ArcView 3-D Analyst

Triangulated Irregular Network (TIN)

A Mesh of Triangles Triangle is the only polygon that is always planar in 3-D Points Lines Surfaces

Tin Triangles in 3-D (x3, y3, z3) (x1, y1, z1) (x2, y2, z2) z y Projection in (x,y) plane x

Delauney Triangulation Maximize the minimum interior angle of triangles No point lies within the circumcircle of a triangle Yes No

Circumcircle of Triangle Draw the perpendicular bisectors of each edge of the triangle Circumcircle is centered on their intersection point Radial lines from center have equal length

Inputs for Creating a TIN Mass Points Soft Breaklines Hard Breaklines Hard breaklines define locations of abrupt surface change (e.g. streams, ridges, road kerbs, building footprints, dams) Soft breaklines are used to ensure that known z values along a linear feature are maintained in the tin.

TIN for Waller Creek

TIN with Surface Features Classroom UT Football Stadium Waller Creek

A Portion of the TIN

Input Data for this Portion Mass Points Soft Breaklines Hard Breaklines

TIN Vertices and Triangles

TIN Surface Model Waller Creek Street and Bridge

3-D Scene

3-D Scene with Buildings

Watershed Modeling With TINs Slides from Dr James Nelson Brigham Young University Sponsored by National Highway Institute US Department of Transportation

Work Flow Tin-based Watershed Delineation This lesson focuses on TIN based watershed delineation. You can see where it fits into the WMS work flow in the diagram shown in this slide.

Flow On a Triangle 2.0 13.0 9.0 10.0 5.0 Any three XYZ points that make up a triangle form a planar surface. Contouring a triangle is straightforward since we only need to linearly interpolate along each edge to discover where a specified contour interval lies (such as 5.0 and 10.0 in this figure). Flow will always be in the direction of steepest descent, or perpendicular to the contours.

Flow On a TIN Flow can be traced across a TIN (series of triangles) by repeatedly tracing flow across individual triangles as explained in the previous slide. In this example flow begins at the point marked with an X. The path of steepest descent is determined from the planar surface defined by the triangle and is traced until it intersects with one of the triangle edges. From the intersection point flow is traced across the adjacent triangle in a similar manner. Flow may also follow a triangle edge if the two adjacent triangles slope together as is the case with the last two flow path segments in this slide.

Defining Basins Drainage basins are defined on a TIN by first defining a stream network and then outlet points where the watershed or sub-basin confluence exist. When outlet points are created a sub-basin for each upstream branch is created. Each triangle is then assigned to a basin by initiating a flow path at its centroid and tracing the flow path until the first stream branch is encountered. The process is repeated for all triangles to fully define the watershed and sub-basins.

Computing Basin Data Area Slope Flow Distances Aspect Stream Lengths Slopes Aspect Stream Lengths Others Once triangles have been assigned to basins, several geometric parameters including area, slope, flow distance lengths and slopes, aspect, and stream lengths and slopes can be automatically computed. These are the variables of interest to most hydrologic simulation programs.

Modifying Basins Add Outlets Refine Boundaries Merge Basins Delete Outlets Recompute Data Split Basins Merge Basins Add Outlets Refine Boundaries After the initial basin delineation it is easy to modify the watershed to include additional outlets (sub-basins). Since triangles are assigned drainage basins based on flow from their centroids it is possible to have a triangle actually straddle a basin boundary. While the overall area of a sub-basin typically is not affected, refining the boundaries will enforce triangle edges along actual basin boundaries so that they are exactly defined from the TIN data (a basin usually ends up gaining as much area as it loses in this process). You can also merge or split basins that share a common outlet point, delete outlets to “collapse” a sub-basin. Each time you modify the sub-basin definition you must recompute the basin data in order to update areas, slopes, and other values.

Ten Steps Using TINs 1. Background Elevation 2. Smooth Elevations 3. Conceptual Model 4. Redistribute Vertices 5. Create TIN 6. Edit TIN 7. Add Interior Outlets 8. Define Basins 9. Refine TIN 10. Compute Basin Data These are the 10 effective habits of WMS TIN Modeling. Each model will have slight variations, but this should provide a guide from which most models can be successfully created.

1: Background Elevation TINs Digitized XYZ Data DEMs It is useful to outline the process typically used when performing watershed modeling and delineation with TINs. The next series of slides outline a 10-step process that serves as a guide (not all problems are alike, but these steps form a guide to solving most TIN delineation problems). The first step is to obtain digital elevation data, which will be referred to often in this training manual as “background” elevation data. The background elevation data can either be TIN or DEM data. NOTE: If you begin with TIN data you will likely be tempted to begin basin delineation, but it is strongly recommended that you use the initial TIN as a background data source from which a new TIN, triangulated specifically for basin delineation as described on the next several slides, will be created.

2: Smooth Elevations TINs or DEMs Whether you are using a TIN or DEM as the background elevation it is a good idea to smooth the data. Because DEM elevations are often rounded to the nearest whole integer value a “stair-step” effect can result which leaves large areas as being “flat.” While it is a good practice to smooth the DEM when using the DEM or gridded methods for delineation, it is even more important in the TIN based method because flow is computed directly from triangle gradients.

3: Conceptual Model TOPAZ Contours Image Importing GIS DXF The conceptual model is a set of feature objects that define important linear hydrologic features such as streams, roads, and ridges as well as the outer boundary of the TIN. The conceptual model can be created by using the results of basin delineation from a DEM using TOPAZ, by digitizing from contours or a registered image, or by importing existing data. The outer boundary of the conceptual model does not need to correspond to the watershed boundary (although it will if you are using the results of TOPAZ), but should be larger than the actual boundary. Often imported data such as DXF files, or GIS data contain a lot more information (resolution) than you have available in your elevation data. Further, you may not have the computing resources to model a watershed at the resolution provided by the imported data. For these reasons it is often better to use the imported data simply as a general coverage for a backdrop and then create the feature objects by digitizing from them.

4: Redistribute Vertices From Coarse to Fine From Fine to Coarse Unequal Distribution The distribution of the vertices along the arcs will determine the size of triangles created. It is important to have enough resolution to define your watershed, without having so much resolution that computing resources are over-burdened. The best resolution is often model dependent, but the following are some rule of thumb guidelines: It won’t help you to redistribute denser than the spacing of the original data. For example if you have 30 meter DEM data don’t redistribute to something smaller than 30 meters. DEM data are redundant by nature, so unless you are working with a watershed that is 1 sq. mile or less you will want to have a spacing larger (often much larger) than the original DEM spacing. 1-5 sq. miles – 100 meter spacing 5-10 sq. miles – 150 meter spacing 10-20 sq. miles – 200 meter spacing 20-50 sq. miles – 250-300 meter spacing 50 sq. miles and larger – 300-500 meter spacing The key is that the important features such as streams are enforced as breakline. The overall resolution of the points on the interior of the basin is far less important.

5: Create TIN Conceptual Model Triangulate Interpolate Z Enforce Breaklines The conceptual model is then filled with triangles at a density proportional to the spacing of feature arc vertices (notice that the spacing of vertices does not have to be uniform on all arcs). The bounding feature polygon determines the limit, and all interior feature arcs are forced as breaklines. Stream arcs are used to create a stream of triangle edges for the TIN. Elevations for TIN vertices are mapped from the background elevation source. Elevation data can be interpolated before or after creation of the TIN when using DEM data.

6: Edit TIN Flat Triangles Pits When using the conceptual modeling approach (and if you have previously smoothed your background data), the number of manual edits required will be small, but inevitably you will need to correct a few of the TIN anomalies such as Flat Triangles and Pits as discussed in the previous lesson.

7: Add Sub-basin Outlets If you define outlet locations on the feature arcs prior to creating the TIN, they will transfer to outlet points on the TIN stream. However, you can also add (or delete) outlets on the TIN after it has been created.

8: Define Basins With the stream network and outlets in place, you can define the watershed and sub-basins.

9: Refine TIN Split Flow Refine NULL Triangles The original basin definition may result in a few small problems that need to be resolved. First of all there may be some vertices that cause split flow. WMS ignores split flow if both paths end up in the same basin, but if the two flow paths end up in separate basins (or one is out of the basin). This is typically corrected by swapping the edge just upstream of the split flow vertex and is handled automatically when using the Correct Split Flow command. Refining boundaries won’t likely change the area of a sub-basin appreciably, but it does help the overall appearance. Once you are sure the entire watershed is delineated and appropriately refined you can delete all triangles not belonging to any sub-basin. These triangles are referred to in WMS as NULL triangles because they do not belong to a basin.

10: Compute Basin Data Basins Streams Area Slope Avg. Elevation Length The final step is to compute the many geometric parameters that are available. By default WMS will display the area of the computed sub-basin after each time basin data is computed. If you edit the TIN or alter the sub-basins in any way the display of area (and/or any other variable currently being displayed) will not be shown. This signifies that basin data must be re-computed in order to accurately reflect the edits made.

Ten Steps Using TINs 1. Background Elevation 2. Smooth Elevations 3. Conceptual Model 4. Redistribute Vertices 5. Create TIN 6. Edit TIN 7. Add Interior Outlets 8. Define Basins 9. Refine TIN 10. Compute Basin Data These are the 10 effective habits of WMS TIN Modeling. Each model will have slight variations, but this should provide a guide from which most models can be successfully created.

TIN Strengths Automated Basin Delineation with Parameter Calculations “Adaptive” Resolution you can use most any elevation data source Urban Areas where small variations in flow can be significant It Was in WMS First reservoir definition, storage capacity curves, time area curves, flood-plain delineation TINs may appear to be more troublesome to work with, but the tools developed to support TIN model creation in WMS are well established and easy to use. Often the additional power, and speed that comes with using a TIN model far outweighs the minor editing that occur as part of the “initial” set up. Also, there are some things such as reservoir generation, time area curves, and flood plain delineation that are only available with TINs.

TIN Weaknesses Lack of Available Data Extra Steps With conceptual model approach this is not such a big factor anymore Extra Steps Local editing Clearly the need to “regenerate” the TIN from background data can seem like a lot of overhead, but once you learn how to build models from a conceptual model this should not be a big deterrent.