Final Cram

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Hot = short, cool = long. Sun hot → 0.48 µm (visible). Earth cool → 9.66 µm (thermal IR). That's why we use VIS/NIR for reflected solar and thermal IR for emitted Earth.

Wien’s Displacement Law — formula and the two peak wavelengths to know?

Hot things glow short, cool things glow long. That’s the whole law in plain terms.

  • The Sun is super hot, so it glows in visible light (we can see it).
  • The Earth is cool, so it glows in thermal infrared (we can’t see it, but our sensors can).

That’s exactly why we use VIS/NIR sensors to capture reflected sunlight, and thermal infrared sensors to capture Earth’s own heat — at night, in the dark, all the time.

🔬 Science / formula

λ_max = 2897.8 / T (µm, T in K)

  • Sun (~6000 K): λ_max ≈ 0.483 µm (visible)
  • Earth (~300 K): λ_max ≈ 9.66 µm (thermal IR)

Hotter → shorter peak wavelength.

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SB = Super Boost. T to the FOURTH — double the temp, 16× the energy. That's why a 300 K Earth emits radiation at all.

Stefan–Boltzmann Law?

How brightly something glows depends on its temperature to the fourth power — meaning a small temp jump produces a huge brightness jump.

  • Double the temperature → 16× the radiation.
  • Triple it → 81×.

That’s why a campfire feels exponentially warmer than warm tea, and why thermal satellite sensors can detect 1°C differences across a landscape — the signal isn’t subtle once you know to look at the right wavelength.

🔬 Science / formula

M_λ = σ · T⁴ — total emitted power per m² from a blackbody.

  • σ = 5.6697 × 10⁻⁸ W/(m²·K⁴)
  • T in Kelvin
  • Real objects: ε · σ · T⁴ (ε = emissivity)
  • Emitted energy scales with T⁴ — why thermal sensors are so sensitive.
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Rayleigh → blue sky (short wins). Mie → haze (particles match wavelength). Non-selective → white clouds (big droplets scatter ALL colors equally = white).

Three types of atmospheric scattering?

Classified by particle size relative to wavelength:

  • 🟦 Rayleigh — particles ≪ λ
    • Source: air molecules (N₂, O₂)
    • Affects: short wavelengths most (1/λ⁴ dependence)
    • Result: blue sky at noon, red at sunset
  • 🌫️ Mie — particles ≈ λ
    • Source: dust, smoke, aerosols, pollen
    • Affects: longer wavelengths and all of visible
    • Result: hazy skies
  • ☁️ Non-selective — particles ≫ λ
    • Source: water droplets, ice crystals
    • Affects: all wavelengths equally
    • Result: white clouds (B + G + R scattered equally → white)
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705 km, 2021. OLI-2 + TIRS-2 (the '-2' matches Landsat-9). With L8 flying opposite, combined revisit ≈ 8 days.

Landsat 9 — launch date, altitude, sensors?

  • 🚀 Launch: Sept 27, 2021
  • 🛰️ Orbit
    • Altitude: 705 km
    • Sun-synchronous, 10 AM equator crossing
    • 16-day repeat (8-day combined with Landsat 8)
  • 📷 Sensors (the “-2” matches Landsat-9)
    • OLI-2 — Operational Land Imager: 9 bands, 30 m VSWIR, 15 m pan
    • TIRS-2 — Thermal Infrared Sensor: 2 thermal bands at 100 m
  • 🎚️ Radiometric: 14-bit (vs 12-bit on L8, 8-bit on L5/7)
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Bands 1-2-3-4-5-7-6. Yes, 7 before 6. All 30 m except thermal band 6 at 120 m. Watch for 'Band 4 = NIR' (on TM) vs 'Band 5 = NIR' (on OLI).

Landsat TM — 7 bands and their resolutions?

TM has 7 spectral bands. All 30 m except thermal at 120 m.

  • 🟦🟩🟥 Visible (30 m)
    • Band 1 · Blue · 0.45–0.52 µm
    • Band 2 · Green · 0.52–0.60 µm
    • Band 3 · Red · 0.63–0.69 µm
  • 🟪 Near-infrared (30 m)
    • Band 4 · NIR · 0.76–0.90 µm
  • 🟫 Shortwave infrared (30 m)
    • Band 5 · SWIR-1 · 1.55–1.75 µm
    • Band 7 · SWIR-2 · 2.08–2.35 µm
  • 🔥 Thermal — coarser: 120 m
    • Band 6 · Thermal IR · 10.4–12.5 µm

⚠️ Numbering oddity: 1-2-3-4-5-7-6. Band 7 was added later and squeezed in spectrally between 5 and 6 but numbered last.

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Multi = few (tens), Hyper = many (hundreds), Thermal = heat only. 'Hyper' literally means MORE — that's the clue.

The three types of optical remote sensing?

  • 📊 Multispectral — a few broad discrete bands
    • Examples: Landsat OLI, SPOT HRV, IKONOS, MODIS
    • Typical: 4–10 bands across visible + NIR + SWIR
  • 🔥 Thermal — one or more bands in 3–14 µm IR
    • Examples: Landsat TIRS, ASTER thermal
    • Detects emitted heat (works day and night)
  • 🌈 Hyperspectral — hundreds of narrow contiguous bands
    • Examples: Hyperion (220 bands), AVIRIS
    • Identifies specific minerals, plant species, pollutants
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Whiskbroom WIGGLES a mirror (Landsat 1–7). Pushbroom PUSHES a linear array straight ahead (SPOT, IKONOS, Landsat 8/9 OLI). No wiggle, no breaking part.

Across-track vs along-track scanners — examples?

Two scanning geometries used by multispectral sensors:

  • 🔄 Across-track (whiskbroom)
    • How: discrete detectors + scanning mirror sweeps perpendicular to flight
    • Examples: Landsat MSS, TM, ETM+
    • Drawback: moving mirror = mechanical wear
  • ➡️ Along-track (pushbroom)
    • How: linear array of detectors — no moving parts
    • Examples: SPOT HRV, IRS LISS, IKONOS, QuickBird, Landsat 8/9 OLI
    • Wins on: longer dwell time → better SNR, more reliable
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IKONOS = 1 meter pan, 4 meter MS, 11-bit, at 681 km. Sub-meter commercial pioneer. Tilts ±45° (more than SPOT's ±27°).

IKONOS — altitude, bands, radiometric resolution?

  • 🛰️ Orbit
    • Altitude: 681 km
    • Sun-synchronous, 10:30 AM equator crossing
  • 📷 Bands
    • 🩶 Panchromatic (0.45–0.90 µm) → 1 m detail
    • 🟦🟩🟥🟪 Multispectral 4 bands (Blue/Green/Red/NIR) → 4 m detail
    • Pan-sharpening fuses them → effective 1 m color
  • 🎚️ Radiometric: 11-bit → 2 048 grey levels
  • 🎯 Off-nadir pointing: up to ±45° (along + across track)
  • 🏆 Heritage: first U.S. commercial sub-meter satellite (1999–2015)
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SPOT 1-3: 832 km (higher than IKONOS 681), 10 m pan / 20 m MS, no blue (Green-Red-NIR only). Off-nadir ±27°. French (CNES).

SPOT 1–3 — altitude, bands, orbit?

  • 🛰️ Orbit
    • Altitude: 832 km
    • Sun-synchronous, 10:30 AM equator crossing
  • ⏱️ Revisit
    • Nadir: 26 days
    • With off-nadir tilt (±27°): 1–4 days at mid-latitudes
  • 📷 Bands — no blue!
    • 🩶 Panchromatic (0.51–0.73 µm) — 10 m
    • 🟩 XS1 — Green (0.50–0.59 µm) — 20 m
    • 🟥 XS2 — Red (0.61–0.68 µm) — 20 m
    • 🟪 XS3 — NIR (0.79–0.89 µm) — 20 m

⚠️ No blue band on SPOT 1–3 → can’t make natural-color composites.

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NDVI = Normalized to −1..+1. Unlike SR which has no upper bound, and unlike EVI which adds the Blue band.

NDVI — formula and range?

Plants pull a sneaky trick with light: chlorophyll drinks red light for photosynthesis but bounces back invisible near-infrared. NDVI just compares the two bands — the bigger the gap, the healthier the vegetation. Numbers land between −1 (water / shadow) and +1 (lush rainforest). The middle is bare ground.

It’s basically a ‘how green is this place’ score that NASA, USDA, and every satellite ag company uses every day.

🔬 Science / formula

NDVI = (NIR − Red) / (NIR + Red). Range −1 to +1. Rouse et al. (1974).

  • Well-vegetated: high (0.6–0.8)
  • Bare rock/sand/snow: ≤ 0.1
  • Water: negative
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Simple Ratio = Simple division. No subtraction, no normalization — just NIR/Red. Unbounded. Cohen 1991 (not Rouse, that's NDVI).

Simple Ratio (SR) — formula and who’s credited?

The first vegetation index. Divide NIR by Red — see how much more NIR came back. A jungle gives you 30+, a parking lot gives you 1. Simple but the number has no upper limit, so you can’t easily compare scenes against each other.

That’s why NDVI replaced it for most modern work — same idea, but locked between −1 and +1.

🔬 Science / formula

SR = NIR / Red. Cohen (1991) identified it as the first true vegetation index. On Landsat TM: Band 4 / Band 3.

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EVI = Enhanced with the Blue band. Coefficients 6-7-1 (six-seven-one). Doesn't saturate in dense canopy like NDVI does.

EVI — formula and coefficients?

Think of EVI as NDVI’s smarter cousin. It does two extra tricks:

  • Uses the blue band to subtract atmospheric haze that fools NDVI on smoggy days.
  • Adds a soil-adjustment factor so dry dirt doesn’t artificially inflate the score.

Use EVI when NDVI flatlines — i.e., over thick rainforest canopy where every leaf already maxes NDVI out. EVI keeps climbing where NDVI gets stuck.

🔬 Science / formula

EVI = [(NIR − Red) / (NIR + C₁·Red − C₂·Blue + L)] · (1 + L)

C₁ = 6.0, C₂ = 7.5, L = 1.0 (MODIS standard). Corrects NDVI for atmosphere (blue band) and soil (L).

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Leaves DRINK red (chlorophyll eats it), BOUNCE NIR. That 'red dip, NIR jump' is THE vegetation fingerprint.

Spectral signature of healthy vegetation?

  • Low red reflectance — chlorophyll absorbs red for photosynthesis.
  • High NIR reflectance — scattered by spongy mesophyll leaf structure.

That contrast is why NDVI, SR, and EVI all work.

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Supervised needs a TEACHER (training samples). Unsupervised is CLUSTERING — the computer invents the classes, you label afterward.

Supervised vs. unsupervised classification — key differences?

Two camps of pixel classification:

  • 👨‍🏫 Supervised — needs a teacher
    • Algorithm: Maximum Likelihood (most common)
    • A priori knowledge: required — you give it training samples
    • Control: user-driven — you set the class scheme
    • Strength: more accurate when training is good
  • 🤖 Unsupervised — clusters on its own
    • Algorithm: ISODATA (or K-means)
    • A priori knowledge: not required — no training
    • Control: computer-automated — it finds the groupings
    • Strength: reveals natural groupings, fast first pass

After unsupervised you still label the clusters by hand — that’s where Recode comes in.

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N-T-M: Number (clusters), Threshold (convergence %), Max-iterations. Terminates on whichever hits first: T reached or M hit.

ISODATA — three parameters the user must set?

  • N — max number of clusters (= max classes).
  • T — convergence threshold: % of pixels unchanged between iterations to declare convergence.
  • M — max iterations (safety cap).
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ML uses **mean + covariance**, not just the mean. Min Distance ignores shape (just the mean). Mahalanobis adds shape. Max Likelihood adds priors on top. The full discriminant formula lives in the long-form review — the *concept* lives here.

Maximum Likelihood classifier — how it works and its main assumption?

Picture each land-cover class (forest, water, city) as a fuzzy cloud floating in spectral space. Max Likelihood asks the question:

“Which cloud is this pixel most likely sitting inside?”

Crucially, it considers each cloud’s shape (covariance), not just its center. Min Distance only looks at the center — it’s like deciding which city you’re closest to without checking which one’s borders you’re inside.

That’s why ML usually wins on accuracy: it understands a tightly-grouped class is more confident, while a wide loose class lets in more variety.

🔬 Science / formula

For each pixel, compute the probability it belongs to each class. Assign to the most likely class.

  • Key assumption: each class is multivariate Gaussian (each band normally distributed inside the class).
  • Uses the class mean AND covariance matrix — that’s how it accounts for class shape, not just position.
  • Strength: most accurate of the four decision rules when classes are well-sampled and bands are roughly normal.
  • Weakness: needs enough training samples to estimate covariance; fails on non-Gaussian classes.
  • Bayesian variant (Hord 1982): supply per-class prior probabilities instead of assuming equal priors.
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Train → Stats → Classify. You TEACH the computer with samples, it LEARNS signatures (mean + covariance), then APPLIES a decision rule to every pixel.

Supervised classification — three-step procedure?

  1. Select training samples — homogeneous AOIs per class.
  2. Generate & evaluate statistical signatures — mean, std, covariance per band.
  3. Class assignment via a decision rule (Min Distance, Max Likelihood, etc.).
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3-5-2: three statute miles visibility, five hundred feet below clouds, two thousand feet horizontal.

Part 107 weather minimums?

  • Visibility: 3 statute miles.
  • Cloud clearance: 500 ft below + 2 000 ft horizontal from clouds.
  • Daylight only (civil twilight with waiver).
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Four hundred and no more — unless you're inspecting a tall structure, then stay within 400 ft of it.

Part 107 maximum altitude for sUAS?

400 ft AGL above ground, or within 400 ft of a structure (above the structure’s height).

Max ground speed: 100 mph.

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A = Airliners. Above FL180. Never a drone's problem.

Class A airspace — altitude?

FL 180 – FL 600 MSL (18 000 ft to 60 000 ft MSL). IFR only. Not a drone concern — sUAS capped at 400 ft AGL.

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B = Big, Busy, Blue. Solid Blue lines. Wedding-cake tiers to 10 000 MSL.

Class B airspace — altitudes, sectional marking, drone rule?

B = Big, Busy, Blue.

  • 📐 Altitudes
    • Floor: surface (SFC)
    • Ceiling: typically 10 000 ft MSL
  • 🎨 Sectional marking: 🟦 solid blue lines
  • 🏛️ Shape: inverted wedding cake — tiers expand upward and outward
  • 🛸 sUAS rule: ATC authorization required (via LAANC)
  • 🏙️ Found at: the busiest US airports — JFK, ORD, ATL, LAX, BOS, SFO
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C = Solid magenta (think 'Cs = solid'). 4000 AGL ceiling. Rings 5/10 NM.

Class C airspace — altitudes, sectional marking, drone rule?

  • 📐 Altitudes
    • Floor: surface (in core)
    • Ceiling: typically 4 000 ft AGL
  • 🎨 Sectional marking: 🟪 solid magenta lines
  • 🏛️ Shape: two-ring layer cake
    • Inner ring: 5 NM radius, SFC – 4 000 AGL
    • Outer shelf: 10 NM radius, 1 200 AGL – 4 000 AGL
  • 🛸 sUAS rule: ATC authorization required
  • 🏛️ Found at: Syracuse, Cleveland, Albany — mid-size towered airports
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D = Dashed blue Donut. Small 4-5 NM cylinder, 2500 AGL.

Class D airspace — altitudes, sectional marking?

D = Dashed blue Donut.

  • 📐 Altitudes
    • Floor: surface
    • Ceiling: typically 2 500 ft AGL
  • 🎨 Sectional marking: 🟦 dashed blue lines
  • 🏛️ Shape: single cylinder, ~4–5 NM radius
  • 🛸 sUAS rule: ATC authorization required (via LAANC)
  • 🏛️ Found at: small towered airports
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E = Everywhere-else controlled. Dashed magenta = surface E (authorization). Shaded magenta = 700 AGL floor. Shaded blue = 1200 AGL floor.

Class E airspace — three common variants and their sectional markings?

E = Everywhere-else controlled. Three flavors:

  • 🟪 Surface-designated (dashed magenta line)
    • Floor: surface
    • Around airports without towers
    • sUAS rule: authorization required
  • 🟪 700 AGL floor (shaded magenta)
    • Floor: 700 ft AGL
    • Drones under 400 AGL stay below E → no authorization needed
  • 🟦 1 200 AGL floor (shaded blue)
    • Floor: 1 200 ft AGL
    • “Default” controlled airspace away from airports
    • No authorization needed for sUAS

⚠️ Only the surface-designated version requires LAANC.

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Parens = AGL. No parens = MSL. Always add 00. So 70/30 = 7000/3000 MSL; (12) = 1200 AGL.

MSL vs AGL — definitions and sectional chart rule?

  • AGL — Above Ground Level (height above terrain).
  • MSL — Mean Sea Level (absolute elevation).
  • On sectional charts: all altitudes MSL unless in parentheses — (12) means 1 200 ft AGL.
  • Add 00 to the printed number.

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