Unit 2 — Atmosphere, infiltration and the soil zone

How do precipitation, soil structure, vegetation and energy partition rainfall between runoff, storage and vapor? The case-study setting is: Diagnose soil-water response to two contrasting storm sequences.. The central difficulty is that the same observed water level, hydrograph, concentration or land-surface change can arise from multiple physical causes. A course in hydrology becomes useful when students learn to infer processes cautiously rather than replacing a missing measurement with a convenient story. This unit integrates conservation laws, field observables and independent checks in a coherent investigation.

Background and field context

The same rainfall distributed over different soil, canopy and energy conditions. The investigation asks students to define a measurement support, write the governing equation with correct units, and make a prediction before inspecting hypothetical data. A high rainfall intensity does not guarantee high catchment runoff: infiltration capacity varies through an event, saturation patches can expand, and surface runoff may be disconnected from streams. Draw routing pathways through litter, upper soil, preferential macropores, lateral horizons and channels. Students should keep a concise field ledger indicating which variables were measured, which were derived, and which were assigned because the problem did not provide enough data.

The unifying tools are dimensional reasoning, boundary diagrams and comparison of rival conceptual models. Rainfall intensity, soil moisture, infiltration capacity, potential and actual evapotranspiration all become difficult when scales are mixed, when a sensor's datum is omitted, or when statistical fit is confused with causal evidence. Draw one section or plan view that labels land surface, relevant geological horizons, the stream or well network, and the water-transfer pathways under discussion. Give a sign convention to every flux. For quantities reported as volumes, identify the integration interval and contributing area. Explain why the chosen model domain includes or excludes neighboring exchanges.

Reading and learning outcomes

Students should be able to calculate a conditional result, describe at least two competing processes, identify limitations of measurement, and write a short reproducible report. Alongside the five lessons, the unit includes a synthetic laboratory dataset and two illustrative slider-driven equations. These models are deliberately simple: use them to see parameter sensitivity, not to recommend operational changes. Any inference about actual water quality, flood hazard or well yield requires site data, qualified review and the relevant authorities.

How the process works

Storm-total rainfall does not specify peak intensity or antecedent wetness. Short bursts may overwhelm infiltration or pipe capacity even when a daily total is moderate. Begin with a drawing of the physical stores and fluxes relevant to rain intensity and storm structure, showing both the water-bearing materials and the chosen observation boundary. Explain which forces move the water, solute or energy; identify the reference datum if hydraulic head or elevation is involved. A catchment outlet, soil column, well screen and river reach measure different domains. Never describe the value at one instrument as a universal property without a scaling argument. Distinguish a conservation relationship, which must hold for a correctly bounded system, from a constitutive equation, whose coefficients require calibration and whose validity is conditional on site conditions.

Evidence, ambiguity and falsifiable alternatives

Intensity-duration plots, radar time series, tipping-bucket tips and synoptic context help identify event structure. For every proposed observation, record units, location, date, time step, instrument support and an independent quality check. Sketch what is measured directly and what must be inferred. Estimate an error or detection limit if the result will be compared across sites or dates. Changes that are smaller than the relevant error should not be described as robust physical trends.

High measured intensity may arise from a partly blocked tipping-bucket that empties abruptly after sticking. A scientifically serious explanation must accommodate rival mechanisms. Identify what the preferred mechanism would predict at another time, depth or location. Choose a second type of evidence—geological context, temperature, chemical tracers, parallel reference catchments or independently surveyed elevations—rather than only refitting the same data. An observation that both models predict equally well is not a discriminating test.

Worked calculation — Rainfall intensity

Illustrative data: 66 mm precipitation over a 2.5 hour period. Equation or arithmetic: 66/2.5. Answer: 26.4 mm/hour. State why the inputs have compatible units, and explain which water store, flux, property, probability or statistic the output actually represents. For mixed units, write intermediate conversions explicitly. Distinguish the numerical answer from a claim about the real-world process: the answer follows from the invented inputs and the chosen equation, not from measurements of an actual catchment or aquifer.

Sensitivity and limits: This mean cannot reveal a 10-minute burst capable of exceeding infiltration capacity. If an input is changed by 20%, calculate the new output and describe whether the response is linear or nonlinear. Where appropriate, identify an excluded term or an assumption about spatial uniformity, stationarity, constant flow, conservative chemistry, or homogeneous porous media. This calculation cannot establish the excluded term is zero merely because it produces a tidy result.

Field or data investigation

Compare two storms with equal depths but contrasting temporal patterns; predict the runoff response under stated soil moisture. Put this in the unit investigation setting: The same rainfall distributed over different soil, canopy and energy conditions. Storm comparison; Separate depth, intensity, duration and initial moisture. The monitoring sheet should retain raw values, calibration and a flag for missing or questionable samples. Before interpreting a change, ask whether an independent instrument would observe the same sign and magnitude. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use a baseline scenario and an alternative scenario with an explicit change in just one assumption, so that the cause of the model's different output remains visible.

Interpretation and practical constraints

Design storms are statistical abstractions and should not be treated as guaranteed future storm sequences. Explain how equal totals can still generate different runoff peaks; Rework an event calculation with a shorter burst and longer recession. Break uncertainty into instrumental accuracy, insufficient temporal or spatial sampling, uncertain model coefficients and uncertainty about the governing mechanism itself. These sources can dominate in different circumstances. Report what could make a conclusion false, not merely a plus–minus range attached to a fitted number. An actual abstraction limit, well safety decision, contamination assessment or flood warning requires locally measured and professionally reviewed evidence.

Problems and answer checks

1. Calculation and units: reproduce the example and then change one input by 20%. Retain units at every line and verify that the result is dimensionally meaningful.

2. Scientific discrimination: write two competing explanations for the described observations, and give the exact sampling location, instrument and predicted difference that could resolve them.

3. Transferability: explain which key assumption is most likely to break in a different soil, geology, season, flow regime or monitoring technology. Design a quick test.

4. Evidence memo: distinguish observations, computed quantities and interpretations in a five-sentence note. State a follow-up observation that could reverse the judgment.

Answer guidance: a sound answer includes the governing relationship, a physically appropriate measurement boundary, checks on units and uncertainty, and one genuinely differentiating field test. Numerical precision alone does not strengthen an unsupported hydrologic interpretation.

How the process works

Infiltration is the downward crossing of the soil surface; percolation through the profile and recharge at the water table are later, distinct processes. Infiltration-excess and saturation-excess runoff have different controls. Begin with a drawing of the physical stores and fluxes relevant to infiltration and runoff partitioning, showing both the water-bearing materials and the chosen observation boundary. Explain which forces move the water, solute or energy; identify the reference datum if hydraulic head or elevation is involved. A catchment outlet, soil column, well screen and river reach measure different domains. Never describe the value at one instrument as a universal property without a scaling argument. Distinguish a conservation relationship, which must hold for a correctly bounded system, from a constitutive equation, whose coefficients require calibration and whose validity is conditional on site conditions.

Evidence, ambiguity and falsifiable alternatives

Tension infiltrometers, ring tests, soil-water sensors, ponding observations and runoff plots sample different scales and hydrologic conditions. For every proposed observation, record units, location, date, time step, instrument support and an independent quality check. Sketch what is measured directly and what must be inferred. Estimate an error or detection limit if the result will be compared across sites or dates. Changes that are smaller than the relevant error should not be described as robust physical trends.

Observed pooling may reflect low permeability, a perched saturated layer or surface sealing; a ring infiltrometer cannot diagnose all three. A scientifically serious explanation must accommodate rival mechanisms. Identify what the preferred mechanism would predict at another time, depth or location. Choose a second type of evidence—geological context, temperature, chemical tracers, parallel reference catchments or independently surveyed elevations—rather than only refitting the same data. An observation that both models predict equally well is not a discriminating test.

Worked calculation — Infiltration excess proxy

Illustrative data: Rain intensity 31 mm/hour and assumed infiltration capacity 19 mm/hour. Equation or arithmetic: 31-19. Answer: 12 mm/hour. State why the inputs have compatible units, and explain which water store, flux, property, probability or statistic the output actually represents. For mixed units, write intermediate conversions explicitly. Distinguish the numerical answer from a claim about the real-world process: the answer follows from the invented inputs and the chosen equation, not from measurements of an actual catchment or aquifer.

Sensitivity and limits: When antecedent saturation changes capacity, the fixed-capacity proxy fails. If an input is changed by 20%, calculate the new output and describe whether the response is linear or nonlinear. Where appropriate, identify an excluded term or an assumption about spatial uniformity, stationarity, constant flow, conservative chemistry, or homogeneous porous media. This calculation cannot establish the excluded term is zero merely because it produces a tidy result.

Field or data investigation

Run a hypothetical rainfall simulator at two intensities with paired soil profiles, then compare runoff onset. Put this in the unit investigation setting: The same rainfall distributed over different soil, canopy and energy conditions. Surface versus subsurface; Distinguish infiltration, percolation and recharge boundaries. The monitoring sheet should retain raw values, calibration and a flag for missing or questionable samples. Before interpreting a change, ask whether an independent instrument would observe the same sign and magnitude. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use a baseline scenario and an alternative scenario with an explicit change in just one assumption, so that the cause of the model's different output remains visible.

Interpretation and practical constraints

A plot-scale infiltration rate is not a universal catchment-wide constant. Explain what ponding means under multiple hydrologic mechanisms; Test predictions for a compacted and a permeable reference plot. Break uncertainty into instrumental accuracy, insufficient temporal or spatial sampling, uncertain model coefficients and uncertainty about the governing mechanism itself. These sources can dominate in different circumstances. Report what could make a conclusion false, not merely a plus–minus range attached to a fitted number. An actual abstraction limit, well safety decision, contamination assessment or flood warning requires locally measured and professionally reviewed evidence.

Problems and answer checks

1. Calculation and units: reproduce the example and then change one input by 20%. Retain units at every line and verify that the result is dimensionally meaningful.

2. Scientific discrimination: write two competing explanations for the described observations, and give the exact sampling location, instrument and predicted difference that could resolve them.

3. Transferability: explain which key assumption is most likely to break in a different soil, geology, season, flow regime or monitoring technology. Design a quick test.

4. Evidence memo: distinguish observations, computed quantities and interpretations in a five-sentence note. State a follow-up observation that could reverse the judgment.

Answer guidance: a sound answer includes the governing relationship, a physically appropriate measurement boundary, checks on units and uncertainty, and one genuinely differentiating field test. Numerical precision alone does not strengthen an unsupported hydrologic interpretation.

How the process works

Capillary and matric forces hold unsaturated water; hydraulic conductivity drops as pores drain. Field capacity and wilting point are practical conventions, not invariant material constants. Begin with a drawing of the physical stores and fluxes relevant to soil water potential and retention, showing both the water-bearing materials and the chosen observation boundary. Explain which forces move the water, solute or energy; identify the reference datum if hydraulic head or elevation is involved. A catchment outlet, soil column, well screen and river reach measure different domains. Never describe the value at one instrument as a universal property without a scaling argument. Distinguish a conservation relationship, which must hold for a correctly bounded system, from a constitutive equation, whose coefficients require calibration and whose validity is conditional on site conditions.

Evidence, ambiguity and falsifiable alternatives

Soil-water retention curves, tensiometers, time-domain reflectometry and texture descriptions jointly constrain soil-state interpretation. For every proposed observation, record units, location, date, time step, instrument support and an independent quality check. Sketch what is measured directly and what must be inferred. Estimate an error or detection limit if the result will be compared across sites or dates. Changes that are smaller than the relevant error should not be described as robust physical trends.

Low sensor readings may arise from poor contact, salinity effects or calibration drift rather than severe drying. A scientifically serious explanation must accommodate rival mechanisms. Identify what the preferred mechanism would predict at another time, depth or location. Choose a second type of evidence—geological context, temperature, chemical tracers, parallel reference catchments or independently surveyed elevations—rather than only refitting the same data. An observation that both models predict equally well is not a discriminating test.

Worked calculation — Root-zone available water

Illustrative data: Water contents 0.30 and 0.13 m³/m³ with 0.8 m effective rooting depth. Equation or arithmetic: (0.30-0.13)0.81000. Answer: 136 mm. State why the inputs have compatible units, and explain which water store, flux, property, probability or statistic the output actually represents. For mixed units, write intermediate conversions explicitly. Distinguish the numerical answer from a claim about the real-world process: the answer follows from the invented inputs and the chosen equation, not from measurements of an actual catchment or aquifer.

Sensitivity and limits: Not all calculated storage is accessible if roots are distributed unevenly. If an input is changed by 20%, calculate the new output and describe whether the response is linear or nonlinear. Where appropriate, identify an excluded term or an assumption about spatial uniformity, stationarity, constant flow, conservative chemistry, or homogeneous porous media. This calculation cannot establish the excluded term is zero merely because it produces a tidy result.

Field or data investigation

Calculate plant-available water within a rooted depth and compare sands with clays under declared thresholds. Put this in the unit investigation setting: The same rainfall distributed over different soil, canopy and energy conditions. Root-zone water; Compare potential, moisture and root-accessible storage. The monitoring sheet should retain raw values, calibration and a flag for missing or questionable samples. Before interpreting a change, ask whether an independent instrument would observe the same sign and magnitude. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use a baseline scenario and an alternative scenario with an explicit change in just one assumption, so that the cause of the model's different output remains visible.

Interpretation and practical constraints

Volumetric water content is not pressure head; equal contents can have different potentials. Explain why a specific sensor calibration may fail in saline soil; Recalculate available storage after changing the effective rooting depth. Break uncertainty into instrumental accuracy, insufficient temporal or spatial sampling, uncertain model coefficients and uncertainty about the governing mechanism itself. These sources can dominate in different circumstances. Report what could make a conclusion false, not merely a plus–minus range attached to a fitted number. An actual abstraction limit, well safety decision, contamination assessment or flood warning requires locally measured and professionally reviewed evidence.

Problems and answer checks

1. Calculation and units: reproduce the example and then change one input by 20%. Retain units at every line and verify that the result is dimensionally meaningful.

2. Scientific discrimination: write two competing explanations for the described observations, and give the exact sampling location, instrument and predicted difference that could resolve them.

3. Transferability: explain which key assumption is most likely to break in a different soil, geology, season, flow regime or monitoring technology. Design a quick test.

4. Evidence memo: distinguish observations, computed quantities and interpretations in a five-sentence note. State a follow-up observation that could reverse the judgment.

Answer guidance: a sound answer includes the governing relationship, a physically appropriate measurement boundary, checks on units and uncertainty, and one genuinely differentiating field test. Numerical precision alone does not strengthen an unsupported hydrologic interpretation.

How the process works

Evaporation requires both available energy and vapor removal. Net radiation, sensible heat, latent heat and ground storage share an energy balance whose closure is often imperfect in observations. Begin with a drawing of the physical stores and fluxes relevant to evaporation and energy balance, showing both the water-bearing materials and the chosen observation boundary. Explain which forces move the water, solute or energy; identify the reference datum if hydraulic head or elevation is involved. A catchment outlet, soil column, well screen and river reach measure different domains. Never describe the value at one instrument as a universal property without a scaling argument. Distinguish a conservation relationship, which must hold for a correctly bounded system, from a constitutive equation, whose coefficients require calibration and whose validity is conditional on site conditions.

Evidence, ambiguity and falsifiable alternatives

Radiometers, humidity and wind instruments, lysimeters and eddy-covariance towers measure complementary quantities. For every proposed observation, record units, location, date, time step, instrument support and an independent quality check. Sketch what is measured directly and what must be inferred. Estimate an error or detection limit if the result will be compared across sites or dates. Changes that are smaller than the relevant error should not be described as robust physical trends.

A high evaporation estimate may be an instrument footprint error or an energy-closure correction rather than a change in available water. A scientifically serious explanation must accommodate rival mechanisms. Identify what the preferred mechanism would predict at another time, depth or location. Choose a second type of evidence—geological context, temperature, chemical tracers, parallel reference catchments or independently surveyed elevations—rather than only refitting the same data. An observation that both models predict equally well is not a discriminating test.

Worked calculation — Energy-equivalent evaporation

Illustrative data: Average latent heat flux 100 W/m² for one day with 2.45 MJ/kg latent heat. Equation or arithmetic: 100*86400/2.45e6. Answer: 3.5265 mm/day. State why the inputs have compatible units, and explain which water store, flux, property, probability or statistic the output actually represents. For mixed units, write intermediate conversions explicitly. Distinguish the numerical answer from a claim about the real-world process: the answer follows from the invented inputs and the chosen equation, not from measurements of an actual catchment or aquifer.

Sensitivity and limits: Energy availability may be different from actual flux under strong soil-water limitation. If an input is changed by 20%, calculate the new output and describe whether the response is linear or nonlinear. Where appropriate, identify an excluded term or an assumption about spatial uniformity, stationarity, constant flow, conservative chemistry, or homogeneous porous media. This calculation cannot establish the excluded term is zero merely because it produces a tidy result.

Field or data investigation

Convert a net energy flux to an equivalent evaporated depth with a declared latent heat value and exposure interval. Put this in the unit investigation setting: The same rainfall distributed over different soil, canopy and energy conditions. Energy limitation; Convert energy flux to latent-heat equivalent depth. The monitoring sheet should retain raw values, calibration and a flag for missing or questionable samples. Before interpreting a change, ask whether an independent instrument would observe the same sign and magnitude. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use a baseline scenario and an alternative scenario with an explicit change in just one assumption, so that the cause of the model's different output remains visible.

Interpretation and practical constraints

Potential evapotranspiration differs from actual water-limited flux; a reference-crop value is not all vegetation. Separate energy-limited and soil-water-limited evaporation; Compare an open-water evaporation assumption with a dry field. Break uncertainty into instrumental accuracy, insufficient temporal or spatial sampling, uncertain model coefficients and uncertainty about the governing mechanism itself. These sources can dominate in different circumstances. Report what could make a conclusion false, not merely a plus–minus range attached to a fitted number. An actual abstraction limit, well safety decision, contamination assessment or flood warning requires locally measured and professionally reviewed evidence.

Problems and answer checks

1. Calculation and units: reproduce the example and then change one input by 20%. Retain units at every line and verify that the result is dimensionally meaningful.

2. Scientific discrimination: write two competing explanations for the described observations, and give the exact sampling location, instrument and predicted difference that could resolve them.

3. Transferability: explain which key assumption is most likely to break in a different soil, geology, season, flow regime or monitoring technology. Design a quick test.

4. Evidence memo: distinguish observations, computed quantities and interpretations in a five-sentence note. State a follow-up observation that could reverse the judgment.

Answer guidance: a sound answer includes the governing relationship, a physically appropriate measurement boundary, checks on units and uncertainty, and one genuinely differentiating field test. Numerical precision alone does not strengthen an unsupported hydrologic interpretation.

How the process works

Canopy interception can evaporate without wetting the soil; root uptake and stomatal regulation influence transpiration and soil-water depletion. Vegetation also changes aerodynamic roughness and infiltration. Begin with a drawing of the physical stores and fluxes relevant to vegetation, interception and transpiration, showing both the water-bearing materials and the chosen observation boundary. Explain which forces move the water, solute or energy; identify the reference datum if hydraulic head or elevation is involved. A catchment outlet, soil column, well screen and river reach measure different domains. Never describe the value at one instrument as a universal property without a scaling argument. Distinguish a conservation relationship, which must hold for a correctly bounded system, from a constitutive equation, whose coefficients require calibration and whose validity is conditional on site conditions.

Evidence, ambiguity and falsifiable alternatives

Throughfall gauges, sap-flux measurements, lysimeters and soil-moisture profiles provide different partitions of ecosystem water use. For every proposed observation, record units, location, date, time step, instrument support and an independent quality check. Sketch what is measured directly and what must be inferred. Estimate an error or detection limit if the result will be compared across sites or dates. Changes that are smaller than the relevant error should not be described as robust physical trends.

A post-clearing streamflow increase may be influenced by rainfall variability, road compaction or catchment disturbance. A scientifically serious explanation must accommodate rival mechanisms. Identify what the preferred mechanism would predict at another time, depth or location. Choose a second type of evidence—geological context, temperature, chemical tracers, parallel reference catchments or independently surveyed elevations—rather than only refitting the same data. An observation that both models predict equally well is not a discriminating test.

Worked calculation — Canopy interception estimate

Illustrative data: 20 mm open-field rainfall, 14 mm throughfall and 1 mm stemflow. Equation or arithmetic: 20-14-1. Answer: 5 mm. State why the inputs have compatible units, and explain which water store, flux, property, probability or statistic the output actually represents. For mixed units, write intermediate conversions explicitly. Distinguish the numerical answer from a claim about the real-world process: the answer follows from the invented inputs and the chosen equation, not from measurements of an actual catchment or aquifer.

Sensitivity and limits: A single event cannot establish an annual interception fraction. If an input is changed by 20%, calculate the new output and describe whether the response is linear or nonlinear. Where appropriate, identify an excluded term or an assumption about spatial uniformity, stationarity, constant flow, conservative chemistry, or homogeneous porous media. This calculation cannot establish the excluded term is zero merely because it produces a tidy result.

Field or data investigation

Construct a paired-plot canopy water balance and propose a controlled comparison to identify interception loss. Put this in the unit investigation setting: The same rainfall distributed over different soil, canopy and energy conditions. Land-cover influence; Account for canopy, soil and root water stores separately. The monitoring sheet should retain raw values, calibration and a flag for missing or questionable samples. Before interpreting a change, ask whether an independent instrument would observe the same sign and magnitude. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use a baseline scenario and an alternative scenario with an explicit change in just one assumption, so that the cause of the model's different output remains visible.

Interpretation and practical constraints

Sap flux does not directly measure whole-catchment evapotranspiration without scaling and calibration. Explain confounding by roads, clearing and changed rainfall; Design a paired-plot comparison with throughfall and sap measurements. Break uncertainty into instrumental accuracy, insufficient temporal or spatial sampling, uncertain model coefficients and uncertainty about the governing mechanism itself. These sources can dominate in different circumstances. Report what could make a conclusion false, not merely a plus–minus range attached to a fitted number. An actual abstraction limit, well safety decision, contamination assessment or flood warning requires locally measured and professionally reviewed evidence.

Problems and answer checks

1. Calculation and units: reproduce the example and then change one input by 20%. Retain units at every line and verify that the result is dimensionally meaningful.

2. Scientific discrimination: write two competing explanations for the described observations, and give the exact sampling location, instrument and predicted difference that could resolve them.

3. Transferability: explain which key assumption is most likely to break in a different soil, geology, season, flow regime or monitoring technology. Design a quick test.

4. Evidence memo: distinguish observations, computed quantities and interpretations in a five-sentence note. State a follow-up observation that could reverse the judgment.

Answer guidance: a sound answer includes the governing relationship, a physically appropriate measurement boundary, checks on units and uncertainty, and one genuinely differentiating field test. Numerical precision alone does not strengthen an unsupported hydrologic interpretation.

Research task. The same rainfall distributed over different soil, canopy and energy conditions Start from the attached datasets/unit-02-synthetic.csv. The records are deliberately fictional and provide no local environmental observations. The learner's deliverable is a short technical notebook, a table of measurements and conversions, a controlled comparison between two interpretations, and a one-page statement of residual uncertainty.

Phase A — conceptual diagram. A high rainfall intensity does not guarantee high catchment runoff: infiltration capacity varies through an event, saturation patches can expand, and surface runoff may be disconnected from streams. Draw routing pathways through litter, upper soil, preferential macropores, lateral horizons and channels. Each observation has a spatial footprint; annotate which terms would require a point sample, area-average estimate or volumetric balance. For groundwater, show screened intervals and vertical datum. For rivers, mark the measurement section and route. For water chemistry, identify concentration, flow and analyte units. A diagram that omits the boundary often hides the missing flux that later produces an apparently anomalous numerical result.

Phase B — independent calculation. A patch of surface water after a storm might be locally saturated, mechanically compacted or underlain by a shallow impermeable layer. A one-hour infiltration experiment does not distinguish them without additional depth observations. Use at least two independent calculation approaches where possible. Compare the result against a sanity bound: storage cannot be below a declared physically admissible minimum, chemical mixing fractions should lie between zero and one under the assumed ideal endmembers, and a probability cannot exceed unity. Round only after combining inputs; retain raw values and intermediate results in a reproducible notebook.

Phase C — evaluate the alternative. Mass balance applies at each vertical boundary: throughfall, infiltration at surface, drainage below root zone and recharge at groundwater level are physically distinct quantities. Replace one assumption at a time. Include a small scenario table showing baseline, lower plausible input and upper plausible input, then a separate table for structural alternatives where equations themselves differ. Explain whether the compared outcomes cross a chosen decision threshold. If no real-world decision threshold has been justified, label the result descriptive only rather than declaring a policy winner.

Phase D — submit a traceable report. Include the following in one coherent narrative: (a) research question and ethical scope, (b) boundary and major water or solute pathways, (c) original invented records, (d) exact equation and dimensional checks, (e) rival mechanisms and discriminating observations, (f) sensitivity or uncertainty table, and (g) a short conclusion distinguishing the measurement from its interpretation. State why the data cannot justify a real-world site decision.

Unit synthesis

Every lesson above contributes a different constraint to the integrated investigation. Cross-check a mass balance against a physically plausible flow path; cross-check a statistical summary against a documented measurement interval; and cross-check a model-derived conclusion against an independent observation wherever feasible. Report what evidence would overturn the preferred conclusion. The appropriate scientific endpoint is not a graph that looks convincing, but an interpretation that remains defensible when another researcher can inspect its data, assumptions and alternatives.