## Standard Hydrologic Grid (SHG) and ModClark Structured Discretization In HEC-HMS

The standard hydrologic grid (SHG) is a grid system developed by USACE Hydrologic Engineering Center (HEC) to cover the conterminous United States for hydrologic modeling purpose in HEC-HMS. SHG is defined on the basis of Albers equal-area conic map projection on NDA83 datum (EPSG 5070 or ESRI 102039) – see ** Figure 1**. It is worth emphasizing that SHG is

**NOT**a new kind of map projection, and instead it is a grid system established on EPSG 5070 and thus it uses EPSG 5070’s projection parameters (

**). Other sources may refer SHG to EPSG 5071 or EPSG 5072, which is also correct since EPSG 5071 or EPSG 5072 uses a refined version of NAD83 datum such as NAD83 (HARN) or NAD83(NSRS2007), and the differences between them and NAD83 are negligible for H&H applications.**

*Table 1*The SHG grid cells are squares and their sizes vary. In SHG, the default grid cell size is 2000-meter x 2000-meter (SHG two-kilometer) and other supported grid cell sizes include 10,000-meter x 10,000-meter, 1000-meter x 1000-meter, 500-meter x 500-meter, 200-meter x 200-meter, 100-meter x 100-meter, 50-meter x 50-meter, 20-meter x 20-meter, and 10-meter x 10-meter. For easy discussion purpose, from now on all the discussions in this post assume the SHG grid cell size is 2000-meter x 2000-meter.

SHG grid cells are arranged relative to the origin point (intersection of 96^{0}W and 23^{0}N where) and indexed by cell counts (**i, j**) of the southwest (lower left) corners as shown in ** Figure 2**. For Grid Cell (-5,4) in

**, its southwest corner easting/northing coordinates are -10000m, 8000m (the easting is negative because this cell is on the west side of 96**

*Figure 2*^{0}W).

A point’s location is defined in EPSG 5070 by its easting/northing (or X, Y) coordinates with unit of meter. In SHG, a point’s location is described by which cell it is located in. To find the indices of the cell to which a point belongs, divide the point’s easting and northing by cell size (2000M for default SHG) and the indices are the quotients (See equations in ** Figure 3**). An example: if a point X, Y coordinates are -9000m, 9000m in EPSG 5070, its index of i=floor(-9000/2000)=floor(-4.5)=-5 and its index of j=floor(9000/2000)=floor(4.5)=4. The results means this point is located within Grid Cell (-5,4) as shown in

**.**

*Figure 2*Gridded data (either static gridded data or gridsets) are normally imported and stored in a HEC-DSS file in the format of SHG, which means the gridded data is projected to EPSG 5070 with grid cell sizes defined by SHG, either 2000-meter x 2000 meter by default, or other sizes. Refer to this post for more details about gridded data and HEC-DSS.

Two types of hydrology modeling methods are available in HEC-HMS: lumped methods and spatially variant distributed methods. For lumped hydrology methods, average values of a watershed are inputs and the entire watershed is to be modeled as one single element (Example: Clark Unit Hydrograph transform method, TOC and Storage Coefficient R, as well as watershed time-area relationship are provided). For distributed hydrology methods, a watershed is subdivided into a gridded system and each grid cell is a small sub-watershed where hydrology calculation happens (ModClark transform method, each cell has its own travel time).

ModClark requires subbasins in HEC-HMS to be discretized using “Structured Discretization” which usually employs SHG grid system as shown in ** Figure 4** and

*.*

**Figure 5**After setting up** ****Projection** (SHG is the default option) & **Cell size** for each subbasin as shown in ** Figure 5**, a terrain file needs to be linked with the basin (

**) and preprocessed by tools in the menu of GIS including**

*Figure 6***Step 1: Preprocess Sinks**and

**Step 2: Preprocess Drainage**(

**) – if these two steps have not been performed before.**

*Figure 7*Finally, go to **GIS—>Compute—>Grid Cells** (** Figure 8**) to generate the grid systems.

In this example, the created grid system is saved in **PistolCreek.sqlite** with cell sizes of 50-meter x 50-meter. **PistolCreek.sqlite** includes data such as cell index i & J, cell areas, and cell travel distances which are to be used for travel time calculation for each cell in ModClark method (** Figure 9**).

Other discretization methods in HEC-HMS, such as Unstructured Discretization, can be viewed here or here. Unstructured Discretization is usually used for the 2D Diffusion Wave transform method.

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