Stratigraphy Deposition & Occupation Phase Calculator

Thickness-to-Time Modeling for Archaeological Stratigraphy

Translating observed stratigraphic sequences into plausible calendar ages is one of the most challenging tasks in field archaeology and cultural resource management. Excavators often have direct measurements of layer thicknesses, notes on hiatuses, and a handful of diagnostic finds or radiocarbon samples. Yet assembling these disparate clues into a coherent occupational history usually requires spreadsheet gymnastics or slow, bespoke modeling. This calculator streamlines the process by combining measured thickness, deposition rates, erosion allowances, and chronological constraints into a single view. It not only estimates the start and end ages of each layer but also aggregates cultural phases and highlights conflicts with terminus post quem (TPQ), terminus ante quem (TAQ), or calibrated ranges.

The workflow is intentionally pragmatic. Field teams can enter measured thicknesses in centimeters, select reasonable deposition rates in millimeters per year, and flag hiatuses or erosion events. The reference surface age anchors the top of the sequence, so all deeper units automatically shift older (more negative calendar years) as durations accumulate. Because deposition rarely proceeds at a perfectly steady pace, each rate accepts an uncertainty percentage. The calculator propagates that uncertainty into minimum and maximum duration bands, preserving transparency about the plausible age envelopes. Cultural layers can then be grouped into occupation phases, producing composite windows that summarize how long the site was actively used.

Mathematics of Layer Durations

Effective deposition time is calculated by converting net thickness (after erosion) from centimeters to millimeters and dividing by the selected rate. The following MathML expression encapsulates the base equation and the uncertainty propagation used by the calculator:

$$\begin{gathered} \mathrm{\Delta t}=\frac{T}{r},\text{with}T=10·t,\text{where}t=\text{thickness (cm) − erosion (cm)},r=\text{rate (mm/yr)} \\ \mathrm{\Delta t}{\_}_{\text{min}}=\frac{T}{r},\mathrm{\Delta t}{\_}_{\text{max}}=\frac{T}{r},\text{for}0<u<1 \end{gathered}$$

Rates entered as zero or negative are automatically rejected, while uncertainties greater than 100% are clipped to preserve meaningful bounds. If erosion equals or exceeds thickness, the effective duration collapses to zero, which the results note explicitly. Hiatus durations are treated as additive gaps after each layer, pushing older layers further back in time without altering the duration of the layer itself. This approach matches how archaeologists narrate sequences in reports: “After the abandonment of US 103 there was a 40-year hiatus before the deposition of US 104.”

Occupation Phases and Cultural Aggregation

Stratigraphic profiles often mix sterile depositional units with cultural surfaces, hearths, or construction episodes. To better understand human activity, the calculator merges consecutive cultural layers into broader occupation phases. Each phase captures the youngest boundary from the uppermost cultural layer and the oldest boundary from the deepest cultural layer in the run. The total occupation duration sums the modeled times of all cultural layers. The MathML snippet below expresses this aggregation:

$$\Phi =\underset{i=a}{\sum }\stackrel{i\in \text{phase}}{\mathrm{\Delta t}}$$

Phases aid in reporting because they condense multiple stratigraphic units into a single occupational story. Rather than listing five thin living surfaces individually, a CRM report can state that “Occupation Phase 2 spans 120 to 60 cal BCE with a best-estimate duration of 60 years.” The calculator automatically performs this roll-up while preserving per-layer details and total cultural versus sterile time slices.

Understanding Hiatuses and Erosion

Hiatus durations represent pauses in deposition or occupation. They may reflect abandonment episodes, natural stabilization, or unexcavated intervals. Entering a hiatus after a layer shifts all deeper layers to older ages by the specified number of years. Erosion losses, by contrast, reduce the effective thickness of a layer. When a profile shows that the upper part of a deposit has been truncated, subtracting that thickness avoids overestimating the duration of the surviving portion. The calculator prevents erosion from exceeding the recorded thickness and highlights layers where the adjustment yields zero time. In practice, archaeologists interpret hiatuses cautiously: anything longer than a generation (20–30 years) usually leaves some surface development or cultural markers, while shorter gaps might reflect seasonal pauses.

Constraints: TPQ, TAQ, and Calibrated Ranges

Chronological constraints anchor stratigraphic estimates. A terminus post quem (TPQ) indicates the earliest possible time a deposit could have formed, typically derived from diagnostic artifacts or radiocarbon assays. If modeled ages fall entirely before the TPQ, the result conflicts with the physical evidence. A terminus ante quem (TAQ) provides the latest permissible age, often from overlying structures or dated events. Calibrated date ranges give a probabilistic window for a sample. The calculator checks whether the modeled interval overlaps the provided range and flags any layers that sit wholly outside. When conflicts emerge, archaeologists can adjust deposition rates, hiatus assumptions, or re-examine the stratigraphic interpretation.

Worked Example Using the Default Values

The default dataset depicts a six-layer sequence anchored at the present (0 cal year) with a mix of cultural and sterile units. Layer 1 (US 100 Topsoil) is eight centimeters thick with a deposition rate of 1.8 mm/yr and an uncertainty of 20%. After accounting for a 25-year hiatus, the younger boundary remains at 0 cal year, while the older boundary shifts to approximately −44 years with min/max brackets of −37 to −55 cal years. Because it is sterile, the occupation duration contributes zero.

Layer 2 (US 101 Floor) is five centimeters thick, deposited at 0.9 mm/yr with a 15% uncertainty and no hiatus. The calculator subtracts the duration from the inherited boundary of −44 cal years, yielding an older boundary around −100 cal years. Since the layer is marked cultural, its roughly 56-year duration contributes entirely to occupation time. The provided TPQ of −120 cal years fits comfortably within the modeled interval, and the calibrated range from −150 to −30 cal years overlaps the estimate, so the constraint status is OK.

Layer 3 (US 102 Levelling Fill) thickens to fourteen centimeters at 1.1 mm/yr and includes a 40-year hiatus afterward. Its best estimate spans about 127 years, moving the boundary from −100 to roughly −227 cal years before the hiatus pushes subsequent layers even older. Because it is sterile, the duration adds to the sterile total. Layer 4 (US 103 Hearth Lens) is a thin cultural layer three centimeters thick with a slow deposition rate of 0.6 mm/yr. Its 50-year modeled duration falls between −227 and −277 cal years, comfortably matching the associated radiocarbon interval.

Layer 5 (US 104 Collapse) includes an erosion loss of two centimeters out of eighteen. The effective sixteen-centimeter thickness at 1.4 mm/yr yields about 114 years. A 60-year hiatus afterward creates a notable gap in the sequence. Because this layer is non-cultural, it adds to sterile time. Finally, Layer 6 (US 105 Sterile Clay) accumulates 25 centimeters at 0.7 mm/yr with 20% uncertainty, producing a duration of roughly 357 years and pushing the base of the excavated sequence to around −808 cal years. The cumulative occupation time sums the cultural durations of layers 2 and 4, while sterile time includes the other four layers plus all hiatus periods when calculating totals.

The results table also reports min and max ages. For example, if the deposition rate of the hearth lens were 25% faster than the best estimate, the occupation could compress to roughly 40 years, while a 25% slower rate would extend it beyond 65 years. These ranges help archaeologists gauge whether their interpretive narrative remains plausible across reasonable rate variations.

Scenario Comparisons

Adjusting deposition rates or hiatus values reveals how sensitive the timeline is. Suppose we increase all cultural layer rates by 20% while keeping sterile layers unchanged. The total occupation duration shrinks, and the phase windows tighten. Conversely, adding a 30-year hiatus after Layer 2 creates a noticeable gap that might correspond to temporary abandonment. The tables below compare three scenarios: the default inputs, accelerated cultural rates, and an added hiatus.

A second comparison explores uncertainty bands. If the uncertainty for Layer 5 increases from 35% to 80%, the max duration nearly doubles, dragging the basal age much older while the minimum remains stable. High uncertainty is useful when little is known about deposition rates, but the expanded window should be clearly communicated in reporting.

Practical Caveats

Rate-based modeling assumes consistent accumulation within each layer, yet natural deposits often fluctuate due to seasonal floods, anthropogenic dumping, or bioturbation. Cultural surfaces can build up rapidly during intense occupation and then remain stable for years. Compaction may shrink the observed thickness relative to the original deposit, especially for organic-rich layers. Re-deposition can mix older materials into younger contexts, complicating TPQ and TAQ logic. The calculator cannot resolve these complexities automatically, but it makes the assumptions explicit so archaeologists can defend or revise them.

Another caveat involves lateral variability. A layer that thins toward the edge of a trench may reflect localized erosion or slope wash. Entering a single thickness value assumes the measured point is representative. Teams can run multiple scenarios using minimum and maximum observed thicknesses to understand the envelope of possibilities. Similarly, variable sedimentation within a layer might warrant splitting it into sublayers with different rates.

Differential preservation is also critical. If post-depositional processes removed the top of a cultural layer, the remaining thickness underestimates occupation duration. Adding an erosion loss approximates this effect, but the user must estimate how much material is missing. When in doubt, pairing this calculator with micromorphology studies or additional dating samples can refine interpretations.

Adapting the Model

Some researchers may prefer separate deposition rates for cultural versus sterile layers. The calculator already supports this by allowing per-layer rate entries. For more sophisticated modeling, users can export the results (via the copy button) and feed them into Bayesian chronological frameworks such as OxCal or ChronoModel. The min and max ages provided here can serve as priors or plausibility checks. Another adaptation is to treat occupation duration as a minimum slice: the “Minimum Occupation Slice” input lets teams specify a floor for cultural durations, rounding very thin surfaces up to a reasonable interpretive unit, such as a single season or year.

Frequently Asked Questions

How should I choose deposition rates?

Rates can be derived from local studies, micromorphology, or published analogues. Urban trash pits might accumulate at 5–10 mm/yr, while natural alluvium could build at 0.5–2 mm/yr. When uncertain, enter a best guess with a generous uncertainty percentage to reveal how much the timeline could vary.

What if I only know the calibrated date range?

Enter the range start and end. The calculator checks whether the modeled interval overlaps the range. If the layer falls entirely outside, the status flags “Needs Review” so you can re-examine assumptions or consider re-dating.

Can hiatus durations represent occupation?

Hiatuses simply add gaps between layers. If you believe people occupied the site during a hiatus, consider modeling that time as a thin cultural layer with minimal thickness instead of a hiatus. This preserves the distinction between human activity and sedimentation pauses.

How do BCE and CE years work?

Negative numbers represent BCE (e.g., −500 = 500 BCE), while positive numbers represent CE. The calculator maintains these conventions across inputs and results. When summarizing results, specify the sign or convert to BCE/CE notation for clarity.

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