SWMM 1 Runoff Engine — the 1971 Fortran, rebuilt from the printed listing, running as WebAssembly

Start with what the machine was

In 1971 a storm-water model was a box of punched cards, a reel of tape and a line printer. You read the cards once, in order, through unit 5; you wrote your report to unit 6, one line at a time, with the first character of each line telling the printer whether to skip to a new page; and you left your real results on a tape for the next program in the chain. The Runoff Block of SWMM Version 1 is about a thousand cards of Fortran IV written for an IBM 360, and every design decision in it comes from that environment. Keep that in mind and the code stops looking odd and starts looking sensible.

This app runs that code. Not a re-derivation of it, not a modern model with a 1971 label — the same statements, in the same order, translated into C with the names and labels kept, compiled to WebAssembly, fed the same 80-column cards. If the original authors could watch, they would recognize every line of the printout.

The watershed as three buckets

A subarea in SWMM 1 is not one surface. RHYDRO splits every subarea into three planes and WSHED solves each of them separately (figure 1). Plane 1 is the impervious ground that holds some water before it runs off — roofs and pavement with their puddles. Plane 2 is the pervious ground, the only one that infiltrates. Plane 3 is the share of the impervious area the modeler says has no depression storage at all: the default is a quarter of it, PCTZER = 25, and it starts running off the instant the rain starts. That third plane is why a SWMM 1 hydrograph rises at the first drop instead of waiting for the puddles to fill. It is a small idea with a big effect on the first ten minutes.

All three planes share the subarea width W1 and slope W4. The width is the one number a modeler has to think about: it is the length of the imaginary curb the sheet of water flows over, and it sets how fast the plane drains. The 1971 manual told you to take the area divided by the average overland flow length, and that advice has not changed in fifty years.

Rain in, water out: the nonlinear reservoir

Each plane is a reservoir with a leak that depends on how full it is. Water depth d on the plane rises with rain i, falls with infiltration f, and falls with outflow, and the outflow is Manning's equation applied to the sheet of water above the depression storage dp:

There is no closed form for that, so WSHED does what an engineer with a desk calculator would do: guess the change in depth over the step, evaluate the balance at the midpoint depth, correct the guess by Newton's method, and stop when the correction is under one percent of the change. Eleven passes are allowed; it usually needs two or three. The sign convention is worth a second look — WCON is stored negative, so the whole Manning term carries its own minus sign, and D0 is the depth above the puddles at mid-step, clamped at zero. If the rain and the stored water together cannot even fill the depression storage, the code skips the solver entirely and just adds the water to the puddle (WSHE 62, 285). Nothing runs off a plane until its puddles are full. Figure 2 shows how steep that leak is: outflow goes with the five-thirds power of the excess depth, so a plane that has a quarter inch standing on it drains an order of magnitude faster than one with a tenth.

Horton's law of diminishing returns

The pervious plane loses water to the soil at a rate that starts high and decays to a floor — Horton's equation, with the three numbers that every SWMM user since has typed in: a maximum rate (3 in/hr), a minimum rate (0.52 in/hr) and a decay constant (0.00115 per second, which is 4.14 per hour). SWMM 1 evaluates it against time since the start of the storm, not against cumulative infiltration, and it does not recover during dry spells — the decay runs on the clock, which is the right model for a single storm and the wrong one for a week of weather. There is one more guard: if the loss over a step would take more water than the plane has, the loss is cut to what is there (WSHE 52–58). That keeps the mass balance honest when a light shower falls on dry ground.

Gutters and pipes: the same trick with geometry

A gutter in SWMM 1 is also a reservoir with a Manning leak, only the geometry is honest about the cross section. GUTTER takes the inflow from the subareas and the upstream elements that drain to it, and solves for the depth at the end of the step so that the change in stored volume equals inflow minus the average outflow over the step. Newton again, up to thirty passes, converged when the volume residual is under a tenth of a cubic foot.

Two choices in that routine deserve attention. First, the pipe is never allowed to fill. DFULL for a pipe is 2.62 radians, which is a depth of 93 percent of the diameter — just about where the flow in a circular pipe is greatest, and comfortably away from the place where Manning's equation goes to pieces as the top of the pipe closes in. Second, when a gutter or pipe hits its full depth the excess is not lost; it is parked in QSUR, printed as a surcharge in cubic feet, and fed back as inflow on the next step (GUTT 162–164). That is a storage node at every manhole, done in three cards. The modern dynamic-wave engine does it with a pressurization slot and a full momentum equation; the 1971 engine did it with a bucket, and for a 5-minute step on a small system the bucket is not a bad answer.

The tree, upside down

The elements have to be solved upstream first, so each gutter knows its inflow before it is asked for its outflow. HYDRO does not ask you to order the cards. It finds the elements that discharge to the inlet, puts them at the far end of NGUT, then walks back up the tree prepending each element's feeders, and finally slides the whole list to the front (figure 5). Thirty cards, no recursion, no stack — just an array walked from the back. The same routine also invents a dummy element, NPG = 3, for any manhole number that subareas or gutters drain to but no gutter card describes; a dummy element passes its inflow straight through. That is how a subarea can drain to a manhole rather than a pipe.

The walk has a limit that the manual does not advertise. RHYDRO collects the elements that discharge to the inlet in two small arrays, NWTOI and NGTOI, and fills them with a loop that runs J = 1 to NIN, and NIN is 10 (RHYD 181). The eleventh subarea or gutter that drains straight to the inlet is reported as "LARGER THAN THE ALLOWED NO" — a message written for a different mistake — and the run stops. In 1971 this was a modelling rule you learned once: collect your laterals into a trunk before the inlet. The converters in this app learn it for you. When a SWMM 5 or SWMM 4 model has more than ten links reaching the outfall, they add pass-through collector elements, ten feeders each, and chain them, so the deck runs and each inlet keeps its own saved hydrograph. The Lancaster example, SWDAT1 from the SWMM 4 distribution, needs one such collector for its fifteen Transport inlets.

Tapes, and what the next block got

The printout is for the engineer. The results are on tape. At every step GUTTER writes the time and the inflow to each saved element to unit NOUT, after a three-record header (figure 6). The Transport Block read that tape as its inflow hydrographs; the quality routine SFQUAL read a second copy on a scratch unit. This app reads the same records back and draws them — the charts you see are not re-computed from the printout; they are the tape.

Dirt, by land use

The second half of the Runoff Block is SFQUAL, Metcalf & Eddy's surface quality model, and it is the part of SWMM 1 that had no precedent. The premise is blunt: what washes off a street is the dust and dirt that accumulated in the gutter since it was last cleaned, and how much accumulated depends on the land use and the length of curb. The Chicago APWA study gave the rates — 0.7 to 4.6 pounds per day per hundred feet of gutter for single-family through industrial land — and the BOD and coliform content of that dirt. Street sweeping takes a fixed fraction each pass (60 to 98 percent, by sweeping interval and number of passes), so the load at the start of the storm is a geometric series over the dry days. Catch basins add a second source: a tank of stale liquid of known BOD that the first runoff flushes out, with an exponential that saturates after about one and a half basin volumes have passed through.

Here r is the runoff rate in inches per hour over the area draining to the input, and the washoff fraction is a power law in it. Look at the exponent D before you trust a pollutograph: it is 1.0 above one inch per hour and climbs toward 2.6 as the flow dies away, so the solids removed per step can rise again on the recession, when the exponent outruns the falling flow. That is not a transcription error — the cards say it — it is what the 1971 authors fitted, and it is one reason later versions replaced this function with the exponential washoff SWMM uses today. SFQUAL reads the hydrographs back from the scratch tape GUTTER left, works per sewer input, writes a per-step table of flow, BOD and solids, and then overwrites the interface tape with NQUAL = 3 so the Transport Block received quality as well as flow (figure 7).

Reading the printout

The report ends with four totals and a number worth trusting more than any single hydrograph: the error in continuity as a percentage of rainfall (HYDR 139). Rainfall in, minus infiltration, minus flow that reached the inlet, minus water still standing on the planes, should be zero. On sample deck 1 it is 0.14 percent; on deck 2, 0.9 percent. A 1971 engineer would have been pleased with either. The error has three sources — the midpoint depth in the planes, the averaged outflow in the gutters, and the fact that the surcharge bucket is not counted as storage — and it grows with the time step. Halve DELT and watch it fall; that is the oldest convergence test there is and it still works.

A model that keeps its mass balance in a visible number on the last page is a model that expects to be checked. Keep that habit.

What this rebuild changed, and what it did not

The Fortran was read from the page images of the listing — the OCR layer in the PDF turns WDEPTH into WOEPTH and 160 into 16O often enough to be useless as a source and good enough to be a scaffold. Each of the seven routines was typed back into fixed form with its identification field in columns 73–80, then translated to C one statement at a time. Blank COMMON is a single array of four-byte words, so the layout, the column-major arrays and even the one place the code deliberately clears past the end of HGRAPH behave exactly as they did on the 360. REAL is a 32-bit float; the 360 used hexadecimal floating point with a slightly different precision, and no one should expect the sixth digit to agree with a 1971 run. Blanks in numeric fields are ignored here, where the 360 read them as zeros; a card punched correctly reads the same either way, and a card typed carelessly now reads the way you meant it.

• Included: RUNOFF, HYDRO, RHYDRO, WSHED, GUTTER, HCURVE — the whole quantity side, the card reader, the report, the interface tape.
• Included: SFQUAL, the surface-quality model, with its scratch-tape read-back and the NQUAL = 3 interface tape. Not included: the Executive Block printer plots that HCURVE sets up. Transport, Storage and Receiving Water are separate volumes of work.
• Imported: SWMM 5 .inp files and SWMM 4 .DAT files with a $RUNOFF block, including the SWDAT series that shipped with SWMM 4. Decks whose rain comes from a Rain Block file, or that only call EXTRAN, Storage or Stats, are shown but not run.
• Verified: wasm and native builds produce byte-identical printouts; the engine is re-entrant; continuity closes within a percent on both sample decks. On the Lancaster deck the reported error is 29 percent, and that is water in transit: the SWMM 4 run ends at 60 minutes while the rain lasts to 65, and HYDR133–139 count rain, infiltration, inlet flow and subcatchment storage but not what is sitting in the gutters and pipes. Not verified: against an actual 1971 run, because none survives in this reconstruction.

Your run

Change a width, halve the slope, move PCTZER to zero and run again. It takes two milliseconds. In 1971 it took a trip to the card punch, a place in the queue and a wait for the printer. The physics did not change in between; the patience required did.