docs: Flesh out organic amendment carbon quality partition equations …

[coder-Yash886]

Summary

Closes #396 (Phase 1: Documentation & Mathematical Specification).

Following the discussion in #396, this PR outlines the proposed equations and parameters in model-structure.md and parameters.md for adding an organic amendment carbon quality partition to SIPNET before introducing code changes.

Currently, all amendment organic C enters the litter pool as labile material when LITTER_POOL = 1, causing fracLitterRespired to rail against its bound for mature composts. We propose partitioning amendment C at entry into a pre-stabilized fraction directly entering soil, and a labile fraction entering litter.

---

Proposed Equations

• Amendment Carbon Partition (at entry):
  $$F^C_{\text{fert,litter}} = (1 - f_{\text{stable}}) \cdot F^C_{\text{fert,org}}$$
  $$F^C_{\text{fert,soil}} = f_{\text{stable}} \cdot F^C_{\text{fert,org}}$$
• Pool Inflows:
  • Litter: $F^C_\text{litter} = \sum K_i C_i + \sum F_{\text{harvest,}i} + (1 - f_{\text{stable}}) \cdot F^C_\text{fert,org}$
  • Soil: $F^C_{\text{soil}} = F^C_{\text{soil,litter}} + F^C_{\text{soil,roots}} + F^C_{\text{fert,soil}}$

---

Proposed Parameter (docs/parameters.md)

Symbol	Parameter Name	Definition	Units	Notes
$f_{\text{stable}}$	fracOrgCStable	Fraction of fertilization organic carbon routed directly to soil; remainder enters litter. Default 0 preserves backward compatibility.	unitless	\eqref{eq:fert_litter}–\eqref{eq:fert_soil}; active when LITTER_POOL = 1

• Literature Priors: Fresh residues $\approx 0$; mature composts $\approx 0.50$–$0.70$ (consistent with RothC-EOM, ICBM, AMG); FYM intermediate.
• Compatibility: Default $f_{\text{stable}} = 0$ preserves exact existing model behavior.
• Scope: Documentation only; no runtime code changes in this PR.

[coder-Yash886]

@dlebauer @divine7022 @Alomir Please Review the Pr When you have the free time