Sediments, tracers and the critical zone

When do observed chemical fingerprints genuinely identify sediment sources and reaction histories?

Synthetic field investigation. A synthetic river delta receives upland and urban sediment; grain-size sorting, chemical weathering and hydrodynamic transport act together. The setting, sampling values and numerical observations are invented for instruction; they do not describe a monitored site or an operational geochemical assessment. Compare at least two hypotheses before drawing conclusions, and make every material balance dimensionally explicit.

By the end of this unit, students should be able to name the relevant reservoirs, express governing relations with units, calculate at least one interpretable quantity, check a competing explanation, and specify what extra observation would increase confidence. The worked calculations are tightly simplified and do not constitute a validated geochemical speciation model, a professional environmental investigation or a public-health threshold determination.

Mechanism and why it matters

Elemental and isotopic compositions can help constrain sediment origins when endmembers differ and signatures are conserved. Identify the named chemical phase and its exchange boundaries. Distinguish measured species totals from inferred reactions; one pattern can have several mechanisms.

Sampling and measurement protocol

Analyze grain-size fractions consistently and include mineralogical and transport indicators. Record phase, sampling support, date, concentration or ratio units, calibration and detection limit. Define which quantities are observed and which depend on an assumed model.

Competing explanations and identifiability

Hydraulic sorting can change a bulk chemical signal without a change in sediment source. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Provenance mixing fraction

Problem. Sample tracer is 70 mg/kg, source A 40 and B 100; conservative A fraction=(B-sample)/(B-A).

Mathematical setup: (100-70)/(100-40). After checking the listed mass, time and amount units, the calculated answer is 0.5 fraction. Write down the inputs separately from the chosen constant or reference so an independent reviewer can recompute the result. If the expression uses a logarithm or a ratio, confirm that its argument is dimensionless; if a molar amount is involved, convert grams to moles before applying reaction coefficients. Because the values are invented for this lesson, the arithmetic demonstrates the physical scale and not a measurement-derived regional conclusion.

Sensitivity check. Compare the sign and magnitude with a limiting case and perturb the main input by ten percent. Report whether the relationship is linear or nonlinear, and avoid overstating numerical precision.

Targeted investigation and practical interpretation

Solve a two-endmember concentration mixing fraction. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Provenance limitation

Chemical fingerprints are sensitive to particle size, mineral sorting and post-depositional change. A mixing result is conditional on source endmembers being correctly sampled, stable and sufficiently distinct. Check the result against isotopic, petrographic or mineralogical evidence before interpreting a fractional contribution.

Knowledge check and research questions

1. Recalculate the numerical example using consistent units.
2. Which competing physical process could reproduce the observation?
3. Which new measurement would discriminate the mechanisms?
4. Which assumed parameter creates the greatest model sensitivity?

Instructor benchmark. 0.5 fraction, conditional on the stated model and units.

Mechanism and why it matters

Fine particles, oxides and organic matter commonly concentrate some elements relative to coarse quartz-rich fractions. Identify the named chemical phase and its exchange boundaries. Distinguish measured species totals from inferred reactions; one pattern can have several mechanisms.

Sampling and measurement protocol

Compare size-normalized concentrations and use appropriate background values rather than universal thresholds. Record phase, sampling support, date, concentration or ratio units, calibration and detection limit. Define which quantities are observed and which depend on an assumed model.

Competing explanations and identifiability

High elemental abundance may reflect natural mineralogy and does not itself establish biological exposure. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Partition coefficient

Problem. Sediment has 50 mg/kg, overlying water 0.5 mg/L; calculate Kd.

Mathematical setup: 50/0.5. After checking the listed mass, time and amount units, the calculated answer is 100 L/kg. Write down the inputs separately from the chosen constant or reference so an independent reviewer can recompute the result. If the expression uses a logarithm or a ratio, confirm that its argument is dimensionless; if a molar amount is involved, convert grams to moles before applying reaction coefficients. Because the values are invented for this lesson, the arithmetic demonstrates the physical scale and not a measurement-derived regional conclusion.

Sensitivity check. Compare the sign and magnitude with a limiting case and perturb the main input by ten percent. Report whether the relationship is linear or nonlinear, and avoid overstating numerical precision.

Targeted investigation and practical interpretation

Calculate a sediment–water partition coefficient. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Provenance limitation

Chemical fingerprints are sensitive to particle size, mineral sorting and post-depositional change. A mixing result is conditional on source endmembers being correctly sampled, stable and sufficiently distinct. Check the result against isotopic, petrographic or mineralogical evidence before interpreting a fractional contribution.

Knowledge check and research questions

1. Recalculate the numerical example using consistent units.
2. Which competing physical process could reproduce the observation?
3. Which new measurement would discriminate the mechanisms?
4. Which assumed parameter creates the greatest model sensitivity?

Instructor benchmark. 100 L/kg, conditional on the stated model and units.

Mechanism and why it matters

Rare-earth element patterns are convention-dependent tools for comparative interpretation, with anomalies sensitive to redox and minerals. Identify the named chemical phase and its exchange boundaries. Distinguish measured species totals from inferred reactions; one pattern can have several mechanisms.

Sampling and measurement protocol

Keep the normalization reference and handling of below-detection measurements explicit. Record phase, sampling support, date, concentration or ratio units, calibration and detection limit. Define which quantities are observed and which depend on an assumed model.

Competing explanations and identifiability

Eu and Ce anomalies are not single-process labels; redox and mineral sorting may both matter. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Normalized ideal anomaly

Problem. Element Eu_N = 0.75; adjacent references Sm_N=1.0 and Gd_N=1.0; anomaly Eu_N/sqrt(Sm_N*Gd_N).

Mathematical setup: 0.75/math.sqrt(1.0*1.0). After checking the listed mass, time and amount units, the calculated answer is 0.75 dimensionless. Write down the inputs separately from the chosen constant or reference so an independent reviewer can recompute the result. If the expression uses a logarithm or a ratio, confirm that its argument is dimensionless; if a molar amount is involved, convert grams to moles before applying reaction coefficients. Because the values are invented for this lesson, the arithmetic demonstrates the physical scale and not a measurement-derived regional conclusion.

Sensitivity check. Compare the sign and magnitude with a limiting case and perturb the main input by ten percent. Report whether the relationship is linear or nonlinear, and avoid overstating numerical precision.

Targeted investigation and practical interpretation

Compute an idealized normalized anomaly. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Provenance limitation

Chemical fingerprints are sensitive to particle size, mineral sorting and post-depositional change. A mixing result is conditional on source endmembers being correctly sampled, stable and sufficiently distinct. Check the result against isotopic, petrographic or mineralogical evidence before interpreting a fractional contribution.

Knowledge check and research questions

1. Recalculate the numerical example using consistent units.
2. Which competing physical process could reproduce the observation?
3. Which new measurement would discriminate the mechanisms?
4. Which assumed parameter creates the greatest model sensitivity?

Instructor benchmark. 0.75 dimensionless, conditional on the stated model and units.

Mechanism and why it matters

Dry and wet deposition add external material that may later be stored, dissolved or remobilized. Identify the named chemical phase and its exchange boundaries. Distinguish measured species totals from inferred reactions; one pattern can have several mechanisms.

Sampling and measurement protocol

Deploy paired collectors, use blanks and measure area plus exposure duration. Record phase, sampling support, date, concentration or ratio units, calibration and detection limit. Define which quantities are observed and which depend on an assumed model.

Competing explanations and identifiability

A collector can overestimate dust deposition if resuspended local soil dominates its catch. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Deposition flux

Problem. Collector area 0.5 m2 catches 1.5 g over 30 days; compute g/m2/day.

Mathematical setup: 1.5/(0.5*30). After checking the listed mass, time and amount units, the calculated answer is 0.1 g/m2/day. Write down the inputs separately from the chosen constant or reference so an independent reviewer can recompute the result. If the expression uses a logarithm or a ratio, confirm that its argument is dimensionless; if a molar amount is involved, convert grams to moles before applying reaction coefficients. Because the values are invented for this lesson, the arithmetic demonstrates the physical scale and not a measurement-derived regional conclusion.

Sensitivity check. Compare the sign and magnitude with a limiting case and perturb the main input by ten percent. Report whether the relationship is linear or nonlinear, and avoid overstating numerical precision.

Targeted investigation and practical interpretation

Calculate annualized deposition flux from collector mass. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Provenance limitation

Chemical fingerprints are sensitive to particle size, mineral sorting and post-depositional change. A mixing result is conditional on source endmembers being correctly sampled, stable and sufficiently distinct. Check the result against isotopic, petrographic or mineralogical evidence before interpreting a fractional contribution.

Knowledge check and research questions

1. Recalculate the numerical example using consistent units.
2. Which competing physical process could reproduce the observation?
3. Which new measurement would discriminate the mechanisms?
4. Which assumed parameter creates the greatest model sensitivity?

Instructor benchmark. 0.1 g/m2/day, conditional on the stated model and units.

Mechanism and why it matters

Soil, regolith, plants and streams form coupled stores with residence times and flow paths. Identify the named chemical phase and its exchange boundaries. Distinguish measured species totals from inferred reactions; one pattern can have several mechanisms.

Sampling and measurement protocol

Write a system balance and separate storage change, incoming fluxes, outgoing fluxes and unobserved pathways. Record phase, sampling support, date, concentration or ratio units, calibration and detection limit. Define which quantities are observed and which depend on an assumed model.

Competing explanations and identifiability

Instantaneous output composition rarely identifies a single source uniquely in a spatially heterogeneous watershed. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Critical-zone storage residual

Problem. Input 120 kg/y, output 92 kg/y, estimated gaseous loss 8 kg/y; compute accumulation.

Mathematical setup: 120-92-8. After checking the listed mass, time and amount units, the calculated answer is 20 kg/year. Write down the inputs separately from the chosen constant or reference so an independent reviewer can recompute the result. If the expression uses a logarithm or a ratio, confirm that its argument is dimensionless; if a molar amount is involved, convert grams to moles before applying reaction coefficients. Because the values are invented for this lesson, the arithmetic demonstrates the physical scale and not a measurement-derived regional conclusion.

Sensitivity check. Compare the sign and magnitude with a limiting case and perturb the main input by ten percent. Report whether the relationship is linear or nonlinear, and avoid overstating numerical precision.

Targeted investigation and practical interpretation

Calculate a residual storage term and discuss its physical meaning. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Provenance limitation

Chemical fingerprints are sensitive to particle size, mineral sorting and post-depositional change. A mixing result is conditional on source endmembers being correctly sampled, stable and sufficiently distinct. Check the result against isotopic, petrographic or mineralogical evidence before interpreting a fractional contribution.

Knowledge check and research questions

1. Recalculate the numerical example using consistent units.
2. Which competing physical process could reproduce the observation?
3. Which new measurement would discriminate the mechanisms?
4. Which assumed parameter creates the greatest model sensitivity?

Instructor benchmark. 20 kg/year, conditional on the stated model and units.

('Delta sediment fingerprinting', 'Synthesize two sediment sources that differ in element concentration and grain-size distribution. Mix the endmembers at known mass fractions, then add quartz sorting and an oxide sorption factor. Compare chemical-source solutions before and after size normalization. Discuss whether normalization to an immobile element improves source attribution. Write a validation plan using mineralogy and an isotope marker not included in the fit.')

Design and controls

Before computing any numbers, list the intended mechanistic question, the sampling unit, plausible confounding influences and the criteria for rejecting a proposed explanation. Separate control treatments from replicates. Specify one independent check that was not used to choose model coefficients, since a model cannot be validated merely by predicting its own calibration inputs. Synthetic scenarios are safe for classroom inference but do not replace field permissions, contamination control or specialist laboratory work.

A complete synthetic data record

Use a header with the following fields: sample_id, phase, dry_mass_g or volume_L, chemical_species, measured_value, analytical_unit, uncertainty, model_assumption, replicate_id and observation_status. Every derived column should include a formula and an audit trail. Avoid blanks that could ambiguously mean zero; label missing or below-quantification values explicitly. The class should archive its original input table and a derived working table so updates to calculations cannot overwrite evidence.

Expected result and alternatives

Analyze the invented measurements with the simplest mass balance or equilibrium relationship appropriate to the question. Choose plausible parameter ranges before looking at the pattern. Next deliberately generate an alternative dataset under a different process that yields a similar headline gradient. Explain which additional variable, sampling depth, time series or reference material would distinguish them. This step addresses the practical reality that geological and chemical processes are often nonunique when seen through sparse observations.

Sensitivity and uncertainty

Build a one-at-a-time sensitivity table varying at least two inputs by 5%, 10% and 20%. Use a separate scenario for systematic calibration shift, because correlated bias does not vanish by averaging independent samples. Include sampling uncertainty when a large reservoir is represented by a few rock chips or bottles. Report the resulting range as a model-conditioned bound rather than an objectively measured confidence interval unless a statistical sampling model was justified.

Interpretation and reporting

The final deliverable is a short field-style memo with a figure, a unit-checked table, a reproducible calculation and two rival explanations. Distinguish measured variables from estimated parameters by typography or column label. Provide the domain where the simple model is defensible, including temperature, composition and phase assumptions. Avoid making health, engineering or management decisions from synthetic data; those require validated data and appropriate regulatory and professional guidance.

Further experimental design

Propose two follow-up observations and rank them by discrimination power, cost and likelihood of analytical bias. A new sample that merely repeats the same confounded measurement may reduce noise without reducing the ambiguity of the hypothesis. A strategically chosen cross-phase, isotope or seasonal measurement can be more informative. Set a stopping rule: what numerical discrepancy or missing diagnostic signature would be sufficient to reject the favored model?

Research notebook prompts

1. At checkpoint 1, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
2. At checkpoint 2, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
3. At checkpoint 3, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
4. At checkpoint 4, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
5. At checkpoint 5, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
6. At checkpoint 6, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
7. At checkpoint 7, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.
8. At checkpoint 8, identify which assumptions in investigation 7 are directly tested, which still require external constraints, and how one alternative reaction or transport pathway could change the conclusion without necessarily altering the measured primary tracer. Record the expected sign of the change and the observation that would distinguish it.

The correct output of a geochemical investigation is not just a fitted number. A defensible conclusion links an observation to a specific physical or chemical mechanism while making conditional assumptions explicit. In this unit, write a three-column comparison: observed or invented data, quantitative model result, and possible geological explanation. Any statement that relies on a presumed endmember, reference standard or equilibrium assumption belongs in the last two columns. For a stronger claim, propose observations that would separate mechanism from coincidence.

Independent short assessment

• Choose one of the five numerical cases and reconstruct it using a different sequence of unit conversions. Confirm that the dimensions still cancel.
• Choose the most important environmental, geological or laboratory confounder from the five lessons. Explain whether it creates random scatter, systematic bias or a genuine alternative Earth process.
• Choose two variables of different spatial scales and explain why plotting them on the same grid would not establish causation.
• Write a transparent uncertainty statement: data are fictional, reference assumptions are specified, sensitivity has been tested, and a professional application requires additional measurements.

Suggested group discussion

Compare a precise but unrepresentative measurement with a noisy but representative sampling design. The former may look more convincing in a graph yet produce a more biased inventory or flux. Discuss a case where adding more significant digits does not improve geological accuracy. Discuss whether a model with a near-perfect fit has proved its reaction pathway or merely fitted several free parameters. End by identifying one prediction not used in the original fit, and describe how a prospective measurement could potentially falsify the process model.