A Vectorial Model to Compute Terrain Parameters and Solar Radiation
on TIN Domains.Hernan A. Moreno
Fred OgdenRobert C. Steinke
Nels Frazier
Department of Civil and Architectural EngineeringUniversity of Wyoming
EPSCoREPS1135483
3rd Conference on Hydroinformatics-2015
Outline
Motivation Application Basin TIN Properties Solar Vector Computation Radiation on Inclined Surfaces Local and Remote Shading Next Steps
Motivation TINs provide economy and
versatility. Tessellations improve
representation of topography. Fewer data points allow storage
and processing economy. Faster processing times than
DEMs which scale well with parallel runs.
Model large basins or small basins with very fine resolution.
Motivation Preserving high resolution at process-active areas is
critical for accurate modeling.
-Elevation - Slope- Aspect- Solar radiation- Evaporation- Transpiration
- Runoff & surface flow- Erosion & transport- Infiltration- Subsurface flow- Channel formation- Energy balance
- Surface-subsurface water interactions- Variable saturated areas- Solar energy potential- Snow accumulation and melt- Contaminant fate and transport- Soil moisture
Insolation modeling
Measurement Pro ConInterpolation of point measurements
Highly accurate source to interpolate.
Expensive. Poorly performance in complex topography.
Meteorologicgeostationary satellites
Large areal coverage at relatively low cost.
Low spatio-temporal resolution.Only work under clear sky conditions.
Spatially-based solar radiation models
Cost-efficient way with high spatio-temporalresolution
So far they have only been tested in DEMs with time-expensive routines.
We propose an efficient and novel methodology for rapid calculation of topographic parameters (slope and aspect) and to better estimate INSOLATION on TIN elements for hydrologic applications.
INSOLATION=SWdir + SWremote + SWdiffuse
Study Basin
Basin Area: 1220 km2
THANKS
Green River, Wyoming
TIN properties
DEM=158,325 cellsTIN=36,436 elements
DEM
TIN
P1
P2
P3
n=(P3-P1)x(P2-P1)
z
x
y
Normal Unit Vector
nx
nz
S
S
kn+jn+in=n uzuyuxu
nn+jnn+inn=n zyxu 0> zzyx nk;n+jn+in=nSlope of plane from normal vector
Slope of plane from eq. plane
Equation of the plane
( )uzn=S arccos
0=d+Zn+Yn+Xn zyx
22
yz+
xz=S'
nux
Mean Median St. Dev. Skewness
-0.012 -0.0005 0.042 -0.003
nuy
Mean Median St. Dev. Skewness
-0.0024 -0.0037 0.0454 0.00026
nuz
Mean Median St. Dev. Skewness
0.9504 0.9879 0.9125 0.8811
Slope S
( )uzn=S arccos
Slope S'
22
yz+
xz=S'
S'- S
S' Vs S
SS'
Slope 1st Quartile Mean Median 3rd Quartile Std. Dev. Skewness
S 4.146 13.2406 8.9125 18.386 340.861 12757
S' 4.153 14.5406 8.9851 19.044 463.487 22877
Slope Aspect
| |
nxny
nxnx=A arctan
2
Solar Vector
Topocentric Spheric System
At noon sun is at:
( )ozoyoxo S,S,S=S( ) ( )( ),So = cossin0,
latitude Triangle=9090
ndeclinatio Solar=
23.4523.45
System RotationAs Earth rotates, So needs to be multiplied by three rotational matrices. Thus solar vector will be
( ) ( ) ( ) oxzx Srwrr=S ( )
=rx
cossin0
sincos0
001
( )
100
0
0
cossin
sincos=wrz
anglehour=
+cosw
sincos
cossin=S
sinsincoscos
coscossin
Cosine lawLambert's cosine law determines the energy flux to each TIN element:
( )
+cos
sincos
cossinn,n,n= uzuyuxs
sinsincoscos
coscossin
cos
nu
Ss
Direct Radiation(w/m2)
Sn= us .cos
When cos s
Incoming Solar Radiation
Spring or fall Equinox
Incoming Solar Radiation
Winter Solstice
Incoming Solar Radiation
Summer Solstice
Remote ShelteringIn process of application. Groups of mesh elements are organized along the sun light path and their projections tested for remote shading.
z
x
S
TIN centroids
T1 T2 T3 T4 T5 T6 T7
Shaded elements
SP
d( )h+Rh=d 2
Next Steps Include a diffuse radiation model based on sky-view
factors.
Add a remote reflected radiation for short wave or high albedo areas.
Include a module for canopy light reduction and below-canopy long wave radiation.
Include an energy balance model. Couple a snow and evapotranspiration module. Couple modules to ADHydro infiltration and routing
schemes.
THANKS
Green River, Wyoming
Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27