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Topographic Metrics

Topographic Metrics

Nov 27, 2015

Topographic metrics that we considered for our analysis were derived from the first order digital elevation model (DEM) produced by OpenTopography and exported as .TIF files. 

Elevation above mean sea level (m aμsl)

The first order unit of topography is given as the vertical elevation above mean sea level in meters (m aμsl). The elevation is derived from a LiDAR point cloud using ground classified returns. The elevations for each of the six length scale DEMs were calculated in OpenTopography using the Triangulated Irregular Network (TIN) and TauDEM (Tarboton XXXX) method with the hydrologically corrected pit filling turned on. Length scales that were used in this analysis:

  • 1m
  • 3m
  • 5m
  • 10m
  • 15m
  • 30m 

 The change in length scales was intended to represent the variation in topography at an ecologically relevant scale, e.g. the total distance an individual tree's roots can spread radially away from its bole. 

Slope

For each of the six DEM models we calculated the slope of the terrain in radians and degrees. The slope was calculated using SAGA Topography Morphometry > Slope, Aspect, Curvature. 

Load GeoTiff layers into SAGA 2.1.4

In SAGA Topography Morphometry > Slope, Aspect, Curvature. 

Selecte the Grid System and Elevation models for a given TIF.

I enerated all of the possible output options:

  • Slope
  • Aspect
  • General Curvature
  • Profile curvature
  • Plan Curvature
  • Tangential Curvature
  • Longitudinal Curvature
  • Cross-Sectional Curvature
  • Minimal Curvature
  • Maximal Curvature
  • Total Curvature
  • Flow Line curvature

The Options were set to:

  • Method: 9 parameter 2nd order polynomial (Zevenbergen & Thorne 1987)
  • Slope Units: Radians
  • Aspect Units: Radians

Aspect

The aspect of exposure was also calculated using SAGA Topography Morphometry > Slope, Aspect, Curvature. 

Curvature

The topographic curvatures were calculated using SAGA Topography Morphometry > Slope, Aspect, Curvature. Curvature can be calculated with six different profile axes ( Alkhasawneh et al. 2013):

  • Planimetric: curvature in the horizontal plane, proxy for convergent/divergent flow paths
  • Profile: proxy for accelerated/decelerated flow velocity
  • Tangential curvature: nearly equivalent to planimetric, proxy for convergent/divergent flow paths
  • Longitudinal: curvature explaining whether a flowing substance will be accelerating or decelerating as it travels across a point.
  • Cross-sectional: similar to plan curvature, explains convergent vs divergent flow path
  • General: the combination of both plan and profile curvatures. 

The measure of curvature is scale dependent. The length scale of the DEM alters curvatures and reveals different landscape properties. For example, the profile curvature of a 1 meter DEM reveals what are essentially microtopographic variations amongst individual trees where the swell of their root balls change the local surface shape. At longer length scales, e.g. 10-30m these features are smoothed out and larger topographic properties of the landscape become more apparent.

For our analysis we chose to look at Profile, Planiform, and General Curvatures. Profile curvatures explain the curvature of the vertical plane, e.g. concave, flat, or convex slopes. Planiform curvatures explain the contour curvature where lateral positions are convergent or divergent. General curvature is the sum of both the profile and planiform curvature measured together. 

In exploring the question about ground water subsidy and its affect on overall tree biomass (estimated from height and canopy diameter) I generated topographic curvatures at multiple length scales (e.g. 1m, 3m, 5m, 10m, 15m, 30m). 

It can be readily observed local profile curvature exhibits concave and convex shapes that appear as terracing above and below clusters of trees, which are in general aligned perpendicular to the hill slope.

Curvatures are one of three values:

Convex > 0

Concave  < 0

Flat = 0

The root swell around trees growing on steep slopes results in a positive feedback where water is slowed across a concave slope on the uphill side, resulting in deposition and greater wetness. This may also have an affect on the snow on south facing aspects, as is also observable in the Valles Caldera data. 

Curvature calculations are typically conducted upon a 3x3 moving window at varying length scales. 

Plan curvature is defined as curvature in a horizontal plane. 


Profile curvature is the curvature of the surface in the direction of the steepest slope (with respect to the vertical plane of a flow line). 


General curvature (also called total curvature) is the curvature of the surface itself (not the curvature of a line formed by the intersection of the surface with a plane).  General curvature = plan curvature + profile curvature


Preliminary Results



Deep ground water is less likely to be affected by variations in short length scale, e.g. 1-5 m, and individual tree responses to deep ground water may not be apparent at those scales. We compared a range of length scales to determine which scales have the greatest influence on biomass accretion.    

 Catchment Area

Catchment area was calculated using SAGA Topography Hydrology > Catchment Area (Recursive) method. The recursive catchment area method (XXXX) 

Catchment area serves as a proxy for redistribution of surface overland flow.

Topographic Wetness Index

Topographic Wetness Index (TWI) was calculated using the TOPMODEL (Beven and Kirkby 1979) method in SAGA Terrain Analysis - Hydrology > Topographic Wetness Index (TWI)

Topographic Position Index

Topographic Position Index (TPI) was calculated using the SAGA Terrain Analysis - Morphometry > Topographic Position Index. The function used the default parameters for the module (inverse distance weighting (IDW) and a 150 m moving window). 

Relative Heights and Slope Positions

The relative heights and slope positions were calculated using the SAGA Terrain Analysis - Morphometry > Relative Heights and Slope Positions.

The module was written by Dietrich and Böhner (2008) - "Cold Air Production and Flow in a Low Mountain Range Landscape in Hessia (Germany)." The outputs of the modules are:

  • Slope Height (m) - vertical change above the channel
  • Valley Depth (m) - the vertical change below the ridge
  • Normalized Height (unitless) - the ratio position between the channel and the ridge (values between 0 and 1).
  • Standardized Height (m amsl) - the position between the channel and the ridge (values in meters above sea level standardized for the catchment)
  • Mid-slope Position (unitless) - the ratio position between either channel or ridge (values of 0 to 1 to 0 for channel to mid-slope to ridge). 

Matlab Scripts

Next, I calculated the group statistics of each topographic variable to the standing aboveground biomass as estimated from the individual tree segmentation.

I downloaded a Shaded Error Bar plot plot script from Matlab Central and generated error bars using the standard deviation about the mean.

%Betasso Preserve slope and elevation characteristics of AGC
%imports the the AGC as bet_agc, slope as bet_slope, and elevation as bet_dem 
[mean_bet_agc_aspect,median_bet_agc_aspect,std_bet_agc_aspect,pred99_bet_agc_aspect,sem_bet_aspect,bet_aspect_grp]=grpstats(bet_agc,round(bet_aspect.*10)./10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
bet_aspect_ngrps=length(bet_aspect_grp);
d=0:0.1:6.2;
d=transpose(d);
d=rad2deg(d);
figure
subplot(2,1,1);
hold on;
shadedErrorBar(d,mean_bet_agc_aspect,std_bet_agc_aspect,'r-',1)
[bet_hist_y_asp,bet_hist_x_asp]=hist(rad2deg(bet_aspect),d);
subplot(2,1,2);
hold on;
s=size(bet_aspect);
bet_hist_y_norm_asp=bet_hist_y_asp./s(1);
stairs(bet_hist_x_asp,bet_hist_y_norm_asp,'r');
%Gordon Gulch slope and elevation characteristics of AGC
[mean_gg_agc_aspect,median_gg_agc_aspect,std_gg_agc_aspect,pred99_gg_agc_aspect,sem_gg_aspect,gg_aspect_grp]=grpstats(gg_agc,round(gg_aspect.*10)./10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
gg_aspect_ngrps=length(gg_aspect_grp);
d=0:0.1:6.3;
d=transpose(d);
d=rad2deg(d);
subplot(2,1,1);
shadedErrorBar(d,mean_gg_agc_aspect,std_gg_agc_aspect,'g-',1)
[gg_hist_y_asp,gg_hist_x_asp]=hist(rad2deg(gg_aspect),d);
subplot(2,1,2)
hold on;
s=size(gg_aspect);
gg_hist_y_norm_asp=gg_hist_y_asp./s(1);
stairs(gg_hist_x_asp,gg_hist_y_norm_asp,'g');
%Como Creek slope and elevation characteristics of AGC
[mean_cc_agc_aspect,median_cc_agc_aspect,std_cc_agc_aspect,pred99_cc_agc_aspect,sem_cc_aspect,cc_aspect_grp]=grpstats(cc_agc,round(cc_aspect.*10)./10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
cc_aspect_ngrps=length(cc_aspect_grp);
d=0:0.1:6.3;
d=transpose(d);
d=rad2deg(d);
subplot(2,1,1);
shadedErrorBar(d,mean_cc_agc_aspect,std_cc_agc_aspect,'b-',1)
[cc_hist_y_asp,cc_hist_x_asp]=hist(rad2deg(cc_aspect),d);
subplot(2,1,2);
hold on;
s=size(cc_aspect);
cc_hist_y_norm_asp=cc_hist_y_asp./s(1);
stairs(cc_hist_x_asp,cc_hist_y_norm_asp,'b');
%Betasso Preserve AGC by DEM
[mean_bet_agc_dem,median_bet_agc_dem,std_bet_agc_dem,pred99_bet_agc_dem,sem_bet_dem,bet_dem_grp]=grpstats(bet_agc,round(bet_dem./10).*10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
bet_dem_ngrps=length(bet_dem_grp);
dem = str2num(cell2mat(bet_dem_grp));
figure
subplot(2,1,1);
hold on;
shadedErrorBar(dem,mean_bet_agc_dem,std_bet_agc_dem,'r-',1)
bet_lr_agc_dem_x=-0.19*bet_hist_x_dem+820;
plot(bet_hist_x_dem,bet_lr_agc_dem_x);
[bet_hist_y_dem,bet_hist_x_dem]=hist(bet_dem,dem);
subplot(2,1,2);
hold on;
s=size(bet_dem);
bet_hist_y_norm_dem=bet_hist_y_dem./s(1);
stairs(bet_hist_x_dem,bet_hist_y_norm_dem,'r');

%Gordon Gulch
[mean_gg_agc_dem,median_gg_agc_dem,std_gg_agc_dem,pred99_gg_agc_dem,sem_gg_dem,gg_dem_grp]=grpstats(gg_agc,round(gg_dem./10).*10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
gg_dem_ngrps=length(gg_dem_grp);
dem = str2num(cell2mat(gg_dem_grp));
subplot(2,1,1);
shadedErrorBar(dem,mean_gg_agc_dem,std_gg_agc_dem,'g-',1)
gg_lr_agc_dem_x=-1.6*gg_hist_x_dem+4503;
plot(gg_hist_x_dem,gg_lr_agc_dem_x,'k-');
[gg_hist_y_dem,gg_hist_x_dem]=hist(gg_dem,dem);
subplot(2,1,2);
hold on;
s=size(gg_dem);
gg_hist_y_norm_dem=gg_hist_y_dem./s(1);
stairs(gg_hist_x_dem,gg_hist_y_norm_dem,'g');
%Como Creek
[mean_cc_agc_dem,median_cc_agc_dem,std_cc_agc_dem,pred99_cc_agc_dem,sem_cc_dem,cc_dem_grp]=grpstats(cc_agc,round(cc_dem./10).*10,{'mean','median','std','predci','sem','gname'},'Alpha',0.01);
cc_dem_ngrps=length(cc_dem_grp);
dem = str2num(cell2mat(cc_dem_grp));
subplot(2,1,1);
shadedErrorBar(dem,mean_cc_agc_dem,std_cc_agc_dem,'b-',1)
cc_lr_agc_dem_x=-1.2*cc_hist_x_dem+4300;
plot(cc_hist_x_dem,cc_lr_agc_dem_x);
[cc_hist_y_dem,cc_hist_x_dem]=hist(cc_dem,dem);
subplot(2,1,2);
hold on;
s=size(cc_dem);
cc_hist_y_norm_dem=cc_hist_y_dem./s(1);
stairs(cc_hist_x_dem,cc_hist_y_norm_dem,'b');

 

References

Beven, K.J., Kirkby, M.J. (1979) A physically-based variable contributing area model of basin hydrology' Hydrology Science Bulletin 24(1), p.43-69

Guisan, A., Weiss, S.B., Weiss, A.D. (1999): GLM versus CCA spatial modeling of plant species distribution. Plant Ecology 143: 107-122.

Tarboton, D.G. (1997) 'A new method for the determination of flow directions and upslope areas in grid digital elevation models', Water Resources Research, Vol.33, No.2, p.309-319

Hurst et al. (2012)