52620_mesquit.tif

Ref: J. M. Rusk Report of the Secretary of Agriculture for the year 1891 (Washington, DC: Government Printing Office, 1892)

image source: http://etc.usf.edu/clipart/52600/52620/52620_mesquit.htm

Meeting with Joel and Adam

Does McClaran et al. 2013 take into account increasing tree age as a possible source of increasing divergence from an idealized allometric state?

• Divergence in the height to basal area height to canopy area vs predicted allometry with increasing age
• Divergence related to disturbance (wildfires), disease, damage.

Are we focused on biomass, component biomass partitioning?

• What are the limitations of the airborne lidar for measuring mesquite biomass and structure (morphology)?
• What are the limitations of the airborne lidar for measuring under the mesquites (species diversity + herbaceous biomass)?
  • Adam will establish the relationship using his field measurements (observed).
  • Compare his model to the lidar estimated canopy area/volume (estimated).
• What are the limitations of the SfM?

Do we want to expand to include species diversity (α, β, γ)?

We need to build a Google.Drive document.

I need to share the lidar data files for the trees.

Need to establish figures.

• Figure 1: Site map
• Figure 2: LiDAR examples of mesquite
• Figure 3: Regression of biomass vs height
• Figure 4: Regression of canopy vs height
• Figure 5: Cumulative density function of biomass across area by tree size (Joel)
• Figure 6: Regression of the field derived canopy volume vs the LiDAR derived canopy volume.
• Figure 7: Regression of the species diversity to tree size
• Figure 8: Regression of the observed diversity (Adam's model) vs the LiDAR estimated diversity

LiDAR Canopy Height Modelling and stem segmentation

First I generate a 1 foot canopy height model in FUSION from the Windows CMD command line:

cd\fusion
## Digital Surface Model
CanopyModel /ascii F:\SRER\DSM\19S15E06_1ft.dtm 1 f f 2 0 2 2 F:\SRER\LAS\19S15E06_LDRY11.las
## Canopy Height Model
CanopyModel /outlier:-1,50 /ground:F:\SRER\DTM\19S15E06_LDRY11.dtm /ascii F:\SRER\CHM\19S15E06_1ft.dtm 1 f f 2 0 2 2 F:\SRER\LAS\19S15E06_LDRY11.las

Next, I open Matlab and select a working directory where my VLM script is saved. I then execute a process to segment out the individual trees at multiple canopy diameter-to-stem height ratio:

% Imports canopy height model (2-ft resolution) and generates stem map
tile19s15e06=asc_import('E:\PAG2011\CHM\ASC\19S15E06_LDRY11.ASC');
% Assigns a 0.75 canopy diameter to height ratio 
tile_v=vlm(tile19s15e06,0.75,2);
vlm_ex=export_utm(tile_v,tile19s15e06);
col_header={'ID','UTME','UTMN','HT','PRED','AREA','EQDIAM','MAJAX','MINAX','MAXHT','MINHT','MEANHT'};
xlswrite('F:\SRER\STEMS\cd0p75_19s15e06.xlsx',vlm_ex,1,'A2');
xlswrite('F:\SRER\STEMS\cd0p75_19s15e06.xlsx',col_header,1,'A1');
% Assigns a 1 canopy diameter to height ratio 
tile_v=vlm(tile19s15e06,1,2);
vlm_ex=export_utm(tile_v,tile19s15e06);
col_header={'ID','UTME','UTMN','HT','PRED','AREA','EQDIAM','MAJAX','MINAX','MAXHT','MINHT','MEANHT'};
xlswrite('F:\SRER\STEMS\cd1_19s15e06.xlsx',vlm_ex,1,'A2');
xlswrite('F:\SRER\STEMS\cd1_19s15e06.xlsx',col_header,1,'A1');
% Assigns a 1.25 canopy diameter to height ratio
tile_v=vlm(tile19s15e06,1.25,2);
vlm_ex=export_utm(tile_v,tile19s15e06);
col_header={'ID','UTME','UTMN','HT','PRED','AREA','EQDIAM','MAJAX','MINAX','MAXHT','MINHT','MEANHT'};
xlswrite('F:\SRER\STEMS\cd1p25_19s15e06.xlsx',vlm_ex,1,'A2');
xlswrite('F:\SRER\STEMS\cd1p25_19s15e06.xlsx',col_header,1,'A1');
% Assigns a 1.5 canopy diameter to height ratio 
tile_v=vlm(tile19s15e06,1.5,2);
vlm_ex=export_utm(tile_v,tile19s15e06);
col_header={'ID','UTME','UTMN','HT','PRED','AREA','EQDIAM','MAJAX','MINAX','MAXHT','MINHT','MEANHT'};
xlswrite('F:\SRER\STEMS\cd1p5_19s15e06.xlsx',vlm_ex,1,'A2');
xlswrite('F:\SRER\STEMS\cd1p5_19s15e06.xlsx',col_header,1,'A1');

Allometric Models

McClaran et al. (2013) reported allometric models for mesquite that include biomass and foliar leaf area (Table 2):

Table 3 reported the structural measure to biomass models as:

Because the LiDAR does not measure basal diameter we must estimate biomass from other canopy metrics, like height, canopy area, or canopy volume (McClaran et al. 2013 used a Cylinder).

Recently, Biederman et al. (in prep) collected information about canopy volume characteristics and basal diameters for several transects located around the Santa Rita Experimental Range (SRER)

Biederman et al. report an allometric scaling exponent α = 0.6 for their height regression, while McClaran et al. (2014) reported scaling of height with basal diameter (α = 0.52)

Notes

Figure: The variation in size between diameter measured at or below root crown near ground level and the equivalent diameter (the sum of all basal areas for each minor stem converted to diameter). The dashed black line is a 1:1 reference point. The solid line is a least square regression fit to an α equal to 1.

Figure: The canopy scaling of individual trees' canopy height. Data are from the SRER collected by Biederman and Naito. The dashed black line is a 1:1 reference point. The solid line is a least square regression fit to an α equal to 1.

Joel has already collected:

1) The belt transects were 60 m long radii from the tower in 8 directions and represent about 9% of the area of a circle with the same radius.

Based on both Joel's and Adam's measurements, the canopy diameter (CD) versus max tree height (HT) of individual mesquites is approximately: CD=HT*1.41 - for the segmentation I set the parameter to 1.5; the minimum height cut-off is 1 foot.

tile19s15e06=asc_import('E:\PAG2011\CHM\ASC\19S15E06_LDRY11.ASC');
tile_v=vlm(tile19s15e06,1.5,2);
vlm_ex=export_utm(tile_v,tile19s15e06);
col_header={'ID','UTME','UTMN','HT','PRED','AREA','EQDIAM','MAJAX','MINAX','MAXHT','MINHT','MEANHT'};
xlswrite('G:\SRER\STEMS\19s15e06.xlsx',vlm_ex,1,'A2');
xlswrite('G:\SRER\STEMS\19s15e06.xlsx',col_header,1,'A1');

Figure: Canopy height model in black to white color ramp. Naito field measured stems are yellow and VLM isolation stems are orange.

Next I generated voronoi polygons in QGIS using the r.voronoi module. The voronoi polygon was the first step in segmenting the individual point clouds using FUSION PolyClipData.

Figure: Canopy height model in black to white color ramp. Naito field measured stems are red, VLM isolation are green, and voronoi polygons are visible. Tree heights are given in units of meters.

Created a FUSION Batch script to segment the original LAS data into polygon segments. The PolyClipData tool can only take in ~32k polygons at a time, so I clipped the extent of stems for analysis to the area around where Adam sampled. 

PolyClipData /multifile /shape:1,* D:\mesquite_allometry\voronoi.shp D:\mesquite_allometry\LAS\stems.las D:\mesquite_allometry\LAS\19S15E06_LDRY11.las

PolyClip was able to segment out the 7165 stems in the local area, but it took quite a long time (96 minutes) to do a partial tile.  

After running PolyClip I ran the ClipData function to further isolate individual trees from within the voronoi footprint. This extra step was done to ensure that (1) trees which share canopies are split by the voronoi polygon, (2) footprints that are larger than the expected canopy area are further reduced, and (3) to normalize the elevation of the points into units of height. The ClipData function was run individually for each tree after I created a spreadsheet in Excel and copy pasted the files into a text editor (TextPad).

ClipData /shape:1 /dtm:D:\mesquite_allometry\19S15E06_LDRY11.dtm /height  D:\mesquite_allometry\LAS\stems_1455.las D:\mesquite_allometry\LAS_clipped_data\tree_1455.las 1029635.002 298975.0019 1029656.998 298996.9981

Estimating the volume of a parabolic ellipsoid cone.

The filled volume space of each mesquite includes its total canopy area, which can be simulated as a half parabolic ellipsoid. However, the angle of the branches that reach up from the ground level create an empty space beneath each mesquite (estimated angle of 30-45 degrees). This results in a leafy volume space that is only a part of the total ellipsoid, while they underlying volume is a cone.

%Volume of a 1/2 ellipsoid
V=((4/3)*pi*x*y*z1)/2
 
%Volume of a cone
V=1/3*pi*x*y*z2
 

Figure: Transverse view of a point cloud extraction from the voronoi polygon for an individual mesquite, ID9980.

Estimating the convex hull volume of the mesquite based on it's elliptical canopy diameter, height, and base height to live canopy.

The LiDAR measures the canopy height, minor and major axes, as well as a cloud metric of the overall canopy dimension.

CloudMetrics /above:2 /new /id /minht:1 D:\mesquite_allometry\LAS_clipped_data\*.las D:\mesquite_allometry\cloud_metrics_full.csv

From the FUSION manual:

CloudMetrics computes the following statistics using elevation and intensity values for each LIDAR sample:

• Total number of returns
• Count of returns by return number (support for up to 9 discrete returns)
• Minimum 
• Maximum 
• Mean 
• Median (output as 50th percentile) 
• Mode 
• Standard deviation 
• Variance 
• Coefficient of variation 
• Interquartile distance 
• Skewness 
• Kurtosis 
• AAD (Average Absolute Deviation) 
• MADMedian (Median of the absolute deviations from the overall median) 
• MADMode (Median of the absolute deviations from the overall mode) 
• L-moments (L1, L2, L3, L4) 
• L-moment skewness 
• L-moment kurtosis 
• Percentile values (1st, 5th, 10th , 20th, 25th, 30th, 40th, 50th, 60th, 70th, 75th, 80th, 90th, 95th, 99th percentiles) 
• Canopy relief ratio ((mean - min) / (max – min)) 
• Generalized means for the 2nd and 3rd power (Elev quadratic mean and Elev cubic mean)

In addition to the above metrics, CloudMetrics also computes various ratios of returns above a heightbreak when the /above:# switch is used:

• Percentage of first returns above a specified height (canopy cover estimate) 
• Percentage of first returns above the mean height/elevation 
• Percentage of first returns above the mode height/elevation 
• Percentage of all returns above a specified height 
• Percentage of all returns above the mean height/elevation 
• Percentage of all returns above the mode height/elevation 
• Number of returns above a specified height / total first returns * 100 
• Number of returns above the mean height / total first returns * 100 
• Number of returns above the mode height / total first returns * 100

In addition to the ratios above, the point counts used to compute these ratios are also included in the output.