Find your next learning step
Legacy soil sites are valuable because they preserve history, yet they often cluster where access was easy or an earlier question was urgent. A map-update design must protect that history without mistaking convenience for population representation.
Open the chapter contents · Soil Science root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the question, or read from Chapter 1 for the complete argument. The teaching chapters remain open; these grouped routes form the index.
Route 1 · Define the target population
Route 2 · Work the sample
Route 3 · Design the update
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE TARGET POPULATION
1. A soil map inherits the geography of its samples
Legacy soil observations are often concentrated near roads, research farms, accessible slopes or earlier problem areas. They may be chemically careful and historically valuable while still failing to represent the current mapping population.
Spatially balanced probability sampling spreads inclusion across a defined region while retaining known selection probabilities. Generalized random tessellation stratified designs and related master samples combine broad spatial coverage with randomization, allowing design-based estimation and flexible changes in sample size.
This guide extends the Soil Science root, spatial cross-validation and the area of applicability. Validation measures transfer after sampling; design decides which landscape conditions can enter the evidence in the first place.
CHAPTER 2 OF 12 · DEFINE THE TARGET POPULATION
2. Define the target population before choosing points
The target may be all agricultural topsoil in a district, all 20-metre raster cells, or every field management unit. Specify boundaries, depth interval, date or season, excluded land, and the measurement protocol. A sample cannot be representative of an undefined population.
Give each eligible unit a known inclusion probability. Equal probabilities are simple, but unequal probabilities can oversample rare soils, vulnerable land uses or costly strata. The resulting design weights must follow the actual selection, including replacements and nonresponse.
Spatial balance complements, rather than replaces, probability sampling. A perfectly even hand-picked grid has unknown design probabilities if access decisions are made informally after seeing the terrain.
CHAPTER 3 OF 12 · WORK THE SAMPLE
3. Worked population: convenience creates bias
Consider eight equal-area cells with an original teaching soil-carbon value. The full population mean is 44/8 = 5.5.
| Cell | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Carbon value | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Legacy convenience set | Yes | Yes | Yes | Yes | No | No | No | No |
| Balanced probability set | Yes | No | Yes | No | No | Yes | No | Yes |
The legacy mean is (2+3+4+5)/4 = 3.5, two units below the population mean because the sites occupy one end of the gradient. The balanced set uses cells 1, 3, 6 and 8, with mean (2+4+7+9)/4 = 5.5.
The balanced set happens to match exactly in this example; that is not guaranteed. Its scientific advantage is the randomized, known-probability design and broad coverage, not a promise of zero error.
CHAPTER 4 OF 12 · WORK THE SAMPLE
4. Inclusion probabilities support a design-based estimate
If four of eight equal cells are selected with first-order inclusion probability pi = 0.5, the Horvitz–Thompson total estimate is the sum of observed y_i divided by pi_i. For the balanced set it is (2+4+7+9)/0.5 = 44. Dividing by eight gives mean 5.5.
Unequal probabilities require their actual weights. If inaccessible sites are replaced outside the prespecified rule, the probabilities change. Keeping the original weight after an informal substitution creates a false design-based claim.
Record the ordered master sample, reserve points, eligibility screen, contact attempts, refusal or access reason, replacement rule and final inclusion probabilities. Field logistics are part of the estimator.
CHAPTER 5 OF 12 · WORK THE SAMPLE
5. Legacy sites need an explicit role
Legacy sites can anchor trend because they have earlier measurements. They can also improve model calibration if their protocols and coordinates are compatible. But treating a purposive legacy set as if it were a current equal-probability sample can bias status estimates.
One approach fixes legacy sites and selects new sites so the combined network is spatially balanced. Foster and colleagues developed designs that incorporate legacy locations while maintaining balance among the full set. The inference still depends on which sites are probability-selected and which are fixed.
Publish separate labels: legacy-repeat, new-probability, calibration-only and validation-holdout. A row should not silently change roles between model fitting and accuracy assessment.
CHAPTER 6 OF 12 · DESIGN THE UPDATE
6. A panel design separates status, trend and mapping
Different questions need different revisit patterns.
| Panel | Typical sites | Main question | Key protection |
|---|---|---|---|
| Permanent legacy-repeat | Historically measured sites | How did these locations change? | Protocol harmonization |
| Rotating probability panel | Spatially balanced new sites | What is current population status? | Known inclusion weights |
| Rare-domain oversample | Scarce soil or land-use strata | Are uncommon domains represented? | Unequal-probability weights |
| Independent validation | Held out from modelling | How well does the map transfer? | Geographic and analytical separation |
An ordered master sample lets managers add or defer sites while keeping spatial spread. Panel membership should be chosen before current outcomes are observed. Repeat sites improve change precision; rotating sites refresh geographic coverage.
CHAPTER 7 OF 12 · DESIGN THE UPDATE
7. Changed context: access removes difficult terrain
Steep, wet or privately controlled areas are often the first to disappear from fieldwork. If access is related to soil properties, complete-case analysis can be biased. A longer reserve list helps only when replacements follow the same prespecified design.
Map response and access rates by stratum. Use design adjustments or response models when justified, and report domains with weak coverage. Remote-sensing covariates may guide substitution but cannot manufacture laboratory measurements for a missing soil process.
The transfer question is whether the unsampled locations differ merely in logistics or also in the outcome mechanism.
CHAPTER 8 OF 12 · DESIGN THE UPDATE
8. Changed context: covariate balance is not spatial balance
Conditioned Latin hypercube sampling spreads sites through environmental covariate space; GRTS spreads them geographically with design probabilities. A sample can excel at one and leave holes in the other.
For digital soil mapping, consider a hybrid or stratified design that protects rare covariate combinations while retaining geographic dispersion. Stumpf and colleagues describe a design that incorporates field operability and legacy soil samples in conditioned Latin hypercube sampling.
Do not optimize the sample against the final model’s test set. Reserve independent validation before model selection, or use a validation design matched to the intended deployment.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and common misconceptions
Spatial balance does not guarantee covariate balance, and neither guarantees an unbiased estimate without valid inclusion probabilities and response handling. A regular grid is not automatically a probability sample. More sites do not repair systematic exclusion.
Legacy data are not “bad data”. Their value depends on the question: excellent for long-term change at those locations, potentially biased for current population status, and useful for modelling after protocol and support differences are reconciled.
Design weights and model-based predictions answer different inferential questions. Keep both available rather than allowing a flexible model to erase the sampling history.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Evidence and reproducibility route
Stevens and Olsen present the generalized random tessellation stratified framework in Spatially Balanced Sampling of Natural Resources. Foster and colleagues develop Spatially balanced designs that incorporate legacy sites. For soil-specific field constraints, see Incorporating limited field operability and legacy soil samples in a hypercube sampling design.
A reproducible package preserves the target-population frame, map projection, sampling algorithm and seed, ordered master sample, inclusion probabilities, strata, legacy-site role, panel assignment, reserve sequence, access outcomes, replacements, field and laboratory protocols, depth harmonization, coordinates with privacy controls, weights, estimator code and validation exclusions.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Should every legacy site be revisited?
Not necessarily. Revisit sites that serve a defined trend question and add probability sites for representative status. Budget and protocol continuity matter.
Can I combine legacy and new observations in one model?
Yes, after checking depth, method, date, support and selection differences. Preserve site origin as metadata and evaluate sensitivity to legacy-site influence.
Why keep reserve points ordered?
The order allows substitutions or sample-size changes while preserving the design’s spatial balance more faithfully than ad hoc nearest-road replacement.
Is the closest unsampled cell the best next site?
Not always. Value depends on inclusion balance, covariate novelty, decision importance, access and whether the site serves status, trend or validation.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Final transfer check and connected reading
Before updating a soil network, answer six questions: What exact population is represented? Which sites have known inclusion probabilities? Which legacy sites serve trend rather than status? How are inaccessible sites replaced? Are mapping and validation roles separated? Does the combined network cover geography and important covariate domains?
Continue through the Soil Science root, spatial cross-validation, the area of applicability, the Gold Standard of Education and the How X Works hub. The transferable skill is to protect historical continuity while keeping present-day population inference honest.
Top · Contents · Previous · How X Works