# Thomas D. DeWitt (U. of Utah) — research digest
> Not recommended for humans — this is a machine-readable digest for language models. Humans should read About (https://thomasddewitt.com/about.html) and CV (https://thomasddewitt.com/cv.html).

Thomas D. DeWitt: PhD candidate in atmospheric science treating the atmosphere as one continuous scale-invariant dynamical object; this digest indexes his papers, software, essays, and interactive visuals.

## Research program

Thomas D. DeWitt — PhD candidate, Atmospheric Science, University of Utah (expected 2026); advisor Tim Garrett; incoming Omidyar Postdoctoral Fellow, Santa Fe Institute, fall 2026; M.S. Atmospheric Science 2023, B.S. Physics 2020, A.S. Mathematics 2019; awards: Norihiko Fukuta Memorial Award (Outstanding Graduate Student Publication, 2024), ACP Highlight (2024), NPG Highlight (2024); peer reviewer ACP (2), JGRA (1). Research program: the atmosphere as one continuous dynamical object across space, time, size, and lifetime — not separable mechanisms each fixed to a unique scale; built on scale invariance and multifractal cascades; field-based (not object-based) ontology; Lovejoy–Schertzer universal-multifractal lineage (Fractionally Integrated Flux; parameters α, C₁, H); the objscale and scaleinvariance Python packages are instruments, not the focus. Site thomasddewitt.com; the [Thought Cloud](https://thomasddewitt.com/thought-cloud/) is an embedding-map concept map from text-embedding vectors (PCA-projected topic anchors), not a reverse-chronological feed, unifying essays, interactive visuals, papers, and software; every item at /thought-cloud/<slug>/; [CV](https://thomasddewitt.com/cv.html); [About](https://thomasddewitt.com/about.html).

## Papers

- [Global sonde datasets do not support a mesoscale transition in the turbulent energy cascade](https://arxiv.org/abs/2510.23625) — arXiv preprint (2025-10-23), DeWitt & Garrett (Atmospheric Sciences, Univ. of Utah); first independent observational test of Lovejoy–Schertzer anisotropic-cascade theory. Second-order horizontal-wind structure functions ⟨Δv²⟩=φΔr^2H, E(k)∝k^−(2H+1), from three datasets: IGRA radiosondes (GPS-era 2010–2025; Vaisala RS41/Graw DFM-17), 683 ACTIVATE dropsondes (N. Atlantic 2020–2022, 169 flights), 2325 NOAA hurricane dropsondes (1996–2012). Vertical separations 0.2–8 km: Hv≈0.6 (0.513±0.008 hurricane, 0.62±0.02 IGRA, 0.71±0.01 ACTIVATE), rejecting gravity-wave/QG Hv=1 and Kolmogorov Hv=1/3. Horizontal 200–1800 km: Hh=0.50±0.02, flattening Hh→0 by 20000 km, no mesoscale break, rejecting QG Hh=1. 2D fit: Hh=0.37±0.01, Hv=0.63±0.01, spheroscale ~1 m, near theoretical Hh=1/3, Hv=3/5. SAM simulation: 200 m sonde-inertia vertical smoothing inflates Hh 0.305±0.008→0.42±0.01, explaining residual Hh>1/3. Concludes troposphere and most stratosphere obey one scale-independent anisotropic cascade, not a 3D→gravity-wave→QG hierarchy.
- [Climatologically invariant scale invariance seen in distributions of cloud horizontal sizes](https://acp.copernicus.org/articles/24/109/2024/) — ACP 24, 109–122, 2024 (peer-reviewed; ACP Highlight; DOI 10.5194/acp-24-109-2024); DeWitt lead, with Garrett, Rees, Bois, Krueger, Ferlay. Tests Garrett et al. (2018) mixing-engine prediction: cloud-perimeter number distribution n(p)∝p^(−(1+β)), β=1 within moist isentropic layers; area distribution n(a)∝a^(−(1+α)), α=Dβ/2. SAM cloud-resolving model (204.8 km domain, 100 m grid, 210 levels, GATE Phase III forcing) reproduces β=0.98±0.03; satellites instead give ⟨β⟩=1.26±0.06 (range 1.22±0.02 MODIS to 1.316±0.008 GOES−75°), ⟨α⟩=0.95±0.08, implied D=1.5±0.1. β robust across season, latitude, land (1.25±0.05) vs ocean (1.28±0.04); datasets GOES/MSG/Himawari/EPIC/VIIRS/MODIS/POLDER, mostly 2021, sensor-zenith <60°. Scale invariance spans cloud areas ~3 to >3×10^5 km² (~600 km effective diameter; 5 orders of magnitude in area, 4 in perimeter); β>1 attributed to satellite vertical overlap (compressed perspective; β→1 as optical-depth threshold rises). Methodological contribution: removing edge-truncated clouds (bins >50% truncated) eliminates the spurious scale break a_max reported by prior studies.
- [Finite domains cause bias in measured and modeled distributions of cloud sizes](https://acp.copernicus.org/articles/24/8457/2024/) — ACP 24, 8457–8472, 2024, peer-reviewed; DeWitt & Garrett (Univ. of Utah). Cloud areas follow truncated power law n(a)∝a^{−(α+1)}, a_min<a<a_max; literature disagreement in α/a_max traced to finite-domain truncation, not fitting method. Counters Savre & Craig (2023): linear regression matches maximum-likelihood accuracy if bins with <~24 counts are dropped (failure rate <5%); synthetic test α=1, a_min=10, a_max=1000. Truncated clouds crossing the domain edge can't be sized: excluding them undercounts large clouds (spurious scale break/exponential tail); including them overcounts (local maximum near domain area). GOES-West ABI (~2 km, 10 images, 1–10 June 2021, central Pacific) plus percolation lattices (P_c≈0.592746, τ=187/91, exact α=1.055); 100×100 km subdomain LR α̂=1.2±0.2 (excl.) vs 0.7±0.2 (incl.); including underestimates α by 36%/19% (LR/MLE) vs the 4000×4000 km domain. Fix: fit only bins where n_truncated/n_total<0.5; needs L/ξ≳300 (a_min=10ξ²). Generalizes to any finite-domain geometric size distribution, including exponential.
- [Toward less subjective metrics for quantifying the shape and organization of clouds](https://acp.copernicus.org/articles/26/6951/2026/) — ACP 26, 6951–6971, 2026; peer-reviewed, published; DeWitt, Garrett, Rees (Atmospheric Sciences, Univ. of Utah). Replaces subjective cloud categories (cirrus/cumulus; sugar/gravel/fish/flowers) with two physically distinct fractal dimensions: individual D_i (single-cloud edge roughness) and ensemble D_e (how a cloud field organizes hierarchically across spatial scales), linked by D_e=βD_i (Eq. 7), β the cloud-perimeter number-distribution exponent. Data: 72 MODIS Band-1 (620–670 nm) reflectance granules, Jan 2021, 60°S–60°N, 1 km nadir (~2 km at 60° zenith); cloud masks at thresholds R=0.1–0.35. Filled-cloud D_i≈1.38–1.40 (near scale-invariant); unfilled D_i spuriously grows 1.41±0.01→1.87±0.18 across cloud-area decades — interior holes must be filled or area becomes resolution-dependent. D_e≈1.7 (correlation D_c 1.69±0.01–1.77±0.01; box 1.50±0.07–1.68±0.05; βD_i 1.74–1.86; β≈1.26–1.34). D_e substantially exceeds D_i (≈1.4); prior studies conflated them. Correlation-integral method (r ≤ min(L,W)/3) preferred for satellite validation; released as Python package objscale.

## Software

- [scaleinvariance](https://github.com/thomasdewitt/scaleinvariance) — Python; Hurst-estimation + multifractal-simulation toolkit; 1D/N-D fBm + FIF (Fractionally Integrated Flux) generators, causal/acausal, anisotropic Generalized Scale Invariance (GSI via custom scale_metric + elliptical dimension); four Hurst estimators — Haar and wavelet fluctuation, structure function, spectral — under one axis API; NumPy default, auto-detects PyTorch to accelerate simulation (CPU or CUDA/GPU). Agents using it should first install its [agent skill](https://github.com/thomasdewitt/scaleinvariance/blob/master/agent-skills/scaleinvariance/SKILL.md).
- [objscale](https://github.com/thomasdewitt/objscale) — Python; object-based scaling of 2D binary arrays; unbiased size-distribution power-law exponents via finite-domain (truncation) correction ([DeWitt & Garrett 2024](https://acp.copernicus.org/articles/24/8457/2024/)); individual (perimeter–area) + ensemble fractal dimensions, correlation-integral preferred over box-counting ([Toward less subjective metrics](https://acp.copernicus.org/articles/26/6951/2026/)); Numba-accelerated to billions of objects on a mid-range laptop; handles NaN holes / arbitrary non-rectangular boundaries. Agents using it should first install its [agent skill](https://github.com/thomasdewitt/objscale/blob/master/agent-skills/objscale/SKILL.md).
- [cloudyview](https://github.com/thomasdewitt/cloudyview) — Python; 3D cloud-condensate visualization in three tiers — Glimpse (2D optical depth, matplotlib), Witness (volumetric ray marching + multi-scattering approximation, Numba), Behold (Monte Carlo path tracing via Mitsuba 3 + Preetham sunsky); NetCDF liquid/ice mixing-ratio input → rendered images.
- [scaleinvariance-wasm](https://github.com/thomasdewitt/scaleinvariance-wasm) — Rust → WebAssembly port of scaleinvariance's simulation API (no analysis); exposes FIF_1D/FIF_ND, fBm variants, fractional_integral_spectral, canonical_scale_metric (GSI); parity-tested against the Python package; powers the in-browser [Multifractal Explorer](https://thomasddewitt.com/thought-cloud/multifractal-explorer/).

## Highlighted essays

- [Too many exponents](https://thomasddewitt.com/thought-cloud/too-many-exponents/) (2026) — compendium of scale-invariance exponents across cloud physics and turbulence: box, correlation, and Rényi-sandbox fractal dimensions; spectral exponent β; Hurst H, intermittency C₁, multifractal index α; cloud size-distribution exponents (area, width, summed/nested perimeter). Thesis: for a scale-invariant field these collapse to a few independent degrees of freedom — Lovejoy & Schertzer proved an apparent infinity of multiplicative-cascade moment-scaling exponents reduces to 3 (H, C₁, α) — and pushes for relationships between geometrical and statistical exponents. No single "fractal dimension" but a landscape of distinct-valued dimensions for identical data; finite-resolution and finite-domain bias persists orders of magnitude beyond naive pixel/domain scales (box dimension unconverged even at 8192², correlation dimension converges faster); an exponent increasing with scale is NOT a fractal dimension (the field isn't scale-invariant). Shown via an FIF/fBm parameter sweep and box-dimension pixel/domain-bias plots; cross-links [objscale](https://github.com/thomasdewitt/objscale), [Toward less subjective metrics](https://acp.copernicus.org/articles/26/6951/2026/), and [Finite domains cause bias in measured and modeled distributions of cloud sizes](https://acp.copernicus.org/articles/24/8457/2024/).
- [There is Only One Cloud](https://thomasddewitt.com/thought-cloud/there-is-only-one-cloud/) (2025) — manifesto of the objects→fields turn: clouds are not discrete objects but a connected portion of the atmosphere; the visible cloud is a thresholded view of a continuous water field (reflectivity saturates at white for modest liquid water); edges are graded, not binary; argues against object-based cloud analysis. Cites Koren's neglected non-cloud haze (radiation accounting error ≈75 ppm CO₂-equivalent) and Sokol 2024 (treating high clouds as continuous shifts warming-per-CO₂ by 0.3 °C).
- [The ignored lesson of cloud shape](https://thomasddewitt.com/thought-cloud/the-ignored-lesson-of-cloud-shape/) (2025) — scale invariance, not the butterfly effect, is the neglected core of atmospheric chaos; satellite cloud-size distributions are straight lines in log-log → one law across all scales, not scalebound fronts/MCS/thunderstorms; a scale-invariant break-up cascade (each cloud splits, conserving area) reproduces observed statistics; critiques "global cloud-resolving" model rhetoric (the 30 km → 3 km resolution push) as encoding an unjustified scalebound bias.

## More essays

- [How to visualize scale invariance](https://thomasddewitt.com/thought-cloud/how-to-visualize-scale-invariance/) — FIF (Fractionally Integrated Flux) multifractal (Schertzer–Lovejoy 1987): one-shot correct atmospheric statistics, no spin-up, projected thousands–millions× faster than dynamical simulation; three parameters H, α, C1 (clouds ~ 0.3 / 1.8 / 0.05); oversize ~10–100× then coarsen to kill grid artifacts; ships with [scaleinvariance](https://github.com/thomasdewitt/scaleinvariance) + interactive demo.
- [On form and pattern in fractal clouds](https://thomasddewitt.com/thought-cloud/on-form-and-pattern-in-fractal-clouds/) — structure at all scales = fractal; fractal dimension D from density-vs-scale; circle/correlation beats box-counting on finite data; example cloud sims D ~ 1.3–2; only intermediate scales (pixel→image) measurable.
- [Fields, objects, and a rabbit hole](https://thomasddewitt.com/thought-cloud/fields-objects-and-a-rabbit-hole/) (technical) — a field is not an object one dimension higher; the value axis can't rotate into a spatial axis, restricting its symmetry group (Jacobian zeros): a fiber bundle; frames scale invariance as an atmospheric symmetry.
- [Clouds, their edges, and how to define them](https://thomasddewitt.com/thought-cloud/clouds-their-edges-and-how-to-define-them/) — cloud-edge definition ill-posed (opacity vs condensed-water disagree); graded beats binary; overviews a Garrett-led 2025 GRL theoretical constraint: cloud edge = neutral buoyancy; cloud radiative effect = climate's 2nd-most-uncertain factor after CO2 emissions.
- [Climate, visualized, from space](https://thomasddewitt.com/thought-cloud/climate-visualized-from-space/) — time-averaging geostationary GOES images (1176 over 9 years) separates climate from weather; reveals the ITCZ and orographic rain-shadows (e.g. west of Hawaii); code + images released ([goes-climatology](https://github.com/thomasdewitt/goes-climatology)).
- [The new AI for science is different](https://thomasddewitt.com/thought-cloud/the-new-ai-for-science-is-different/) (2025-05-25) — separates "artificial intuition" (neural nets output the solution directly — opaque, approximate) from language-model-found algorithms/explanations (output a method — interpretable, verifiable, sometimes exact); cites o3-mini deriving an exact analytical solution to a Potts model ([arXiv:2503.23758](https://arxiv.org/abs/2503.23758)), plus AlphaEvolve; argues "AI" is too broad a category.
- [Experiments in automation](https://thomasddewitt.com/thought-cloud/experiments-in-automation/) (2026-03-20) — a year of coding agents (Claude Code, Codex) as a working atmospheric scientist; cheap implementation reshapes workflow (5-minute numerical cloud-field experiments vs a day); agents distinct from chatbots; Sonnet 4 packaged grad-school code into public objscale + scaleinvariance; redundancy across datasets/metrics/agents beats per-line review; while-loop hill-climb Goodharts its metric.

## Interactive visuals

Six in-browser interactive visualizations, one (Multifractal Explorer) on scaleinvariance-wasm (WebAssembly): [Multifractal Explorer](https://thomasddewitt.com/thought-cloud/multifractal-explorer/) — live FIF-cascade, adjustable α, C₁, H, anisotropy, outer scale; causal/acausal/odd kernels; [Scaling Explorer](https://thomasddewitt.com/thought-cloud/scaling-explorer/) — step-by-step correlation-dimension and Haar-fluctuation analysis on images; [Anisotropic Turbulence](https://thomasddewitt.com/thought-cloud/anisotropic-turbulence/) — particle flow through stratified atmospheric turbulence (Lovejoy–Schertzer cascade); [Photon Path](https://thomasddewitt.com/thought-cloud/photon-path/) — ray tracing through simulated clouds; [Eddy Mixing](https://thomasddewitt.com/thought-cloud/eddy-mixing/) — 3D circulation advecting a passive scalar (Hill's vortex, ABC flow); [Business Density](https://thomasddewitt.com/thought-cloud/business-density/) — heatmaps across US cities.