SCIENCE · INVESTIGATE AND EXPLAIN

Track initial water and remaining capacity

Distinguish final inventory from storage change and locate filling within an hour.

Learning outcome: Compare wet and dry initial conditions without changing the storm.

Starting recap

Initial water remains in the sealed store; real saturated soils can transmit water.

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Try

Initial 5 mm under uniform rain fills the 40 mm store at hour 3.5.

Open the experiment

Predict

Will equal final storage mean equal event infiltration?

Your prediction and reason

Experiment

Compare uniform storms at initial 0, 5 and 20 mm, then test light and dry profiles.

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

Give the initial condition a place in the ledger

Two identical storms need not produce the same modeled runoff if the store begins with different amounts of water. Before changing a control, predict whether a wetter initial store leaves more or less room for new rain. Initial storage is an inventory, not rain that fell during the current six-hour experiment.

Choose Uniform: 60 mm over six hours. Compare initial storage 0 and 20 mm while leaving every other rule unchanged. Capacity remains 40 mm and entry is capped at 15 mm/hour. The profile supplies 10 mm/hour, below the entry-rate cap while storage space remains.

Calculate the available space

With 0 mm initially stored, space is 40 mm; total event infiltration is 40 mm and runoff is 20 mm. With 20 mm initially stored, only 20 mm of space remains. Two uniform hours fill it, and the remaining 40 mm of rain leaves as runoff. Both end at 40 mm, but their storage increases differ.

Write final storage and storage change in separate columns. In the wetter case, final storage 40 mm minus initial 20 mm equals a 20 mm increase. Treating all final storage as new infiltration would count pre-existing water again. This sealed model retains the initial water; it does not release it as baseflow or runoff.

The event balance is rain = runoff + storage change. A fuller inventory statement is initial storage + rain = final storage + runoff. Both give the same answer under the model’s omitted-flow assumptions. This differs from the earlier monthly watershed budget, where outflow and evapotranspiration were separately supplied.

Locate a filling time within an hour

Set initial storage to 5 mm under the uniform storm. Space is 35 mm. At 10 mm/hour, filling takes 35/10 = 3.5 hours. During the fourth hour, the first half adds the last 5 mm and the second half produces 5 mm runoff. Total six-hour runoff is 25 mm.

The hourly ledger contains totals, but the rate display splits at the actual filling time. Do not describe infiltration as a constant 5 mm/hour throughout that fourth hour: it is 10 mm/hour for half the hour and zero afterward. Averages and within-interval changes are different representations of the same accounting.

Compare that with the concentrated storm at initial storage 20 mm. Fifteen millimeters enters during its first rainy hour, leaving 5 mm of space. At the 15 mm/hour entry cap, those 5 mm fill during one third of the next hour. The store becomes full at hour 3⅓, not at the end of hour four.

Test light rain and no rain

Choose Light: 20 mm over four hours with initial storage 0 mm. All 20 mm can enter, runoff is zero and final storage is 20 mm. Repeat at 30 mm initially stored: only 10 mm can enter and 10 mm becomes runoff. This isolates the remaining-capacity limit with a rain rate below the maximum entry rate.

Now choose Dry: no rain. Storage stays at its initial amount and runoff stays zero, even if the store begins full. Full storage does not manufacture an output. USGS infiltration context includes real drainage and groundwater pathways that are deliberately absent here. Real saturated soil can transmit water; this sealed store cannot.

Transfer: audit an unfamiliar inventory

A paper event starts with 15 mm, receives 20 mm rain and ends with 35 mm stored under the same no-loss assumptions. A report claims 35 mm infiltrated during the event. Repair the infiltration and runoff totals without assuming a new rainfall profile.

Check the runoff-storage transfer

Storage increased by 35 − 15 = 20 mm, so event infiltration is 20 mm and runoff is zero. The final inventory includes 15 mm already present. This endpoint balance does not reconstruct the rainfall timing or prove that every possible profile could produce those endpoints.

Apply

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

Explain the within-hour rate split and why a full no-rain store produces no runoff.

Your explanation and limitations

Continue

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

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Previous: Compare rainfall timing with water entry Next: Bound a runoff interpretation

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