SCIENCE · INVESTIGATE AND EXPLAIN

Bound a runoff interpretation

Separate controlled water-budget results from erosion, intervention and flood claims.

Learning outcome: Defend a model comparison and identify observations needed for a field inference.

Starting recap

The simulation supplies no sediment chemistry, channel routing or calibrated catchment forecast.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

Twenty mm over a separately stipulated 100 square meters is two cubic meters, not a travel time.

Open the experiment

Predict

Does more runoff establish an erosion mass or downstream flood arrival?

Your prediction and reason

Experiment

Compare paired captures with one changed input, calculate runoff fractions only when rain is nonzero and build a supported/missing-evidence ledger.

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

Make a claim about the experiment you actually ran

A modeled runoff difference can explain a mechanism under stated rules without predicting the response of an actual catchment. Start a report with the initial inventory, rainfall profile, storage capacity and entry-rate limit. Add the boundary assumptions before interpreting the result: no drainage, evapotranspiration, ponding or downstream routing.

All rainfall profiles and constants are original teaching choices. The weathering cards are fictional evidence descriptions, and the cube demonstration is ideal geometry. None is a newly measured field dataset. A complete notebook should preserve that distinction rather than presenting a precise calculation as an observed result.

Compare like with like

At initial storage 0 mm, the uniform 60 mm storm gives 20 mm runoff, while the concentrated 60 mm storm gives 30 mm. The changed input is rainfall timing. Calculate runoff fractions by dividing runoff by rain: 20/60 is one third, while 30/60 is one half.

Those fractions summarize this model’s particular event responses. They are not universal coefficients for a soil, land cover or region. If you change initial storage at the same time, the comparison no longer isolates timing. Use paired captures with one chosen difference and explain any other assumptions that remain fixed.

For the dry profile, both rainfall and runoff are zero. A runoff fraction would be 0/0, which is undefined rather than zero. The valid statement is zero modeled runoff during a no-rain interval. A ratio needs a meaningful nonzero denominator.

Keep water amount separate from a flood forecast

The model reports runoff as water-equivalent depth leaving the surface store immediately. It does not route that water along hillslopes, drains or channels. Consequently a high hourly local runoff rate is not a predicted river discharge peak, arrival time or flood depth at a town.

If an independently stated hypothetical plot area is 100 m², 20 mm runoff corresponds to 0.020 m × 100 m² = 2 m³. This paper conversion supplies a volume, not a flow speed or travel time. No fixed area is needed to compare the browser’s depth budgets, and the conversion does not add a routing model.

The USGS runoff overview describes real dependence on rainfall, prior moisture, land cover and landscape properties. Those relationships motivate further investigation; they do not make this single fixed-capacity store a calibrated representation of all those effects.

Do not infer weathering or erosion from runoff alone

A larger modeled runoff amount does not specify newly eroded sediment mass or chemical-weathering rate. Material availability, detachment, transport capacity and temporary storage are unresolved. The earlier sediment lesson required both discharge and representative concentration even to estimate suspended mass passing a particular section.

Likewise, more exposed cube area is not a measured reaction rate. Physical fragmentation, mineral alteration and transport need distinct evidence. The NPS weathering explanation provides the conceptual distinction; the storm simulation contains no mineral chemistry or sediment source attribution.

Write one supported result and two stronger claims that need further observations. For a real catchment comparison, useful records could include time-resolved rainfall, initial water conditions, soil entry or drainage measurements and discharge with consistent boundaries. An intervention claim would also need a design that addresses other differences, rather than assigning a causal land-cover label to our unchanged parameters.

Transfer: repair a universal-rule claim

A report says, “The concentrated storm produces 30 mm runoff, so every site receiving 60 mm in two hours must export 30 mm, erode the same soil mass and flood at the same time.” Replace this with a supported statement and identify the missing mechanisms.

Check the runoff-claims transfer

The original sealed-store model at zero initial storage produces 30 mm runoff for that profile under its 15 mm/hour entry cap and 40 mm capacity. Other initial conditions and processes can change the result. Sediment production/transport and downstream routing are absent, so soil mass and flood timing do not follow. This public explanation is practice, not independent field-model validation.

Apply

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

Distinguish accurate accounting from empirical validation or independent mastery.

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: Track initial water and remaining capacity Next: Why does air move?

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