2. Surface Functions FE 423 - Lecture 2b

3. From Tuesday: Gridding contours and contouring grids

4. From Tuesday: HJ Andrews Topography Download Import71.exe TOPOGRID

5. SCHEDULE

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

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

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

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

10. 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

11. SLOPE IN GRID

12. ASPECT IN GRID

13. 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

14. 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)

15. CURVATURE out_slopeout_aspect out_pro_gridout_plan_grid

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

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

18. 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.

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

20. Practice Problem 2: Identify the aspect of each square

21. Practice Problem 3: Estimate slope for each cell

22. Practice Problem 4: Estimate aspect for each cell

23. Practice Problem 5: Shade convergent topography

24. Practice Problem 6: Shade convergent topography