docs: clarify TAI method boundary

analysis/issues/issue_29_tai_method_note.md

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+## Issue #29 TAI method note
+
+Current conclusion:
+
+- `TAI` should remain **unimplemented** until the package names the exact index and
+  fixes the PET basis, aggregation surface, and threshold provenance.
+
+Why this remains blocked:
+
+- the repo comment history and Sammy issue context point toward a
+  **Thornthwaite moisture-deficit style aridity index**
+- local `xclim` only provides `aridity_index(pr, pet)`, which is a
+  **UNEP-style `P / PET` ratio**
+- those are **not interchangeable metrics**
+
+## What we verified
+
+### 1. `xclim` is not a drop-in `TAI`
+
+Local installed `xclim.indices.aridity_index` is documented as:
+
+- ratio of total precipitation over potential evapotranspiration
+- classification in the `hyperarid` to `dry subhumid` UNEP-style framing
+- wetter conditions have **higher** values
+
+Implication:
+
+- `xclim.aridity_index` is useful if we later want a separate
+  **UNEP aridity ratio**
+- it should **not** be exposed as the toolkit's intended Thornthwaite-style `TAI`
+
+### 2. Current toolkit PET path does not settle the method
+
+Current package drought/water-balance path already has useful components:
+
+- `climate_tookit.climatology.spei.prepare_monthly_climatic_water_balance(...)`
+  aggregates monthly precipitation and monthly ET totals
+- when ET is not supplied, that path derives daily `ET0_mm_day`
+  from `season_analysis.add_et0(...)`
+- current metadata explicitly labels that derived path as
+  `season_analysis.add_et0_hargreaves`
+
+Implication:
+
+- current package backbone is **Hargreaves reference ET0**, not a named
+  Thornthwaite PET implementation
+- that may still be useful later, but it is a **method choice** and should not be
+  silently treated as equivalent to Thornthwaite PET
+
+### 3. Thornthwaite-family naming is overloaded
+
+Secondary references checked during this issue pass separate at least two
+ commonly conflated ideas:
+
+- Thornthwaite climate-classification aridity / humidity indices based on
+  water deficit or surplus relative to PET
+- UNEP / dryland-style aridity ratio `P / PET`
+
+In practice this means a generic public metric name like `tai` is too ambiguous.
+
+## Recommended package decision
+
+### Public naming
+
+- do **not** add a generic public metric named only `TAI`
+- if implemented later, use an explicit name such as:
+  - `thornthwaite_aridity_index`
+  - and, separately if desired, `unep_aridity_index`
+
+### First implementation target
+
+- first home should be `climatology`, not `calculate_hazards`
+- reason:
+  - this is primarily a **climate context / dryness** metric
+  - hazard-band outputs should only come after formula and threshold provenance are signed off
+
+### Aggregation surface
+
+- compute **monthly first**
+- do **not** define this directly from daily values
+
+Suggested workflow:
+
+1. monthly precipitation total
+2. monthly PET total using an explicitly named PET method
+3. monthly deficit `max(PET - P, 0)`
+4. aggregate to annual / climatology window
+5. compute whichever Thornthwaite-style index the project explicitly adopts
+
+### PET method choice must be explicit
+
+Open options:
+
+- implement a true Thornthwaite monthly PET path
+- or adopt current Hargreaves-derived ET0 as a documented approximation / alternate method
+
+But the package must not blur these into one unnamed `TAI`.
+
+### Thresholds
+
+- no validated threshold set was found in current code
+- do not ship hazard classes until threshold source is documented and accepted
+
+## Conservative implementation plan
+
+1. Add a method design note first.
+2. Decide whether the package wants:
+   - Thornthwaite deficit index
+   - UNEP `P / PET` ratio
+   - or both under different names
+3. Fix PET method and denominator definition.
+4. Add one validated example calculation.
+5. Only then expose CLI / hazard integration.
+
+## Recommendation for issue status
+
+- keep `#29` open until:
+  - metric name is fixed
+  - PET method is fixed
+  - aggregation definition is fixed
+  - threshold provenance is fixed