Regression-based mapping of forest aboveground biomass

Authors: Akpona Okujeni, Sam Cooper, Patrick Hostert, Clemens Jaenicke, Benjamin Jakimow, Andreas Rabe, Fabian Thiel & Sebastian van der Linden

Date: 03/07/2020

Introduction

1. Background

hyperEDU logo

This tutorial is part of the HYPERedu online learning platform, an education initiative within the EnMAP mission hosted on EO College. HYPERedu provides annotated slide collections and hands-on tutorials using the open-source EnMAP-Box software, targeting basic principles, methods as well as applications of imaging spectroscopy.

Annotated slide collections for the tutorial Regression-based mapping of forest aboveground biomass and a software description unit for the EnMAP-Box are provided here:

2. Content

Forest aboveground biomass (AGB) is a measure of the living and dead plant material in a given area. As such, it is often used for forest management, assessing fire potential, and is an important metric used in modelling carbon and nutrient cycles. AGB can be directly measured at a plot level by harvesting and weighing vegetation, but this is both an expensive and highly invasive process. Through the use of statistical modelling and remotely sensed imagery, AGB can be mapped across broad, spatially continuous areas using only a small number of directly measured biomass plots. This tutorial focuses on regression-based modeling of forest biomass using the EnMAP-Box. A hyperspectral image mosaic from the EnMAP sensor (here simulated from AVIRIS imagery) and a corresponding vector dataset containing aboveground biomass estimates are used for this tutorial. The aim is to provide an introduction into the functionality of the EnMAP-Box, as well as hands-on training for implementing regression-based mapping.

3. Requirements

This tutorial requires at least version 3.5 of the EnMAP-Box 3. There might be some minor changes for higher versions (e.g., changed menu labels, added parameter options, etc.).

4. Further reading

We recommend [1] and [2] for a comprehensive overview of imaging spectroscopy of terrestrial ecosystems, and [3] for an overview of remote sensing of forest aboveground biomass.

[1]Foerster, S., Guanter, L., Lopez, T., Moreno, J., Rast, M., Schaepman, M.E. (2019) Exploring the Earth System with Imaging Spectroscopy. Springer International Publishing
[2]Thenkabail, P. S., & Lyon, J. G. (2016). Hyperspectral remote sensing of vegetation. CRC press.
[3]Lu, D., Chen, Q., Wang, G., Liu, L., Li, G., & Moran, E. (2016). A survey of remote sensing-based aboveground biomass estimation methods in forest ecosystems. International Journal of Digital Earth, 9(1), 63-105.

5. Data

You can download the data for this exercise here: https://box.hu-berlin.de/f/997b6737226e4e7bbcef/?dl=1

The tutorial dataset contains a hyperspectral image mosaic in Sonoma County, California, USA, as well as a shapefile containing point based biomass estimates sampled from an existing LiDAR derived biomass map [4].

Data type Filename Description
Raster enmap_sonoma.bsq Simulated spaceborne hyperspectral data from the EnMAP sensor with a spatial resolution of 30m, 195 bands, and 1000x200 pixels (ENVI Standard Band Sequential bsq)
Raster NLCD_sonoma.bsq National Land Cover Database 30m classification for the study region (ENVI Standard Band Sequential bsq)
Vector biomass_sonoma.shp 3000 biomass reference points sampled from an existing LiDAR derived biomass map [4] (ESRI Shapefile bsq)
[4](1, 2) Dubayah, R.O., A. Swatantran, W. Huang, L. Duncanson, H. Tang, K. Johnson, J.O. Dunne, and G.C. Hurtt. 2017. CMS: LiDAR-derived Biomass, Canopy Height and Cover, Sonoma County, California, 2013. ORNL DAAC, Oak Ridge, Tennessee, USA. https://doi.org/10.3334/ORNLDAAC/1523

The tutorial dataset is a subset extracted from the “2013 Simulated EnMAP Mosaics for the San Francisco Bay Area, USA” dataset [5]. Please cite the dataset as follows:

[5]Cooper, Sam; Okujeni, Akpona; Jänicke, Clemens; Segl, Karl; van der Linden, Sebastian; Hostert, Patrick (2020): 2013 Simulated EnMAP Mosaics for the San Francisco Bay Area, USA. GFZ Data Services. https://doi.org/10.5880/enmap.2020.002

Exercise A: Remote sensing of terrestrial ecosystems with the EnMAP-Box

Description

This exercise introduces basic functionalities of the EnMAP-Box for this tutorial. You will get to know the graphical user interface and will learn how to load data, visualize raster and vector data, and use the basic navigation tools. Additionally, you will learn to work with multiple map views and how to visualize image spectra using Spectral Library Windows.

Duration: 45 min

1. Start the EnMAP-Box

  • Start QGIS and click the enmapbox icon in the toolbar to open the EnMAP-Box. The GUI of the EnMAP-Box consists of a Menu and a Toolbar, panels for Data Sources and Data Views, and the QGIS Processing Toolbox including the EnMAP-Box algorithms.
../../../_images/Slide1_BoxScreenCap.PNG

2. Load data

  • To load new datasets into the EnMAP-Box, click the mActionDataSourceManager icon and navigate to the file directory containing your data. Select biomass_sonoma.shp from the Open data source dialogue and select Open.

  • Alternatively, the EnMAP-Box offers simple drag & drop capabilities to load data from an external file manager (e.g. Windows File Explorer). Open enmap_sonoma.bsq by dragging and dropping the file from your file manager into the Data Sources panel.

  • All data currently open in the EnMAP-Box will appear in the Data Sources panel.

    ../../../_images/Slide2_DataLoaded.PNG

3. Visualize raster data

  • The EnMAP-Box offers Map Views (Map #) for visualizing raster and vector data. Click the viewlist_mapdock icon to open a new Map View and drag enmap_sonoma.bsq from the Data Sources panel into Map #1.

  • In addition to a new Map View opening, a corresponding Data View entry is created in the Data Views panel which shows all data currently loaded in a given Map View.

  • By default, the first three bands are assigned to the RGB channels when displaying a new raster dataset. To assign a custom RGB combination to a raster image, right click on the dataset in the Data Views panel, select Layer Properties and navigate to Symbology. Set Render type to Multiband color and select bands to display in the red, green and blue color channels. Common combinations are listed below.

    Combination Red Green Blue
    TrueColor 658 nm 569 nm 479 nm
    nIR 847 nm 658 nm 569 nm
    swIR 847 nm 1645 nm 658 nm
  • Display enmap_sonoma.bsq as true color composite. Under Min/Max Value Settings, select the radio button for Cumulative count cut and set the stretch to 2-98%. Select OK.

    ../../../_images/Slide3_RasterSymbology.PNG

4. Basic navigation tools

  • The Toolbar offers common navigation tools for exploring visualized datasets. Make yourself familiar with the following navigation tools: navtools Note that the mouse wheel can be used alternatively for zooming (roll mouse wheel forward/backward) and panning (press and hold mouse wheel).

5. Multiple map views

  • The EnMAP-Box enables users to work with multiple Map Views, which can be flexibly organized and geospatially linked. Open a new Map View by clicking the viewlist_mapdock icon. Note a Data View entry appears corresponding to the new Map View.
  • Display enmap_sonoma.bsq as an RGB composite of your choice in Map #2.

Tip

When loading a raster image to a map view, you may also right click the filename in the Data Sources panel and select either Open in existing map or Open in new map. If the raster image has wavelength information associated with it, you may also select a predefined composite from the context menu.

  • For geospatial linking, click on View in the Menu and select Set Map Linking. In the Map Linking window, select the link_mapscale_center Link Map Scale and Center option and close the dialog. You may also right click a map window you wish to link and select Link with other maps.
  • Display enmap_sonoma.bsq as a true color composite Map #1 and as an RGB composite of your choice in Map #2. Move the map views to best fit the orientation of the data.
../../../_images/Slide5_LinkingMultipleViews.PNG

Tip

Map Windows can be re-arranged by clicking on the blue Map title bar and dragging it to the desired position. A transparent blue rectangle will appear indicating the docking position once you release the mouse button. You may also undock map views from the EnMAP-Box window by selecting float_window from the blue Map title bar. To re-dock a Map View, click and drag the blue Map title bar to an open Map View already docked in the EnMAP-Box window.

6. Visualize vector data

  • Close Map #2 from the previous step.
  • Load biomass_sonoma.shp to Map #1.
  • To change the order of stacked layers, go to the Data Views panel and drag one layer on top or below another one. Arrange the layer stack so that biomass_sonoma.shp is displayed on top of enmap_sonoma.bsq.
  • By default, vector files are displayed with a single uniform symbol. To change this symbology, right click on biomass_sonoma.shp in the Data Views panel, select Layer Properties and navigate to Symbology in the LayerProperties window. You can now change the symbology in accordance to the QGIS functionality. Select Graduated from the dropdown menu, and select biomass in Column and Color in Method. Set the Color ramp to run from white to green.
  • Press Classify and then OK to display the relative biomass values associated with each point. Explore the different ways you can display this information using the QGIS symbology functionality.
../../../_images/Slide6_VectorSymbology.PNG
  • Use the metadata tool on the toolbar to view displayed raster and vector data. When activated, a new Cursor Location Values window will open displaying data from the selected pixel or feature. Note: select_location Identify Cursor Info must be activated to access this tool.

7. Extract & visualize image spectra

  • The EnMAP-Box offers Spectral Library Windows (SpectralLibrary #) for visualizing spectra and handling their metadata. A detailed introduction to the Spectral Library Window can be found in Exercises B and C of the Regression-based unmixing tutorial.
  • This tool may also be used to extract and visualize spectra which are spatially associated with vector data open in the EnMAP-Box, i.e., the biomass reference points. To do this, open a new Spectral Library window by selecting the viewlist_spectrumdock icon on the toolbar.
  • Next, select Import profiles from raster + vector sources from the dropdown menu by the plus_green icon in SpectralLibrary #1 and select the appropriate raster and vector sources. Activate the option cb1 Copy Attributes. A spectral library is automatically built based on the geographic location of each point in the vector file. The associated attribute information is displayed in the table on the right.
  • Change the spectral profile colors to reflect the biomass values associated with them. Do this by selecting system in lower right corner of the Spectral Library Viewer. Then use the QGIS symbology functionality to change the color scheme of the spectral profiles to reflect the associated biomass values in the attribute table (see Exercise A6 if needed).
  • In the Exercise B, you will learn how to create and apply regression models based on this information to predict biomass across the whole image.
../../../_images/Slide7_SpecLibColored.PNG

Learning Activities

  • A1: What land cover types are present in the imagery? How are the biomass training plots distributed throughout the scene?
  • A2: What different information can you see when switching from a true color composite to a NIR false color composite?
  • A3: Compare spectra from high biomass plots and low biomass plots. What differences can you see?

Exercise B: Regression based mapping of aboveground forest biomass

Description

One of the strengths of remote sensing comes from its ability to take high-quality point measurements of a variable of interest and building statistical models with which wall to wall maps of this variable can be created. One of the most common ways of doing this is to create regression models based on the optical properties of the training data and applying it to large scale imagery. This exercise…

  • Introduces a regression-based mapping approach for taking point measurements of biomass and generating spatial biomass estimates using an input raster of hyperspectral imagery.
  • Demonstrates the Regression-based mapping application of the EnMAP-Box.
  • Conduct an accuracy assessment of our biomass estimates using the EnMAP-Box algorithms.

Duration: 20 min

1. Start the Application

  • Close all opened Map and Spectral Library Windows. For this exercise you must have enmap_sonoma.bsq and biomass_sonoma.shp open in the Data Sources panel.
  • Click on Applications in the Menu and select Regression Workflow. The graphical widget of the Regression Workflow consists of sections for specifying Inputs, for setting Sampling schemes, for selecting the regression algorithm used for model Training, and for specifying the Mapping and Cross-validation parameters.
../../../_images/Slide8_RegressionWorkflow.PNG

2. Inputs

  • The first step in the Regression Workflow is defining the inputs. This includes a Raster dataset as well as a Reference vector file with attributes containing a variable of interest to map, in our case, biomass.
  • Select the following inputs:
    • Raster: enmap_sonoma.bsq
    • Reference: biomass_sonoma.shp
    • Attribute: biomass

3. Stratified Sampling

  • In the case of uneven distribution of training data, you may choose to subset your training data by stratifying the variable of interest and sampling from within each stratum. By default, the Number of Strata is set to one and the Sample Size is set to 100%, meaning that all training data is used.
  • As our training data is not evenly distributed across the range of observed biomass, we will implement an equalized sampling scheme to ensure an appropriate model fit.
../../../_images/8-distribution.png
  • Change the Number of Strata to 5 and click Apply. You will see five strata appear below, showing the minimum and maximum biomass values, the number of samples which will be drawn, and the total number of samples in each strata in parentheses.
  • Change the Sample Size to 20% and click Apply. You will now see the number of samples drawn from each strata automatically update to include 20% of the total size of each strata. To set an equalized sampling scheme, select Pixel from the dropdown menu and sample 20 pixels per strata. You can also manually define the sample size from each bin if desired. For now, sample 20 pixels for each of 5 strata.
  • Select the option to cb1 Save Sample and define an output file name and location (e.g. biomassSample.bsq). This saves a raster containing the biomass samples used to train the model, as well as a complementary raster of the samples left out of the training. We can later use these complementary samples for validation of the model.
../../../_images/9-sampling.png

4. Regression Algorithm

  • Next, we must define a regression method. The EnMAP-Box makes use of the scikit-learn library (see https://scikit-learn.org/stable/index.html) to implement several state-of-the-art algorithms offered in the Regressor drop menu. Note that the different algorithms lead to varying accuracies and processing times. Advanced Model Parameters may also be set here. Refer to the scikit-learn documentation for more information.
  • Select RandomForestRegressor (default, due to the low processing time), and use the default model parameters.

5. Mapping

  • The Input Raster is by default the same as the raster used to generate training spectra. However, if you wish to apply the model to another image you may specify this here.
  • Select Output Regression, and in the adjacent box specify a file location and name to which you will save the biomass estimation.

6. Cross-validation Accuracy Assessment

  • If you lack independent validation data, you may select to run cross-validation of the dataset with a desired number of folds. Leave this unchecked.

Attention

Note that the cross-validation is conducted only on the training sample defined in the sampling panel. Future versions will also allow users to validate models based on the withheld samples.

7. Run the application

  • Click on the action button to run the application. The outputs appear in the Data Sources panel.
usr_section/application_tutorials/biomass_regression/img/workflow_newFig.png

8. Visualize biomass results

  • The outputs from the Regression Workflow will appear in the Data Sources panel:
    • biomass_estimation.bsq: spatially continuous biomass estimation based on the spectral information contained within each EnMAP pixel.
    • biomassSample.bsq: biomass information used for training the regression model, rasterized to the EnMAP grid and spatially aligning with pixels from which training spectra were sampled.
    • biomassSample_compliment.bsq: rasterized biomass values of withheld samples.
  • Open enmap_sonoma.bsq as an RGB composite of your choice (refer to Exercise A3 if needed)
  • Open the biomass_estimation.bsq in a new Map View and link to the Map #1 (refer to Exercise A5 if needed). Use the Layer Properties to change the color ramp to white-green (Singleband pseudocolor).
../../../_images/biomass_result.png

9. Validation of biomass maps

  • When training the biomass regression model, we withheld a number of samples, biomassSample_compliment.bsq, which we will now use to validate the biomass predictions. Open and link these withheld samples in a new Map View. Compare the biomass values in the withheld samples to the model predicted biomass estimates. We will use the reference values in the withheld samples to statistically evaluate our biomass predictions.
  • In the Processing Toolbox, go to EnMAP-Box ‣ Accuracy Assessment ‣ Regression Performance. Run the Regression Performance algorithm with the following inputs:
    • Prediction: biomass_estimation.bsq
    • Reference: biomassSample_compliment.bsq
../../../_images/Slide12_RegressionPerformance.PNG
  • After selecting Run, an HTML report with scatterplots and statistical measures will open in your default browser. Make yourself familiar with the HTML report.
../../../_images/13-performance.png

Learning Activities

Learning Activities

  • B1: What general trends do you see in the biomass estimations? How do they compare to landscape features seen in the EnMAP imagery?
  • B2: How do the biomass estimates compare to the withheld samples? How do they compare to the training samples?
  • B3: Discuss the accuracy results, both in terms of the statistical measures, as well as the form of the scatterplot and histograms.

Exercise C: Introduction to ImageMath

Description

In this exercise, you will learn how to use the ImageMath tool to calculate NDVI and generate a tree mask based on NDVI thresholding. You will then assess the biomass prediction from Exercise B using the new tree mask. Duration: 30 min

1. ImageMath introduction

  • The ImageMath tool in the EnMAP-Box allows users to apply a mathematical operation, python function or user defined function to an image.
  • For this exercise, you will need biomass_estimation.bsq, NLCD_sonoma.bsq and enmap_sonoma.bsq from the previous exercises open in the Data Sources panel.
  • Open the ImageMath application by going to Applications then selecting numpy ImageMath
  • The ImageMath Calculator consists of several panels:
    • Inputs: defines input variables and variable names
    • Outputs: defines output variable names and locations to be saved to.
    • Code editor: Text editor in which programmatic manipulation of the input datasets can be defined using Python scripting syntax.
    • Output Grid: Allows users to manually set output grid following calculations done in the editor.
    • Processing: Allows users to select block sizes for processing large datasets with limited memory
    • Log Window: Displays the status (and error messages) of executed code
    • Additionally, a tab for Routines allows users to select a number of common python-based tools for manipulating spatial datasets with linked documentation.
../../../_images/Slide14_ImageMathEmpty.PNG

Attention

Input and output variable names in the Editor must exactly match corresponding names defined in the Inputs and Outputs panels.

  • The ImageMath tool allows for quick implementation of python-like code, treating input raster datasets as numpy n-dimensional arrays.
  • In the following sections, we will utilize standard numpy array processing protocols to analyse our raster image to
    1. calculate NDVI from two bands of our EnMAP imagery
    2. apply a forest mask to both the NDVI and biomass images

2. Calculate NDVI

  • The Normalized Difference Vegetation Index (NDVI) is a commonly used vegetation index that is correlated with both vegetation cover and biomass. The formula for NDVI is:

    \[NDVI = \frac{NIR-Red}{NIR+Red}\]

    where NIR is the near-infrared band reflectance (~850nm) and Red is the red band reflectance (~660nm). We will now calculate NDVI from the EnMAP imagery using the ImageMath tool.

  • In the Inputs panel, select enmap_sonoma.bsq from the dropdown menu. The variable name is automatically taken from the filename, but may be changed if desired. Note: if you wish to process multiple rasters with different grids, you can also define a resampling method from the dropdown menu and the grid to be sampled to in the Output Grid panel.

  • In the Editor panel, define the RED and NIR bands in our imagery. These correspond to bands 42 and 73 in our imagery, respectively, and we can define them using python indexing syntax (i.e. 0 indexed array slicing):

    RED = enmap_sonoma[41]
    NIR = enmap_sonoma[72]
    

    Next, we define the formula we wish to run:

    NDVI = (NIR - RED)/(NIR + RED)
    

    In the Outputs panel, define the output variable name as NDVI, and select an output file path and file name (e.g. C:\Users\USERNAME\Desktop\NDVI.bsq). Note, if you leave the file name black, the output variable will be saved to memory.

  • Finally, click on the action button to run the script.

Tip

For spectral images, metadata such as projection information may be missing. If this is the case, such information may be added to the output raster using the setMetaData command. See the imageMath manual for more information.

../../../_images/Slide15_ImageMathNDVI.PNG
  • A new raster dataset NDVI.bsq will appear in the Data Sources panel. Open this in a new Map Viewer and link to the biomass estimates (see Exercise A5).
../../../_images/ndvi_result.png

3. Create a forest mask

  • Open NLCD_sonoma.bsq in Map #1.
  • As the biomass map was only trained using forested biomass plots, only limited inference can be made of the non-forest biomass estimates. We will therefore apply a forest mask to our biomass map.
  • The forest mask will ignore any pixels that are Deciduous (41), Evergreen (42), or Mixed (43) forest according to the NLCD classification.
  • Below are the NLCD classes and color legend represented in the raster data. We will consider any pixel to be forest which is labelled as Deciduous (41), Evergreen (42), or Mixed (43) forest according to the NLCD classification.
../../../_images/17-NLCD.png
  • Open the ImageMath tool and set NLCD_sonoma.bsq as the input file.

  • Enter the following code into the code editor:

    ForestMask_sonoma = NLCD_sonoma
    forest_classes = [42, 43, 44]
    
    for x in range(ForestMask_sonoma.shape[1]):
        for y in range(ForestMask_sonoma.shape[2]):
            if ForestMask_sonoma[0, x, y] in forest_classes:
                ForestMask_sonoma[0, x, y] = 0
            else:
                ForestMask_sonoma[0, x, y] = 1
    
  • Line by line, this

    1. Copies the NLCD information to a new object we will manipulate to create the mask
    2. Creates a list of classes which we consider forest
    3. Loops through the x dimension of the raster. For each loop, x will be an integer representing the current location in the x dimension.
    4. Loops through the y dimension of the raster. For each loop, y will be an integer representing the current location in the y dimension. These two loops allow us to look at each element in the array individually. While numpy offers more efficient ways to analyse arrays (See section C4), this is one basic approach.
    5. Check if the element at the current x and y position is in the forest_classes list
    6. If it is, set that value to 0
    7. If it is not
    8. Set that value to 1
  • Set ForestMask_sonoma as the output and define the path to your working directory.

  • Run the script by clicking action. The resulting mask now has a value of 0 for forested pixels, and 1 for non-forested pixels.

../../../_images/18-Masking_imgmath.png

4. Apply a mask

  • Open the ImageMath tool and set NDVI.bsq, biomass_estimation.bsq, and ForestMask_sonoma.bsq as the input files.

  • Enter the following code into the Console to apply the forest mask to the NDVI and biomass images.

    ForestMask_sonoma = ForestMask_sonoma.astype(bool)
    
    biomassMasked = biomass_estimation
    biomassMasked[ForestMask_sonoma] = -99
    setNoDataValue(biomassMasked, -99)
    
    NDVI_Masked = NDVI
    NDVI_Masked[ForestMask_sonoma] = -99
    setNoDataValue(NDVI_Masked, -99)
    
  • Line by line, this script:

    1. First sets the mask to a Boolean data type (i.e. True/False). The mask file contains binary values where 0 indicates forest (i.e. non-masked pixels) and 1 indicates non-forest (i.e. pixels to be ignored). In Python, 1 also represents True while 0 represents False, and by setting the datatype to bool, we explicitly tell Python to treat these values in this manner.
    2. Copies the biomass values to a new array.
    3. Steps through each value in the new array and sets the value to -99 if the mask value is True. In numpy array speak, this line can therefore read: “For each value in biomassMasked, if the corresponding value in ForestMask_sonoma is True (i.e. non-forest), then set that value to -99”. If mask value is False (i.e. forested), nothing will happen, and the biomass value will remain in the array.
    4. Sets the no data value for the masked array to -99. This helps the EnMAP-Box to automatically display the data correctly, and since it is not a realistic value for both biomass and NDVI, we can safely ignore it.
    5. Steps 2-4 are then repeated for NDVI.
  • Set biomassMasked and NDVI_Masked as the outputs and define the path to your working directory. Run the script by clicking action.

5. Visualize the masked raster

  • Open an RGB composite of enmap_sonoma.bsq in Map #1 and open and link the masked biomass image in a new Map window. Refer to Exercise A5 if needed.
  • Open NDVI.bsq in Map #1. Compare patterns of NDVI and estimated AGB.
../../../_images/masked_biomass.png

6. Visualize NDVI vs Biomass with the Scatterplot tool

  • To investigate the relationship NDVI has with forest AGB, we will make use of the EnMAP-box’s Scatterplot tool. This is one of a number of tools integrated into the EnMAP-Box to help aid with data visualization and assessment.

  • Open the Scatterplot tool by going to Tools then selecting Scatterplot.

    • Select biomass_Masked.bsq for Band X and NDVI_Masked.bsq for Band Y from the dropdown menus.

      • If a selected raster has multiple bands, you would specify the desired band from the dropdown Band menu.
      • You may also specify the Min and Max values to be displayed for each band, but if left blank these will be calculated automatically.
    • If you wish to apply another mask to both images, you may specify this with the Mask option. As we have already masked both images, leave this blank.

    • Under Accuracy you may choose to display Estimated or Actual. Actual will display all available data, while Estimated will only display a random subset. For large raster extents, Estimated is much faster, and for that reason is the default. Leave Accuracy as Estimated.

    • Next, you may choose how to Plot the data: either as binned data or plotting all the data points individually. Leave the default selection as binned data with 100 bins.

    • Optionally, you may include the ‘Min-max line’, which represents the linear 1:1 relationship between the two variables if they were perfectly correlated, and a ‘Fitted line’, which represents the linear regression line fitted between the actual data from the two variables. Activate the ‘Min-max line’ by checking the box to its left.

  • Run the Scatter Plot tool by clicking action in the lower right of the window. You may adjust the color scale by right clicking on the color bar to the right of the plot, and you can change the stretch by adjusting the size and position of the blue box next to it.

../../../_images/20-scatter.png

Learning Activities

Learning Activities

  • C1: Why was it necessary to mask the biomass results?
  • C2: What relationships can you see between NDVI and AGB? Do these relationships hold true if you look at the un-masked AGB and NDVI maps?
  • C3: Given the relationships between NDVI and AGB, do you think NDVI could be used to map AGB? What limitations would you expect from such a model?

Additional Exercises

Learning Activities

  • AE1: Use the ImageStatistics tool in the Tools menu to look at the band statistics for the biomass predictions both with and without the tree mask applied.
  • AE2: Because we randomly subsetted the training data prior to model training, the performance of the model has an element of uncertainty to it. To better understand this, rerun the regression workflow 3-5 times. Then use the ImageMath tool to calculate the average estimate and variance. How does running the regression in such an ensemble approach affect the results? What is the spatial pattern of variation in estimates?
  • AE3: Rerun regression (Exercise B) using NDVI as the input rather than the hyperspectral imagery.