SCIENCE · INVESTIGATE AND EXPLAIN

Compare rainfall timing with water entry

Contrast equal-total storms under explicit entry and storage limits.

Learning outcome: Calculate hourly rain partition while preserving event water balance.

Starting recap

The original store has 40 mm capacity and 15 mm/hour maximum entry, with no drainage or ponding.

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Try

At zero initial storage, uniform 60 mm produces 20 mm runoff; concentrated 60 mm produces 30 mm.

Open the experiment

Predict

Must equal rain totals produce equal modeled runoff?

Your prediction and reason

Experiment

Capture uniform and concentrated storms with initial storage zero; calculate each hourly ledger and total.

Compare storm timing and initial water storage

Original sealed-store experiment · separate weathering evidence practice · Original synthetic plot with 40 mm storage capacity and maximum entry 15 mm/hour. Rain is piecewise constant by hour. Infiltration is limited by rain supply, entry limit and remaining storage; unentered rain leaves immediately as runoff. No drainage, evapotranspiration, surface ponding, routing or empirical soil forecast. Entry stops at a full store only because this store has no drainage; real saturated soil can transmit water. Exact rate segments split at filling time; stored water is not runoff.

Initial water in teaching store: 0 mm Six-hour rain profile: Uniform: 60 mm over six hours

Reset keeps your prediction, captures and practice history.

Weathering changes material; erosion moves it

Original fictional observation cards. The rain controls do not change these cards or simulate weathering. Before revealing an interpretation, identify whether the evidence supports physical fragmentation, chemical alteration, transport, or an unresolved mechanism. Real exposures may show several processes together.

Supplied qualitative evidence, not measurements from a field site
Case	Evidence to explain	Prediction task
A: broken sample	A rock breaks along cracks into smaller pieces. Mineral tests before and after show the same mineral constituents.	What changed, and what was conserved?
B: altered minerals	Mineral tests show loss of some original feldspar and formation of clay minerals; dissolved constituents occur in water leaving the sample.	Does fragmentation alone explain all observations?
C: relocated grains	Marked grains leave one patch during flowing water and accumulate downstream; their tested mineral constituents remain unchanged.	Separate removal, transport and deposition.
D: a brown surface	A photograph shows a brown coating. No mineral or chemical analysis is supplied.	What additional evidence distinguishes oxidation, staining or another coating?

Compare the weathering interpretations

A supports mechanical fragmentation; the stated evidence does not establish chemical alteration. B supports chemical weathering, including mineral transformation and dissolved export; real reactions require appropriate conditions and cannot be identified from color alone. C supplies erosion, transport and deposition evidence, not proof of new chemical weathering. D remains ambiguous: obtain compositional evidence and compare coated material with the underlying rock.

Water entering cracks, crystal growth and roots can contribute to physical breakdown under suitable conditions. Chemical weathering includes dissolution and reactions involving water, oxygen or acids. These processes can interact: new cracks expose surfaces, while alteration can weaken rock. A crack or weather event by itself does not establish an exact weathering rate.

Fragmentation exposes more surface

Original geometry: begin with a cube 2 cm on each edge. Cut every edge into equal divisions and separate all pieces so every face is accessible. Predict the total exposed area before opening the table. Cutting changes shape and exposure; it does not itself change mineral identity or create material.

Reveal area and volume calculations

All faces exposed; no material lost and no chemical reaction modeled
Divisions per original edge n	Pieces n³	Piece edge cm	Total volume cm³	Total area cm²
1	1	2	8	24
2	8	1	8	48
4	64	0.5	8	96

Each of n³ pieces has edge 2/n cm and six faces. Total area = n³ × 6 × (2/n)² = 24n cm². Total volume = n³ × (2/n)³ = 8 cm³. The area grows in proportion to n, while volume stays fixed. More available surface can change reaction opportunities, but temperature, composition, water supply, chemistry and accessible contact also matter. Twice the area does not guarantee twice the observed weathering rate.

Transfer: use a 3 cm starting cube divided into three pieces per edge. Calculate piece count, total volume and area, then identify why tightly packed pieces might not expose every face to moving water.

Background: National Park Service weathering mechanisms and USGS explanation of clay formation and weathering. These sources explain real processes; the cards and cubes here are teaching constructions.

Original storm experiment: entry and storage are different limits

Uniform: 60 mm over six hours. The receiving store holds at most 40 mm of water equivalent and admits at most 15 mm/hour while space remains. Rain that does not enter leaves the plot immediately. This is an intentionally sealed teaching store: no drainage, evapotranspiration, surface ponding or travel time is included. Real saturated soil can transmit water; these parameters are not measured soil properties.

Conservation: initial storage + rain = final storage + runoff. For this case, 0 + 60.0 = 40.0 + 20.0 mm. Newly infiltrated water equals the storage increase only because this model has no store outflow. Initial water is not counted again as new infiltration.

Read rates and accumulated water separately

The model store first fills at hour 4.0000. A full store and an exceeded entry-rate limit are distinct reasons why rain may leave as runoff.

One-hour totals; quantities are mm of water equivalent
Hour interval	Rain	Initial store	Infiltration	Runoff	Final store
0–1	10.0	0.0	10.0	0.0	10.0
1–2	10.0	10.0	10.0	0.0	20.0
2–3	10.0	20.0	10.0	0.0	30.0
3–4	10.0	30.0	10.0	0.0	40.0
4–5	10.0	40.0	0.0	10.0	40.0
5–6	10.0	40.0	0.0	10.0	40.0

Inspect exact rate intervals and the filling event

Within-hour rate changes occur at calculated filling times
Start–end hours	Rain mm/hour	Infiltration mm/hour	Runoff mm/hour	Store start–end mm
0.0000–1.0000	10	10	0	0.00–10.00
1.0000–2.0000	10	10	0	10.00–20.00
2.0000–3.0000	10	10	0	20.00–30.00
3.0000–4.0000	10	10	0	30.00–40.00
4.0000–5.0000	10	0	10	40.00–40.00
5.0000–6.0000	10	0	10	40.00–40.00

For a one-hour bin, entry depth is the minimum of rain depth, 15 mm and remaining storage. Before filling, entry rate is the smaller of rain rate and 15 mm/hour. Time to fill is remaining storage divided by that rate. If the rate is zero, no filling time is calculated from division by zero. At filling, entry stops and the rest of the rain leaves; the plot is not drawn as though the average hourly entry occurred uniformly.

Choose a fair comparison and explain its limits

Compare uniform and concentrated storms from the same initial storage: both supply 60 mm, isolating timing in this model. Light rain supplies 20 mm and the dry case supplies zero, so those comparisons also change total input. With initial storage zero, uniform rain admits 40 mm and exports 20 mm; the concentrated storm admits 30 mm and exports 30 mm. With 20 mm initially stored, both export 40 mm, but the time patterns differ.

Real runoff depends on drainage, surface storage, soil structure, vegetation, slope and spatial connections omitted here. This plot's immediate export is not a catchment outlet hydrograph. Runoff depth alone does not determine sediment mass; that requires concentration or sediment-process evidence. Background: USGS surface runoff and USACE infiltration and runoff-volume concepts.

Rain 60.0 mm = runoff 20.0 mm + storage increase 40.0 mm.

Initial store 0 mm; final store 40.0 mm. Store first full at hour 4.000. Full means the sealed teaching store is full, not a diagnosis of real soil saturation; real saturated soil can transmit water. Synthetic bounded accounting, not a catchment forecast.

Observation to attach to a capture

Captures preserve initial water storage and the synthetic storm profile. Replay recalculates the sealed-store comparison; it does not measure real runoff, simulate weathering or establish an independent field result.

Understand

Compare storms with the same total rain

A steady storm and a short intense storm can deliver the same rain total without producing the same runoff in a specified system. Predict the comparison before choosing the profiles. This experiment uses an original sealed teaching store, not a measured watershed or a forecast for a particular soil.

Set Initial water in teaching store to 0 mm. Choose Uniform: 60 mm over six hours. Each hour supplies 10 mm. Then compare Concentrated: 60 mm in two hours, which supplies 30 mm/hour during hours two to four and no rain during the other four hours. The six-hour totals agree; the rates and timing differ.

State the storage and entry rules

The store has capacity 40 mm of water-equivalent depth. Water can enter at no more than 15 mm/hour while space remains. Actual entry is also limited by available rain. Any rain that does not enter leaves immediately as modeled runoff. There is no drainage, evaporation, transpiration, surface ponding or downstream routing.

These are chosen teaching assumptions, not empirical coefficients for a named soil. Water-equivalent millimeters describe an amount per unit area; they do not specify a physical soil-layer thickness or a water-table elevation. The USGS infiltration explanation provides real-process context, including effects of rainfall and ground conditions, without making these particular constants universal.

For one hour before the store fills, compare three limits: rain supplied, maximum entry of 15 mm, and remaining capacity. The smallest determines the infiltrated amount during that hour. Runoff is rain minus infiltration; storage increases by the infiltrated amount.

Work through the uniform storm

With no starting water, the first four uniform hours each add 10 mm. Storage reaches 40 mm at hour four. The final two hours cannot enter this full, sealed store, so 20 mm leaves as runoff. Total infiltration is 40 mm and final storage is 40 mm.

Make six paper rows with rain, starting storage, entry, runoff and ending storage. Check each row and then the event total: 60 mm rain equals 40 mm storage increase plus 20 mm runoff. Zero balance error verifies the bookkeeping, not the realism of the chosen parameters.

A real saturated soil can still transmit water. Entry stops at full capacity here because the store has no outlet or drainage, not because every saturated material is impermeable. Keep that model boundary in the conclusion.

Work through the concentrated storm

The two rainy hours each supply 30 mm. At most 15 mm enters per hour, so each contributes 15 mm runoff even while storage has room. After both hours the store contains 30 mm, and total runoff is 30 mm. It never fills during the six-hour window.

Capture both storms with initial storage unchanged. Explain why the more concentrated case has greater runoff despite lower ending storage. An entry-rate limit can reject rain before the total capacity is exhausted. Rain that already left as runoff cannot return during the subsequent dry hours because this model has no ponded surface reservoir.

The USGS runoff overview discusses rainfall intensity and other controls in real settings. Our comparison isolates selected mechanisms; it does not estimate an outlet flood peak, flow travel time or erosion load.

Transfer: one unfamiliar rain interval

For a paper-only hour, start with 25 mm stored and supply 20 mm of rain uniformly over that hour. Keep capacity 40 mm and maximum entry 15 mm/hour. Predict infiltration, runoff and ending storage, then explain which limits matter.

Check the storm-runoff transfer

Remaining capacity is 15 mm and maximum hourly entry is 15 mm, so 15 mm enters and 5 mm runs off. Ending storage is 40 mm. This is a one-hour paper calculation, not an additional selectable storm or a measured soil response.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Distinguish entry limitation before filling from rejection by the full sealed store.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Compare exposed area after fragmentation Next: Track initial water and remaining capacity

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