C3 · Publication Volume 13

Sampling Design

orientation surveys, spacing, support, duplicates and field practice

Learning goals

The learner should be able to convert a decision into a target population and sampling frame; use an orientation survey to estimate footprint, variance and failure conditions; set location, spacing, direction, support and field practice coherently; distinguish duplicates from independent samples; and write acceptance, redesign and stopping rules before seeing the production data.

Sampling design is not a regular grid drawn over a map. It is the joint design of inference, material support, spatial selection, field execution, quality control and follow-up. A dense but biased sample frame can be less informative than a sparse probability-based or process-stratified design. The correct density depends on footprint, variability and action, not on a customary number.

Decision, population and measurand

Begin with the action the survey may change. Regional screening, catchment prioritisation, anomaly boundary definition, process discrimination and baseline characterisation require different populations and error tolerances. Define the target population as material units, not just coordinates: for example, a specified horizon and size fraction within residual process domains over the accessible study area.

The sampling frame is the operational list or geometry from which locations can be selected. Coverage gaps, inaccessible ground, missing streams and disturbed areas make it differ from the target population. Record those gaps as unknown or out-of-frame; do not colour them as background. A design-based inference requires known inclusion logic, while a model-based inference requires an explicit spatial or process model. Convenience selection supports only limited claims.

Define the measurand as quantity, material, preparation, extraction and unit. “Element X concentration” is incomplete. “Mass fraction of X recovered from the less-than-specified fraction of the stated horizon by the stated extraction, on a dry-mass basis” is auditable. If method or fraction changes, the measurand changes even if the column name does not.

Orientation surveys and adaptive learning

An orientation survey tests the entire signal chain over contrasting source, background, transported and disturbed settings. It asks whether the medium exists consistently; which horizon and fraction carry a coherent response; how signal changes across and along expected dispersion; what mass and spacing control variance; whether preservation and limits are adequate; and which control samples diagnose expected failures.

Predefine alternatives. A strong response over the source supports sensitivity, but a similarly strong response in transported or disturbed controls may destroy specificity. A weak response may reflect unsuitable medium, support or method rather than absence of a source. Include repeat visits or nested increments where temporal or small-scale variation is expected.

Adaptive redesign is legitimate when versioned. Freeze orientation data, decision rules and lessons before changing production design. Do not merge an early coarse design with a later refined design without recording phase, inclusion probability and support. Prospective validation should use new areas or samples that were not used to tune the rule.

Geometry, spacing and support

Design direction across the expected footprint where possible. Line spacing controls the chance of crossing an elongated feature; station spacing controls resolution along a line. In drainage designs, tributary topology and catchment area replace Euclidean spacing as primary geometry. In irregular terrains, stratification by process domain may be more defensible than forcing a uniform grid.

Sampling design connects the decision, orientation evidence, spatial geometry, physical support and staged quality controls
Sampling design connects the decision, orientation evidence, spatial geometry, physical support and staged quality controls

Support includes collected footprint, depth or horizon, number of increments, total field mass, retained fraction, split mass and analytical aliquot. Increasing composite increments can reduce local heterogeneity but also averages narrow signals. Larger support is not automatically better. Match support to the minimum footprint that must influence the action.

Randomisation protects against batch and time trends. Randomise or balance analytical order across spatial blocks and expected concentration groups, while preserving control placement. If field collection order follows geography for safety and efficiency, analytical randomisation can reduce confounding between location and instrument drift. Retain both orders.

Field practice, duplicates and control placement

A field protocol specifies site selection tolerance, material acceptance, horizon or depth, tools, cleaning, increment pattern, mass, container, label, observations, photographs, coordinates, preservation, transport and exceptions. Train with real materials before production. The protocol should say when not to collect, when to relocate, and when a sample is non-comparable.

A field duplicate is a second sample collected under a defined duplicate protocol. Adjacent independent grabs, split field material and repeated measurements estimate different variance components. Label roles in hidden or neutral ways where practical, but never lose their identity in the audit record. Duplicate frequency alone is not quality; spatial distribution and stage coverage matter.

Insert blanks where contamination can occur, reference materials where accuracy and batch comparability can be evaluated, and duplicates where precision matters. Distribute them through the sequence. Controls clustered at the batch end cannot reveal a short early drift. Include enough controls to detect the failure size that would change the survey decision, not merely to satisfy a percentage convention.

Worked synthetic example

A synthetic orientation line crosses a predicted 120 m-wide footprint. Samples are collected every 40 m, so an unfavourable offset still yields at least two or three stations within the footprint. Observed log-concentration standard deviation within a uniform background subdomain is 0.36. A four-increment composite is proposed. If increments are approximately independent at that small scale, the standard deviation of their mean log signal is

$0.36/\sqrt{4}=0.18.$

If nearby increments have average pairwise correlation \rho=0.30, the variance of a four-increment mean becomes

$\sigma_{\bar{x}}^2=\frac{\sigma^2}{4}\left[1+(4-1)\rho\right],$

giving standard deviation 0.36\sqrt{(1+0.9)/4}=0.248. The independence assumption was optimistic. The composite still reduces local variability, but less than expected.

Suppose the footprint could narrow to 50 m. A 40 m station interval may yield one or two points and provide poor boundary definition. The response is not automatically to sample the whole project at 20 m. A staged design can retain 40 m screening and infill only lines with coherent process evidence. The decision rule, not visual preference, determines infill.

Design audit workflow

  1. Name the decision, target population and smallest relevant footprint.
  2. Define medium, horizon, fraction, mass, preparation, extraction and unit.
  3. Map frame exclusions, process domains and expected signal direction.
  4. Design orientation contrasts and predefine sensitivity and specificity tests.
  5. Choose line, station or network geometry relative to the footprint.
  6. Set support using heterogeneity, particle size and required resolution.
  7. Place controls across field, preparation and analytical stages.
  8. Separate collection order, submission order and analytical order.
  9. Predefine acceptance, infill, redesign and stop rules.
  10. Version the design and validate tuned rules on genuinely new observations.

Practice and review

  1. Design an orientation survey that compares two soil horizons, two fractions and a transported control domain without confounding method and location.
  2. Recalculate the composite standard deviation for six increments and pairwise correlation 0.20.
  3. Explain why a field duplicate placed beside every twentieth routine sample may still fail to cover the important variance.
  4. Draw a sampling frame that shows inaccessible areas and state what inference remains valid.
  5. Write a staged infill rule for a narrow synthetic footprint.

Review questions: What population is being inferred? What does one sample physically support? Does geometry cross the predicted footprint? Which variance component does each duplicate estimate? What change would trigger redesign?

Sources and further reading