Lecture slides for GIS/MEA582

Viewshed analysis and solar radiation

Helena Mitasova

GIS/MEA582 Geospatial Modeling and Analysis NCSU

Learning objectives

understand line of sight
define viewshed, cumulative viewshed and viewscape
explain components of solar radiation in complex terrain
understand cast shadow and solar inclination angle
explain cumulative solar radiation, solar energy potential

Line of sight

Line of sight (LoS) analysis is used to identify points on the terrain surface along a given line that are visible from an observer point on this line
LoS analysis or ray-tracing is used for:
- 3D visualization
- visibility and viewshed analysis
- emitor-receptor systems design taking into account decay of signal with distance, for example, to optimize locations of cell towers

Computing Line of sight

Given a viewing point $A$ and a target point $B$, $B$ is visible from $A$ if:
all lines $AC_i$ are below the line $AB$
where the set of points $C_i$ represents projection of the line $AB$ on the surface

Computing Line of sight

any line $AC_i$ is above the line $AB$
where the set of points $C_i$ represents projection of $AB$ on the surface

Viewshed

region defined by a set of grid cells (or triangles) visible from a given viewing point
computed by applying LOS analysis from the viewing point to each cell within a given distance
can be implemented for TIN or raster DEMs
binary visibility map (yes/no)
angle above/below horizontal plane
relative elevation above/under horizontal plane
shows what is visible from the given point or
from where one can see the given point

Viewshed example 1

Visibility analysis from buildings, 30m resolution DTM
Relative height above the surface: 4 and 32 story building

Compute and compare land cover composition for each viewshed in the assignment

Viewshed example 2

Visibility analysis from balcony of the Hunt library
10m resolution DTM and 1m resolution DSM

Viewshed example 2

Visibility analysis from buildings, 1m resolution DSM
Observer point at a balcony of the Hunt library and on upper floor of Jordan hall

Viewshed example 3

Visibility analysis for finding a location for a webcam to support real-time monitoring of a watershed
Above-ground height 1.75 and 6m, 1m resolution DTM

Starek, M.J., et al., 2020, Viewshed simulation and optimization for digital terrain modelling with terrestrial laser scanning, International Journal of Re-mote Sensing, 41:16, 6409-6426

Viewshed example 4

High resolution viewshed analysis input

Replacing "tree mounds" in DSM with tree trunks. Tabrizian et al. 2020, High Resolution Viewscape Modeling Evaluated Through Immersive Virtual Environments. ISPRS Int. J. Geo-Inf. 9, 445.

Viewshed example 4

High resolution viewshed analysis with improved representation of trees: Dix park application

Tabrizian et al. 2020, High Resolution Viewscape Modeling Evaluated Through Immersive Virtual Environments. ISPRS Int. J. Geo-Inf. 9, 445.

Cumulative Viewshed

Set of grid cells visible from a set of points:

find a path that has minimum or maximum visibility
optimize distribution of signal sources to achieve the maximum coverage
limit development to areas that are not visible - e.g. from the Blue Ridge Parkway minimize visibility of wind turbines

Starek, M.J., et al., 2020, Viewshed simulation and optimization for digital terrain modelling with terrestrial laser scanning, International Journal of Re-mote Sensing, 41:16, 6409-6426

Solar radiation

controls surface energy and water balance
affects atmospheric, biophysical and hydrologic processes
provides a source of renewable energy

Surface net radiation

Spatially and temporally variable and depends on

orientation of Earth relative to Sun (or position of Sun relative to a given point on Earth)
topography: slope, aspect and shadowing
clouds and other atmospheric properties
surrounding surface properties (land cover)

Solar radiation components

Sun position

Given a date, time, and a location, for example:

2001.12.22, day number 356, time: 14:25:00

long: -78.678856, lat: 35.736160, timezone: -5.000

sun position is given by

solar azimuth (measured in horizontal plane ): 212.7934...
solar altitude (sun angle above horizon): 23.1924

Sun position parameters

2001-12-22, day number 356, time: 14:25:00, long: -78.678856, lat: 35.736160, timezone: -5.000

solar azimuth: 212.7934...
solar altitude or inclination: 23.1924
sun declination - angle between solar beam and earth equator: -23.4405 (winter solstice, sun above the Tropic of Capricorn)
sunrise time (without refraction cor.): 07:26:30
sunset time (without refraction cor.): 17:00:28
atm. refraction correction: inclination > 0 before sunrise

Solar incidence angle

Angle between the terrain normal and solar beam

solar beam: defined by solar inclination and azimuth
terrain normal: 3D vector orthogonal to the plane tangent to terrain surface,
terrain normal: function of slope and aspect, horizontal projection of terrain normal is gradient $\nabla z = (f_x,f_y)$

Modified from Batson et al., 1975, see also 8.1.8 in Hengl et al., 2008, Geomorphometry or A.62 in Neteler et al., 2008 Appendix

Solar incidence angle map

Solar incidence angle for winter solstice around 2pm, lat=35.736160, including a building with cast shadow

Solar incidence angle dynamics

Solar incidence angle dynamics during summer and winter solstice for a small valley at 45 deg lat.

Solar incidence angle dynamics

Solar incidence angle dynamics during summer and winter solstice for a small valley at 45 deg lat.

Solar irradiance

Solar beam (direct) irradiance for inclined plane in $W/m^2$ is function of:

solar incidence angle
solar constant $[W/m^2]$
atmospheric factors (clear sky):
- Linke turbidity factor (atm. turbidity due to aerosols - reduces direct radiation)
- Rayleigh optical thickness (thickness of clear atm., function of surface pressure)
cloud cover
computed as cumulative solar irradiance: daily $Wh/(m^2.day)$, monthly, seasonal, annual