cs249r_book/mlsysim/docs/tutorials/07_geography.qmd

---
title: "Geography is a Systems Variable"
subtitle: "Same cluster, same model, same duration — but does location change the cost?"
description: "Compare identical training runs across four grid regions to discover whether geography matters more than hardware choice or training duration for carbon footprint."
categories: ["ops", "intermediate"]
---

## The Question

You have a 256-GPU cluster training a model for 30 days. Does it matter *where* that
cluster is located? Not for latency or throughput — those are fixed by the hardware. But
for carbon emissions, water usage, and total cost of ownership, does geography matter —
and if so, by how much?

::: {.callout-note}
## Prerequisites
Complete [Tutorial 1: The Memory Wall](01_memory_wall.qmd). No other prerequisites
are required — this tutorial can be completed independently.
:::

::: {.callout-note}
## What You Will Learn

- **Calculate** the carbon footprint of identical training runs in different regions
- **Quantify** the gap between the cleanest and dirtiest electricity grids
- **Compare** geography vs. training duration as levers for sustainability
- **Apply** the `EconomicsModel` to show how carbon pricing changes the cheapest option
:::

::: {.callout-tip}
## Background: Grid Carbon Intensity

Every kilowatt-hour of electricity has a carbon cost, measured in grams of CO2 per kWh
(gCO2/kWh). This number depends entirely on how the electricity is generated:

| Region | Primary Source | Carbon Intensity |
|:-------|:---------------|:-----------------|
| Quebec | Hydroelectric | ~20 gCO2/kWh |
| Norway | Hydroelectric | ~29 gCO2/kWh |
| US Average | Mixed (gas, coal, renewables) | ~390 gCO2/kWh |
| Poland | Coal-dominated | ~820 gCO2/kWh |

The range is wide. How wide — and whether it matters more than other levers like
training duration or hardware choice — is what this tutorial quantifies.
:::

---

## 1. Setup

```{python}
#| echo: false
#| output: false
import mlsysim  # installed via `pip install mlsysim` (see workflow)
Engine = mlsysim.Engine
```

```python
import mlsysim
from mlsysim import Engine
```

---

## 2. Two-Region Comparison

Let's run the same training job in two locations: Quebec (hydroelectric) and Poland
(coal-dominated). Same fleet, same model, same 30-day duration. The only variable
is where the electricity comes from.

```{python}
from mlsysim import Systems
from mlsysim.solvers import SustainabilityModel
from mlsysim.systems.types import Fleet, Node, NetworkFabric
from mlsysim.core.units import Q_
from mlsysim.show import table, info

# 256-GPU cluster: 32 DGX H100 nodes
fleet = Fleet(
    name="256-GPU Training Cluster",
    node=Systems.Nodes.DGX_H100,
    count=32,
    fabric=Systems.Fabrics.InfiniBand_NDR
)

solver = SustainabilityModel()

# Quebec: hydroelectric grid
res_quebec = solver.solve(
    fleet=fleet, duration_days=30,
    datacenter=mlsysim.Infrastructure.Grids.Quebec
)

# Poland: coal-heavy grid
res_poland = solver.solve(
    fleet=fleet, duration_days=30,
    datacenter=mlsysim.Infrastructure.Grids.Poland
)

carbon_q = res_quebec.carbon_footprint_kg / 1000  # tonnes
carbon_p = res_poland.carbon_footprint_kg / 1000
ratio = carbon_p / carbon_q if carbon_q > 0 else 0

table(
    ["Region", "Carbon (tonnes CO2)"],
    [
        ["Quebec (Hydro)", f"{carbon_q:.1f}"],
        ["Poland (Coal)", f"{carbon_p:.1f}"],
    ]
)
info(Ratio=f"{ratio:.0f}x")
```

Same cluster. Same model. Same duration. The carbon footprint differs by roughly
**40x** depending on the electricity grid. This is not an optimization — it is a
location decision.

---

## 3. All-Region Sweep

Let's expand the comparison to all four grid regions in the Infrastructure Zoo,
adding energy consumption, water usage, and PUE to the picture.

```{python}
grids = [
    mlsysim.Infrastructure.Grids.Quebec,
    mlsysim.Infrastructure.Grids.Norway,
    mlsysim.Infrastructure.Grids.US_Avg,
    mlsysim.Infrastructure.Grids.Poland,
]

region_results = {}
rows = []
for grid in grids:
    r = solver.solve(fleet=fleet, duration_days=30, datacenter=grid)
    energy_mwh = r.total_energy_kwh.magnitude / 1000
    carbon_t = r.carbon_footprint_kg / 1000
    water_kl = r.water_usage_liters / 1000
    region_results[r.region_name] = r
    rows.append([r.region_name, f"{energy_mwh:,.1f}", f"{carbon_t:,.1f}", f"{water_kl:,.1f}", f"{r.pue:.2f}"])

table(["Region", "Energy (MWh)", "Carbon (t)", "Water (kL)", "PUE"], rows)
```

Notice that energy consumption also varies between regions because of different PUE
values. A modern liquid-cooled facility (PUE 1.1) wastes less energy on cooling than
a legacy air-cooled datacenter (PUE 1.6). But the dominant factor is carbon intensity
— it creates the 40x gap.

---

## 4. Geography vs. Training Duration

Is it better to train longer in a clean region or shorter in a dirty region? Let's
compare 30 days in Quebec against just 10 days in Poland.

```{python}
# 30 days in Quebec
res_30d_quebec = solver.solve(
    fleet=fleet, duration_days=30,
    datacenter=mlsysim.Infrastructure.Grids.Quebec
)

# 10 days in Poland (1/3 the training time)
res_10d_poland = solver.solve(
    fleet=fleet, duration_days=10,
    datacenter=mlsysim.Infrastructure.Grids.Poland
)

c_q = res_30d_quebec.carbon_footprint_kg / 1000
c_p = res_10d_poland.carbon_footprint_kg / 1000

table(
    ["Scenario", "Carbon (tonnes CO2)"],
    [
        ["30 days in Quebec", f"{c_q:.1f}"],
        ["10 days in Poland", f"{c_p:.1f}"],
    ]
)
info(Ratio=f"{c_p/c_q:.1f}x")
```

::: {.callout-important}
## Key Insight

**Geography is a larger lever than training duration for carbon footprint.** Even
training for one-third the time in Poland produces more carbon than the full 30-day
run in Quebec. The carbon intensity gap between hydro and coal grids is so large that
no reasonable reduction in training time can compensate. For any organization serious
about sustainable AI, datacenter location is not a logistics detail — it is a
first-order systems design decision with 40x impact.
:::

---

## 5. Economic Angle: When Carbon Has a Price

What happens when carbon emissions carry a financial cost? Carbon pricing (through
taxes or cap-and-trade) changes the economics of datacenter location. Let's compute
TCO with a carbon price of $50/tonne.

```{python}
from mlsysim.solvers import EconomicsModel

econ = EconomicsModel()
carbon_price = 50  # USD per tonne CO2

rows = []
for grid in grids:
    tco = econ.solve(fleet=fleet, duration_days=30, grid=grid)
    carbon_cost = (tco.carbon_footprint_kg / 1000) * carbon_price
    total = tco.tco_usd + carbon_cost
    rows.append([tco.region_name, f"${tco.tco_usd:,.0f}", f"${carbon_cost:,.0f}", f"${total:,.0f}"])

table(["Region", "TCO ($)", "Carbon Cost ($)", "Total ($)"], rows)
```

At $50/tonne, carbon pricing adds a visible cost differential between regions. At
higher carbon prices (some jurisdictions already charge $100+/tonne), the difference
becomes even more pronounced, potentially shifting which region offers the lowest TCO.

---

## Your Turn

::: {.callout-caution}
## Exercises

**Exercise 1: Predict before you compute.**
Training for 30 days in Quebec vs. 10 days in Poland — which produces more carbon?
Write your prediction, then run both scenarios. Were you right? What does this tell
you about the relative magnitude of grid carbon intensity vs. training duration?

**Exercise 2: At what carbon price does geography change the cheapest option?**
Sweep carbon price from $0 to $500/tonne in steps of $50. For each price, calculate
the total cost (TCO + carbon cost) for all four regions. At what price does a region
other than the default cheapest become the best option? Print a table showing the
crossover.

**Exercise 3: Sweep PUE from 1.0 to 2.0.**
Create custom grid profiles using `from mlsysim.infrastructure.types import GridProfile` with
US Average carbon intensity but varying PUE. Sweep PUE from 1.0 to 2.0 in steps of
0.1. How much does total energy increase? At what PUE does facility overhead exceed
the IT energy itself?

**Self-check:** If you train for 30 days in Quebec (20 gCO2/kWh) vs. 15 days in
Poland (820 gCO2/kWh), and both use the same fleet and power, which produces more
total carbon? Show the mental calculation: the ratio of carbon intensities is 41x,
and the ratio of durations is 2x, so Poland is still 41/2 = ~20x worse.
:::

---

## Key Takeaways

::: {.callout-tip}
## Summary

- **Grid carbon intensity creates a 40x gap** between the cleanest (Quebec, ~20 gCO2/kWh) and dirtiest (Poland, ~820 gCO2/kWh) regions
- **Geography dominates training duration** as a sustainability lever: 10 days in Poland emits more than 30 days in Quebec
- **PUE amplifies energy use** but carbon intensity is the dominant factor in emissions
- **Carbon pricing changes the economics**: at $50-100/tonne, location becomes a financial variable, not just an environmental one
- **Datacenter location is a systems design decision** with first-order impact on sustainability and, increasingly, on cost
:::

---

## Next Steps

- **[The $9M Question](08_nine_million_dollar.qmd)** -- Quantify the infrastructure cost of chain-of-thought reasoning
- **[Scaling to 1000 GPUs](06_scaling_1000_gpus.qmd)** -- Discover the hidden reliability cost at scale
- **[Sensitivity Analysis](09_sensitivity.qmd)** -- Use sensitivity sweeps to find which parameter matters most
- **[Infrastructure Zoo](../zoo/infra.qmd)** -- Browse all regional grid profiles and datacenter configurations