Hydrology 2

This program is a hydrology toolkit that offers three computational modules via a menu: rainfall distribution (“RAIN D”), flood hydrograph generation (“Fld Hyd”), and storage/discharge function rates (“FUNC RATES”). The menu dispatches to subroutines using the computed GO TO at line 395 (`GO TO Number*10`), where the user enters 40, 45, or 55 to jump to lines 400, 450, or 550 respectively. The flood hydrograph section implements a unit hydrograph convolution, multiplying rainfall excess values against unit graph ordinates and summing them to produce a flow time series. The program embeds all its test data in DATA statements and uses DIM arrays for intermediate storage, with the storage-routing section computing S+Q/2 and S-Q/2 routing function values scaled by acre-feet conversion factors (43560 sq ft per acre, 10800-second time steps).

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Program Analysis

Program Structure

The program is organised as a menu dispatcher plus three self-contained computational modules, each terminated by a GO TO 372 (or GO TO 370) to return to the menu. The overall flow is:

1. Lines 350–395: Title, menu display, and computed branch (GO TO Number*10)
2. Lines 400–430: Module 1 — Rainfall Distribution (“RAIN D”)
3. Lines 450–525: Module 2 — Flood Hydrograph (“Fld Hyd”)
4. Lines 550–595: Module 3 — Storage/Routing Function Rates (“FUNC RATES”)
5. Line 1000: STOP (reached when user enters 100)

Computed GO TO Dispatch

Line 395 uses GO TO Number*10 to branch: entering 40 jumps to line 400, 45 to line 450, 55 to line 550, and 100 to line 1000. This is a compact menu-dispatch idiom that avoids a chain of IF statements. No bounds checking is performed, so any other input will cause an error due to jumping to a non-existent line.

Module 1 — Rainfall Distribution (Lines 400–430)

Reads a count N, total rainfall R, and two label strings from DATA, then reads N fractional distribution values into array F. For each period it computes E(I) = R * F(I) (rainfall excess per period) and prints a table of time period, fraction, and excess depth. The DATA at lines 417–418 encodes a 6-period, 6.00-inch, 100-year event for “Luther Lake”.

Module 2 — Flood Hydrograph (Lines 450–525)

Implements a discrete unit hydrograph convolution to generate a flood hydrograph from rainfall excess and unit graph ordinates. The convolution loop runs from J=1 to NQ = NP + NUHGQ - 1, the expected length of the output hydrograph. A conditional at line 478 splits the inner loop into two cases depending on whether J ≤ NUHGQ or not.

There is a significant bug in the convolution logic: inside the first branch (lines 479–483), Q(J) is overwritten on each iteration of the inner I loop rather than accumulating. The correct formulation would add P(K)*U(I) to a running sum rather than assigning it to Q(J) and then adding Q(J). As a result SUMF does not correctly accumulate the convolution sum. The same error appears in the parallel dead-code section at lines 492–505.

Lines 492–505 are entirely unreachable dead code: line 491 unconditionally branches to line 506, so lines 492–505 can never execute. These appear to be remnants of an earlier version of the algorithm that was not fully removed.

Module 3 — Storage Routing Function Rates (Lines 550–595)

Computes the storage-routing working curves S/TR, S/TR − Q/2, and S/TR + Q/2 for reservoir routing using Muskingum or level-pool methods. Storage S(I) is built up cumulatively from trapezoidal area integration scaled by the elevation increment ELEVD. The conversion at line 563 applies the factor 43560/10800 (square feet per acre divided by seconds per time-step) to convert acre-feet storage to a compatible flow unit.

Line 565 uses LET B(I) = INT NUM/10 to round B(I) to one decimal place via an intermediate variable NUM = B(I)*10, a common BASIC rounding idiom since INT only truncates toward zero.

Notable Anomalies and Bugs

• Convolution overwrite bug (line 481, 488, 495, 503): Q(J) = P(K)*U(I) should accumulate (i.e. LET Q(J) = Q(J) + P(K)*U(I)); the current assignment discards previous iterations, making SUMF incorrect.
• Dead code (lines 492–505): Unconditional GO TO 506 at line 491 makes these lines permanently unreachable.
• Operator precedence at line 565: INT NUM/10 is parsed as (INT NUM)/10 in Sinclair BASIC, which is the intended behaviour here, but could be misleading to a reader expecting INT(NUM/10).
• Module 2 DATA misalignment: READ NUHGQ,TR,NP at line 458 expects the unit graph to have 12 ordinates and 12 rainfall excesses, but lines 512–515 supply only 12 unit graph values split across two DATA lines and 12 rainfall values split across two more — the counts match but the split across lines is worth noting for maintainability.
• REM at line 1: The author acknowledges bugs directly in the source: REM This program has "bug problems"--doesn't run completely.

Variable Summary

Variable	Module	Purpose
Number	Menu	User menu selection (40/45/55/100)
N, R, T$, Y$	RAIN D	Period count, total rainfall, title strings
F(24), E(24)	RAIN D	Fractional distribution and excess depth arrays
NUHGQ, TR, NP	Fld Hyd	Unit graph ordinate count, time interval, rainfall period count
U(15), P(15), Q(30)	Fld Hyd	Unit graph ordinates, rainfall excesses, convolution output
SUMF, IHR, NQ	Fld Hyd	Accumulated flow, current hour, total output periods
H(10), A(10), Q(10)	FUNC RATES	Head, area, and discharge arrays
S(10), B(10), C(10), D(10)	FUNC RATES	Storage, S/TR, S/TR−Q/2, S/TR+Q/2 arrays
ELEVD, SUM, NUM	FUNC RATES	Elevation increment, cumulative storage, rounding intermediate