Air, Water, Energy, Earth: Footprints, Plumes, Rain, and Geodesy

Environment search mixes indexes, inventories, and geophysics. AQI is not a stack model. kWh × emission factor is not a lifestyle ecological footprint. Tsunami speed in shallow water is not earthquake energy in joules. This hub is the ecology-earth silo on pancalc: air, carbon, water, and energy systems on one shelf; sphere-and-fault teaching tools on the other. Education and scenario math — not carbon-offset advice, not earthquake safety, not drinking-water certification.

If you only remember one sentence: index, inventory, physical dispersion, and geodesy are four jobs.

Air: index vs plume

The air quality index calculator maps concentrations to a piecewise public index (breakpoint tables differ by agency and year). It is a communication tool. It is not personal exposure, indoor air, or a medical diagnosis.

The Gaussian plume calculator is a teaching Gaussian dispersion: source Q, wind, stability class, downwind x, maybe reflection. Real terrain, calm winds, and chemistry eat the model. Use it to understand why “the stack is 2 km west” is not an AQI.

Do not convert AQI 120 into a plume Q.

Carbon and land: three inventories

A carbon footprint calculator sketches CO₂e from activities. Factors are region- and year-specific. It is not a tax form.

Carbon offset / travel focuses on trips. Aviation radiative forcing multipliers are a debate; the page is a scenario, not a purchase recommendation. Subtracting a tree sketch from a flight is not a protocol we endorse as advice.

Ecological footprint uses land-equivalent language (global hectares in many classroom versions). A small carbon number with a huge land number (or the reverse) is possible depending on diet and energy. Do not report gha as kg CO₂e.

Electricity CO₂ is kWh × grid factor. It is the cleanest of the four if you actually have a kWh. Lifestyle footprint tools often embed this plus car plus food. Use electricity CO₂ when the bill is the object; use the lifestyle tool when the object is a bundle.

Water, rain, diversity

Water pollutant dilution is a mixing identity: load into a flow. Rivers have dead zones and non-conservative pollutants (decay, sorption). Teaching C = mass/volume after mix is not a discharge permit.

Rainfall volume is depth × area (unit hell: mm over hectares). It feeds a rain barrel or a runoff sketch. It is not a dilution unless you then mix that volume with a spill — two steps.

Simpson’s diversity index is a classroom biodiversity statistic from counts of types. It is not AQI and not carbon. Ecology students land on “index” and pick the air page; that is the bug this hub exists to stop.

Energy machines: solar, wind, trees as sketches

Solar panel array uses panel watts, sun hours, derate. Sun position tells you where the sun is in the sky at a time and place — geometry, not kWh. Tilt talk can mention both; only one sizes an inverter sketch.

Wind turbine power is ½ρAv³Cp in the teaching form. v³ means small speed errors dominate. Not a Reynolds-number fluid homework (physics hub) unless you are actually doing blade CFD.

Tree carbon sequestration is a growth/allometry sketch. Species, climate, and mortality wreck simple annual kg. Use it to understand order of magnitude, not to greenwash a turbine.

Earth science: sphere, faults, water waves

Earth curvature is a sphere (sometimes refraction) sketch for “how much of that mountain is hidden?” It is a magnet for internet arguments. State the radius and observer height.

Geodesic distance is the path length on the ellipsoid/sphere between coordinates. Flight planning 101. Curvature hidden-height is not this length.

Earthquake energy maps magnitude scales to energy-order sketches (and sometimes TNT equivalent as a metaphor). Magnitude is logarithmic; +1 is not +10% energy. This is not a tsunami speed and not a building code.

Tsunami speed in the shallow-water teaching limit is √(g h). Deep-ocean 4–7 km depth gives aircraft-like speeds in the cartoon; coastal slowing is a different h. Not a rainfall volume.

Sun position, already contrasted with PV, also feeds “when is noon solar vs clock noon” — that is astronomy, not a date-of-week household tool.

Worked mix-ups

A rooftop: rainfall volume for gutter load versus solar array for energy versus sun position for a shading sketch. Three pages.

A factory: electricity CO₂ from the meter versus Gaussian plume from a stack versus dilution if the story is wastewater. AQI might be what the city app shows that afternoon — still not the stack model.

A news story: earthquake energy (joules) versus tsunami speed (m/s) versus geodesic distance from epicenter to a city. None of these is Simpson’s D from a reef survey.

Factors, logs, and why v³ hurts

Grid factors: 0.2 kg CO₂/kWh vs 0.8 kg CO₂/kWh is a four-times story for the same bill. Electricity CO₂ is honest when the kWh is measured. Lifestyle carbon tools that assume a diet you do not eat are theatre. Ecological footprint land factors from a 2000s textbook are not your city’s 2026 zoning.

Travel: a short-haul sketch might use kg/passenger-km; a long-haul different. Offsets in tonnes are a market instrument. Tree kg C / year × 40 years is not a tonne of aviation CO₂e without a method paper.

Plume: double the wind speed, concentration at a point often drops (more dilution) in the Gaussian cartoon; real fumigation events do the opposite. Dilution in a river: 1 kg of conservative dye in 1000 m³ well mixed is 1 mg/L. Rain: 10 mm on 100 m² is 1 m³ (0.01 m × 100 m²). Those 1 m³ on a spill pad are a volume, not a Simpson index.

Solar: 400 W panel × 4 sun-hours × 0.75 derate ≈ 1.2 kWh/day teaching. Wind: if speed is 10% high, power is ~33% high because of v³. Turbine Cp cannot exceed Betz 16/27 ≈ 0.59 in the ideal disc story.

Magnitude 6 vs 7: energy order jumps far more than 10%. Tsunami √(9.81×4000) ≈ 198 m/s in the deep-water cartoon (~700 km/h). Geodesic Warsaw–Tokyo is a long-haul number; curvature drop over 5 km of road is centimetres-to-metres depending on the sketch — do not use it to deny a mountain.

Sun elevation 0° is a geometric horizon, not weather. AQI 50 vs 150 is an index jump with breakpoint tables; it is not “three times the plume.”

Field notebook, one site

You stand on a roof near a small factory and a river.

Air: the city app AQI is 85 (index). A stack 800 m upwind is a Gaussian plume homework if you have Q and wind; you still do not “correct” AQI with Q. Electricity on the roof: 24 kWh/day × a grid factor 0.4 kg/kWh = 9.6 kg CO₂/day (electricity CO₂). A lifestyle carbon form that also adds flights is a broader inventory. A flight next month is the travel sketch. Planting a tree in the yard is sequestration order-of-magnitude, not an airline ticket. Ecological footprint might still be large because of food land — a different unit.

Water: 18 mm rain on 180 m² roof = 3.24 m³ (rainfall volume). A 0.5 m³ rain barrel overflows; that is storage, not dilution. If a student dumps 10 g of salt in the barrel, concentration is a dilution/mix identity after you know volume. Simpson D from counting insect types on the green roof is ecology classroom, not AQI.

Machines: 8 × 400 W panels, 4 peak-sun-hours, derate 0.75 → 9.6 kWh/day in the cartoon — coincidentally the bill above, which does not prove the model. A small turbine at 6 m/s vs 7 m/s: (7/6)³ ≈ 1.59 times power. Sun elevation at 10:00 determines shading on the facade, not the kWh identity.

Looking out: geodesic km to the airport; curvature drop to a distant crane; sun azimuth for a photo. News on the phone: magnitude 6.8 energy sketch; if the event is under water, tsunami speed uses local depth, not the energy joules.

Write “index / inventory / mix / machine / geodesy” in the margin. Circle one.

What this hub will not do

It will not sell you an offset, site a turbine, or tell you to evacuate. It will not replace EPA/EEA inventory rules or a seismologist. It will not turn Simpson’s D into a conservation status. It will not make AQI into a personal dose. It will not forecast rain — only convert depth × area once you have a depth.

What it will do is keep public indexes, greenhouse inventories, mixing models, machine sketches, and geodesy from sharing a cell. Search for “carbon calculator” still splits lifestyle vs travel vs kWh vs trees. Search for “distance calculator” splits geodesic km vs curvature drop vs tsunami travel-time cartoons. Search for “wind calculator” might even mean Reynolds in the physics hub if the student is in a fluids lab, not a turbine sketch.

If your assignment is “compare two cities’ electricity CO₂ for 100 kWh,” you do not need a plume. If your assignment is “estimate concentration 1 km downwind,” you do not need Simpson’s D. If your assignment is “how far is the horizon,” you do not need geodesic distance to Tokyo. If your assignment is “kWh from wind at 8 m/s,” you do not need AQI. Write the assignment verb on the page: report an index, inventory a factor, mix a fluid, size a machine, or measure the Earth. Neighbor hubs: physics-stats owns Ohm and Reynolds (lab fluids, not turbines); homework-math owns area of a roof polygon before rainfall volume; dates-household owns “how many days until the storm” as a countdown, not millimetres of rain; kitchen-math owns grams, not CO₂e of a steak unless you intentionally opened the lifestyle carbon form. Keep those doors labeled. One more roof check: millimetres of rain are not kWh; azimuth is not AQI; a city index is not a stack Q. If you cannot name the output unit in SI or “index points,” you are not ready to click. Inventory vs index: kilograms are not AQI points; global hectares are not kilograms; millimetres of rain are not milligrams per litre until you mix. Machine vs geodesy: watts are not degrees of azimuth; tsunami metres per second are not geodesic kilometres. Keep a physical notebook line: “I am reporting an index / a mass of CO₂e / a concentration / a wattage / a length on the Earth.” If two of those appear, you have two jobs and two URLs, which is the session we want — stacked, not blended. That line is the whole article.

Practical takeaway

Pick index (AQI, Simpson), inventory (carbon, ecological, kWh factor, travel, tree), fluid mixing (plume, dilution, rain volume), machine sketch (solar, wind), or geophysics/geodesy (curvature, geodesic, quake, sun, tsunami). Never subtract a tree from a plume. When the job is Ohm’s law or a t-test, use the physics-stats hub instead.