# Numeric Attributes

##### Area (A)

Total area of the unit calculated from shape geometry.

##### Width (W)

Average width of unit calculated as the area of the unit divided by length.

##### Length (L)

Maximum length of minimum bounding rectangle.

##### Perimeter (P)

Total length of unit boundary calculated from shape geometry.

##### LtoWRatio

Length of the unit divided by the width of the unit.

##### ElongRatio

ElongRatio=2 x(sqrt(Area/pi)/L)

Elongation ratio calculated as the diameter of a circle with the same area as that of the shape divided by maximum shape length.

##### Orient

Orientation of the unit relative to the centerline. orientations are calculated using minimum bounding geometry.

##### bfSlope

Bankfull stage water surface slope. Calculated in degrees.

##### bfSlopeSm

Average bankfull stage water surface slope. Calculated over a bankfull width x bankfull width window

##### bedSlope

Average bed slope of the unit.

##### bfwRatio

Width of the unit divided by the reach averaged bankfull width.

##### Roundess

Roundness=Area/Pc^2

Where Pc is the convex perimeter of the shape (the perimeter of a rubber band if it was stretched around the shape, resting on the shapes most prominent vertices)

The maximum value is 1, shapes with irregular boundaries have lower values (van der Werff and van der Meer, 2008; Williams, 2014; Meshkova and Carling, 2013).

##### Convexity

Convexity= Pc/P

where Pc is the convex perimeter of the shape (the perimeter of a rubber band if it was stretched around the shape, resting on the shapes most prominent vertices)

Values of 1 indicate that the curvature of any location on the perimeter is convex (van der Werff and van der Meer, 2008; Williams, 2014; Meshkova and Carling, 2013)

##### Compactness

Compactness=4pi(A/P^2)

Denotes how similar the shape is to a circle. If compactness is one it is a perfect circle. Lower values are associated with deviations from circles. (van der Werff and van der Meer, 2008; Williams, 2014; Meshkova and Carling, 2013)

##### Relief (R)

Maximum elevation of unit minus minimum elevation of unit using DEM

##### Vcompact

Vertical Compactness as a ratio of relief over maximum length of the unit. Units greater than one are thicker than they are long (Sneed and Folk, 1958; Williams, 2014)

##### Platyness

Ratio of relief compared to width. For values greater than one the unit is thicker than it is wide (Krumbein, 1941; Williams, 2014)

##### Sphericity

Sphericity=(Area/(Length x width))/Relief

Closeness of the shape to a perfect sphere (Krumbein, 1941; Williams, 2014)

##### ProfCurv

Curvature in direction of maximum slope per cell in the DEM averaged over the unit (ESRI, 2016).

##### PlanCurv

Curvature perpendicular to maximum slope per cell averaged over the unit (ESRI, 2016)

##### mBend

Bankfull channel meander bend index value nearest to the unit centroid. The meander bend index is calculated over a bankfull width by bankfull width moving window. For each bankfull channel edge cell, difference the number of dry (out-of-channel) and wet (in-channel) cells. Positive values indicate outside of bends, negative values indicate inside of bends, and values near zero indicate straight sections of the channel. (add citation)

ESRI, 2016. Curvature Function. ArcMap10.3. Accessed Dec., 19, 2017. http://desktop.arcgis.com/en/arcmap/10.3/manage-data/raster-and-images/curvature-function.htm

Krumbein, W. C., 1941. Measurement and geological significance of shape and roundness of sedimentary particles, Journal of Sedimentary Petrology, 11(2), 64- 72.

Meshkova, L.V. & Carling, P.A., 2012. The geomorphological characteristics of the Mekong River in northern Cambodia: A mixed bedrock-alluvial multi-channel network. Geomorphology, 147, pp.2–17.

Sneed, E.D. & Folk, R.L., 1958. Pebbles in the lower Colorado River, Texas a study in particle morphogenesis. The Journal of Geology, 66(2), pp.114–150.

Van der Werff, H. & Van der Meer, F., 2008. Shape-based classification of spectrally identical objects. ISPRS Journal of Photogrammetry and Remote Sensing, 63(2), pp.251–258.

Williams, R., 2014. Two-dimensional numerical modelling of natural braided river morphodynamics.