BE Civil Engineering (IOE, TU) Remote Sensing and GIS (IOE, CE 754) Question Paper 2076 Nepal

1. The EM spectrum in remote sensing

Remote sensing relies on detecting electromagnetic energy that is reflected or emitted from the Earth's surface. The energy travels as waves characterised by wavelength $\lambda$ and frequency $\nu$, related by $c = \lambda\nu$, where $c = 3\times10^{8}\ \text{m/s}$.

Labelled sketch (increasing wavelength to the right)

 Gamma | X-ray | UV | VISIBLE | Near-IR | Mid-IR | Thermal-IR | Microwave | Radio
             0.4um  0.7um    1.3um    3um      14um        1mm        1m
           |<------ optical / reflective ------>|<-emissive->|<- radar ->|

Major spectral regions and civil applications

Atmospheric windows

The atmosphere absorbs EM energy selectively (mainly via H2O, CO2, O3). The wavelength bands where transmission is high are called atmospheric windows; sensors are designed to operate within them. Major windows lie in the visible/NIR (0.4-1.3 um), several in the mid/thermal IR (3-5 um and 8-14 um), and a very wide window in the microwave region (> 2 cm), which is why radar is essentially all-weather.

2. Wien's displacement law calculation

Wien's law gives the wavelength of peak spectral exitance of a blackbody:

$$\lambda_{max} = \frac{b}{T}$$

Given $b = 2898\ \mu\text{m}\cdot\text{K}$ and $T = 320\ \text{K}$:

$$\lambda_{max} = \frac{2898\ \mu\text{m}\cdot\text{K}}{320\ \text{K}} = 9.056\ \mu\text{m}$$

The peak emission occurs at $\lambda_{max} \approx 9.06\ \mu\text{m}$, which lies in the thermal-infrared region (8-14 um window). This confirms that a thermal sensor operating in the 8-14 um window is the correct choice for sensing emitted heat from a pavement at ambient road temperature.

Four types of resolution

• Spatial resolution — the smallest ground area represented by one pixel (the GSD); governs how much fine detail can be seen.
• Spectral resolution — the number and width of wavelength bands the sensor records; finer (narrower, more) bands allow better material discrimination.
• Radiometric resolution — the number of digital quantisation levels (bit depth) used to record brightness; higher bit depth resolves subtle reflectance differences.
• Temporal resolution — the revisit interval, i.e. how often the same area is imaged; important for change-detection and disaster monitoring.

Trade-offs

For a fixed sensor/data-rate budget, improving one resolution usually degrades another. A small IFOV (fine spatial resolution) collects less energy per pixel, so to keep signal-to-noise acceptable the band must be widened (coarser spectral resolution) or dwell time increased. Higher radiometric and spectral resolution increase data volume, often forcing a narrower swath that lengthens the revisit time (coarser temporal resolution).

(a) Ground Sampling Distance

For a frame/pushbroom optical system the GSD at nadir follows from similar triangles:

$$\text{GSD} = \frac{p \cdot H}{f}$$

Convert to consistent SI units: $p = 13\ \mu\text{m} = 13\times10^{-6}\ \text{m}$, $H = 700\ \text{km} = 7.0\times10^{5}\ \text{m}$, $f = 10\ \text{m}$.

$$\text{GSD} = \frac{(13\times10^{-6}\ \text{m})(7.0\times10^{5}\ \text{m})}{10\ \text{m}} = \frac{9.1}{10}\ \text{m} = 0.91\ \text{m}$$

GSD = 0.91 m (i.e. about 0.91 m per pixel at nadir).

(b) Grey levels

For a 12-bit quantisation the number of discrete grey levels is:

$$2^{12} = 4096\ \text{levels (0 to 4095)}$$

Each pixel can store 4096 grey levels. This property is the sensor's radiometric resolution.

Major steps of digital image processing

1. Pre-processing (restoration): corrects sensor and platform-induced errors before analysis.

• Radiometric correction: removes striping, line dropout, sensor-gain errors and atmospheric haze; converts DN to radiance/reflectance.
• Geometric correction: removes distortions from Earth curvature, relief and platform attitude; includes georeferencing and resampling to a map projection.

2. Enhancement: improves visual interpretability without changing information content.

• Contrast stretching, density slicing, spatial filtering (smoothing/edge detection), band ratioing and principal component analysis.

3. Classification: assigns pixels to thematic land-cover classes.

• Supervised (training samples + maximum-likelihood / SVM) and unsupervised (clustering, e.g. ISODATA, K-means), followed by accuracy assessment.

Linear contrast stretch

The min-max linear stretch maps the input range $[DN_{min}, DN_{max}]$ onto the full display range $[0, 255]$:

$$DN_{out} = \left(\frac{DN_{in} - DN_{min}}{DN_{max} - DN_{min}}\right)\times 255$$

Here $DN_{min} = 60$, $DN_{max} = 158$, so $DN_{max} - DN_{min} = 98$.

How contrast improves

Before stretching the data used only $158-60 = 98$ of the available 256 levels (about 38% of the dynamic range), so the image appeared flat and low-contrast. After stretching, the same scene spans the full 0-255 range; differences between adjacent features are spread over a wider brightness span, making edges and tonal variations far more distinguishable.

Stretched values: DN(60) = 0, DN(100) = 104, DN(158) = 255.

Raster vs vector data models

Representation of a road and a forest polygon

VECTOR                          RASTER (R = road cell, F = forest cell, . = other)
 Road = polyline:               . . R . . .
  (2,1)-(2,3)-(4,4)             . . R . . .
 Forest = polygon:              . . R F F .
  closed ring of vertices       . . . F F .
                                . . . F F .

In vector the road is one line feature (an ordered vertex list) and the forest is one polygon (a closed ring); in raster both are approximated by sets of coded cells.

(a) Grid dimensions

Area = 4 km (E-W) x 3 km (N-S), cell size = 20 m.

• Columns = $\dfrac{4000\ \text{m}}{20\ \text{m}} = 200$ columns
• Rows = $\dfrac{3000\ \text{m}}{20\ \text{m}} = 150$ rows
• Total cells = $200 \times 150 = 30{,}000$ cells

(b) Uncompressed file size

Each cell = 8 bits = 1 byte.

$$\text{Size} = 30{,}000\ \text{cells} \times 1\ \text{byte} = 30{,}000\ \text{bytes}$$ $$= \frac{30{,}000}{1024}\ \text{KB} = 29.30\ \text{KB}$$

Grid = 150 rows x 200 columns = 30,000 cells; uncompressed size = 30,000 bytes ≈ 29.30 KB.

Working principle of GPS

GPS is a satellite-based positioning system organised in three segments:

• Space segment — a constellation of ≥ 24 satellites in ~20,200 km medium Earth orbit, each broadcasting coded timing signals and ephemeris data.
• Control segment — ground monitoring/master control stations that track the satellites, compute orbit/clock corrections and upload them.
• User segment — the receivers that decode signals and compute position, velocity and time.

Trilateration

The receiver measures the distance to each satellite from the signal travel time ($d = c\,t$). One distance defines a sphere of possible positions around the satellite. The intersection of three spheres narrows the position to (generally) two points, one of which is rejected as non-physical (off the Earth). This geometric method of fixing position from multiple known distances is trilateration.

Why four satellites?

Three satellites suffice for the three unknowns of position ($X, Y, Z$). However, the inexpensive receiver clock is not perfectly synchronised with the atomic satellite clocks, introducing a fourth unknown — the receiver clock bias ($\Delta t$). A fourth satellite provides the extra equation needed to solve simultaneously for $X, Y, Z$ and $\Delta t$. That is why the measured ranges are called pseudoranges (range plus clock-bias error) and why four satellites are the minimum for a 3-D fix.

(a) Pseudorange

$$d = c \cdot t = (3\times10^{8}\ \text{m/s})(0.07\ \text{s}) = 2.1\times10^{7}\ \text{m}$$

Pseudorange d = 2.1 × 10⁷ m = 21,000 km. (This is consistent with the ~20,200 km GPS orbit altitude plus slant range.)

(b) Dilution of Precision (DOP)

DOP is a dimensionless number describing how the geometric arrangement of the satellites amplifies measurement error into position error: $\sigma_{position} = \text{DOP}\times\sigma_{measurement}$. Satellites spread widely across the sky give strong geometry and a low DOP; satellites clustered together give weak geometry and a high DOP.

A low DOP value is desirable because it corresponds to better satellite geometry and a more accurate position fix.

NDVI

NDVI exploits the contrast between strong chlorophyll absorption in the red band and strong leaf-mesophyll scattering (high reflectance) in the near-infrared (NIR) band. It is defined as:

$$\text{NDVI} = \frac{\rho_{NIR} - \rho_{Red}}{\rho_{NIR} + \rho_{Red}}$$

The index is bounded in the range −1 to +1. Healthy, dense vegetation gives high positive values (~0.6-0.9); bare soil gives low positive values (~0.1-0.2); water and clouds typically give values around 0 or negative.

Calculation

Given $\rho_{NIR} = 0.52$ and $\rho_{Red} = 0.08$:

$$\text{NDVI} = \frac{0.52 - 0.08}{0.52 + 0.08} = \frac{0.44}{0.60} = 0.733$$

Interpretation

NDVI ≈ 0.73. This high positive value indicates dense, healthy, photosynthetically active vegetation — consistent with a well-grown agricultural crop. The large NIR/red contrast confirms vigorous green biomass rather than bare soil or stressed plants.

(a) Overall accuracy

Overall accuracy = (sum of diagonal correctly classified pixels) / (total reference pixels):

$$\text{OA} = \frac{45 + 70 + 62}{200} = \frac{177}{200} = 0.885 = 88.5\%$$

Overall accuracy = 88.5%.

(b) Forest-class accuracies

For the Forest class: diagonal (correct) = 70, classified-as-Forest row total = 80, reference Forest column total = 80.

Producer's accuracy (omission viewpoint — of all true Forest points, how many were correctly mapped):

$$\text{PA}_{Forest} = \frac{70}{\text{column total}} = \frac{70}{80} = 0.875 = 87.5\%$$

User's accuracy (commission viewpoint — of all points mapped as Forest, how many are truly Forest):

$$\text{UA}_{Forest} = \frac{70}{\text{row total}} = \frac{70}{80} = 0.875 = 87.5\%$$

Producer's accuracy (Forest) = 87.5%; User's accuracy (Forest) = 87.5%. (Here both equal 87.5% only because the Forest row and column totals happen to be identical at 80; in general they differ.)

Buffer analysis

A buffer creates a zone of a specified distance around point, line or polygon features. It answers proximity questions such as "what lies within X metres of this feature?". Civil use: defining right-of-way / setback corridors along roads, rivers or transmission lines, or protection zones around water-supply intakes.

Overlay analysis

Overlay combines two or more spatial layers to create new features and attributes, using operations such as union, intersect, and clip (vector) or map algebra (raster). Civil use: site suitability analysis — overlaying slope, land-use, soil and proximity layers to select a suitable site for a landfill, reservoir or building.

Buffer corridor area

The corridor is a rectangle: length = centreline length, width = buffer on both sides.

• Length $L = 5\ \text{km} = 5000\ \text{m}$
• Width $W = 30\ \text{m} + 30\ \text{m} = 60\ \text{m}$ (both sides)

$$A = L \times W = 5000\ \text{m} \times 60\ \text{m} = 300{,}000\ \text{m}^2$$

Convert to hectares ($1\ \text{ha} = 10{,}000\ \text{m}^2$):

$$A = \frac{300{,}000}{10{,}000} = 30\ \text{ha}$$

Buffer corridor area = 30 hectares.

Digital Elevation Model

A DEM is a raster representation of the bare-earth terrain surface, where each cell stores a ground elevation value. (When surface features such as buildings and trees are included it is a Digital Surface Model, DSM.)

Two methods of generation:

1. Stereo-photogrammetry / stereo satellite imagery (e.g. parallax from overlapping stereo pairs).
2. Active sensing — LiDAR or radar interferometry (InSAR); also ground survey / digitised contours interpolated to a grid.

Slope at the centre cell (steepest adjacent drop)

Centre elevation $z_c = 1255\ \text{m}$. The 8 neighbours and their elevation differences ($z_c - z_{neighbour}$, positive = downhill) are:

Slope to each downhill neighbour = drop / horizontal distance. The candidates:

• W: $7/30 = 0.2333$
• S: $8/30 = 0.2667$
• SW: $15/42.43 = 0.3536$ ← steepest
• NW: $5/42.43 = 0.1179$

The maximum gradient is toward the SW cell:

$$\tan\theta = \frac{\Delta z}{\text{distance}} = \frac{15\ \text{m}}{42.43\ \text{m}} = 0.3536$$ $$\theta = \tan^{-1}(0.3536) = 19.47^{\circ}$$

Slope at the centre cell ≈ 19.5° (steepest descent toward the south-west neighbour).

Elements of visual image interpretation

The standard elements are: tone/colour, shape, size, pattern, texture, shadow, site/association, and height/depth (stereo). An interpreter combines these clues to identify and delineate features.

(a) Photo scale

For a vertical photograph over flat terrain the scale is:

$$S = \frac{f}{H} = \frac{0.152\ \text{m}}{2280\ \text{m}} = \frac{1}{15{,}000}$$

Check: $2280 / 0.152 = 15{,}000$.

Scale = 1 : 15,000.

(b) True ground length of the road

Ground distance = photo distance / scale = photo distance × scale denominator:

$$D_{ground} = 84\ \text{mm} \times 15{,}000 = 1{,}260{,}000\ \text{mm}$$ $$= 1260\ \text{m}$$

True ground length of the road = 1260 m (1.26 km).

Integrated RS and GIS in civil engineering (Nepalese context)

Remote sensing supplies up-to-date spatial data (imagery, DEMs, change detection) over large and often inaccessible terrain; GIS stores, integrates, analyses and models that data with other layers to support decisions. In Nepal's rugged, hazard-prone geography the combination is especially valuable.

1. Landslide and flood hazard mapping — RS provides multitemporal imagery and DEMs to map slope, aspect, lineaments, land cover and rainfall-triggered changes; GIS overlays these factors (weighted overlay / AHP) to produce hazard-susceptibility maps. Critical in the mid-hills and for GLOF/flood risk in river basins such as the Koshi and Karnali.

2. Watershed and water-resource planning — DEM-derived drainage networks, catchment delineation and slope analysis in GIS support hydropower siting, irrigation command-area planning and soil-erosion (RUSLE) modelling, which is central to Nepal's hydropower-driven development.

3. Infrastructure and route (road/transmission) alignment — RS imagery and DEMs feed GIS least-cost-path and corridor analysis to select road and transmission-line alignments that minimise cut/fill, avoid unstable slopes and reduce land acquisition — important for strategic and rural road networks in difficult terrain.

4. Land-use / urban planning — classified satellite imagery monitors urban sprawl (e.g. Kathmandu Valley), encroachment and land-cover change; GIS supports zoning, utility planning, cadastre and earthquake-risk-sensitive land-use planning following the 2015 Gorkha earthquake.

Role summary: Remote sensing is the primary data-acquisition tool (synoptic, repetitive, all-terrain coverage); GIS is the integration, analysis and decision-support platform. Together they enable faster, cheaper and more objective planning, monitoring and disaster response than ground survey alone.