Walker Circulation Dynamics @ PKU

Basic Info

• Period: Nov 2020 — Oct 2021 (~12 months active research; paper draft v6 finalized 2021-10-22)
• Role: Undergraduate independent research (First author)
• Organization: School of Physics, Department of Atmospheric and Oceanic Sciences, Peking University
• Advisors: Ji Nie (primary PI) + (co-advisor, Hu-group discussion platform)
• Location: Beijing / Tianhe-II NSCC-GZ
• Support: PKU President Fellowship (undergraduate research)

Core Problem

Systematic response of the Walker Circulation to oceanic-forcing width: in CAM3 aqua-planet, vary the distance D between the warm-pool source and cold-pool sink from 60° to 180° (step 20°), plus Warm-only / Cold-only / Aqua baseline — 10 cases × 30-year runs total — exploring the regularities of Walker strength + large-scale SST/precip/ω/SW responses.

Zhenyu’s Core Original Contribution (2021-07-13 breakthrough)

Linear Superposition framework — apply a 2nd-order Taylor expansion to the forcing-response operator, drop the interaction term when the forcings are far apart, yielding:

$\mathrm{Response}(W+C)\approx \mathrm{Response}(W)+\mathrm{Response}(C)$

4-field quantitative validation (D80-D180 bulk):

• SST corr 0.9063
• Precip corr 0.9215
• ω@500mb corr 0.8282
• SW corr 0.9324 (all > 0.82)

2021-07-13 breakthrough verbatim (see slide 24):

After advisor discussion, the linear superposition framework proposed by Zhenyu provided a satisfactory explanation, and was endorsed.

Emergent prediction: Walker strength is non-monotonic and peaks at D80-100° — that peak corresponds exactly to the location where Wonly’s natural descending area (200-220°E) geometrically overlaps with the cold pool. No nonlinear mechanism is needed to explain it.

Linear-superposition failure boundary (D60-D80): low-cloud positive-feedback loop — CP descending↑ → suppress convection → trap humidity → low cloud↑ → albedo↑ → SW absorption↓ → SST↓ → ΔSST↑ → loop; 4-term energy budget diagnosed (SW + LH dominate; ΔSW D60: -66.5141 W/m² → D180: -110.6316 W/m²).

7-Month Intuition Accumulation Trajectory (from framing to breakthrough)

Time	Event	Cumulative state
2020-12-29 slide 5	Walker left-right asymmetry framing (7-width sweep)	Early framework seed
2021-04-26 master PPT 295 slides	Collage seedlings slides 32-65 (3 months BEFORE breakthrough)	First systematic superposition attempt
2021-05-16 Hu group 15 slides	D180 self-consistent linear superposition explicit	Explicit 3 months before
2021-05-26 / 5-28 / 6-2 progress reports	84 figure groups systematic (5-28 collage systematized to 6 fields)	Near-complete 2 months before
2021-07-13 progress report 29 slides	breakthrough — Zhenyu proposed linear superposition on the spot + Ji Nie endorsement	”Then we can start writing the paper”
2021-07-16 Hu group 28 slides	Post-breakthrough echo to Hu group (slide 20 “linear superposition can explain Q1”)	Multi-advisor platform delivery

Key Achievements

1. Linear Superposition framework proposal + 4-field 0.83-0.93 correlation validation (framework-level contribution, not incremental); see Linear Superposition Framework
2. Emergent non-monotonic Walker-strength explanation (D80-100° peak = natural-descending and cold-pool overlap)
3. Low-cloud feedback failure-boundary diagnosis (4-term energy budget, SW + LH dominate)
4. ω-based vs u-based methodology bug catch (4-26 slide 26 found ω does not satisfy “non-divergence”; both NCL modules preserved side by side: msf_top2bottom_u2_Walker.ncl 61 lines + msf_top2bottom_omega2_WalkerStream.ncl 63 lines) — engineering-rigor signature, attributed to Multi-Method Comparison Spine (2019-2025)
5. Paper draft v6 (3,663 words, 11 refs, 2021-10-22): Zhenyu He¹, Ji Nie¹*, supported by the PKU President Fellowship — unpublished:

Project not submitted by mutual decision.

Not a research failure but a co-author publishing decision. The paper-draft archive is at . 6. 8-week / 9-version paper auto-diff: v1 → v2_2 → v2_2-nj (Ji Nie round 1, +13 Chinese inline comments) → v3 (Zhenyu implements +3 equation tables) → v4 (+465 words / +8 refs in 2 days, big expansion) → v5 → v5-nj (Ji Nie round 2) → v6 (+3 refs, final) 7. Ji Nie methodology arc arc signature: Project paper draft retained internally; advisor and student arrived at a mutual decision not to submit.

Technical Depth (resume-grade specifics)

• 5-stage HPC pipeline architecture: (1) CAM3 aqua-planet with prescribed Q-flux → (2) 30-year spin-up on Tianhe-II (undergraduate Tianhe-II account) account (yhrun -p work -n 48 48-PE SLURM) → (3) 25 cal_X/ MATLAB diagnostic folders → (4) NCL stream function + ω analysis → (5) paper figure refinement in MATLAB + Python
• 27,882 MATLAB+NCL lines / 5 languages: MATLAB (main diagnostics) + NCL (stream function) + Fortran (namelist + CAM3 source mods) + Bash (SLURM runscripts) + Python (paper figure polish)
• 14 Q-flux variants preserved (D60 / D80 / D100 / D120 / D140 / D160 / D180 + Wonly + Conly + Aqua + variations)
• 20 NCAR CAM3 .F90 source mods (SourceMods.zip 143 KB in Walker cam3_task/), aggregate: cldinti / cldsav / cloud_fraction / comctl / ghg_defaults / hb_diff / history / hycoef / ice_constants / inidat / initext / ocn_srf / physpkg / radiation / radlw / runtime_opts / somoce (MLDANN 50→30m slab ocean, key dep) / stratiform / tphysbc — undergraduate-level source-code modifications to a GCM

Academic / Career Significance

• Together with Aerosol Joint Retrieval Senior Thesis @ PKU + DSCOVR Inverse Problem + Regularization Methods @ Caltech / UCR, constitutes a 3-track parallel Sep-Dec 2021 senior fall (Walker paper v3→v6 + DSCOVR HBP + nwp_hw 4 assignments ≈ 3-4 deliverable/week)
• Successor to Walker/Hadley Circulation Response Under Global Warming @ PKU (Oct 2019 — May 2020, the first project in Ji Nie’s group), and competence foundation for the multi-model work in PhD phase (3-D LES + 1-D DSE+SWTG quasi-2D etc.)
• The research-grade specificity of Walker paper v6 became the bedrock of Zhenyu’s later UC Berkeley PhD application + Caltech/UCR Yuk Yung/King-Fai Li collaboration + Princeton SGS invitation
• Moment 2 of the Independent Judgment narrative (held until 2026-06-10) spine (2021-07-13: after the advisor’s MSE-budget explanation failed, Zhenyu proposed linear superposition and defended it to Ji Nie’s endorsement)

Skills Used

• Climate Physics & Atmospheric Science (Walker/Hadley + 4-term energy budget + low-cloud feedback)
• High Performance Computing (Tianhe-II (undergraduate Tianhe-II account) 48-PE + CAM3 aqua-planet 30-yr)
• Python Scientific Computing (paper figures + part of the diagnostics)
• Numerical Model Source Code Modification (20 NCAR CAM3 .F90 mods)

Related Pages

• Undergraduate Research @ Peking University & Caltech/UCR — undergraduate-research umbrella page
• Walker/Hadley Circulation Response Under Global Warming @ PKU — predecessor Ji Nie group project (Oct 2019 — May 2020)
• Ji Nie — Walker project primary PI
• — Walker co-advisor, Hu-group discussion platform
• Linear Superposition Framework — Zhenyu’s original framework concept page
• — breakthrough artifact source page
• — paper-draft source page
• PKU advisor methodology companion (private) — acknowledgment-edit arc, paired with Jing Li
• Multi-Method Comparison Spine (2019-2025) — ω-vs-u methodology rigor attributed to this spine
• Independent Judgment narrative (held until 2026-06-10) — Moment 2 (meta-level)
• Academic Honors @ PKU (2018-2022) — supported by the PKU President Fellowship

Sources

• research_wiki/projects/walker_hadley/overview.md (~55k words / 1303 lines)
• research_wiki/resume_angles/problem_solving.md §Project 5
• research_wiki/resume_angles/technical_depth.md §Section 9