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

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