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Hydrologic analysis

Understanding drainage systems

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The area upon which water falls and the network through which it travels to an outlet are referred to as a drainage system. The flow of water through a drainage system is only a subset of what is commonly referred to as the hydrologic cycle, which also includes precipitation, evapotranspiration, and groundwater. This topic focuses on the movement of water across a surface.

A drainage basin is an area that drains water and other substances to a common outlet. Other common terms for a drainage basin are watershed, basin, catchment, or contributing area. This area is normally defined as the total area flowing to a given outlet, or pour point. A pour point is the point at which water flows out of an area. This is usually the lowest point along the boundary of the drainage basin. The boundary between two basins is referred to as a drainage divide or watershed boundary. The terms watershed, pour point, and watershed boundary will be used in this material.

Components of drainage basin

The network through which water travels to the outlet can be visualized as a tree, with the base of the tree being the outlet. The branches of the tree are stream channels. The intersection of two stream channels is referred to as a node or junction. The sections of a stream channel connecting two successive junctions or a junction and the outlet are referred to as stream links.


Exploring Digital Elevation Models (DEM)

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The most common digital data of the shape of the earth¨s surface is cell-based digital elevation models (DEMs). This data is used as input to quantify the characteristics of the land surface.

A DEM is a raster representation of a continuous surface, usually referencing the surface of the earth. The accuracy of this data is determined primarily by the resolution (the distance between sample points). Other factors affecting accuracy are data type (integer or floating point) and the actual sampling of the surface when creating the original DEM.

Raster DEM surface

Errors in DEMs are usually classified as either sinks or peaks. A sink is an area surrounded by higher elevation values and is also referred to as a depression or pit. This is an area of internal drainage. Some of these may be natural, particularly in glacial or karst areas (Mark, 1988), although many sinks are imperfections in the DEM. Likewise, a spike or peak is an area surrounded by cells of lower value. These are more commonly natural features and are less detrimental to the calculation of flow direction.

Errors such as these, especially sinks, should be removed before attempting to derive any surface information. Sinks, being areas of internal drainage, prevent downslope flow routing of water.
Learn more about removing or filling sinks

The number of sinks in a given DEM is normally higher for coarser resolution DEMs. Another common cause of sinks results from storing the elevation data as an integer number. This can be particularly troublesome in areas of low vertical relief. It is not uncommon to find 1 percent of the cells in a 30-meter-resolution DEM to be sinks. This can increase as much as 5 percent for a 3 arc–second DEM.

DEMs may also contain noticeable horizontal striping, a result of systematic sampling errors when creating the DEM. Again, this is most noticeable on integer data in flat areas.

The hydrologic analysis functions described here are designed to model the convergence of flow across a natural terrain surface. There is an assumption that the surface contains sufficient vertical relief that a flow path can be determined. The functions assume that water can flow in from many cells but out through only one cell.


Deriving runoff characteristics

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When delineating watersheds or defining stream networks, you proceed through a series of steps. Some steps are mandatory, while others are optional depending on the characteristics of the input data. Flow across a surface will always be in the steepest downslope direction. Once the direction of flow out of each cell is known, it is possible to determine which and how many cells flow into any given cell. This information can be used to define watershed boundaries and stream networks. The following flowchart shows the process of extracting hydrologic information, such as watershed boundaries and stream networks, from a digital elevation model (DEM).

Hydrological modelling flowchart


Regardless of your goal, start with an elevation model. The elevation model is used to determine which cells flow into other cells (the flow direction). However, if there are errors in the elevation model or if you are modeling karst geology, there may be some cell locations that are lower than the surrounding cells. If this is the case, all water traveling into the cell will not travel out. These depressions are called sinks. The hydrologic analysis functions allow you to identify the sinks and give you tools to fill them. The result is a depressionless elevation model. You can then determine the flow direction on this depressionless elevation model.

If you are delineating watersheds, you need to identify pour points (locations for which you want to know the contributing watershed). Usually these locations are mouths of streams or other hydrologic points of interest, such as a gauging station. Using the hydrologic analysis functions, you can specify the pour points, or you can use the stream network as the pour points. This will create watersheds for each stream segment between stream junctions. To create the stream network, you must first calculate the flow accumulation for each cell location.

If you are defining stream networks, you will not only need to know the direction water flows from cell to cell but also how much water flows through a cell, or how many cells flow into another cell. When enough water flows through a cell, the location is considered to have a stream passing through it.


Creating a depressionless DEM

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A digital elevation model (DEM) free of sinks—a depressionless DEM—is the desired input to the flow direction process. The presence of sinks may result in an erroneous flow–direction raster. In some cases, there may be legitimate sinks in the data. It is important to understand the morphology of the area well enough to know what features may truly be sinks on the surface of the earth and which are merely errors in the data.


Identifying sinks

Sinks can be located using the Sink function. This function requires a direction raster that is created by the Flow Direction function. The result is a raster that identifies any existing sinks in the data. Depending on the results, you can fill the sinks, or you can use the output to help determine the fill limit. Sinks can be filled using the Fill function. To use the output from Sink to determine the fill limit, refer to ¨Finding sink depth¨ in this topic (below).

Profile view of a sink
Profile view of a sink.



Filling sinks

The Fill function uses a variety of ArcGIS Spatial Analyst functions, including several of the hydrologic analysis functions discussed earlier, to create a depressionless DEM. This function requires an input surface, a fill limit, and an output raster. When a sink is filled, it is filled to its pour point, the minimum elevation along its watershed boundary.

The identification and removal of sinks when creating a depressionless DEM is an iterative process. When a sink is filled, the boundaries of the filled area may create new sinks, which then need to be filled. For a large DEM or one with many sinks, this can take minutes to hours.


Finding sink depth

It is useful to know the depth of a sink or group of sinks. This information can be used to determine an appropriate z-limit for the Fill function, to understand the type of errors present in the data, and to determine if the sinks are legitimate morphological features. The following steps outline the process to find sink depth.

  1. Create a raster of sinks with values that identify their depth by running the Sink function to locate sinks in the raster.

  2. Use the Watershed function to create a raster of the contributing area for each sink using the flow direction from the elevation raster and the output from the Sink function as input for pour points.

  3. Use the Map Algebra tools or ArcGIS Spatial Analyst Raster Calculator to create a raster of the minimum elevation in the watershed of each sink.
  4.     sink_min = zonalmin (sink_areas, elevation)



    The sink_areas will be the output from the Watershed function.

  5. Create a raster containing the lowest elevation along the boundary of each watershed using Map Algebra tools or the Raster Calculator. This corresponds to the elevation at which flow would leave the basin after filling to the rim.
  6.     sink_max = zonalfill (sink_areas, elevation)



  7. Using Map Algebra or the Raster Calculator, subtract the minimum value from the maximum value to find the depth again.
  8.     sink_depth = sink_max – sink_min



The above sequence can also be completed using the Sink, Watershed, Zonal Statistics, Zonal Fill, and Minus geoprocessing tools.


Determining flow direction

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One of the keys to deriving hydrologic characteristics about a surface is the ability to determine the direction of flow from every cell in the raster. This is done with the Flow Direction function.

This function takes a surface as input and outputs a raster showing the direction of flow out of each cell. If the output drop raster option is chosen, an output raster is created showing a ratio of the maximum change in elevation from each cell along the direction of flow to the path length between centers of cells and is expressed in percentages. If the force all edge cells to flow outward option is chosen, all cells at the edge of the surface raster will flow outward from the surface raster.

Coding of the direction of flow


There are eight valid output directions relating to the eight adjacent cells into which flow could travel. This approach is commonly referred to as an eight direction (D8) flow model and follows an approach presented in Jensen and Domingue (1988).

The direction of flow is determined by finding the direction of steepest descent, or maximum drop, from each cell. This is calculated as
    maximum drop = change in z-value / distance



The distance is determined between cell centers. Therefore if the cell size is one, the distance between two orthogonal cells is one and the distance between two diagonal cells is 1.414216, the square root of two. If the maximum descent to several cells is the same, the neighborhood is enlarged until the steepest descent is found.

When a direction of steepest descent is found, the output cell is coded with the value representing that direction.

If all neighbors are higher than the processing cell, the processing cell is a sink and has an undefined flow direction. Cells with undefined flow direction can be flagged as sinks using the Sink function. To obtain an accurate representation of flow direction across a surface, the sinks should be filled.

Learn more about filling sinks


Calculating flow accumulation

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The Flow Accumulation function calculates accumulated flow as the accumulated weight of all cells flowing into each downslope cell in the output raster. If no weight raster is provided, a weight of one is applied to each cell, and the value of cells in the output raster will be the number of cells that flow into each cell.

In the graphic below, the top left image shows the direction of travel from each cell and the top right the number of cells that flow into each cell.

Determining the accumulation of flow


Cells with a high flow accumulation are areas of concentrated flow and may be used to identify stream channels. This is discussed in Identifying stream networks. Cells with a flow accumulation of zero are local topographic highs and may be used to identify ridges.

An example of using a weight raster in the Flow Accumulation function is determining how much rain has fallen within a given watershed. In such a case, the weight raster may be a continuous raster representing average rainfall during a given storm.

The output from the Flow Accumulation function would represent the amount of rain that would flow into each cell, assuming that all rain became runoff and there was no interception, evapotranspiration, or loss to groundwater. This could also be viewed as the amount of rain that fell on the surface, upslope from each cell.


Delineating watersheds

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A watershed is the upslope area contributing flow to a given location. Such an area is also referred to as a basin, catchment, subwatershed, or contributing area. A subwatershed is simply part of a hierarchy, implying that a given watershed is part of a larger watershed. Watersheds can be delineated from a DEM by computing the flow direction and using it in the Watershed function. The Watershed function uses a raster of flow direction to determine contributing area.

Delineating watersheds


You will use a flow accumulation threshold or the pour points to delineate watersheds. When the threshold is used to define a watershed, the pour points for the watershed will be the junctions of a stream network derived from flow accumulation. Therefore, a flow accumulation raster must be specified as well as the minimum number of cells that constitute a stream (the threshold value).

When a feature dataset is used to define a watershed, the features identify the pour points.


Identifying stream networks

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Stream networks can be delineated from a digital elevation model (DEM) using the output from the Flow Accumulation function. Flow accumulation in its simplest form is the number of upslope cells that flow into each cell. By applying a threshold value to the results of the Flow Accumulation function using Map Algebra (or the Con tool in geoprocessing), a stream network can be delineated. For example, the expression to create a raster where the value one represents a stream network on a background of NoData could be:

   streamnet = con (flowacc > 100, 1)



or
   streamnet = setnull (flowacc < 100, 1)



In both examples, all cells with more than 100 cells flowing into them are assigned the value one, and all other cells are assigned NoData. For future processing, it is important that the stream network, a set of raster linear features, be represented as values on a background of NoData. Once created, the stream network can be further analyzed using the Stream Order, Stream Link, and Stream to Feature (or Map Algebra StreamLine) functions, for ordering (ranking) the streams, assigning unique IDs to stream links, or creating a feature dataset. Determining a threshold value that represents where a permanent stream or stream channel begins is affected not only by contributing area but also by climate, slope, and soil characteristics. For more information on stream channel initiation, refer to Tarboton and Bras (1991).


Stream ordering

Stream ordering is a method of assigning a numeric order to links in a stream network. This order is a method for identifying and classifying types of streams based on their number of tributaries. Some characteristics of streams can be inferred by simply knowing their order.

For example, first-order streams are dominated by overland flow of water; they have no upstream concentrated flow. Because of this, they are most susceptible to nonpoint source pollution problems and can derive more benefit from wide riparian buffers than other areas of the watershed.

The Stream Order function has two methods you can use to assign orders. These are the methods proposed by Strahler (1957) and Shreve (1966).

Stream ordering methods

In both methods, the most upstream stream segments, or exterior links, are always assigned an order of one. In the Strahler method, stream order increases when streams of the same order intersect. Therefore, the intersection of two first-order links will create a second-order link, and the intersection of two second-order links will create a third-order link. The intersection of two links of different orders, however, will not result in an increase in order. For example, the intersection of a first-order and second-order link will not create a third- order link, but will retain the order of the highest ordered link. The Strahler method is the most common stream ordering method. However, because this method only increases in order at intersections of the same order, it does not account for all links and can be sensitive to the addition or removal of links.

The Shreve method accounts for all links in the network. As with the Strahler method, all exterior links are assigned an order of one. For all interior links in the Shreve method, however, the orders are additive. For example, the intersection of two first-order links creates a second-order link, the intersection of a first-order and second-order link creates a third-order link, and the intersection of a second-order and third-order link creates a fifth-order link.

Because the orders are additive, the numbers from the Shreve method are sometimes referred to as magnitudes instead of orders. The magnitude of a link in the Shreve method is the number of upstream links.


Stream links

The Stream Link function allows you to assign unique values to each of the links in a raster linear network. This is most useful as input to the Watershed function to quickly create watersheds based on stream junctions. It can also be useful for attaching related attribute information to individual segments of a stream.


Vectorizing a stream network

A raster linear network can be accurately converted to features representing the linear network using the Stream to Feature function. The vectorization algorithm is designed primarily for vectorization of raster stream networks or any other raster representing a raster linear network for which directionality is known. In the output feature dataset, all arcs will point downstream.

The Stream to Feature algorithm is optimized to use a direction raster to aid in vectorizing intersecting and adjacent cells. With Stream to Feature, it is possible for two adjacent linear features of the same value to be vectorized as two parallel lines instead of being lumped into a single line as they would when using other vectorization methods.

Vectorizing stream network rasters


Hydrologic analysis references

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For a more detailed discussion of material presented on the hydrologic tools, refer to the following publications:

Jenson S. K. and J. O. Domingue. 1988. Extracting Topographic Structure from Digital Elevation Data for Geographic Information System Analysis. Photogrammetric Engineering and Remote Sensing 54 (11): 1593-1600.

Mark, D. M. Network Models in Geomorphology. In Modelling in Geomorphological Systems. John Wiley.

Shreve, R. L. 1966. Statistical Law of Stream Number. Journal of Geology. 74: 17-37.

Strahler, A. N. 1957. Quantitative Analysis of Watershed Geomorphology. Transactions of the American Geophysical Union 8 (6): 913-920.

Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe. 1991. On the Extraction of Channel Networks from Digital Elevation Data. Hydrological Processes. 5: 81-100.


Hydrologic analysis sample applications

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The hydrologic modeling functions in ArcGIS Spatial Analyst provide methods for describing the physical components of a surface. The hydrologic tools allow you to identify sinks, determine flow direction, calculate flow accumulation, delineate watersheds, and create stream networks. The image below is of a resulting stream network derived from an elevation model.

Example stream network derived from elevation model

Using an elevation raster or digital elevation model (DEM) as input, it is possible to automatically delineate a drainage system and quantify the characteristics of the system. The following graphics illustrate the steps involved in calculating a watershed and stream network from a DEM.

The DEM on which the hydrologic analysis will be performed:
DEM surface

Using the DEM as input into the Flow Direction tool, the direction in which water would flow out of each cell is determined.
Flow direction is determined

With the Sink function, any sinks in the original DEM are identified. A sink is usually an incorrect value lower than the values of its surroundings. The depressions shown in the graphic above (the scattered colored points) are problematic because any water that flows into them cannot flow out. To ensure proper drainage mapping, these depressions can be filled using the Fill tool.
Sinks identified
Using the Watershed tool, the watersheds are delineated for specified locations. However, if you want to calculate only the stream network, this step can be ignored.
Watersheds delineated

To create a stream network, use the Flow Accumulation tool to calculate the number of upslope cells flowing to a location. The output of the Flow Direction tool from above is used as input.
Flow accumulation
A threshold can be specified on the raster derived from the Flow Accumulation tool; the initial stage is defining the stream network system. This task can be accomplished with the Con tool or using Map Algebra. An example of Con is newraster = con(accum > 100, 1). All cells with more than 100 cells flowing into them will be part of the stream network.

To represent the order of each of the segments in a network, apply the Stream Order tool. The available methods for ordering are the Shreve and Strahler techniques.
Stream ordering

Using the Flow Length tool, the length of the flow path, either upslope or downslope, from each cell within a given watershed can be determined. This is useful for calculating the travel time of water through a watershed.
Flow length