# 1. Drainage Area

What is needed ?

• A table that contains two columns: USGS station ID and Drainage area. This table has to be stored as an Arc/Info Info file or as any file that can be converted into Info file, for example, text (ASCII) or dbf.
• Grid of flow direction xxxfdr and
• Grid which cells represent the USGS stations xxxgs. The value of each cell that represents the USGS station must be equal to the station ID. All other cells must contain NO DATA.

### 1) Calculate the grid of drainage area

a) calculate the flow accumulation

xxxfac = flowaccumulation (xxxfdr )

b) find out the multiplication number that is equal to the cell area multiplied by unit conversion factor. For example if the cell size is 500 m and we want area in square kilometers the multiplication factor will be a = 0.5 * 0.5 = 0.25 (If we want area in mi2, a = 0.25 * 0.3861 = 0.096525)

c) calculate area (here in km2)

xxxarea = xxxfac * 0.25

### 2) Determine the drainage area for each gauging station

xxxargs = con (xxxgs > 0 , xxxarea )

### 3) Convert grid into Integer representation,

This step is required to create a value attribute table VAT. The integer grid will not have decimal part, thus if the precision higher than 1 km2 is needed before using INT function, the grid xxxargs must be multiplied by a number large enough to preserve required number of decimal places. For example, to have precision of 1 ha, grid xxxargs must be multiplied by 100. Here, the precision of 1 km2 is high enough.

xxxargsi = int ( xxxargs )

If the VAT has not been created automatically, it must be created by applying buildvat command

buildvat xxxargsi

### 4) Create a table that relates estimated area to the station ID

xxxcom = combine (xxxgs, xxxargsi )

The VAT table should contain the standard items: count and value, as well as the following items:

• xxxgs = station id
• xxxargsi = station drainage area (in km2)

### 5) Use Arc/Info or ArcView to merge two info files,

one that contains USGS estimates of drainage area, and the other that contains drainage area estimated from DEM (grid xxxcom). JOINITEM command requires that the items that contain station id (merge-item) must have identical names, widths, types and other parameters. ArcView does not have such requirements to perform joining two tables.

joinitem xxxcom.vat usgs.pat xxxcom.vat station_id station_id

# 2. Error in Estimations of the Drainage Area

The percentage error is calculated utilizing the following formula:

error = 100 * (A - B ) / B

Where: A is the estimated drainage area and B is the USGS area.

1) The calculations may be performed within ArcInfo TABLES processor.

The dialog may look like follows (usgsarea is the item that contains the drainage area from USGS record):

additem xxxcom.vat xxxcom.vat error 8 12 f 2 usgsarea

tables select xxxcom.vat

calculate error = 100 * ( usgsarea - xxxargsi ) / usgsarea

2) The error can be calculated using grid algebra.

Two grids are required:

• xxxarea (see section 1c for description) and
• usgsgrid - same as xxxgs, but cell values equal to drainage area from USGS data.

The following line shows exemplary GRID dialog that calculate the percentage error:

error = 100 * ( usgsgrid - xxxarea ) / usgsgrid

where error is the grid that contains error.

# 3. Sources of the Errors

There are three possible causes of the error:

1. Station is located on the wrong flow path (river)
2. Station is on good river but the delineated watershed boundaries are wrong.
3. Both, (1) and (3)

I assume that the numbers published by the USGS are good ( but ... you never know) To solve the problem (1) the stations need to be moved into new location. The problem (2) is more serious. It can not be solved just by deleting the station. It requires editing the flow direction grid (or elevation grid) to create "proper" flow path delineation.

How to find out if the watershed boundaries are correct ?

• Display grid of the delineated watersheds (or polygon coverage of these watersheds) and on the top draw the RF1 (streams). Then check if there are rivers from RF1 that cross the delineated watershed boundaries.
• Display grid of delineated watersheds and the coverage of the HUCs (hydrologic units)

How to correct errors ?

• The "walls" that prevent the flow to go through can be build by changing the elevation of selected cells. For example in ArcInfo tools (grid tools) a line can be drawn on the DEM that is edited. Each cell that represent this line will be assigned a specified value. The "wall" (line) has to be thick enough: If the cells that represent this flow barrier are connected only in corners the flow will get through it!!!
• The flow direction can be adjusted in ArcInfo Grid Editing Tools. If we want to cut the river , we have to change the value in the cell in which the flow path should be disconnected. For example, the selected cell has a value of 4 (flow in South direction) and the major inflow into this cell come from the North-West thus we change the flow direction number into 32.

Pawel, May 1996