The
Precision Farming Primer |
|
Characterizing Micro Terrain
(Part 1) — describes procedures for
identifying convex and concave terrain features
Characterizing Micro Terrain
(Part 2) — investigates localized
variation as measure of surface roughness
Characterizing Micro Terrain
(Part 3) — identifies a procedure for
modeling surface water flow.
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Characterizing Micro-Terrain (Part 1) (return to top of Topic
5)
The past several columns investigated surface modeling
and analysis. The data surfaces
derived in these instances weren't the familiar terrain surfaces you
walk the dog, bike and hike on.
None-the-less they form surfaces that contain all of the recognizable
gullies, hummocks, peaks and depressions we see on most hillsides. The "wrinkled-carpet" look in the
real world is directly transferable to the cognitive realm of the data
world.
However, at least for the moment, let's return to terra firma to investigate
how micro-terrain features can be characterized. As you look at a landscape you easily see the
changes in terrain with some areas bumped up (termed convex) and
others pushed down (termed concave). But how can a computer "see" the
same thing? Since its world is digital
how can the lay of the landscape be transferred into a set of drab numbers?
One of the most frequently used
procedures involves comparing the trend of the surface to the actual elevation
values. Figure 1 shows a terrain profile
extending across a small gully. The
dotted line identifies a smoothed curve fitted to the data, similar to a
draftsman's alignment of a French curve.
It "splits-the-difference" in the succession of elevation
values— half above and half below.
Locations above the trend line identify convex features while locations
below identify concave ones. The further
above or below determines how pronounced the feature is.
In a GIS, simple smoothing of the actual elevation values derives the trend of
the surface. The left side of Fig. 2
shows the actual and smoothed surfaces for a project area. The flat portion at the extreme left is an
area of open water. The terrain rises
sharply from 500 feet to the 2500 feet at the top of the hill. Note the small "saddle" (elevation
dips down then up) between the two hilltops.
Also note the small depression in the relatively flat area in the lower
SW portion.
In generating the smoothed surface, elevation values were averaged for a 4-by-4
window moved throughout the area. Note
the subtle differences between the surfaces—the tendency to pull-down the
hilltops and push-up the gullies.
While you see (imagine?) these differences in the surfaces, the computer
quantifies them by subtracting. The difference surface on the
right contains values from -84 (prominent concave feature) to +94 (prominent
convex feature). The big bump on the
difference surface corresponds to the smaller hilltop on elevation
surface. Its actual elevation is 2016
while the smoothed elevation is 1922 resulting in 2016 - 1922 = +94
difference. In micro-terrain terms,
these areas are likely drier that their surroundings as water flows away.
The other arrows on the surface indicate other interesting locations. The "pockmark" in the foreground is
a small depression (764 - 796 = -32 difference) that is likely wetter as water
flows into it. The "deep cut"
at the opposite end (539 - 623 = -84) suggests a very prominent concavity. However representing the water body as fixed
elevation isn't a true account of terra firma configuration.
The 2-D map of differences identifies areas that are concave (dark red), convex
(light blue) and transition (white portion having only -20 to +20 feet
difference between actual and smoothed elevation values). If it were a map of a farmer's field, the
groupings would likely match a lot of the farmer's recollection of crop
production—more water in the concave areas, less in the convex areas.
A
The idea of variable rate response to spatial conditions has been around for
thousands of years as indigenous peoples adjusted the spacing of holes they
poked in the ground to drop in a seed and a piece of fish. While the mechanical and green revolutions
enable farmers to cultivate much larger areas they do so in part by applying broad
generalizations of micro-terrain and other spatial variables over large
areas. The ability to continuously
adjust management actions to unique spatial conditions on expansive tracks of
land foretells the next revolution.
The ability to identify and investigate the effects of micro-terrain conditions
goes well beyond the farm. For example,
the Universal Soil Loss Equation uses "average" watershed conditions,
such as stream channel length and slope, dominant soil types and existing land
use classes, to predict water runoff and sediment transport from large
areas. These non-spatial models are
routinely used to determine the feasibility of spatial activities, such as
logging, mining, road building and housing development. While the procedures might be applicable to
typical conditions, they less accurately track unusual conditions clumped
throughout an area and provide no spatial guidance within the boundaries of the
modeled area.
GIS-based micro-terrain analysis can help us be more like a "modern
ancient farmer"— responding to site-specific conditions over large
expanses of the landscape. Calculation
of a difference surface simply scratches the surface of micro-terrain
analysis. In the next few columns we'll
look other procedures that let us think like a raindrop while mapping the
micro-terrain.
As depicted in the example calculations for the concave feature, the average
elevation of the surroundings is 106, that computes to a -6.00 deviation when
subtracted from the center's value of 100.
The negative sign denotes a concavity while the magnitude of 6 indicates
it's fairly significant dip (a 6/100= .06).
The protrusion above its surroundings (termed a convex feature)
shown on the right of the figure has a localized deviation of +4.25 indicating
a somewhat pronounced bump (4.25/114= .04).
The implication of the "Localized Deviation" approach goes far beyond
simply an alternative procedure for calculating terrain irregularities. The use of "roving windows"
provides a host of new metrics and map surfaces for assessing micro-terrain
characteristics. For example, consider
the Coefficient of Variation (Coffvar) Surface shown in the
bottom-right portion of figure 2. In
this instance, the standard deviation of the window is compared to its average
elevation—small "coffvar" values indicate areas with minimal
differences in elevation; large values indicate areas with lots of different
elevations. The large ridge in the
Coffvar surface in the figure occurs along the shoreline of a lake. Note that the ridge is largest for the
steeply-rising terrain with big changes in elevation. The other bumps of surface variability noted
in the figure indicate areas of less terrain variation.
While a statistical summary of elevation values is useful as a general
indicator of surface variation or "roughness," it doesn't consider
the pattern of the differences. A
checkerboard pattern of alternating higher and lower values (very rough) cannot
be distinguished from one in which all of the higher values are in one portion
of the window and lower values in another.
As shown in figure 3, there are eight surrounding elevation values in a 3x3
roving window. An individual slope from
the center cell can be calculated for each one.
For example, the percent slope to the north (top of the window) is
((2332 - 2262) / 328) * 100 = 21.3%. The
numerator computes the rise while the denominator of 328 feet is the distance
between the centers of the two cells.
The calculations for the northeast slope is ((2420 - 2262) / 464) * 100
= 34.1%, where the run is increased to account for the diagonal distance (328 *
1.414 = 464).
The eight slope values can be used to identify the Maximum, the Minimum and the
Average slope as reported in the figure.
Note that the large difference between the maximum and minimum slope (53
- 7 = 46) suggests that the overall slope is fairly variable. Also note that the sign of the slope value
indicates the direction of surface flow—positive slopes indicate flows into the
center cell while negative ones indicate flows out. While the flow into the center cell depends
on the uphill conditions (we'll worry about that in a subsequent column), the
flow away from the cell will take the steepest downhill slope (southwest flow
in the example… you do the math).
In practice, the Average slope can be misleading. It is supposed to indicate the overall slope
within the window but fails to account for the spatial arrangement of the slope
values. An alternative technique
"fits a plane" to the nine individual elevation values. The procedure determines the best fitting
plane by minimizing the deviations from the plane to the elevation values. In the example, the Fitted slope is 65%… more
than the maximum individual slope.
At first this might seem a bit fishy—overall slope more than the maximum
slope—but believe me, determination of fitted slope is a different kettle of
fish than simply scrutinizing the individual slopes. Next time we'll look a bit deeper into this
fitted slope thing and its applications in micro-terrain analysis.
_______________________
Author's
Notes: An Excel worksheet
investigating Maximum, Minimum, and Average slope calculations is available
online at the "Column Supplements" page at http://www.innovativegis.com/basis.
In effect, a drop of water is placed at each location and allowed to pick its
path down the terrain surface. Each grid
cell that is traversed gets the value of one added to it. As the paths from other locations are
considered the areas sharing common paths get increasing larger values (one +
one + one, etc.).
The inset on the right side of the figure shows the path taken by a couple of
drops into a slight depression. The
inset on the left shows the considerable inflow for the depression as a high
peak in the 3-D display—a collection point.
The high value indicates that a lot of uphill locations are connected to
this feature. However, note that the
pathways to the depression are concentrated along the southern edge of the
area.
So far, the various spatial analysis techniques for characterizing terrain
surfaces introduced in this series provide a wealth of different perspectives
on surface configuration. Recall that
the Deviation from Trend, Difference Maps and Deviation
Surfaces are used to identify areas that "bump-up" (convex) or
"dip-down" (concave). A Coefficient
of Variation Surface looks at the overall disparity in elevation values occurring
within a small area. A Slope Map
shares a similar algorithm (roving window) but the summary of is different and
reports the "tilt" of the surface.
An Aspect Map extends the analysis to include the direction of
the tilt as well as the magnitude. And
finally, a Confluence Map takes an extended view and characterizes the
number of uphill locations connected to each location to characterize surface
flow.
The coincidence of these varied perspectives can provide valuable input to
decision-making. Areas that are smooth,
steep and coincide with high confluence are strong candidates for gully-washers
that gouge the land. On the other hand,
areas that are rough, gently-sloped and with minimal confluence are relatively
stable. Concave features in these areas
tend to trap water and recharge soil moisture and the water table. Convex features under erosive conditions tend
to become more prominent as the confluence of water flows around it.
While these "rules-of-thumb" make sense in most situations, there are
several exceptions that can undercut them.
Two concerns in particular are important— conditions and
resolution. First, conditions along the
surface can alter the effect of terrain characteristics. For example, soil properties and the vegetation
at a location greatly effects surface runoff and sediment transport. The nature of accumulated distance along the
surface is also a determinant. If the
uphill slopes are long steep, the water flow has accumulated force and
considerable erosion potential.
In addition, the resolution of the elevation grid can effect the
calculations. In the case of water drops
the gridding resolution and accurate "Z" values must be high to
capture the subtle twists and bends that direct water flow. This concern is crucial in the subtle
micro-terrain changes across most agricultural fields. While elevation data within a few meters is
sufficient for planning highways and development, agricultural applications
require much more detail.
Enter RTK (Real Time Kinematic) GPS technology you might have heard about— it
builds terrain maps to centimeter accuracy.
This detail coupled with terrain analysis promises a pretty good picture
of the flows within a field (erosion, accretion, infiltration, runoff, fines,
organic matter, sediment transport, etc.).
In site-specific terms this information could be the next frontier in
the revolutionary field of precision farming.
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