Welcome, Future Space Leaders! 🚀
This guide is designed to help you master the core concepts of Geodesy, Remote Sensing, and GIS for Module 2. Review the key topics, watch the lecture videos, and test yourself with the practice scenarios below.
Good luck with your studies and the upcoming exam!
1. Geodesy & The "Lies" of Mapping
🎯 Learning Objectives
- I can explain why "all maps are lies" (generalization, classification, projection).
- I can describe the 3 Earth models (Sphere, Ellipsoid, Geoid).
- I can list the 4 map distortions.
The Three Layers of Location
To define a location on Earth, we need three stacked layers:
- Geodesy: Modeling the Earth's shape (Ellipsoid).
- Coordinate System: A grid for address (Lat/Long).
- Map Projection: Flattening the 3D grid to 2D.
The Math of Height:
h = H + N
Ellipsoidal Height (h) = Orthometric Height (H) + Geoid Undulation (N)
h = H + N
Ellipsoidal Height (h) = Orthometric Height (H) + Geoid Undulation (N)
Coordinate Systems
Latitude (Phi): Measures angle North/South of the Equator. Lines are parallel "rungs on a ladder".
Longitude (Lambda): Measures angle East/West of the Prime Meridian. Lines converge at the poles (like orange slices).
Map Projections & Distortions
It is impossible to flatten a round earth without distortion. Projections are classified by the surface they use:
- Cylindrical: Good for Equatorial regions (e.g., Mercator).
- Conic: Good for Mid-latitudes (e.g., Albers, LCC).
- Azimuthal (Planar): Good for Polar regions.
Classes of Map Projections
Projections are also defined by what they preserve:
| Property | Preserves... | Use Case | Example |
|---|---|---|---|
| Conformal | Angles & Shapes (Locally) | Navigation, Topographic Maps | Mercator, Lambert Conformal Conic |
| Equal Area (Equivalent) | Areas | Thematic Maps (Population density, Land cover) whereby comparing size is critical. | Albers Equal Area Conic |
| Equidistant | Distance (from a specific point) | Radio ranges, Air travel distances | Azimuthal Equidistant |
Spotlight: The Mercator Projection
The Mercator is a Cylindrical Conformal projection.
- Pro: Preserves direction. A straight line is a constant compass bearing (Rhumb Line). Essential for sailors.
- Con: Distorts area massively at the poles. Greenland looks as big as Africa (it's actually 14x smaller).
The Modifiable Areal Unit Problem (MAUP)
Map results can change dramatically based solely on how you draw the boundaries. This is the "Gerrymandering" of geography.
The Problem: The same underlying data can yield completely opposite results depending on aggregation zones.
- Scenario 1 (Blue Wins): Grouping into vertical rows makes Blue the majority in every district.
- Scenario 2 (Red Wins): "Creative" shape drawing (Gerrymandering) packs Blue into fewer districts, allowing Red to win the majority.
Key Takeaway: Be skeptical of maps that aggregate data into arbitrary units (like zip codes or counties). Are the boundaries masking the truth?
Limits of Representation: Eye, Mind, and Color
Effective mapping requires understanding the limitations of the user and the technology.
| Limit | Concept | Implication for Mapping |
|---|---|---|
| Eye Limit | Visual Acuity & Distinction The human eye has a limit to the detail (spatial resolution) and the number of colors it can distinguish. |
Don't display data at a higher resolution than the screen/eye can resolve. While 8-bit offers 16.7M colors, we can only distinguishing ~10M. |
| Mind's Limit | Cognitive Load (Miller's Law) The human brain can only hold about 7 (±2) items in working memory. |
Classification Rule: Never use more than 5-7 classes in a Choropleth map. Users cannot distinguish or remember 12 different shades of blue. |
| Color Limit | Bit Depth (0-255) Digital images are limited by their bit depth. |
Computers bin the infinite continuity of reality into discrete integers (0-255 for 8-bit). We lose slight variations to "quantization." ➜ Explore Color Brewer Tool |
2. Remote Sensing Fundamentals
🎯 Learning Objectives
- I can define the 4 Resolutions (Spatial, Spectral, Temporal, Radiometric).
- I can interpret a spectral signature graph.
- I can distinguish between Active and Passive sensors.
- I can explain how to create a False Color Composite.
The 4 Resolutions
| Resolution | Definition | Example |
|---|---|---|
| Spatial | Pixel size on ground | 30m (Landsat) vs 1m (Aerial) |
| Spectral | Number/width of bands | Multispectral (10 bands) vs Hyperspectral (200 bands) |
| Temporal | Revisit time | Daily (Weather) vs 16 days (Landsat) |
| Radiometric | Sensitivity (bit depth) | 8-bit (256 levels) vs 12-bit (4096 levels) |
Spectral Signatures
Every material reflects light differently. This "signature" allows us to identify materials.
Active vs. Passive Sensors
- Passive: Uses sun's energy (Photography, Landsat). No data at night.
- Active: Sends own energy pulse (LiDAR, Radar). Works day/night and through clouds (Radar).
3. Data Models & Analysis
🎯 Learning Objectives
- I can calculate and interpret NDVI.
- I can compare Raster vs. Vector data models.
- I can explain Supervised vs. Unsupervised Classification.
Raster vs. Vector
| Model | Best For... | Example |
|---|---|---|
| Raster | Continuous data | Elevation, Temperature, Satellite Imagery |
| Vector | Discrete data | Roads, Property Lines, Cities |
NDVI (Vegetation Index)
Uses the contrast between RED (absorbed by plants) and NIR (reflected by plants) to measure health.
NDVI = (NIR - Red) / (NIR + Red)
Interpretation:
- > 0.5: Healthy Vegetation
- 0.1 - 0.2: Bare Soil
- < 0: Non-vegetated and Impervious Land Cover (Water, Concrete, Snow)
📐 Formula Sheet
DMS to DD Conversion
DD = Degrees + (Minutes / 60) + (Seconds / 3600)
*Make negative for South or West!
DD = Degrees + (Minutes / 60) + (Seconds / 3600)
*Make negative for South or West!
NDVI
NDVI = (NIR - Red) / (NIR + Red)
NDVI = (NIR - Red) / (NIR + Red)
Eratosthenes' Calculation
Circumference = Distance × (360° / Shadow Angle)
Circumference = Distance × (360° / Shadow Angle)
8-bit Image Colors
2⁸ = 256 levels (0-255) per channel
2⁸ = 256 levels (0-255) per channel
📺 Video Lecture Library
Review key concepts with these selected video lectures.
Additional Resources:
➜ Look at Weeks 1 and 2 on "Think" (RSGEE)
➜ Look at Weeks 1 and 2 on "Think" (RSGEE)
Landsat: 25 Years in the Pacific Northwest Forest
What is MODIS Aqua - Vizualization of Data
Everything you want to know about Map Projections
What is GIS Data?
Lying with Maps - MAUPs, Choropleths, and Tornadoes
The Cartographic Communication Channel
How many categories should I choose in a map legend?
Cartographic Generalization - What is it?
Red State, Blue State - The Power of Maps
📝 Practice Questions
Test yourself! Click to reveal the answer.
1. A satellite image has a Spatial Resolution of 30 meters. What does this mean?
Each pixel in the image represents a 30m x 30m square area on the
ground. You cannot distinguish objects smaller than this size.
2. Calculate the NDVI for a pixel with Red=0.1 and NIR=0.5.
NDVI = (0.5 - 0.1) / (0.5 + 0.1) = 0.4 / 0.6 = 0.66
This indicates healthy vegetation.
This indicates healthy vegetation.
3. Why do we divide by (NIR + Red) in the NDVI formula?
To normalize the data. This scales the result
between -1 and +1, allowing us to compare images taken at different
times of day or seasons without lighting differences ruining the
comparison.
4. Name one advantage of LiDAR (Active) over standard Satellite Imagery (Passive).
LiDAR can penetrate gaps in forest canopy to measure the ground
("bare earth" model) using multiple returns. It also works at night!
5. You want to map specific tree species in a forest. Which type of resolution is most critical?
Spectral Resolution. You need many narrow bands
(Hyperspectral) to detect the subtle "signature" differences between
tree species.
6. Convert 30° 30' 00" West to Decimal Degrees.
30 mins / 60 = 0.5 deg.
Total = 30.5.
Since it is WEST, it must be negative.
Answer: -30.50
Total = 30.5.
Since it is WEST, it must be negative.
Answer: -30.50
7. Explain the evolution of Earth Models (Sphere -> Ellipsoid -> Geoid).
- Sphere: Simple, used for small scales (globes). Inaccurate for GPS.
- Ellipsoid (WGS 84): Flattens at poles due to rotation (Centrifugal Force). Used for GPS coordinates.
- Geoid: "Lumpy" model based on gravity/sea level. The most accurate representation of Earth's true shape.
8. Compare SRTM (30m) vs. LiDAR (1m) for flood mapping.
SRTM (30m) is too coarse; it might miss small levees or channels, leading to inaccurate flood predictions.
LiDAR (1m) captures micro-topography, allowing for precise modeling of water flow and flood risks in urban areas.
LiDAR (1m) captures micro-topography, allowing for precise modeling of water flow and flood risks in urban areas.
9. What are the trade-offs between Drone (SfM) and Satellite Imagery?
Drone (SfM): High resolution (cm-level), flexible timing, but small coverage area and short battery life.
Satellite: Global coverage, consistent revisit times, but lower resolution and subject to cloud cover.
Satellite: Global coverage, consistent revisit times, but lower resolution and subject to cloud cover.
10. What is a Geodetic Datum (e.g., WGS 84)?
A reference system that defines the size/shape of the Earth (Ellipsoid) and its position relative to the center of the Earth. It "anchors" coordinates to the planet.
11. Explain the difference between Raster and Vector data.
Raster: Grid of pixels (best for continuous data like elevation/imagery).
Vector: Points, lines, and polygons (best for discrete objects like roads/property boundaries).
Vector: Points, lines, and polygons (best for discrete objects like roads/property boundaries).
12. Why does the Mercator projection distort area at the poles?
It is a Cylindrical projection. To keep lines of longitude parallel (straight up/down) instead of converging at the poles, it stretches the map horizontally and vertically as you move away from the Equator.
13. You have an 8-bit image. What is the maximum pixel value?
255. (2^8 = 256 possible values, ranging from 0 to 255).
14. What is the "Orange Peel Problem" in mapping?
The mathematical impossibility of flattening a 3D sphere onto a 2D plane without tearing, stretching, or compressing it (distortion).
15. True or False: A "Red State / Blue State" map is immune to the MAUP.
False. It is a classic example. Changing the boundaries (e.g., from State to County) completely changes the visual story.
16. What does a "False Color Composite" (NIR, Red, Green) help visualize?
It makes vegetation pop out in bright Red. This leverages the high reflectance of healthy plants in the Near-Infrared (NIR) band.
17. Why is "Temporal Resolution" important for disaster response?
It determines how often a satellite revisits the same spot. In a rapidly changing disaster (flood/fire), you need daily (or hourly) images, not just one every 16 days.
18. In GIS logic, what does "Forest AND Elevation > 1000m" do?
It acts as a filter (Intersection). It selects only those areas that meet *BOTH* criteria simultaneously.
19. Which coordinate system layer uses "Easting and Northing"?
A Projected Coordinate System (like UTM). These are Cartesian coordinates (X, Y) on a flat 2D plane, unlike Lat/Long which are angles.
🚀 Advanced Scenario Practice
20. Scenario: Mapping Air Quality. You have (A) Average pollution levels by city district (Discrete) and (B) Continuous sensor node data (Continuous). Which map type for each?
- (A) By District: Use a Choropleth Map. It colors defined areas (polygons) based on a value.
- (B) Continuous Data: Use an Isopleth Map (Heatmap/Contour). Air pollution drifts continuously across borders; it doesn't stop at a city line.
21. Scenario: Global Forest Map. Why is the Mercator projection a poor choice for comparing the size of the Amazon Rainforest (Equator) vs. the Siberian Taiga (High North)?
Mercator maps are Conformal (good for shapes/angles) but not Equal Area. It severely stretches areas near the poles. The Taiga would look disproportionately huge compared to the Amazon, misleading the viewer about the actual amount of forest cover.
22. Calculate: Convert Sydney Opera House Coordinates (33° 51' 24" S, 151° 12' 36" E) to Decimal Degrees.
- Latitude (South is Negative): -(33 + 51/60 + 24/3600) = -(33 + 0.85 + 0.0067) = -33.8567
- Longitude (East is Positive): 151 + 12/60 + 36/3600 = 151 + 0.2 + 0.01 = 151.21
23. Scenario: The "Fake Grass" Detective. A soccer field looks bright green (RGB) but has a very low NDVI (0.05). Why?
It is likely Artificial Turf (Plastic). While it reflects Green light (looking real to the eye), plastic does NOT have the cell structure to reflect Near-Infrared (NIR) light. Real grass would reflect NIR strongly, resulting in a high NDVI (> 0.6).
24. Scenario: Oil Spill Tracking. You need to monitor a rapidly spreading oil spill. Which two resolutions are critical?
- Temporal Resolution: Critical. You need images *every few hours or days* to see where the oil is moving. A 16-day revisit time is useless here.
- Spectral Resolution: Important. You need specific bands (Thermal/IR) to distinguish oil from water.
25. Scenario: Spy vs. Weather Satellite. Satellite A visits the same spot at the same time every day. Satellite B hovers over one spot constantly. Name their orbits.
- Satellite A (Spy/Monitoring): Sun-Synchronous Orbit (Polar). Good for consistent lighting for comparisons.
- Satellite B (Weather/Comms): Geostationary Orbit. Matches Earth's rotation to "stare" at one hemisphere.
📚 Glossary
Atmospheric Window
Wavelengths of light that can pass through the atmosphere (e.g.,
visible light) without being absorbed. Sensors are designed to look
through these "windows."
Geoid
The most accurate Earth model based on gravity/mean sea level. It is
lumpy and irregular, unlike the smooth mathematical Ellipsoid.
Structure from Motion (SfM)
A technique using drone photography (2D images) to build 3D models.
WGS 84
The standard "Ellipsoid" model used by GPS. It defines the
coordinate system for the planet.
False Color Composite
An image where bands are assigned to wrong colors (e.g., NIR
displayed as Red) to highlight features like vegetation.
MAUP
Modifiable Areal Unit Problem. The statistical bias that occurs when
you aggregate data into arbitrary zones (like states).
Centrifugal Force
The outward force caused by Earth's rotation, making it bulge at the equator (creating an Ellipsoid).
Geodetic Datum
A reference system (like WGS 84) that positions the ellipsoid relative to Earth's center. Essential for GPS.
Point Cloud
A massive collection of X,Y,Z points generated by LiDAR, representing the 3D surface of the world.
Map Algebra
Math applied to raster pixels. Example: (Band 4 - Band 3) to calculate NDVI.
Boolean Logic
True/False logic used in GIS analysis (e.g., Select pixels where Elevation > 100 AND Land Cover = 'Forest').
Impervious Surface
Man-made surfaces (asphalt, concrete) that water cannot penetrate. High runoff, low NDVI.
Lambert Conformal Conic
A "cone-based" projection best for areas extending East-West (like the USA or Tennessee).
Transverse Mercator
A "cylinder-based" projection turned sideways, best for areas extending North-South (like Chile or UTM zones).
Equal Area Projection
A map projection that maintains the correct relative sizes of areas (e.g., Albers Equal Area). Essential for density maps.
Equidistant Projection
A map projection that maintains accurate distances from one or two specific points to all other points.
Conformal Projection
A map projection that preserves local angles and shapes (e.g., Mercator). Grid lines intersect at 90 degrees.
Orthometric Height (H)
The elevation above the Geoid (Mean Sea Level). This is the height found on topographic maps.
Ellipsoidal Height (h)
The height above the reference ellipsoid. This is the raw height measured by a GPS receiver.