2024 · Problem B — Environmental Impact of High-Powered Computing

Carbon Logistic growth Markov Forecasting

The problem in one paragraph

HPC (data centers, AI, crypto) is exploding. Build a model for its total carbon emissions that accounts for the energy mix (coal, gas, renewables, nuclear), project to 2030, and extend to one additional environmental dimension (water, e-waste, resource depletion, land use, etc.). Recommend actionable policy interventions and write a letter to the UN AI Advisory Board.

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Requirements, restated

Estimate annual energy consumption of HPC worldwide — full capacity and average utilization.
Build a model for total carbon emissions, accounting for the energy mix.
(a) Show how the model evolves with HPC growth, other-sector demand, and energy-mix shifts. (b) Bound the 2030 problem.
(a) Model the effect of moving to higher renewables, including 100% renewables. (b) Add one secondary environmental impact (water, e-waste, etc.).
(a) Provide actionable recommendations. (b) Show how one recommendation would slot into the model. (c) Letter to UN Advisory Board urging environmental section in 2030 AI goals.

How to frame the problem

The base model

$E(t) = C(t) \cdot u(t) \cdot 8760$ (annual kWh)
$\text{CO}_2(t) = E(t) \cdot \sum_k m_k(t) \cdot f_k$

Where $C(t)$ is installed HPC capacity (kW), $u(t)$ is average utilization rate, $m_k(t)$ is the share of energy source $k$, and $f_k$ is its emission factor (kgCO₂/kWh). $f_k$ values are well-tabulated: coal ≈ 0.82, gas ≈ 0.49, nuclear ≈ 0.012, solar ≈ 0.05, wind ≈ 0.01, hydro ≈ 0.02.

Growth model

Pure exponential growth (Goldman Sachs: ~160% increase in data-center power by 2030) is the default forecast. But the judges specifically praised teams that recognized this can't continue forever — a logistic growth model with a saturating capacity is more defensible:

$C(t) = \dfrac{K}{1 + ((K - C_0)/C_0) e^{-rt}}$

Energy mix evolution

Use a Markov chain over energy-source shares to model how the mix shifts under different policy scenarios (status-quo, ambitious renewables, nuclear renaissance). Top teams ran 6-state Markov models (coal, gas, oil, nuclear, hydro, other-renewables) with transition matrices calibrated to recent IEA scenarios.

Secondary impact

Pick one and model it cleanly. The most tractable is water: $\text{Water}(t) = E(t) \cdot \text{WUE}$, where WUE (water-use effectiveness) is liters per kWh, typically 1.8 L/kWh for traditional data centers, 0.05–0.5 L/kWh for advanced cooling.

2030 bounds

Run the model under three scenarios — pessimistic (exponential, status-quo mix), central (logistic, mix shifts slowly), optimistic (logistic, ambitious renewables). Report a range. Top teams gave 2030 carbon emissions of ~1.5–3.5 GtCO₂/yr depending on scenario.

What the judges highlighted

One base model that extends, vs. two unrelated models bolted together. The best teams kept extending the same model through every requirement.
Honest about counter-intuitive results — Team 15022 found emissions kept rising despite adding renewables (because total energy demand was growing faster). They explained why instead of dismissing it.
Geographic specificity — Team 15225 included latitude/temperature in their model to explain cooling-energy variation.
Markov chain creativity — Team 15270 used it for scenario evolution.

Pitfalls

Cherry-picking a single forecast (e.g., always-exponential) without sensitivity.
Forgetting that energy mix varies by region, not just by year — a US data center has a very different footprint than one in Iceland or Wyoming.
Treating "100% renewables" as zero-emissions; lifecycle emissions are not zero.
The UN letter is often dry — make it persuasive, not just a summary.

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