HAND, a new terrain descriptor using SRTM-DEM - DPI - Inpe

Table 1
Δ Function definition
Flow direction Δ (Flow direction)
N h0,−1i
NE h1,−1i
E h1,0i
SE h1,1i
S h0,1i
SW h−1,1i
W h−1,0i
NW h−1,−1i
Null h0,0i
Montgomery and Dietrich (1988) discussed the criteria to predict the
point where channels should begin (headwater). One of the first
procedures for delineating drainage networks (O'Callaghan and Mark,
1984) used a minimum contributing area threshold to identify
channel beginning. The drainage network is thus defined by those
grid points that have a contributing area greater than a given
threshold. The contributing area is computed by counting the number
of points whose flow paths converge to the considered point.
Considering a given point h i,j i, we can determine its neighborhood
as
Nðhi; jiÞ
¼ fhk; liaGjk ¼ fi1; i; i 1g;
l ¼ fj1; j; j þ 1g;
hk; liphi; jig
ð2Þ
The points in N(hi,ji) are called the neighbors of h i,j i.Ifpointh i,j i is
not on the border grid (i≠1, i≠c, j≠1 andj≠r), then it has 8 neighbors,
that is
Nðhi; jiÞ
¼ fhi1; j 1i; hi 1; ji; hi 1; j þ 1i; hi; j 1i; hi; j þ 1i;
hi þ 1; j 1i; hi þ 1; ji; hi þ 1; j þ 1ig
otherwise, it will have less than 8 neighbors.
Based on the D8 method, the point hi,ji can be hydrologically
connected to only one of its neighbors. If F(hi,ji) is the point to which hi,ji
flows, it can be defined as:
Fðhi; jiÞ
¼hi; jiþDðLDDðhi; jiÞÞ
ð4Þ
where Δ is a function that represents the relative position hΔi,Δji
between two hydrologically connected points. Table 1 shows the
correspondence between the flow directions and the relative positions.
Note that if point hi, ji is a pit, then F(hi, ji)=hi, ji.
The contributing area of point hi, ji, defined as A(hi,ji), is computed
through an iterative process.
Let A t (hi, ji) be the contributing area of the point hi, ji in the t th
iteration. In the first iteration (t=1)
A 1 ðhi; jiÞ
¼
1 ifhi; jigFðGÞ 0 otherwise
where F(G) represents the set of all upward points connected to any
given point, that is
FG ð Þ ¼ fhk; liaGjahi; jiaNðhk; liÞjFðhi;
jiÞ
¼ hk; lig:
ð6Þ
In this first iteration, the contributing area of all points that initiate
a flow path is equal to one.
For the other iterations (tN1)
A t A
ðhi; jiÞ
¼
t 1ðhi; jiÞ
if At 1ðhi; jiÞp0
1 þ P
F−1ðhi;jiÞAt 1ðhk; liÞ
if 0gAt 1 F 1 8
<
ðhi; jiÞ
:
0 otherwise
ARTICLE IN PRESS
4 C.D. Rennó et al. / Remote Sensing of Environment xxx (2008) xxx-xxx
ð3Þ
ð5Þ
ð7Þ
where F − 1 (hi, ji) represents a set of all neighbors of point hi,ji that flow
to it, that is
F 1 ðhi; jiÞ
¼ fhk; liaNðhi; jiÞjFðhk;
liÞ
¼ hi; jig
ð8Þ
The iteration process stops (t=n) when, for any point hi,ji, A t −1 (hi,ji)≠0,
that is, A(hi,ji)=A n (hi,ji).
The method based on the contributing area is very easy to
implement and therefore widely used. Tarboton (2003) pointed out
that a significant question with this method is the choice of
contributing area threshold. The basic hypothesis is that channel
heads, where there is a transition from convex to concave profiles, is
also where concentrated fluxes begins to dominate over diffusive
fluxes (Tarboton et al., 1991, 1992). Some authors have called for
objective criteria to define channel heads, such as the relationship
between slope and contributing area (Tarboton et al., 1991). Others use
local curvatures to account for spatially variable drainage densities
(Tarboton and Ames, 2001). Montgomery and Foufoula-Georgiou
(1993) compared the constant contributing area with the slopedependent
contributing area. Although these approaches represent
progress towards the automatic determination of channel heads, the
tests we conducted for Central Amazonia showed that the application
of these methodologies to SRTM data did not estimate drainage
density properly. We suspect that vegetation masking ground
topography may be the explanation. For this reason, we decided to
use the contributing area threshold as one of the main criteria to
define the drainage network, validating channel heads with field data.
To define the channel heads we used an additional criteria based on
simplifications of horizontal and vertical geomorphic curvatures.
Firstly, the channel head element should represent a convergent point,
meaning it should have two or more overland flux paths converging to
it (horizontal curvature). Secondly, the channel profile should be
concave, i.e. where the channel head profile point has a smaller
change of elevation than the mean of the elements located uphill and
downhill of it (vertical curvature).
2.2. The height above the nearest drainage terrain descriptor
To quantify relevant parameters that could uniquely identify generalizable
spatial properties of hill slopes there was the need to have a local
frame of variable topographic reference that should be more useful than
the all encompassing and generic height ASL, or the third dimension in
the DEM. Horizontal distances of DEM grid points to connected drainage
channels (slope length) have been computed by a number of approaches
(e.g. Tucker et al., 2001). As the initial interest in this study was to predict
potential hydrological properties for each DEM grid point, especially the
depth to the permanently saturated zone, this approach wasn't useful.
The gravitational potential energy difference between any given grid
point and the other extremity of the hill slope flow path, at the functional
stream outlet (explicit in the LDD), defines a unique and permanent
property of that grid point that we call draining potential. The vertical
distance of a given grid point to its drainage outlet (which is
hydrologically important) can in most cases be expressed as a relative
height, or the height difference between those points. Thus there will be
no gravitationally driven water movement between two hydrologically
connected points that share the same height. Classifying all grid points
according to their respective draining potentials allows them to be
grouped into classes of equipotential (equivalent draining gravitational
potential), defining environments or zones with inferred similar
hydrological properties. The linking of every grid point to its outlet on
the drainage system allows for the whole DEM to be normalized for the
drainage network (adjusting point heights in relation to the drainage),
which in this way becomes a distributed frame of topographic reference.
If D is a set of drainage network points, identified by a number
through a bijective function in order that each point of the drainage
Please cite this article as: Rennó, C. D., et al., HAND, a new terrain descriptor using SRTM-DEM: Mapping terra-firme rainforest environments
in Amazonia, Remote Sensing of Environment (2008), doi:10.1016/j.rse.2008.03.018