Geomorphic Curvature
Curvature is the rate of change of slope, so it is the second derivative of the elevation surface.
Profile  Plan  Cross section  Minimum  Maximum 
The curvature maps are all scaled to show the 5th to 95th percentiles, and they usually have distributions with very large tails.
Curvature (convexity)

Point parameter, from 9 point neighborhood 

Second derivative of elevation First derivative of slope 
Surface Curvature.
Curvature Equations Used in MICRODEM


z1 := znw  z;
z2
:= zn  z;
z3
:= zne  z;
z4
:= zw  z;
z5
:= 0;
z6
:= ze  z;
z7
:= zsw  z;
z8
:= zs  z;
z9
:= zse  z;


A := ((z1 + z3 + z4 +
z6 + z7 + z9) / 6  (z2 + {z5 +} z8) / 3) / XSp / YSp;
B := ((Z1 + z2 + z3 +
z7 + z8 + z9) / 6  (z4 + {z5 +} z6) / 3) / XSp / YSp;
C := (z3 + z7 z1 
z9) / 4 / XSp / YSp;
D := (z3 + z6 + z9 
z1  z4  z7) / 6 / XSp;
E := (z1 + z2 + z3 
z7  z8  z9) / 6 / YSp;
F := (2 * ( z2 + z4 +
z6  z8)  (z1 + z3 + z7 + z9) {+ 5 * z5} ) / 9;


SqABC := sqrt(sqr(AB)
+ sqr(C));
MaxCurve := 20
* (ASp)*(A  B + SqABC);
MinCurve := 20
* (ASp)*(A  B  SqABC);
SqED := (sqr(E) +
sqr(D));
if SqED > 0.000001
then begin
SlopeCurvature {Profile convexity} := 200 * (A * sqr(D)
+ B * sqr(E) + C * D * E) / SqED / Math.Power(1 + SqED, 1.5);
PlanCurvature {Plan convexity} := 200 * (B * sqr(D) + A
* sqr(E)  C * D * E) / Math.Power(1 +SqED, 1.5);
crossc := 20 * (ASp)*(B*D*D + A*E*E  C*D*E)/
SqED;
end
else begin
SlopeCurvature := 0;
PlanCurvature := 0;
CrossC := 0;
end;

XSp and YSp are are the horizontal data spacings in the x and y directions, which can be different (for example SRTM, NED, or DTED), and can be a function of latitude within a single DEM.
References:
The algorithm option computes using four algorithms, with an option to use a larger computation region:
Last revised 1/8/2017