Hydrology

This program is a hydrology toolkit that offers four computational modules selectable from a menu: slope computation, a watershed map drawing routine, unit hydrograph preparation (UHG PREP), and a mathematical unit hydrograph generator (MATH UHG). The menu dispatcher at line 50 uses a single multiply-and-branch idiom (`GO TO 10*Number`) to jump to subroutines at lines 60, 100, 200, and 250 based on the user’s input of 6, 10, 20, or 25. The map-drawing module (line 100) POKEs 12 bytes of machine code into address 23760 and then calls it via `RANDOMIZE USR 23760`, implementing an LDIR block-copy routine (opcodes `ED B0`) capped with a `RET` (`C9`). The MATH UHG section (line 250) implements a lognormal distribution fitting algorithm with an iterative sigma convergence loop and computes either instantaneous or average unit hydrograph ordinates using numerical integration by Simpson’s rule.

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Program Analysis

Program Structure

The program is organized as a menu-driven dispatcher. Lines 1–45 display a menu and read the user’s selection into Number. Line 50 computes GO TO 10*Number, routing to one of four modules:

Input	Target line	Module
6	60	Slope computation
10	100	Map draw
20	200	UHG Prep
25	250	Math UHG
100	1000	STOP

Each module ends with GO TO 18, which jumps to a non-existent line — falling through to line 19 (the blank PRINT). In practice this is effectively a restart of the menu from line 19 onward, since BASIC will run the next available line after an unfound target in some interpreters, though this is noted as a known technique. The REM at line 1 flags the author’s awareness of bugs.

Machine Code Usage

The map-draw module (lines 106–108) POKEs 12 bytes into RAM starting at address 23760 and then invokes them with RANDOMIZE USR 23760 at line 125. The DATA at line 127 decodes as:

Address	Byte (hex)	Z80 mnemonic
23760	33 00 40	LD HL,16384 (start of display)
23763	64 11 00 E3	partial operands / LD DE,…
23767	01 00 1B	LD BC,…
23770	ED B0	LDIR (block copy)
23772	C9	RET

The exact byte sequence is 33,0,64,17,0,230,1,0,27,237,176,201. The LDIR instruction copies a block of memory, and the RET returns cleanly to BASIC. The purpose appears to be a display-area memory operation, consistent with copying or clearing graphics data.

Slope Computation Module (lines 60–90)

This module computes the Taylor-Schwarz channel slope formula used in hydrology. It reads N elevation points, a reach length DL, and a total length L from DATA. For each pair of adjacent elevations it computes D(I) = 1 / SQR(ELDIFF/DL), then calculates overall slope as S = ((N-1) / SUM)^2. The result is truncated to four decimal places using the INT(x*10000)/10000 idiom and converted to ft/mile by multiplying by 5280.

Map Drawing Module (lines 100–136)

This module plots a watershed boundary and stream network using pixel-level PLOT and DRAW commands. Two pairs of 2D arrays (x, y for boundary; z, u for stream) store coordinate sequences read from DATA. The boundary data is at line 132 and stream data at line 134, giving sequences of absolute pixel coordinates. The DRAW calls use relative offsets computed from successive coordinate differences. A sentinel check IF x(c,1)>255 THEN GO TO 135 at line 112 and a similar check at line 120 guard against out-of-range coordinates, though the check at 120 tests z(1,1) (the first element) rather than z(c,1) (the current element), which is likely a bug — it will never trigger mid-loop as intended.

UHG Preparation Module (lines 200–229)

This module implements the Snyder synthetic unit hydrograph method. It computes lag time TP, time-to-peak TPR, and peak discharge QP from basin parameters: drainage area DA, main channel length L, length to centroid LCA, storm duration TR, and empirical coefficients CT and CP640. The formula NUM=(L*LCA)^0.3 is the standard Snyder lag parameter. An urbanization parameter PAR = L*LCA/SQR(S) is also printed for lookup on an external curve.

Mathematical UHG Module (lines 250–326)

This is the most computationally intensive module, implementing a lognormal unit hydrograph. It fits a sigma parameter iteratively by bracketing the solution to match a lognormal CDF target (YO), converging in two passes of decreasing step size (0.0005, then 0.000005). The core loop structure is:

1. Compute YO = TMQ * QMAX / (111.80941 * A) (the lognormal argument)
2. Estimate initial SIGMA from a polynomial approximation using Y = log10(YO)
3. Iteratively refine SIGMA at lines 268–281 until S ≈ YO within 0.0001
4. Compute the mode time T from SIGMA
5. Evaluate ordinates in the FOR loop at lines 293–318

The constant 111.80941 is SQR(12500), a normalisation factor for the lognormal unit hydrograph. When INSTA=0, average flows are computed using a simple trapezoidal/Simpson accumulation (TOT + 2*Q) inside the inner loop, divided by 20 at line 309. The loop exit condition at lines 315–316 terminates when both time has passed the mode and flow has dropped to 2 or below.

Notable Techniques and Idioms

• Computed GO TO: GO TO 10*Number at line 50 is an efficient menu dispatcher, avoiding a chain of IF statements.
• Rounding idiom: INT(x*10000)/10000 and INT(x*100+.5)/100 are used throughout for controlled decimal truncation and rounding respectively.
• DATA reuse: All module parameters are stored in DATA statements local to each module section, so the READ pointer advances naturally as each module is entered once per run. Re-entering a module after a GO TO 18 restart would exhaust the DATA pointer — a latent bug for repeated use within one run.
• Polynomial sigma inversion: Lines 264–267 use a degree-6 polynomial in Y = log10(YO) to approximate the inverse normal, seeding the iterative refinement efficiently.

Bugs and Anomalies

• Line 120 sentinel check: IF z(1,1)>255 always tests the first stream coordinate, not the current loop variable z(c,1). This means the stream loop never terminates early via this guard.
• Line 294 dead code: IF (J-1)>=0 THEN GO TO 296 is always true for J=1 TO 11 (since J starts at 1), so line 295 (LET TT=TT-DT/10) is never executed.
• DATA pointer exhaustion: Modules use READ/DATA without RESTORE, so selecting the same module twice in one session will cause an error when data runs out.
• Line 90 / 136 / 229 / 326 — GO TO 18: Line 18 contains PRINT "MENU SELECTION", so the menu is redisplayed from line 18 rather than from line 15 (which prints the title). This skips the title and the CLS at line 45 is not re-executed, so old output remains on screen.
• Line 72 square root of ratio: SQR(ELDIFF/DL) will produce an error if any adjacent elevations are equal or decrease, as the argument becomes zero or negative.