GISWR 2015 Midterm Review

Definition of Latitude, f

(1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn(2) Define the line pq through S and normal to thetangent plane(3) Angle pqr which this line makes with the equatorialplane is the latitude f, of point S

O f

Sm

nq

p

r

Definition of Longitude, l

0°E, W

90°W(-90 °)

180°E, W

90°E(+90 °)

-120°

-30°

-60°

-150°

30°

-60°

120°

150°

l

l = the angle between a cutting plane on the prime meridianand the cutting plane on the meridian through the point, P

P

Length on Meridians and Parallels

0 N

30 N

DfRe

Re

RR

A

BC

Dl

(Lat, Long) = (f, l)

Length on a Meridian:AB = Re Df(same for all latitudes)

Length on a Parallel:CD = R Dl = Re Dl Cos f(varies with latitude)

D

A map of Texas and a set of map projection parameters for the state are given above. (a) Please draw and label on the map: the central meridian, the latitude of origin, and the two standard parallels. (b) Give the numerical values (in degrees and minutes) for (ϕ0, λ0):

 (c) Give the numerical values for (X0, Y0): (d) What earth datum is used?

 (e) What spheroid is used? (f) What map projection is used? (g) What are the distance units in the coordinate system?

Std Parallel 2

Std Parallel 1

Latitude of Origin

Central MeridianUtah State Plane System (North)

(𝜙0 ,𝜆0 )=(40.33 ° N ,−111.5 W )Origin

Subwatershed Precipitation by Thiessen Polygons

𝑃 𝑖=∑𝑘𝐴𝑖𝑘𝑃𝑘

∑𝑘𝐴𝑖𝑘

• Thiessen Polygons• Intersect with

Subwatersheds• Evaluate A*P Product• Summarize by

subwatershed

WatershedsFlow (cfs)

Flow Volume (ft^3)

Subwater-sheds

Precip volume

subwater-shed sum

Runoff ratio

Plum Ck at Lockhart, TX 49.00 1.5E+09 330 9.49E+09 0.16303Blanco Rv nr Kyle, TX 165.00 5.2E+09 331, 332 3.67E+10 0.14203

San Marcos Rv at Luling, TX 408.00 1.3E+10331, 332, 333, 336 7.43E+10 0.17325

Subwatershed Precip from Thiessen Polygons

HydroID Area (m^2)Mean Precip (in)

Precip Volume (ft^3)

330 2.91E+08 36.37 9.49E+09331 9.21E+08 37.82 3.12E+10332 1.49E+08 40.48 5.42E+09333 1.27E+08 40.48 4.60E+09336 9.80E+08 37.59 3.31E+10

Runoff Coefficients• Interpolated precip for each

subwatershed• Convert to volume, P• Sum over upstream

subwatersheds in Excel• Runoff volume, Q• Ratio of Q/P

Watershed HydroID'sPlum Ck at Lockhart, TX 330Blanco Rv nr Kyle, TX 331, 332San Marcos Rv at Luling, TX 331,332,333,336

7 7 6 7 7 7 7 5 7 7

9 9 8 9 9 9 9 7 9 9

11 11 10 11 11 11 11 9 11 11

12 12 10 12 12 12 12 10 12 12

13 12 10 12 13 13 13 11 13 13

14 10 10 11 14 14 14 12 14 14

15 10 10 10 10 15 15 13 15 15

15 10 10 10 10 16 16 14 16 16

15 11 11 11 11 17 17 14 17 17

15 15 15 15 15 18 18 15 18 18

Pit Filling

7 7 6 7 7 7 7 5 7 7

9 9 8 9 9 9 9 7 9 9

11 11 10 11 11 11 11 9 11 11

12 12 8 12 12 12 12 10 12 12

13 12 7 12 13 13 13 11 13 13

14 7 6 11 14 14 14 12 14 14

15 7 7 8 9 15 15 13 15 15

15 8 8 8 7 16 16 14 16 16

15 11 11 11 11 17 17 6 17 17

15 15 15 15 15 18 18 15 18 18

Pits Pour Points

Original DEM Pits Filled

Grid cells or zones completely surrounded by higher terrain

The lowest grid cell adjacent to a pit

80 74 63

69 67 56

60 52 48

80 74 63

69 67 56

60 52 48

30

45.02304867

=

50.030

5267=

Slope:

Hydrologic Slope - Direction of Steepest Descent

30

0 0 000

0

0

1

0

0

0

0

0

02 2 2

10 1

0 144 1

19 1

0 0 00 0

0

0

1

0

0

0

0

0

0

2 2 2

10 1

0

14

14

191

Flow Accumulation Grid. Area draining in to a grid cell

ArcHydro Page 72

Watershed Draining to Outlet

• Watershed mapped as all grid cells that drain to an outlet

• Streams mapped as grid cells with flow accumulation greater than a threshold

Zonal Average of Raster over Subwatershed

Join

2013 Midterm Questions

Curved Earth Distance(from A to B)

Shortest distance is along a “Great Circle”

A “Great Circle” is the intersection of a sphere with a plane going through its center.

1. Spherical coordinates converted to Cartesian coordinates.

2. Vector dot product used to calculate angle from latitude and longitude

3. Great circle distance is R, where R=6378.137 km2

X

Z

Y•

AB

)]cos(coscossin[sincos 1BABABARDist llffff =

Ref: Meyer, T.H. (2010), Introduction to Geometrical and Physical Geodesy, ESRI Press, Redlands, p. 108

NHDPlus Version 2.1

National Elevation Dataset

National Hydrography DatasetNational Land Cover Dataset

Watershed Boundary Dataset

NHDPlus

Foundation for a Geospatial Hydrologic Framework for the United States

2.7 million reach catchments in USaverage area 3 km2 reach length 2 kmUniquely labelled

Note that behind “networks” in ArcGIS there is a data model that enables the network functionality that you used.

We did not cover that this year as it is hidden from a user so you would not get this question. However you should know how networks work and what they can be used for.

“All geographic information systems are built using formal models that describe how things are located in space. A formal model is an abstract and well-defined system of concepts. A geographic data model defines the vocabulary for describing and reasoning about the things that are located on the earth. Geographic data models serve as the foundation on which all geographic information systems are built.”

Scott Morehouse, Preface to “Modeling our World”, First Edition. He is the chief software engineer at ESRI

Geographic Data Model

Or, more simply: the way that data is organized can enhance or inhibit the analysis that can be done

The connectivity in the network data model enables analyses such as tracing for selection of the upstream network and watershed

Subnetwork analysis enabled by attributes joined with a network

2012 Midterm Questions

gd

ah

eb

if

c∆

𝑎−𝑐2 ∆ 𝑑− 𝑓

2 ∆𝑔−𝑖2∆

2 ∆

Similarly

Slope magnitude =

ArcGIS “Slope” tool

a b c

d e f

g h ix

y

xy

ArcGIS Aspect – the steepest downslope direction

dxdz

dydz

DD

=

yxatan

dy/dzdx/dzatan

x,yatan2 DD

Use atan2 to resolve ambiguity in atan direction

Δ𝑥

Δ 𝑦 𝛼

− Δ 𝑥− Δ𝑦𝛼+180𝑜

Δ 𝑦=¿

Δ𝑥=¿

Example30

80 74 63

69 67 56

60 52 48

a b c

d e f

g h i229.0

30*8)4856*263()6069*280(

dxdz

=

=

=

cingx_mesh_spa * 8i) 2f (c - g) 2d (a

329.030*8

)6374*280()4852*260(acing y_mesh_sp* 8

c) 2b (a -i) 2h (gdydz

=

=

=

o8.21)401.0(atan =

o8.34329.0

229.0atanAspect =

= o

o

2.145

180

145.2o

401.0329.0229.0Slope 22

==

80 74 63

69 67 56

60 52 48

80 74 63

69 67 56

60 52 48

30

45.02304867

=

50.030

5267=

Slope:

Hydrologic Slope (Flow Direction Tool)- Direction of Steepest Descent

30