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Pond capacity

What this page covers: how a Pond capacity result is worked out. That is the capacity and the water spread at each level up to the full tank level (FTL), inside a boundary. It also covers the levels CSE chooses, the bed and the spill check, and the area–capacity curve. At the end is a worked example you can check with a calculator.

For the steps in the program, see Tank and pond capacity. For how the surface is made, see The contour surface (TIN).

What is worked out

For each level in the list:

  • Water spread: the plan area, inside the boundary, where the ground is below the level (m²).
  • Capacity: the volume between the ground and the level wherever the ground is below it, inside the boundary (m³, and in megalitres: m³ ÷ 1,000).
  • Volume of the step: the capacity at this level less the capacity at the level before. The first row's step is its own capacity, from the bed.

Also worked out:

  • The bed: the lowest ground inside the boundary.
  • The boundary's lowest point: the lowest ground along the boundary line, where the water would spill out.

1. Each level straight from the TIN

The capacity at a level is exactly what Volume… would give as the fill against a flat formation at that level, inside the same boundary. The water spread is that fill's area. The method is the one in Site cut and fill, step 2:

  1. Each kept triangle of the TIN is cut to the boundary.
  2. Each piece is split where the ground is at the level. Only the part below the level is kept.
  3. That part gives area × (level − ground at its centroid), the exact volume of water over it. For a whole triangle under water this is area × (level − mean of its three corner levels).
  4. The parts are added up: their volumes give the capacity, their areas the water spread.

No rule between levels. CSE does not use the average end area rule or the prismoidal rule between one level and the next. Every level is worked out on its own from the TIN, so the capacity at 24.000 is the same whether the levels go every 0.10, 0.25 or 0.50 m. The step only decides which rows are in the table. The volume of a step is just the difference of two exact capacities.

This is not how the route's volume abstract works. There, the volume between two cross sections comes from their areas, by Average End Area or Prismoidal (see Volumes: Average End Area and Prismoidal). Here there is a whole surface, so nothing has to be assumed between levels.

2. The levels

In the Pond Capacity dialog, under Levels:

  • From starts at the bed rounded up to the step. Under it, "The bed is at 21.000, the lowest point inside." Use it puts the bed itself in From, to 3 decimals.
  • To starts at the boundary's lowest point rounded down to the step, so the water stays inside. If that is not above From, it starts at the highest ground inside rounded down. Failing that, it is one step above From.
  • Every is 0.10, 0.25 or 0.50 m (0.25 to start with).

The list is From, then every round level (a whole number of steps, counted from 0) above it up to To, then To itself if it is not on the step. Each level is to 3 decimals.

  • If From is off the step (the bed, after Use it), a round level less than half a step above it is skipped, so the first step is never a sliver. From 21.130 every 0.25, the list is 21.130, 21.500, 21.750 …
  • FTL (under Full tank level) is put in as a row of its own if it is not already one of the levels. An FTL below From becomes the first row, and one above To the last. Its row is marked in the Capacity sheet, and the tile, the banner and the water drawn on the plan are at the FTL. With no FTL they are at the top level.
  • At most 500 levels are worked out. More than that, and the dialog asks for a larger step or a smaller range.

3. The bed and the spill check

Inside each triangle the ground is a plane, so the lowest ground inside the boundary is at a corner of one of the pieces. Along the boundary line, the lowest ground is at a place where the line crosses a triangle side, or at a corner of the boundary. Both are found exactly, with no sampling.

If the FTL (or, with no FTL, the top level) is above the boundary's lowest point, as both read to the millimetre, the water would spill out there. The dialog warns: "The FTL is above the boundary's lowest point, 25.410: the water would spill there." Otherwise the checks strip says, for example, "The boundary's lowest point is 25.000, above the FTL".

The capacity is still worked out up to the level asked for, inside the boundary, as if the boundary were a wall. The warning tells you it is not.

4. The area–capacity curve

The printed pond sheet (Print / PDF with the pond shown) has a CAPACITY table (Level, Spread and Capacity) and under it the area–capacity curve:

  • Level is up the side, from the first level to the last.
  • Capacity is along the foot, from 0 to the largest capacity, drawn solid.
  • Water spread is along the top, from 0 to the largest spread, drawn dashed.
  • The FTL is a line across, labelled.

The points of the curve are the levels in the list, joined by straight lines. A finer Every gives a smoother curve, but does not change any point on it. If the table has no room for every level, the print shows a coarser step, and the notes say "Every 0.10 m level is in the Capacity sheet."

5. Rounding and where each figure is shown

  • The tile: "9 levels · 900 m³ at FTL · 900 m² of water", in whole m³ and m².
  • The banner: "At FTL 24.000: capacity 900 m³ (0.90 ML) over 900 m² of water. 9 levels, 21.000 to 25.000." Megalitres are to 2 decimals.
  • The Capacity sheet (Level (m), Water spread (m²), Volume of the step (m³), Capacity (m³), Capacity (ML)): areas and volumes to 2 decimals, levels to 3, the FTL's row in bold.
  • The Summary sheet: the bed, the FTL, the capacity and water spread at it, the levels, the boundary's area and lowest point, and the method ("TIN prisms, as Volume…").
  • Nothing is rounded during the working out. The rounding is only in how a figure is shown.

Things to watch

  • Every hollow inside the boundary counts. The capacity is all the space below the level inside the boundary. A separate hollow (a borrow pit, or ground behind the bund) that the water in the tank could not reach is counted too, if it is inside the boundary. Run the boundary along the top of the bund, round the water you mean.
  • Part of the boundary off the TIN is left out. The checks strip says "… m² of the boundary has no TIN under it and is left out".
  • A flat bed at a level is not under water at that level. Water of no depth counts as neither capacity nor spread, so a tank with a flat bed at 20.000 has 0 m² of spread at 20.000.
  • Out of date: if the points, the surface settings or the job's boundary change, the tile says "Out of date: the surface or boundary has changed." Click Recalculate.

Worked example

A small pond shaped like an upside-down pyramid: a 40 m square at 25.000, with its bed at the centre, 4 m down. The four corners are coded BND, in order round the pond.

Point Easting Northing R.L. Code
1 500.000 800.000 25.000 BND
2 540.000 800.000 25.000 BND
3 540.000 840.000 25.000 BND
4 500.000 840.000 25.000 BND
5 520.000 820.000 21.000 GL

The TIN is four triangles, each from the bed to one side of the square. No side is over 50 m. The boundary is the square, 1,600 m². The bed is 21.000, and the boundary's lowest point is 25.000 (the whole boundary is at 25.000).

The dialog starts with From 21.000 and To 25.000. Set Every to 0.50 and FTL to 24.000. The levels are 21.000, 21.500 … 25.000: 9 levels, with 24.000 among them.

By hand. At a level h, the water is d = h − 21.000 deep at the centre. The sides slope 20 m out for every 4 m up, so the water's edge is a square of side 40 × d / 4 = 10·d.

  • Water spread = (10·d)² = 100·d²
  • Capacity = spread × d / 3 (a pyramid: a third of base × height) = 100·d³ / 3

At the FTL, d = 3: spread = 100 × 9 = 900 m², capacity = 100 × 27 / 3 = 900 m³ (0.90 ML). The banner says "At FTL 24.000: capacity 900 m³ (0.90 ML) over 900 m² of water. 9 levels, 21.000 to 25.000."

Level (m) Water spread (m²) Volume of the step (m³) Capacity (m³) Capacity (ML)
21.000 0.00 0.00 0.00 0.00
21.500 25.00 4.17 4.17 0.00
22.000 100.00 29.17 33.33 0.03
22.500 225.00 79.17 112.50 0.11
23.000 400.00 154.17 266.67 0.27
23.500 625.00 254.17 520.83 0.52
24.000 FTL 900.00 379.17 900.00 0.90
24.500 1,225.00 529.17 1,429.17 1.43
25.000 1,600.00 704.17 2,133.33 2.13

Against the rules between levels. By the average end area rule, the volume from 23.000 to 24.000 would be (400 + 900) / 2 × 1.0 = 650 m³. The true volume is 900 − 266.67 = 633.33 m³, so the rule is 2.6 % high. The prismoidal rule, with 23.500 as the middle level, gives (400 + 4 × 625 + 900) / 6 × 1.0 = 633.33 m³. It is exact here because this pond's sides are straight planes. On real ground neither rule is exact, which is why CSE works each level out from the TIN instead.

To try it in the program, put the five points in a CSV file, make a job and import it. The boundary comes from the BND points. Add a Pond Capacity… with Every 0.50 and FTL 24.000, then open the Capacity sheet.