Weathering, soils and biogeochemical cycles

How do weathering, erosion, life and climate jointly influence element fluxes?

Synthetic field investigation. A constructed upland soil chronosequence receives dust and loses bases in drainage; unmeasured export terms are included in its uncertainty budget. 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

Silicate weathering commonly removes mobile cations relative to less mobile Al, but compositional indices depend on mineralogy. 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

Use molar oxide proportions, correct CaO from non-silicates when possible, and report provenance caveats. 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

Different parent rocks can yield different index values even under identical weathering intensity. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Chemical index of alteration

Problem. Molar Al2O3=0.45, CaO*=0.10, Na2O=0.15, K2O=0.30; CIA percent.

Mathematical setup: 100*0.45/(0.45+0.10+0.15+0.30). After checking the listed mass, time and amount units, the calculated answer is 45 percent. 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 a chemical index of alteration from molar oxide inputs. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Time and transport

Flux follows the product of concentration and carrier transport only when measurements represent the same interval. Inventories describe storage, not instantaneous flow. For annual estimates, storm-driven changes and dry-season gaps should be treated as systematic sources of uncertainty rather than hidden by extra decimal places.

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. 45 percent, conditional on the stated model and units.

Mechanism and why it matters

Clay minerals and organic matter supply exchange sites; base saturation estimates the fraction occupied by specified basic cations. 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 exchange units consistent and document pH-dependent capacity and extraction method. 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 base saturation does not prove low contamination or suitability for agriculture without further evidence. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Base saturation

Problem. Basic exchange cations=8 cmolc/kg, CEC=12 cmolc/kg; percent.

Mathematical setup: 100*8/12. After checking the listed mass, time and amount units, the calculated answer is 66.6667 percent. 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 percent base saturation from exchange equivalents. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Time and transport

Flux follows the product of concentration and carrier transport only when measurements represent the same interval. Inventories describe storage, not instantaneous flow. For annual estimates, storm-driven changes and dry-season gaps should be treated as systematic sources of uncertainty rather than hidden by extra decimal places.

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. 66.6667 percent, conditional on the stated model and units.

Mechanism and why it matters

Annual export depends on both dissolved concentration and discharge, including seasonality and storm pulses. 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

Integrate load over time rather than multiplying a single grab sample by an annual flow. 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 few rainy-season samples can dominate export while being missed by a dry-season monitoring program. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Annual solute export

Problem. Constant 2 mg/L at 0.4 m3/s over 365 days; kilograms exported.

Mathematical setup: 20.4100036524*3600/1e6. After checking the listed mass, time and amount units, the calculated answer is 25228.8 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

Estimate an annual mass export from a constant classroom discharge. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Time and transport

Flux follows the product of concentration and carrier transport only when measurements represent the same interval. Inventories describe storage, not instantaneous flow. For annual estimates, storm-driven changes and dry-season gaps should be treated as systematic sources of uncertainty rather than hidden by extra decimal places.

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. 25228.8 kg, conditional on the stated model and units.

Mechanism and why it matters

Weathering can consume atmospheric CO2 on certain timescales, while carbonate weathering and eventual marine precipitation complicate the net balance. 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

Use balanced reaction stoichiometry and declare geological timescale and carbonate-system boundary. 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

An assumed one-to-one CO2 removal for every mole of dissolved cation often overstates the net effect. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — CO2 stoichiometric upper bound

Problem. Idealized silicate reaction consumes two mol CO2 per mol mineral; for 0.75 mol calculate consumption.

Mathematical setup: 2*0.75. After checking the listed mass, time and amount units, the calculated answer is 1.5 mol CO2. 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 an upper-bound molar CO2 consumption from specified reaction. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Time and transport

Flux follows the product of concentration and carrier transport only when measurements represent the same interval. Inventories describe storage, not instantaneous flow. For annual estimates, storm-driven changes and dry-season gaps should be treated as systematic sources of uncertainty rather than hidden by extra decimal places.

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. 1.5 mol CO2, conditional on the stated model and units.

Mechanism and why it matters

Microbial activity and vegetation influence element cycling through uptake, remineralization and redox transformations. 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

Measure biomass production and elemental content, with a separate pathway for leaching and gaseous loss. 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 nutrient inventory change could arise from external deposition rather than only biological uptake. Specify an independently testable observation capable of distinguishing this explanation from an alternative source, reaction or laboratory bias.

Worked numerical example — Biological elemental uptake

Problem. 20 kg dry plant matter with 1.2 wt% phosphorus; calculate phosphorus mass in kg.

Mathematical setup: 20*1.2/100. After checking the listed mass, time and amount units, the calculated answer is 0.24 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 nutrient uptake from mass and tissue concentration. Create a six-row synthetic table with inputs, predicted outputs and one replicate. Compare a rival process and document a falsifiable difference.

Advanced reasoning: Time and transport

Flux follows the product of concentration and carrier transport only when measurements represent the same interval. Inventories describe storage, not instantaneous flow. For annual estimates, storm-driven changes and dry-season gaps should be treated as systematic sources of uncertainty rather than hidden by extra decimal places.

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. 0.24 kg, conditional on the stated model and units.

('Soil chronosequence', 'Create three hypothetical profiles with oxide composition, cation-exchange measurements, river discharge and wet deposition. Normalize the oxide measurements on a molar basis, correct the Ca component where appropriate and calculate a chemical index of alteration. Construct a material budget with one unresolved incoming dust term. Test whether the same CIA pattern might arise from parent-rock composition rather than only exposure duration.')

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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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.