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Choose a route or read from the beginning. All teaching chapters stay open; the grouped index below is expandable.
Define the climate target
Chapters 1–2. Separate calendar weighting from proxy production.
Work the seasonal cases
Chapters 3–5. Hold the annual mean fixed while changing the proxy.
Explain the apparent trend
Chapters 6–8. Decompose weight changes and test calibration transfer.
Evaluate the evidence
Chapters 9–10. Check seasonality and answer practical questions.
Practise and continue
Chapters 11–12. Use changed seasons and archive-specific reading.
Full chapter index · Practice and worked checks · Palaeoclimatology subject root
A proxy record changes while the annual mean temperature stays the same. That can happen if the warm and cool seasons change differently, or if the archive records a different share of each season.
This guide builds an original two-season forward model, keeps annual climate separate from proxy production and tests what a baseline calibration can legitimately carry into another period. The temperatures and weights are fictional. The example neither reconstructs a real historical interval nor claims that all proxies have the same seasonal response.
Chapter index
Define the climate target · Chapters 1–2
1. Name the climate target before interpreting the proxy
2. Separate calendar weights from production weights
Work the seasonal cases · Chapters 3–5
3. Establish a baseline without declaring it universal
4. Hold the annual mean fixed and change the seasonal contrast
5. Change recording weights without changing annual climate
Explain the apparent trend · Chapters 6–8
6. Decompose the change instead of assigning one cause
7. Keep each anomaly tied to its reference
8. Explain why a modern calibration may transfer incompletely
Evaluate the evidence · Chapters 9–10
9. Seek evidence that distinguishes the explanations
10. Questions readers ask
Practise and continue · Chapters 11–12
11. Transfer checks with worked answers
12. Continue by the missing archive or timing question
CHAPTER 1 OF 12 · Define the climate target
1. Name the climate target before interpreting the proxy
An annual mean, a growing-season mean and a winter temperature are different climate quantities. A record can be useful and accurately measured while being better suited to one target than another.
A proxy’s response can reflect when organisms grow, when material is produced, the habitat represented and how the archive preserves that material. The laboratory measurement also needs a calibration model. A measured isotope ratio or ring width is not literally the weighted temperature used in this teaching example.
We work with a hypothetical temperature-equivalent proxy value P after a stipulated ideal linear conversion. That deliberately removes other complications so the effect of seasonality can be inspected. In a real study, proxy formation and the conversion would need their own evidence and uncertainty account.
CHAPTER 2 OF 12 · Define the climate target
2. Separate calendar weights from production weights
Divide the model year into two equal-duration halves, with warm-half mean S and cool-half mean W. Its true annual mean is A = 0.50S + 0.50W. Equal half-year duration is an assumption, not a claim that every real seasonal division has equal length.
Let the proxy instead weight the warm half by w and the cool half by 1 − w, so P = wS + (1 − w)W. The weights describe the proxy’s stipulated recording process. They do not change the calendar duration of either half.
Subtracting gives P − A = (w − 0.50)(S − W). A seasonally selective proxy differs from the annual target according to both its weighting and the seasonal contrast. Those quantities should not be conflated.
CHAPTER 3 OF 12 · Work the seasonal cases
3. Establish a baseline without declaring it universal
Choose a baseline with S₀ = 20 °C and W₀ = 0 °C. The annual mean is A₀ = 10 °C. With proxy weight w₀ = 0.80, its temperature-equivalent value is P₀ = 0.80 × 20 + 0.20 × 0 = 16 °C.
Suppose the classroom conversion to annual temperature is A_est = P − 6 °C. It reproduces the baseline: 16 − 6 = 10 °C. This one-point agreement does not establish the conversion’s validity for every possible seasonal history.
If both halves warm by the same 1 °C and weights stay fixed, the annual mean and proxy each rise by 1 °C. That particular pattern transfers correctly through the conversion. The next cases change the relationship that made it work.
CHAPTER 4 OF 12 · Work the seasonal cases
4. Hold the annual mean fixed and change the seasonal contrast
Let an earlier fictional state have S₁ = 18 °C and W₁ = 2 °C. Its annual mean is still 10 °C, but seasonal contrast falls from 20 °C to 16 °C.
Keeping w = 0.80 gives P₁ = 0.80 × 18 + 0.20 × 2 = 14.8 °C. The proxy anomaly relative to its baseline is −1.2 °C, while the annual anomaly is zero. The baseline conversion would report A_est = 8.8 °C instead of 10 °C.
| Model state | Warm half S, °C | Cool half W, °C | Warm proxy weight | Annual mean A, °C | Proxy P, °C |
|---|---|---|---|---|---|
| Baseline | 20 | 0 | 0.80 | 10 | 16.0 |
| Reduced contrast, same weight | 18 | 2 | 0.80 | 10 | 14.8 |
| Baseline seasons, changed weight | 20 | 0 | 0.90 | 10 | 18.0 |
| Reduced contrast, changed weight | 18 | 2 | 0.90 | 10 | 16.4 |
The first comparison does not involve changing recording weights. Different seasonal climate changes alone are enough to break this particular fixed-offset annual interpretation.
CHAPTER 5 OF 12 · Work the seasonal cases
5. Change recording weights without changing annual climate
Now retain the baseline temperatures, 20 °C and 0 °C, but shift the proxy’s warm-half weight from 0.80 to 0.90. The annual mean remains 10 °C. The proxy rises from 16 to 18 °C simply because the observation weights changed.
Combining the reduced seasonal contrast, 18 °C and 2 °C, with the new weight 0.90 gives P = 16.4 °C. Its anomaly is now +0.4 °C, reversing the sign from the −1.2 °C obtained with fixed weight, although annual temperature is unchanged in both cases.
These stipulated weights are not inferred from the proxy value itself. A real explanation would need independent support for the production or habitat change. Otherwise the weight shift is a candidate mechanism, not an established correction.
CHAPTER 6 OF 12 · Explain the apparent trend
6. Decompose the change instead of assigning one cause
Write ΔS = S₁ − S₀, ΔW = W₁ − W₀ and Δw = w₁ − w₀. Exact expansion gives ΔP = w₀ΔS + (1 − w₀)ΔW + Δw(S₁ − W₁).
The first two terms describe climate changes seen through the original proxy weights. The last term describes a weight change acting on the new seasonal contrast. Using the final contrast in that term preserves the interaction rather than dropping it accidentally.
For the combined case, ΔS = −2 °C, ΔW = +2 °C and Δw = 0.10. Climate contributes 0.80 × (−2) + 0.20 × 2 = −1.2 °C. Changing weights contributes 0.10 × 16 = +1.6 °C. Total proxy change is +0.4 °C.
The annual change remains 0.50 × (−2) + 0.50 × 2 = 0. A proxy change, a seasonal change and an annual change are therefore three statements that need explicit connections.
CHAPTER 7 OF 12 · Explain the apparent trend
7. Keep each anomaly tied to its reference
| Model case | Annual anomaly, °C | Proxy anomaly, °C | Annual estimate from P − 6, °C |
|---|---|---|---|
| Baseline | 0 | 0 | 10.0 |
| Reduced contrast, fixed weight | 0 | −1.2 | 8.8 |
| Baseline seasons, changed weight | 0 | +2.0 | 12.0 |
| Reduced contrast, changed weight | 0 | +0.4 | 10.4 |
Subtracting a reference mean removes an offset. It does not generally remove seasonal weighting or guarantee that the relationship to an annual target is stationary. Rebaselining a curve is not a substitute for validating its observation model.
Likewise, smoothing to annual plotted points does not make the represented quantity an annual calendar mean. A yearly observation can still represent a particular growth season or a production-weighted part of the year.
CHAPTER 8 OF 12 · Explain the apparent trend
8. Explain why a modern calibration may transfer incompletely
A statistical calibration can learn a relationship between seasonal and annual variation over its fitting period. If those relationships change, predictive performance outside that period may differ even when the measured proxy remains precise.
The primary Last Millennium Reanalysis study with seasonal proxy modelling explicitly compares proxy-system representations and validation approaches. Its results concern the tested records and experiments; they do not supply a universal weight of 0.80 for any archive.
Sedproxy distinguishes seasonal or habitat weights and can represent changes in those weights within a forward model. That is a useful framework for asking what an archive would record under a proposed climate history. Our two-half-year arithmetic isolates just one part of such a process chain.
CHAPTER 9 OF 12 · Evaluate the evidence
9. Seek evidence that distinguishes the explanations
Begin with proxy type, site, target season, formation process and existing seasonality metadata. Check whether temperature, moisture or another influence dominates the measured feature. Production timing and habitat depth can add further distinctions.
Compare observations with a forward model using the appropriate seasonal climate variables, and evaluate held-out information where suitable. Seasonality selected by searching many candidate windows also requires validation; the best fit among many choices can overstate generality.
Complementary records with different well-understood sensitivities may help distinguish annual changes from seasonal or ecological changes. Simply averaging many records with the same seasonal preference does not guarantee cancellation of that shared preference.
Report which effects were measured, modelled, assumed or left unresolved. An honest seasonal interpretation can be more useful than an unsupported annual label. It should also remain separate from claims about geographical representativeness or global climate.
Is a seasonal proxy biased if my question concerns that season?
Seasonal sensitivity may be exactly the information needed. Bias is relative to a target and model. A warm-season record becomes problematic when it is interpreted as an annual mean without an adequate connection.
Does crossdating identify the climate season recorded?
Crossdating helps establish chronological placement. It does not by itself determine which climatic factors or seasons control the measured feature. Timing and climate sensitivity require related but distinct evidence.
Do these examples explain a real disputed climate trend?
No. They establish possibilities within a constructed model. Explaining an actual trend requires its archive data, chronology, calibrations, spatial coverage, physical mechanisms and uncertainty, alongside comparisons with alternative explanations.
Keep the baseline 20 °C and 0 °C, but use warm proxy weight 0.60. The proxy baseline is 12 °C. For the 18 °C and 2 °C state, it becomes 11.6 °C, an anomaly of −0.4 °C while the annual anomaly remains zero. Reduced selectivity reduces this particular contrast effect.
Next let both halves warm by 2 °C at fixed weight 0.80. Annual mean rises from 10 to 12 °C and proxy from 16 to 18 °C. The proxy anomaly now matches the annual anomaly because both seasonal changes are equal under unchanged weights.
Finally combine that uniform warming with a weight shift to 0.90. The new seasons are 22 °C and 2 °C, giving P = 20 °C. The proxy anomaly is +4 °C, while the annual anomaly is +2 °C. The extra 2 °C follows from the changed weight acting on a 20 °C contrast.
CHAPTER 12 OF 12 · Practise and continue
12. Continue by the missing archive or timing question
Archives and seasonal interpretation
Return to the Palaeoclimatology root and the Paleoclimatology subject guide. Use tree rings and past-climate evidence for growth-sensitive records and Teaching Dendrochronology for chronology and crossdating.
Separate other observation limitations
Sampling intervals, aliasing and false periods concerns temporal distinguishability. Shared age anchors and lead–lag uncertainty concerns relative dating. Better dates or denser sampling do not automatically repair an incorrect seasonal target.
Sources and transferable learning
The primary references are seasonal proxy modelling in Last Millennium Reanalysis and Sedproxy’s archive forward model. The constructed temperatures, weights, decompositions and exercises here illustrate the reasoning without reproducing a real reconstruction.
Continue through How X Works and the Gold Standard of Education. The transferable habit is to keep the target’s weighting separate from the process that produced the observations.
Sources checked 21 October 2026. Worked examples are educational models with the assumptions stated above.