Surface Functions FE Lecture 2b

From Tuesday: Gridding contours and contouring grids

From Tuesday: HJ Andrews Topography Download Import71.exe TOPOGRID

SCHEDULE

OUTLINE Why Slope, Aspect, & Curvature Slope/Aspect/Curvature in GRID Hillshade

SLOPE What is Slope? Why do we care about slope? How do we define slope? With points? On TIN? On Contours?

ASPECT What is aspect? Why do we care about aspect? How do we define aspect? With points? On TIN? On Contours?

CURVATURE What is curvature? Why do we care about curvature? How do we define curvature? With points? On TIN? On Contours?

Surface Functions in GRID dZ/dx dZ/dy dZ/ds Z = Ax 2 y 2 + Bx 2 y + Cxy 2 + Dx 2 + Ey 2 + Fxy + Gx + Hy + I Z(0,0) = I Z(0,1) = E + H + I Z(0,-1) = E - H + I dZ/dx = 2Axy 2 + 2Bxy + Cy 2 + 2Dx + Fy + G d 2 Z/dx 2 = 2Ay 2 + 2By + 2D

SLOPE IN GRID

ASPECT IN GRID

CURVATURE IN GRID A = [(Z1 + Z3 + Z7 + Z9) /4 - (Z2 + Z4 + Z6 + Z8) /2 + Z5] /L4 B = [(Z1 + Z3 - Z7 - Z9) /4 - (Z2 - Z8) /2] /L3 C = [(-Z1 + Z3 - Z7 + Z9) /4 + ( Z4 - Z6)] /2] /L3 D = [(Z4 + Z6) /2 - Z5] /L2 E = [(Z2 + Z8) /2 - Z5] /L2 F = (-Z1 + Z3 + Z7 - Z9) /4L2 G = (-Z4 +Z6) /2L H = (Z2 - Z8) /2L I = Z5 Curvature = (D + E) /2

CURVATURE IN GRID In ArcGRID C:> curve_grid = curvature(dem, {out_pro_grid}, {out_plan_grid}, {out_slope}, {out_aspect}) Surface Analyst aGrid.Curvature (proCurvFN, planCurvFN, slopeFN, aspectFN)

CURVATURE out_slopeout_aspect out_pro_gridout_plan_grid

HILLSHADE Angle of sun to the surface examples radiation on snowpack radiation on stream rain ‘shadow’

Reading from ArcDoc Spatial modeling –Cell-based Modeling with GRID GRID algebra and analysis environment GRID operators GRID map algebra rules and syntax

Discussion Problems: Use a sun-angle calculator from the web to identify the sun angle for the beginning and end of this class period. Make a hillshaded image of the UW area for these times. Using a DEM of steep topography, map the areas of steep and convergent topography.

Practice Problem 1: Identify the slope of each square 500m grid

Practice Problem 2: Identify the aspect of each square

Practice Problem 3: Estimate slope for each cell

Practice Problem 4: Estimate aspect for each cell

Practice Problem 5: Shade convergent topography

Practice Problem 6: Shade convergent topography