Groundwater, Rivers and Contaminant Transport

By the end of this unit students should be able to (a) diagram relevant stocks, flows, feedbacks and boundaries; (b) identify at least two mechanisms compatible with incomplete data; (c) compute the unit-consistent screen and recognize its simplifying assumptions; (d) design a measured contrast or control; (e) discuss the difference between evidence for a process and the ethical choice of response; and (f) prepare a short decision note with uncertainty, stakeholder impacts and specific follow-up actions.

2.1 Watersheds and hydrologic budgets

Core mechanism and governing scale. Precipitation is apportioned among evaporation, transpiration, infiltration, streamflow and change in storage. The identity P = ET + Q + ΔS becomes useful only after choosing a consistent area, interval and treatment of subsurface imports and exports. Rain gauges miss spatial gradients; stream gauges measure runoff after routing and storage delays. This is a physical claim about a set of processes, not a description of a single visible feature. To use it rigorously, distinguish the quantity being measured from a proxy and draw an explicit spatial and temporal boundary. If the relevant mass or energy can cross that boundary, the investigator must consider transfers as well as any material produced or consumed internally. A strong explanation predicts how a change in forcing would alter at least two independently observable consequences. Identify those predictions before seeing the sample data, so an initially appealing interpretation can genuinely be rejected.

Site investigation. Use a seasonal watershed with headwater rain, irrigated lowlands and a downstream gauging station. Compare the sign of inferred storage change after a dry season and a wet season. Write the site description in a way that another geoscientist can reconstruct the comparison. Record location, elevation or depth, coordinate system, local time, sampling interval, instrument settings, quality-control flags and any reason observations were excluded. A sample label should distinguish a point from a mixture of points, and a laboratory result should identify the phase analyzed: filtered water, whole water, sediment, porewater or another material. For a process that varies after rainfall, one visit gives a snapshot rather than a stable baseline. Use pre-event and post-event observations where the mechanism makes a temporal prediction.

Working with competing explanations. A residual is not automatically groundwater recharge. It may combine measurement error, unmeasured diversion and a mismatch between rainfall and discharge timing. Formulate two alternative mechanisms that could plausibly produce the observation, then specify a measurement that would discriminate them. Merely collecting more measurements of the same ambiguous quantity may increase precision without increasing explanatory power. Test whether the apparent change can arise from sensor drift, dilution, sample composition, changed boundary conditions or an unrelated common driver. A transparent analysis reports which explanations were evaluated and which remain unresolved. Numerical agreement between a model and data is not a sufficient test if the model parameters were selected using those same data.

Decision interpretation. Close a water balance with uncertainty ranges before using a residual to justify groundwater licensing. State the practical action that could change under the result, then calculate how an error in the parameter would affect that action. For a preliminary screening study, use conservative but explicit uncertainty bounds rather than claim exact compliance. Distinguish a threshold from a causal mechanism: exceeding a screening value may justify follow-up, while remaining below it does not automatically prove no ecological or human-health impact. Prioritize measures that interrupt a credible exposure pathway if an urgent hazard is identified, and refer regulatory or public-health determinations to competent authorities.

Worked quantitative screen (2.1). storage. Use the wholly invented parameters P=1050 mm, ET=590 mm, Q=310 mm. The teaching expression is P − ET − Q; substitute consistently converted units to obtain 1050 − 590 − 310 = 150, or approximately 150 mm storage residual. The arithmetic illustrates the chosen model; it should not be mistaken for a field observation or a calibrated regulatory prediction. Ask whether doubling one input would double the output. If it would not, explain the nonlinearity. Name one missing parameter that could reverse a site decision despite this seemingly precise result.

2.2 Darcy flow and hydraulic gradients

Core mechanism and governing scale. For saturated laminar flow through a porous material, Darcy's relation gives volumetric discharge Q = K i A, with hydraulic conductivity K, gradient i and cross-sectional area A. The seepage velocity is greater than Darcy flux by the inverse of effective porosity. Fractured bedrock and preferential pathways can violate assumptions of homogeneous porous flow. This is a physical claim about a set of processes, not a description of a single visible feature. To use it rigorously, distinguish the quantity being measured from a proxy and draw an explicit spatial and temporal boundary. If the relevant mass or energy can cross that boundary, the investigator must consider transfers as well as any material produced or consumed internally. A strong explanation predicts how a change in forcing would alter at least two independently observable consequences. Identify those predictions before seeing the sample data, so an initially appealing interpretation can genuinely be rejected.

Site investigation. Measure heads at three wells screened in the same aquifer and infer a horizontal gradient. Sketch how a low-permeability lens can bend the flow field and confine a dissolved plume. Write the site description in a way that another geoscientist can reconstruct the comparison. Record location, elevation or depth, coordinate system, local time, sampling interval, instrument settings, quality-control flags and any reason observations were excluded. A sample label should distinguish a point from a mixture of points, and a laboratory result should identify the phase analyzed: filtered water, whole water, sediment, porewater or another material. For a process that varies after rainfall, one visit gives a snapshot rather than a stable baseline. Use pre-event and post-event observations where the mechanism makes a temporal prediction.

Working with competing explanations. Water-table elevation from wells of different screened depths can suggest false horizontal flow. Well construction and pumping status matter as much as map distances. Formulate two alternative mechanisms that could plausibly produce the observation, then specify a measurement that would discriminate them. Merely collecting more measurements of the same ambiguous quantity may increase precision without increasing explanatory power. Test whether the apparent change can arise from sensor drift, dilution, sample composition, changed boundary conditions or an unrelated common driver. A transparent analysis reports which explanations were evaluated and which remain unresolved. Numerical agreement between a model and data is not a sufficient test if the model parameters were selected using those same data.

Decision interpretation. Use pilot testing and lithologic logs to qualify a back-of-envelope travel-time estimate. State the practical action that could change under the result, then calculate how an error in the parameter would affect that action. For a preliminary screening study, use conservative but explicit uncertainty bounds rather than claim exact compliance. Distinguish a threshold from a causal mechanism: exceeding a screening value may justify follow-up, while remaining below it does not automatically prove no ecological or human-health impact. Prioritize measures that interrupt a credible exposure pathway if an urgent hazard is identified, and refer regulatory or public-health determinations to competent authorities.

Worked quantitative screen (2.2). darcy. Use the wholly invented parameters K=0.0002 m/s, i=0.005, A=12 m². The teaching expression is K i A; substitute consistently converted units to obtain 0.0002 × 0.005 × 12 = 0.000012, or approximately 1.2e-05 m³/s. The arithmetic illustrates the chosen model; it should not be mistaken for a field observation or a calibrated regulatory prediction. Ask whether doubling one input would double the output. If it would not, explain the nonlinearity. Name one missing parameter that could reverse a site decision despite this seemingly precise result.

2.3 Advection, dispersion and sorption

Core mechanism and governing scale. Solutes travel through groundwater by bulk movement, molecular diffusion and mechanical dispersion. A retardation factor can represent reversible equilibrium sorption in an ideal linear system; non-equilibrium sorption and heterogeneous geochemistry can produce tails that this approximation misses. Mixing can reduce concentration without destroying contaminant mass. This is a physical claim about a set of processes, not a description of a single visible feature. To use it rigorously, distinguish the quantity being measured from a proxy and draw an explicit spatial and temporal boundary. If the relevant mass or energy can cross that boundary, the investigator must consider transfers as well as any material produced or consumed internally. A strong explanation predicts how a change in forcing would alter at least two independently observable consequences. Identify those predictions before seeing the sample data, so an initially appealing interpretation can genuinely be rejected.

Site investigation. Compare a conservative tracer with a sorbing solute in an artificial sand column. Record breakthrough times and the width of each response rather than only the peak. Write the site description in a way that another geoscientist can reconstruct the comparison. Record location, elevation or depth, coordinate system, local time, sampling interval, instrument settings, quality-control flags and any reason observations were excluded. A sample label should distinguish a point from a mixture of points, and a laboratory result should identify the phase analyzed: filtered water, whole water, sediment, porewater or another material. For a process that varies after rainfall, one visit gives a snapshot rather than a stable baseline. Use pre-event and post-event observations where the mechanism makes a temporal prediction.

Working with competing explanations. An apparent disappearance from the water phase may mean transfer to sediment rather than complete degradation. Inverse inference from one well alone is poorly constrained. Formulate two alternative mechanisms that could plausibly produce the observation, then specify a measurement that would discriminate them. Merely collecting more measurements of the same ambiguous quantity may increase precision without increasing explanatory power. Test whether the apparent change can arise from sensor drift, dilution, sample composition, changed boundary conditions or an unrelated common driver. A transparent analysis reports which explanations were evaluated and which remain unresolved. Numerical agreement between a model and data is not a sufficient test if the model parameters were selected using those same data.

Decision interpretation. Specify whether a remedial objective is lower dissolved concentration, lower transported mass or lower cumulative exposure. State the practical action that could change under the result, then calculate how an error in the parameter would affect that action. For a preliminary screening study, use conservative but explicit uncertainty bounds rather than claim exact compliance. Distinguish a threshold from a causal mechanism: exceeding a screening value may justify follow-up, while remaining below it does not automatically prove no ecological or human-health impact. Prioritize measures that interrupt a credible exposure pathway if an urgent hazard is identified, and refer regulatory or public-health determinations to competent authorities.

Worked quantitative screen (2.3). retard. Use the wholly invented parameters rho=1.5 kg/L, Kd=0.8 L/kg, n=0.3. The teaching expression is 1 + rho Kd / n; substitute consistently converted units to obtain 1 + (1.5 × 0.8) ÷ 0.3 = 5, or approximately 5 dimensionless. The arithmetic illustrates the chosen model; it should not be mistaken for a field observation or a calibrated regulatory prediction. Ask whether doubling one input would double the output. If it would not, explain the nonlinearity. Name one missing parameter that could reverse a site decision despite this seemingly precise result.

2.4 Water quality and geochemical fingerprints

Core mechanism and governing scale. Electrical conductivity, pH, dissolved oxygen, temperature, alkalinity and specific ion ratios help interpret water chemistry, but none uniquely identifies a pollutant source. Oxygen, iron and sulfate reactions vary with redox conditions. Chemical speciation may control toxicity and mobility more strongly than total element concentration. This is a physical claim about a set of processes, not a description of a single visible feature. To use it rigorously, distinguish the quantity being measured from a proxy and draw an explicit spatial and temporal boundary. If the relevant mass or energy can cross that boundary, the investigator must consider transfers as well as any material produced or consumed internally. A strong explanation predicts how a change in forcing would alter at least two independently observable consequences. Identify those predictions before seeing the sample data, so an initially appealing interpretation can genuinely be rejected.

Site investigation. Compare fictional upstream and downstream profiles, preserving field meter calibration checks and duplicate samples. Examine chloride as a possible conservative indicator while checking for other sources. Write the site description in a way that another geoscientist can reconstruct the comparison. Record location, elevation or depth, coordinate system, local time, sampling interval, instrument settings, quality-control flags and any reason observations were excluded. A sample label should distinguish a point from a mixture of points, and a laboratory result should identify the phase analyzed: filtered water, whole water, sediment, porewater or another material. For a process that varies after rainfall, one visit gives a snapshot rather than a stable baseline. Use pre-event and post-event observations where the mechanism makes a temporal prediction.

Working with competing explanations. A laboratory 'non-detect' indicates that concentration was below a stated reporting limit, not necessarily zero. Preserved and unpreserved samples may behave differently. Formulate two alternative mechanisms that could plausibly produce the observation, then specify a measurement that would discriminate them. Merely collecting more measurements of the same ambiguous quantity may increase precision without increasing explanatory power. Test whether the apparent change can arise from sensor drift, dilution, sample composition, changed boundary conditions or an unrelated common driver. A transparent analysis reports which explanations were evaluated and which remain unresolved. Numerical agreement between a model and data is not a sufficient test if the model parameters were selected using those same data.

Decision interpretation. Choose laboratory methods and detection limits with intended exposure decisions in mind, and publish uncertainty alongside concentrations. State the practical action that could change under the result, then calculate how an error in the parameter would affect that action. For a preliminary screening study, use conservative but explicit uncertainty bounds rather than claim exact compliance. Distinguish a threshold from a causal mechanism: exceeding a screening value may justify follow-up, while remaining below it does not automatically prove no ecological or human-health impact. Prioritize measures that interrupt a credible exposure pathway if an urgent hazard is identified, and refer regulatory or public-health determinations to competent authorities.

Worked quantitative screen (2.4). dilution. Use the wholly invented parameters C0=12 mg/L, Q0=20 L/s, Qtotal=100 L/s. The teaching expression is C0 Q0 / Qtotal; substitute consistently converted units to obtain 12 × 20 ÷ 100 = 2.4, or approximately 2.4 mg/L. The arithmetic illustrates the chosen model; it should not be mistaken for a field observation or a calibrated regulatory prediction. Ask whether doubling one input would double the output. If it would not, explain the nonlinearity. Name one missing parameter that could reverse a site decision despite this seemingly precise result.

2.5 Exposure pathways and safe water decisions

Core mechanism and governing scale. A complete exposure pathway links a source, transport medium, contact location, route and receptor. A contaminant in an inaccessible deep horizon may have a different exposure significance from the same concentration in a shallow drinking-water well. Alternative supply, wellhead protection and land-use controls can sometimes reduce exposure before the source is fully remediated. This is a physical claim about a set of processes, not a description of a single visible feature. To use it rigorously, distinguish the quantity being measured from a proxy and draw an explicit spatial and temporal boundary. If the relevant mass or energy can cross that boundary, the investigator must consider transfers as well as any material produced or consumed internally. A strong explanation predicts how a change in forcing would alter at least two independently observable consequences. Identify those predictions before seeing the sample data, so an initially appealing interpretation can genuinely be rejected.

Site investigation. Construct a conceptual model that includes domestic wells, irrigation canals, fish ponds and seasonal flood transfers. Mark hypothetical ingestion, dermal and food-chain pathways separately. Write the site description in a way that another geoscientist can reconstruct the comparison. Record location, elevation or depth, coordinate system, local time, sampling interval, instrument settings, quality-control flags and any reason observations were excluded. A sample label should distinguish a point from a mixture of points, and a laboratory result should identify the phase analyzed: filtered water, whole water, sediment, porewater or another material. For a process that varies after rainfall, one visit gives a snapshot rather than a stable baseline. Use pre-event and post-event observations where the mechanism makes a temporal prediction.

Working with competing explanations. Do not equate screening exceedances automatically with a diagnosed health effect. Site-specific toxicology, duration, background sources and measurement quality require qualified assessment. Formulate two alternative mechanisms that could plausibly produce the observation, then specify a measurement that would discriminate them. Merely collecting more measurements of the same ambiguous quantity may increase precision without increasing explanatory power. Test whether the apparent change can arise from sensor drift, dilution, sample composition, changed boundary conditions or an unrelated common driver. A transparent analysis reports which explanations were evaluated and which remain unresolved. Numerical agreement between a model and data is not a sufficient test if the model parameters were selected using those same data.

Decision interpretation. For a drinking-water concern, favor verified regulatory guidance and public-health expertise over an educational calculator; preserve sample custody records. State the practical action that could change under the result, then calculate how an error in the parameter would affect that action. For a preliminary screening study, use conservative but explicit uncertainty bounds rather than claim exact compliance. Distinguish a threshold from a causal mechanism: exceeding a screening value may justify follow-up, while remaining below it does not automatically prove no ecological or human-health impact. Prioritize measures that interrupt a credible exposure pathway if an urgent hazard is identified, and refer regulatory or public-health determinations to competent authorities.

Worked quantitative screen (2.5). pathways. Use the wholly invented parameters active=3 paths, considered=8 paths. The teaching expression is active / considered × 100; substitute consistently converted units to obtain 3 ÷ 8 × 100 = 37.5, or approximately 37.5 percent of hypothesized pathways. The arithmetic illustrates the chosen model; it should not be mistaken for a field observation or a calibrated regulatory prediction. Ask whether doubling one input would double the output. If it would not, explain the nonlinearity. Name one missing parameter that could reverse a site decision despite this seemingly precise result.

Research brief. Construct cross sections through a fictional fertilized field, old disposal pit, drainage channel and four wells with different screened intervals. Work with the accompanying datasets/unit-02-synthetic.csv file. The data are deliberately synthetic and not observations from a real study. Students must not use the outputs to locate actual pollution or certify safety. Before drawing a graph, write down the spatial and temporal extent of the question, the target population of inference, and the causal alternative being examined. If these differ across competing hypotheses, explicitly state the difference rather than changing the question after plotting the data.

Initial scenario evidence. Peak stream nitrate occurs during storms, yet shallow well solute increases months later. Chloride remains low at a deeper screened location. An appropriate notebook records the stated evidence separately from new calculations and speculative explanations. Construct a table with source, transport medium, receptor, measurement, unit, time stamp and quality flag. Do not automatically interpolate through a gap. Describe what direct observations could distinguish spatial gradients from a measurement artifact. Think carefully about whether measurements made on the same day are independent: weather, laboratory batches and access constraints can introduce common disturbances.

Hypothesis comparison. Separate advective travel, temporary storage, nitrification, denitrification and dilution. A deep well measurement cannot serve as the sole control for a shallow plume. Express each hypothesis as a short process chain, from cause to transport or transformation and then to observable consequence. For each chain, describe a finding that would weaken it even if the original observation remained true. This is more demanding than simply asking students to find supporting evidence. Write a four-row evidence matrix containing current observations, ambiguous clues, missing observations and tests capable of discrimination. Use a mixture of field observations and existing institutional records rather than putting the entire burden on the laboratory assay.

Measurement design. Select a reference location, a likely impact location and at least one location that tests the suspected transport direction. Plan a repeat period long enough to capture the dominant forcing, with a predeclared justification for the number and location of samples. Document the measurement unit, calibration procedure, field duplicate, transport method, chain-of-custody practice when needed and appropriate data-handling permissions. Explain what a non-detect means in relation to the reporting limit. If the accessible sampling locations omit vulnerable groups, state how that limitation affects the conclusion rather than quietly treating data absence as exposure absence.

Quantitative analysis. Read the CSV and calculate the mean, range and a simple temporal contrast for one indicator. Plot indicator against the forcing variable and inspect outliers on the original scale before considering transformation. Report the result with units and avoid inferring causation from one correlation coefficient. Test sensitivity to removal of one observation, alternative grouping of sites and plausible systematic error. If a variable is coded as a toy index, keep it clearly labeled as such; there is no physical unit hiding behind a derived ranking. A good report includes a notebook where a reader can reproduce every number without proprietary data access.

Uncertainty and decision. Compare re-sampling, point-of-use water alternatives and source controls with monitoring criteria. Which first action requires the least uncertain source attribution? List which uncertainties are reducible through new measurements and which depend on social values or future land-use choices. Produce at least two recommendations: a near-term low-regret action and a longer-term investigation or remediation option. For each, state the measurable trigger that would alter the recommendation and the organization that must act. An unexplained rank ordering is weaker than a transparent comparison across environment, health, fairness, time, cost and implementability. If a real-world hazard were suspected, qualified professionals and local authorities would have to replace these toy values with regulatory procedures.

Deliverables and review rubric. Submit a labeled site diagram; a one-page hypothesis table; a reproducible calculation file; a figure whose axis labels include units; a paragraph describing alternative mechanisms; a decision table with at least three choices; and an evidence-quality note. Award 20% for physically plausible mechanisms, 20% for transparent data provenance, 20% for unit-consistent arithmetic and uncertainty checks, 20% for discriminating experiment design and 20% for decision clarity and treatment of affected stakeholders. A polished figure alone receives no substitute credit for missing science.

Construct a two-page dossier for a mixed agricultural–industrial watershed with shallow domestic wells. Start with a map or cross-section of the physical environment, then list stocks, fluxes or forces that operate on multiple time scales. Use one instrument observation, one derived physical quantity, one sensitivity test and one clearly identified decision assumption. Organize claims by evidence quality and specify what additional field or laboratory result would change the conclusion. A scientifically defensible exercise may conclude that the available fictional evidence is insufficient for strong attribution.

For peer review, exchange dossiers and ask a partner to locate unsupported causal leaps, missing mass-balance terms, numerical unit mistakes and hidden stakeholder costs. The reviewer should mark every model parameter as measured, calibrated, hypothesized or fixed for teaching. In a revision note, explain what changed and what remains unknown. Do not substitute an unverified AI summary or a single plotted trend for this explicit review process.

Mastery test: Define the core process in one paragraph, show one correct calculation with units, draw two plausible mechanisms capable of producing the same initial observation and give a measurement that separates them. Make a separate recommendation that identifies who benefits or bears costs; explicitly label which part is scientific inference and which part is a value-based decision.