative Runoff Method from its Method list. Picking SWMM5 (nonlinear reservoir) turns the subcatchment back, and the ARM data goes with it.

• With several subcatchments selected, the multi-selection sheet has one Runoff method list, which changes all of them in one step.
• Every change is one undo step, labelled like runoff method of S1 to Clark UH or ARM parameters of S1.

A converted subcatchment starts from values the model already implies:

Switching between ARM methods keeps the Tc, the Tc inputs and the CN or C, and drops the parameters the new method does not use.

On the map an ARM subcatchment's outline is dashed and its centroid dot is violet. The sheet shows what the method makes of it under the parameters: the Tc and each term that makes it up, the rainfall and runoff depths, and the peak with when it comes. The ARM Hydrographs… button opens the window of §24.7 on this subcatchment.

24.2 The methods

Every method but Snyder needs a Tc (§24.4). Snyder uses one only to default its lag.

24.3 Losses

Curve number. Every unit hydrograph method takes its losses from the NRCS curve number equation (NEH 630 Ch 10, eq. 10-9):

S = 1000/CN − 10 (in),   Ia = λ·S,
Q = (P − Ia)² / (P − Ia + S)   for P > Ia, else 0

• The CN is the composite CN of the whole subcatchment, as TR-55 and TR-20 use it.
• λ is the model-wide initial abstraction ratio in ARM Options, 0.20 by default. If you change it to 0.05, enter CNs that go with that ratio: AquaSWMM does not convert them.
• The equation is applied to cumulative rainfall at every time step. Each step's excess is the difference between successive cumulative runoff depths.
• In SI models rainfall is converted from millimetres to inches for the equation and back.

Runoff coefficient. The Modified Rational method takes its losses as C.

24.4 Time of concentration

The Tc method list:

TR-55 segments. Each segment is sheet flow (length, slope, Manning's n, 2-yr 24-hr rainfall), shallow concentrated flow (length, slope, paved or not), or channel flow (length, slope, n, hydraulic radius). Add segment appends one, and each segment has its own remove button. The segment times are the ones the storm-sewer Tc calculator uses: sheet flow 0.007(nL)^0.8/(P2^0.5 S^0.4) h, shallow flow V = 16.13√S unpaved or 20.33√S paved, and channel flow by Manning.

NRCS lag equation.

• Y is the watershed's average land slope, not the flow path's.
• NEH 630 limits the equation to CN 50–95 and to watersheds up to about 9 mi² (possibly 19 mi²).

Kerby-Kirpich.

• Kerby (overland): t = 0.828 (L·N)^0.467 S^−0.235 min, with L in ft. TxDOT's retardance N values, which it says not to interpolate:
  • pavement 0.02
  • smooth bare packed soil 0.10
  • poor grass, row crops or moderately rough packed surfaces 0.20
  • pasture or average grass 0.40
  • deciduous forest 0.60
  • dense grass, conifers, or deep litter 0.80
• Kirpich (channel): t = 0.0078 L^0.770 S^−0.385 min.
• Low slopes: a slope under 0.002 gets TxDOT's low-slope adjustment, +0.0005, and the Tc lines say so.
• Length limit: an overland length over Kerby's 1,200 ft limit is flagged in the Tc lines.
• Units: lengths are the model's (ft, or m in SI models) and slopes ft/ft.

24.5 How a hydrograph is made

Time grid. Hydrographs are computed on a grid of the ARM time step (1 minute unless ARM Options says otherwise), starting at the simulation start.

Rainfall. Rainfall comes from the subcatchment's rain gage the way SWMM reads it:

• Each reading is spread evenly over the gage's recording interval. INTENSITY readings are rates, VOLUME readings are depths, and CUMULATIVE readings are differenced. A reading below the one before is a reset: it counts as the depth since the reset, as in SWMM.
• The gage's snow catch factor (SCF) multiplies the rainfall.
• Dated readings are placed against START_DATE and START_TIME.
• The gage must read a time series in the model. A gage on a rainfall file, or a series that reads a file, is refused with a finding.

Unit hydrographs. Each unit hydrograph is built for a block of excess one time step (Δt) long. It is then scaled so it holds exactly one inch over the area: Σu·Δt = 645.33·A (cfs·h, with A in mi²). Finally it is convolved with the excess, each block's response starting where the block starts. That is the convolution NEH 630 example 16-1 uses.

• SCS dimensionless.
  • Time to peak: Tp = Δt/2 + L, with the lag L = 0.6·Tc (NEH 630 eqs 16A-7 and 16A-9).
  • At a peak rate factor of 484 the shape is table 16-1, sampled every Δt.
  • Any other peak rate factor uses the gamma curve of eq. 16-1, q/qp = (t/Tp)^m·e^{m(1 − t/Tp)}, with m solved so that 645.33·m^{m+1}e^{−m}/Γ(m+1) is the factor (m = 3.7 gives 484, as in NEH table 16-5). The sheet reports the m used.
• SCS triangular.
  • Rises to its peak at Tp and falls to zero at Tb = Tp·2·645.33/PRF, so it holds one inch. That is 2.67·Tp at 484.
• Delmarva.
  • NEH 630 Ch 16 names this curve but does not tabulate it. Its ordinates here are the Maryland Stormwater Design Manual's table D.14.2, which gives them at 0.02 of a 10·Tp base.
  • Summed, that table's peak rate factor is 282; the manual prints 284.
• Clark. As HEC-HMS computes it (CPD-74B eqs 44–50):
  • One inch is translated over Tc by HMS's synthetic time-area curve: Aₜ/A = 1.414(t/Tc)^1.5 up to Tc/2, then 1 − 1.414(1 − t/Tc)^1.5.
  • It is then routed through a linear reservoir, O = C_A·I + (1 − C_A)·O′, with C_A = Δt/(R + Δt/2).
  • Each ordinate is the average of consecutive outflows.
  • Computation stops once 0.995 inch has passed, and the ordinates are scaled to exactly one.
• Snyder. As HEC-HMS does it:
  • For a duration Δt the lag is tpR = tp − (tr − Δt)/4, with tr = tp/5.5.
  • The peak is UpR = 640·Cp·A/tpR.
  • The ordinates are those of the Clark unit hydrograph with that peak at Δt/2 + tpR. These are the targets HEC-1's eqs 3.39–3.40 check.
  • Two Clark pairs can match one Snyder peak: a storage-heavy one and a translation-heavy one. AquaSWMM takes the storage branch, as HEC-1 does for its manual's example. The sheet reports the Tc and R found.
• Nash.
  • n equal linear reservoirs with constant K.
  • The unit hydrograph is the S-curve difference of the gamma response, u_j = 645.33·A·(P(n, jΔt/K) − P(n, (j−1)Δt/K))/Δt.
  • With K left blank it is 0.6·Tc/n, which puts the lag n·K at 0.6·Tc.

Modified Rational.

• Peak: Q = C·i·A, with i in in/hr, A in acres and Q in cfs. AquaSWMM uses the exact unit conversion, 1.0083, not 1.
• Shape: the area arrives linearly over Tc. A storm of duration D ≥ Tc gives a trapezoid: rise over Tc, hold until D, fall over Tc. A shorter storm peaks at C·i·A·D/Tc.
• Intensity from GAGE: the gage's greatest average intensity over D. The hydrograph starts where that window starts.
• Intensity from an IDF table: the table's intensity at D, interpolated log-log, starting at Storm starts at.

24.6 ARM Options

Project → ARM Options… opens the ARM Options window for the settings every ARM subcatchment shares.

• Initial abstraction ratio Ia/S. λ in §24.3, from 0 to 1.
• Hydrograph time step (min). The grid of §24.5. NEH 630 (eq. 16A-13) asks for a step of at most 0.133·Tc for a unit hydrograph. A subcatchment whose Tc is too short for the step gets a warning.
• IDF tables (Modified Rational).
  • Named duration–intensity tables: minutes, and in/hr or mm/hr. Any agency's curve can be entered point by point.
  • Add table makes one, named in the box beside it (spaces become underscores). Delete table removes the table shown, Add row extends it, and each row has a − button.
  • Rows are kept in order of duration.

24.7 ARM Hydrographs

Results → ARM Hydrographs… opens the ARM Hydrographs window:

• Table: every ARM subcatchment, with its method, outlet, Tc, rainfall and runoff depths, and peak with its time.
• Plot: the chosen subcatchment's hydrograph, with its lines from the property sheet.
• Copy CSV puts every hydrograph on the clipboard, one column per subcatchment. Save CSV… writes the same to a file.

The window works from the model as it is now, so hydrographs can be read before any SWMM run. Subcatchments whose hydrograph cannot be made are listed under the table with the reason.

The results Chart plots nodes and links. An ARM subcatchment's runoff is in this window and, after a run, in its outlet node's lateral inflow.

24.8 What a run does

EPA's engine knows nothing of ARM, so what it is given is the model with the ARM part replaced by what it means:

1. The ARM sections are removed. The engine refuses any section it does not know.

2. ARM subcatchments rain from a dry gage. A rain gage named ARM_DRY, on a series of zeros, replaces their own, so the nonlinear reservoir adds nothing. Their rows in the report's runoff summary are zero (step 5 fills in the .out).

3. Hydrographs enter at the outlet nodes. Each outlet node gets an external FLOW inflow, a time series ARM_<node>, that is the sum of the ARM hydrographs draining to it.

   • If the node already had a FLOW inflow, it is folded in: that series, scaled by its Sfactor, plus the ARM flow over its Mfactor. The baseline and pattern are kept.
   • The report counts the ARM runoff as external inflow, not runoff.
   • Each series starts at the node's first rise: a zero at the start, a zero just before the rise, then the hydrograph.
   • A large model is thinned to fit. Past 5 million points in all, each node's series keeps every k-th point, its peak and its closing zero. The points other than the peak are scaled so the engine still gets the whole volume. The Run Status note gives the step used. A model of 20,000 ARM subcatchments at a 15-second step goes in at about 4 minutes; PCSWMM hands its engine these flows at the report step.

4. The run reads a scratch copy. It runs under %TEMP%\AquaSWMM\run\, and the Run Status window says why.

5. The results file gets the ARM subcatchments. After a run ends cleanly, each ARM subcatchment's record in the .out is written at every reporting period:

   • Rainfall: the gage's intensity. A rational subcatchment shows its design storm instead (intensity i for duration D), whether that came from the gage or an IDF table.
   • Infiltration: the loss rate. For CN methods this is the rainfall intensity times (1 − dQ/dP) on the curve number equation, all of it before Ia. For a rational subcatchment on its gage it is i·(1 − C).
   • Runoff: the ARM hydrograph.

   So the Chart, the results tables, the map's colours and the EPA GUI show them as the method made them. The Model Report adds an ARM Subcatchment Runoff table after the engine's summary tables. It gives each ARM subcatchment's method, CN or C, rain (the gage's depth over the run), losses, runoff depth, and peak runoff with its time. The engine's own runoff summary still lists these subcatchments at zero. Rainfall in the .out follows the engine's convention: at a block's edge it is the next block's rate. The other variables (evaporation, snow, groundwater, washoff) stay as the engine wrote them. So do the system totals, where ARM runoff is external inflow at the outlet nodes, as in the .rpt. While the run is going, the live view shows the ARM subcatchments at zero. Their values arrive when it ends. A run that is stopped is not patched.

The model you edit is untouched by any of this; it happens in the copy the engine reads. Scenarios, calibration runs and coupled 1D-2D runs go through the same step.

Limits of the replacement.

• An ARM subcatchment must drain to a node, since an inflow enters the network there. An ARM subcatchment whose outlet is another subcatchment is an error.
• Water another subcatchment routes onto an ARM subcatchment still passes through the ARM subcatchment's own nonlinear reservoir to its outlet. The ARM hydrograph is its rainfall response only.
• Groundwater, LID, snow and pollutant washoff on an ARM subcatchment see no rain.

24.9 Files

The ARM data is part of the model in the editor. Undo, rename, delete and copy/paste carry it with its subcatchment. On disk it is kept apart, because EPA SWMM and other editors refuse sections they do not know:

• Save writes the .inp without ARM sections, and writes them to a sidecar beside it: model.inp → model.aqarm. When no subcatchment uses ARM, and no option or table is set, the sidecar is removed.

• Open reads model.aqarm back when it is there.

• Not .arm: PCSWMM writes its own binary ARM hydrographs to model.arm (with model.arm.rpt and model.arm.txt) beside the same .inp. AquaSWMM never reads, writes or removes that file. A model.arm that AquaSWMM itself wrote, in the text form below, is still read; the next Save moves it to model.aqarm.

• The sidecar is plain text in .inp syntax:

  [ARM]
  ;;Subcatchment  Method    Parameters
  S1              SCS       CN=78 TC=12.5 PRF=484
  S2              CLARK     CN=70 TC=TR55 R=0.8
  S2              SEGMENT   SHEET L=100 S=0.02 N=0.24 P2=3.6
  S2              SEGMENT   SHALLOW L=600 S=0.015 PAVED=NO
  S3              RATIONAL  C=0.65 TC=10 IDF=10-yr
  
  [ARM_OPTIONS]
  IA_RATIO        0.2
  TIMESTEP        1
  
  [ARM_IDF]
  10-yr           5         7.2
  10-yr           60        2.4

• The keys are the method's parameters: CN, C, PRF, TP, CP, R, N, K, D, IDF, START, and TC. TC is a number of minutes or TR55, LAG (with LEN, Y) or KERBY (with LO, SO, NK, LC, SC).

• Opening the model elsewhere: the .inp alone opens and runs in EPA SWMM or any other editor, with the ARM subcatchments running as the SWMM5 subcatchments they also are. That is a different answer, so send the .aqarm with the model.

Importing a PCSWMM model

PCSWMM keeps ARM subcatchments outside the .inp. They sit in its project database, model.db, table ARM_Subcatchments, and it feeds their flows to the engine through a routing interface file named in the .inp: [FILES] USE INFLOWS "model.arm.txt". Opened here, such a model has none of those subcatchments.

• On open, a model with a model.db holding ARM subcatchments, and none of its own yet, shows Import PCSWMM ARM with how many there are. Not now closes it. Project → Import PCSWMM ARM… offers it again at any time.
• Import makes each row an ordinary subcatchment with its outlet, rain gage, area, slope, polygon and curve number. The width is the area over PCSWMM's flow length. Each also gets its ARM row. It is one undo step.
• It also:
  • sets the ARM time step to the model's wet-weather step, which PCSWMM uses;
  • takes the Ia/S ratio from PCSWMM's 0.2 S;
  • removes the USE INFLOWS … .arm.txt line, since the ARM rows now make those flows and would otherwise enter them twice.
• What is read is what has been checked against PCSWMM 7.7 projects:
  • the SCS dimensionless unit hydrograph at PCSWMM's standard peak rate factor (shown there as 483.4; it is the NEH 630 curve, 484 here);
  • SCS curve-number losses;
  • a Tc from PCSWMM's SCS method, which is the NRCS lag equation (TC=LAG, LEN and Y from its flow length and slope; the Tc comes out the same), or entered by hand.
  • A Tc from any other PCSWMM method is kept as the minutes PCSWMM last computed.
• Anything else (another runoff type, peak rate or loss method, or a name already in the model) is left out. The report lists each one with the reason.
• PCSWMM's files are only read. Save writes the .inp and the .aqarm beside them.

On a 20,249-subcatchment PCSWMM model the import takes under a second, and the hydrographs and peaks agree with PCSWMM's ARM report as in §24.11.

24.10 Checks

ARM findings join the model check, in section [ARM], and select their subcatchment when clicked. A run is refused while any is an error.

• Errors:
  • a missing CN, C, R, n or Cp
  • a CN outside 30–100, a C outside 0–1, a Cp outside 0.1–1, or a peak rate factor outside 50–1000
  • a Tc that cannot be found
  • no rain gage, a gage on a rainfall file, or a series with no values
  • a gage whose recording interval is longer than the time between its series' readings. EPA SWMM refuses such a gage (error 159), but an ARM gage never reaches the engine's check. 15-minute data on a 1-hour gage would count each reading as an hour of rain.
  • an IDF table that is not in ARM Options, or one that gives two intensities for the same duration
  • an outlet that is not a node
  • an ARM row that does not read
• Warnings:
  • a time step coarser than 0.133·Tc
  • a peak rate factor outside about 100–600

24.11 Validation

The computations are tested against published worked examples, and the tests run with every build:

The end-to-end test runs wherever an EPA engine is installed. The build servers have none, so it is skipped there.

Against PCSWMM. A one-off comparison used a PCSWMM 7.7 1D-2D model with 20,249 ARM subcatchments. All were SCS dimensionless UH (PRF 484) under a 24-hour Type II storm at a 15-second step, most with Tc from the NRCS lag equation. The subcatchments were rebuilt in AquaSWMM and compared with PCSWMM's ARM report:

• Tc: identical on a sample of 40 spanning 0.08 to 8.7 min.
• Losses: PCSWMM's match the CN equation to 0.0005 in on all 20,249. That makes the excess 27.346 million gallons, and AquaSWMM's hydrographs hold 27.346.
• Peaks: within 0.5 % wherever the unit hydrograph is resolved (Tc above about 0.7 min at that step).
• Short Tc: below that, PCSWMM's unit hydrographs hold less than an inch. It warns ARM01 on 10,364 of them, and hands its engine 26.925 million gallons, 1.5 % short. AquaSWMM scales every unit hydrograph to one inch, so its volume is the CN volume.
• Scale: the hydrographs take 1.7 s. EPA SWMM 5.2.4 runs the engine text (158 MB, thinned as in §24.8) and reports the full 27.346 million gallons as external inflow.

24.12 Not yet

Planned, in no particular order:

• per-subcatchment Ia/S
• ARM Tc and unit hydrograph parameters in the Model Report
• rainfall-file gages
• routing between ARM subcatchments
• importing PCSWMM's other runoff types, peak rates and loss methods
• the other PCSWMM methods: Desbordes, and the Ventura and Los Angeles County rational variants