Explore dissolved oxygen in 3D

Explore dissolved oxygen in 3D
Deoxygenation of the oceans is one of the most important issues in oceanography today. Oxygen
levels are an important component of ocean ecology, and recent research has established that
global oxygen levels in the ocean have been declining for decades and will continue to decline as
climate change intensifies in the future. To tackle these difficult problems, you must be able to
make accurate three-dimensional models of dissolved oxygen levels in the oceans.
In this lesson, you'll use dissolved oxygen measurements taken at various depths in Monterey Bay,
California, and perform 3D geostatistical interpolation to predict the oxygen levels throughout the
entire bay. You'll learn how to explore 3D data, configure the parameters of Empirical Bayesian
Kriging 3D (EBK3D), and export the results into convenient GIS formats and video animations.
Explora el oxígeno disuelto en 3D
La desoxigenación de los océanos es uno de los problemas más importantes en la oceanografía en
la actualidad. Los niveles de oxígeno son un componente importante de la ecología oceánica, y
una investigación reciente ha establecido que los niveles globales de oxígeno en el océano han
disminuido durante décadas y continuarán disminuyendo a medida que el cambio climático se
intensifique en el futuro.
Para abordar estos problemas difíciles, debe ser capaz de hacer modelos tridimensionales precisos
de los niveles de oxígeno disuelto en los océanos.
En esta lección, utilizará las mediciones de oxígeno disuelto tomadas a diversas profundidades en
la Bahía de Monterey, California, y realizará una interpolación geoestadística 3D para predecir los
niveles de oxígeno en toda la bahía.
Aprenderá a explorar datos en 3D, configurar los parámetros de Empirical Bayesian Kriging 3D
(EBK3D) y exportar los resultados a formatos GIS y animaciones de video convenientes.
You'll start by downloading the project containing the dissolved oxygen
measurements and opening it in ArcGIS Pro.
1. Download the Interpolate3D.zip file.
2. Locate the downloaded file on your computer.
3. Right-click the Interpolate3D.zip file and extract the contents to a convenient location on
your computer.
4. Open the unzipped folder to view the contents.
The folder contains an ArcGIS Pro project package.
5. If you have ArcGIS Pro 2.3 installed on your computer, double-click
Interpolate_3D_Dissolved_Oxygen_Measurements_in_Monterey_Bay.ppkx to open the
project.
Note:
If you don't have ArcGIS Pro 2.3 or an ArcGIS Online account, you can sign up for an
ArcGIS free trial.
6. Sign in using your ArcGIS Online account.
The project opens to display a map and a local scene.
7. If necessary, open the Monterey Bay map and review the layers in the Contents pane.
La capa OxygenPoints es una pequeña muestra de los datos proporcionados por la Base de Datos
del Océano Mundial (WOD) de los Centros Nacionales de Información Ambiental de NOAA. Estos
puntos representan ubicaciones en la Bahía de Monterey donde se observaron y registraron los
niveles de oxígeno disuelto, medidos en micromoles por litro, para varias profundidades.
The OxygenPoints layer is a small sample of the data provided by the NOAA National Centers for
Environmental Information’s World Ocean Database (WOD). These points represent locations in
Monterey Bay where dissolved oxygen levels, measured in micromoles per liter, were observed and
recorded for various depths.
8. In the Contents pane, right-click the OxygenPoints layer and choose Attribute Table.
9. On the Map tab, in the Selection group, click the Select tool.
10. On the map, select any OxygenPoints feature by dragging a box around it.
11. In the OxygenPoints table, click Show selected records to display the record associated with
your selected sample point.
Notice that you have selected multiple sample points that have the same x- and y-coordinate
but different z-values. These represent observed oxygen levels at different depths (z) below
the surface. Your number of selected coincident records may differ as each sample location
may not have the same number of samples at various depths.
Note:
If you were to interpolate a continuous surface of oxygen levels at this time, your
interpolation could only be generated for one depth (z-value) at a time, and you would need
to create multiple interpolated surfaces for the different depths. This would make it difficult
to interpret and understand how oxygen levels differ as depth increases.
Next, you'll explore the OxygenPoints data in a 3D scene.
Observe que ha seleccionado varios puntos de muestra que tienen las mismas coordenadas x e
y pero valores z diferentes. Estos representan los niveles de oxígeno observados a diferentes
profundidades (z) debajo de la superficie. Su número de registros coincidentes seleccionados
puede diferir, ya que cada ubicación de muestra puede no tener el mismo número de muestras
a varias profundidades.
Nota:
Si tuviera que interpolar una superficie continua de niveles de oxígeno en este momento, su
interpolación solo se podría generar para una profundidad (valor z) a la vez, y tendría que
crear múltiples superficies interpoladas para las diferentes profundidades. Esto dificultaría la
interpretación y la comprensión de cómo difieren los niveles de oxígeno a medida que aumenta
la profundidad.
A continuación, explorará los datos de OxygenPoints en una escena 3D.
12. On the ribbon, on the Map tab, in the Selection group, click the Clear button to
unselect OxygenPoints features. Close the table.
13. Open the Monterey Bay 3D scene.
The 3D scene shows Monterey Bay, California, with 10x vertical exaggeration applied.
As a result, the Monterey Canyon appears ten times deeper and steeper than it
actually is. The WorldElevation/TopoBathy layer is used to define the elevation
surface and the World Ocean Base basemap is draped on top of the elevation to
provide a 3D effect. This elevation surface is available in the ArcGIS Living Atlas of the
World.
En la cinta, en la pestaña Mapa, en el grupo Selección, haga clic en el botón Borrar para
deseleccionar las funciones de Puntos de oxígeno. Cierra la mesa.
Abre la escena 3D de la bahía de Monterey.
La escena 3D muestra la Bahía de Monterey, California, con una exageración vertical de
10x aplicada. Como resultado, el Cañón de Monterey aparece diez veces más profundo y
más inclinado de lo que realmente es. La capa WorldElevation / TopoBathy se usa para
definir la superficie de elevación y el mapa base de World Ocean Base se coloca encima
de la elevación para proporcionar un efecto 3D. Esta superficie de elevación está
disponible en el ArcGIS Living Atlas of the World.
1. Note:
This lesson generally refers to the depth of the points in positive numbers, for
example, the point at depth 150 meters. However, the actual z-coordinates of the
feature class are stored as negative numbers and are often referred to as elevation in
the various windows and panes of ArcGIS Pro. Negative elevations indicate that the
point depths are beneath mean sea level.
2. In the Monterey Bay 3D scene in the Contents pane, click and expand the OxygenPoints
layer.
The OxygenPoints points are symbolized by their oxygen level, with the lowest
measurements displayed in blue and the largest measurements displayed in red, and
with green, yellow, and orange in the middle. In addition to the symbology, the points
also have a 10x vertical exaggeration applied to depth to match the exaggeration
applied to the elevation surface.
3. In the Contents pane, collapse and uncheck the OxygenPoints layer.
4. In the Contents pane, check and review the TargetPoints layer.
The TargetPoints layer contains points that are gridded in 3D. They have no
attributes and will serve as target locations in the final lesson.
5. Uncheck the TargetPoints layer and turn on the OxygenPoints layer.
6. On the ribbon, on the Map tab, in the Navigate group, click Explore.
1. Using the Explore tool, rotate, tilt, pan, and zoom around Monterey Canyon and observe the
OxygenPoints points at different locations and depths.
Note:
If you have a mouse with a wheel button, clicking the wheel button allows you to
rotate and tilt in 3D. Click to pan and right-click to zoom. For more information on
using the Explore tool for navigation, see Learn more about navigation in 3D. For
more advanced 3D navigation, you can use the on-screen navigator, which exposes
many camera navigation commands in a single control in the lower left of a scene or
view.
2. To add the onscreen navigator to the scene, on the ribbon, on the View tab, in the Navigation
group, click the Navigator button.
Using the navigator, you can now rotate, move, tilt, pan, and zoom using the control in
the lower left of the map.
Note:
The navigator is useful when well-defined control is needed for camera movements.
The navigator is resizable and provides quick access to controls to tilt and change
direction. Review Use the on-screen navigator to learn more about the camera
navigation commands.
21. In the scene, click any point and review the pop-up.
1. Each point is individually symbolized by its oxygen level value and displays at the
depth it was measured (z-value). As you explore, notice that the highest oxygen
measurements are found near the surface of the ocean, and the lowest measurements
are near the middle of the vertical columns. Also, note how points at the same depth
tend to have roughly the same oxygen level, but that oxygen levels change very
quickly going up and down the vertical columns.
2. Close the pop-up.
3. On the ribbon, on the Map tab, in the Navigate group, click Bookmarks and choose
Monterey Canyon.
Explore the oxygen measurements with
a histogram chart
In this section, you'll use a histogram chart to explore the distribution of the
dissolved oxygen measurements and use transformations to adjust the distribution
to be more suitable for interpolation. The histograms will visually summarize the
distribution of dissolved oxygen measurements by measuring the frequency at
which oxygen measurements occur in the dataset. Interpolation works best when
data is normally distributed; when data is skewed (the distribution is lopsided), you
might want to transform the data to make it normal. Histograms allow you to
explore the effects of logarithmic and square root transformations on the
distribution of your data.
1. In the Contents pane, right-click OxygenPoints, point to Create Chart, and choose
Histogram.
1. The Chart and Chart Properties panes appear. The Chart pane will be empty until
you specify which field you want to investigate.
2. In the Chart Properties pane, on the Data tab, under Variable and Number, choose
Oxygen.
This is the field that stores the dissolved oxygen measurements at each point.
Review the Distribution of Oxygen histogram.
3. The histogram reflects that the distribution is heavily skewed to the left, with many
observations on the lower end of the distribution and few observations at the higher
end.
Note:
The values on the axes of the histogram may be different for you, as the values that
are displayed depend on the size of the pane.
4. In the Chart Properties pane, check the Show Normal distribution box.
The chart updates and you are now able to visually compare the result to a normal
distribution that best fits the histogram.
5. Review the updated Distribution of Oxygen histogram.
While reviewing and comparing the normal distribution curve overlaid on the
histogram, it is clear that the bars of the histogram are not close to the curve. Next,
you’ll use a transformation to try to make the oxygen measurements distribution
closer to a normal distribution.
Note:
Transformations are mathematical operations that are applied to each data
measurement, such as taking the square root or logarithm of each value, and the
distribution of the transformed dataset will be different than the distribution of the
original dataset. Interpolation methods are most effective when the data is close to a
normal (bell-shaped) distribution, and transformations can be used to make a dataset
closer to a normal distribution.
6. In the Chart Properties pane, from the With transformation drop-down menu, choose
Square Root.
The histogram updates to display the distribution with the application of a square
root transformation.
7. Review the transformed Distribution of Oxygen histogram.
8. In the Chart Properties pane, from the With transformation drop-down menu,
choose Logarithmic.
The histogram updates to display the distribution with a logarithmic transformation
applied.
The distribution now appears to be more symmetrical and closer to a bell shape than
in the two previous histograms. You will use the fact that a logarithmic
transformation is effective later when configuring interpolation options and settings.
9. Close the Chart Properties pane and the OxygenPoints – Distribution of Oxygen
table.
Explore the relationship between
oxygen and elevation with a scatterplot
While navigating in 3D, you observed the highest dissolved oxygen levels near the
surface of the bay, and the lowest levels in the middle of the vertical columns. In this
section, you'll use a scatterplot to visualize how the oxygen levels change with
depth.
A scatterplot is used to visualize the relationship between two numeric variables,
where one variable is displayed on the x-axis, and the other variable is displayed on
the y-axis.
1. In the Contents pane, right-click OxygenPoints, click Create Chart, and choose Scatter Plot.
2. In the Chart Properties pane, on the Data tab, for X-axis Number, choose Oxygen.
3. For Y-axis Number, choose z.
The chart name updates to Relationship between Oxygen and z.
4. In the Chart Properties - OxygenPoints pane, under Statistics, uncheck Show linear trend.
5. Review the scatterplot.
The scatterplot shows a clear relationship between oxygen levels and depth. The oxygen
level is highest near the surface and then drops quickly and steadily.
6. The lowest values occur between approximately -600 and -1,000 meters, and at
depths below -1,000 meters, the oxygen levels slowly rise back up.
Note:
Placing depth values on the y-axis is most typical when plotting values measured at
different depths, but in these lessons, you are interested in predicting oxygen levels
based on depth, so it makes more sense to put the depth on the x-axis of the
scatterplot.
7. In the Chart Properties pane, do the following:
1. For X-axis Number, choose z.
2. For Y-axis Number, choose Oxygen.
The scatterplot updates and displays the relationship between depth and oxygen
levels, with depth now represented on the x-axis.
We learned from the histogram earlier that a logarithmic transformation is appropriate, so
it will be helpful to see the scatterplot with the oxygen measurements on a logarithmic
scale.
8. In the Chart Properties pane, click the Axes tab. For the Y-axis properties, under
Scale, check Log axis.
Note:
Using a logarithmic axis is the equivalent of applying a logarithmic transformation to data
on a linear axis. This is similar to what you did to the histogram in the previous section.
The scatterplot updates to show the oxygen values on a logarithmic scale.
9. Review the scatterplot.
With the logarithmic scale applied, you can see the same trend as before, with the
largest values at the surface and smallest values around 800 meters below the
surface.
For this data, only two lines are needed to approximate the scatterplot. In a more
dispersed scatterplot, using more lines would provide an even closer approximation.
This is a very important finding because, as you will learn in the next lesson, local
linear trends can be modeled and removed when performing interpolation.
10. Close the Chart Properties pane and the OxygenPoints – Relationship between
Oxygen and z pane.
Note:
Charts are managed as a property of a layer, so they are not deleted when you close
charting panes. You can view your charts by expanding the OxygenPoints layers
legend in the Contents pane and scrolling to the bottom of the legend. Doubleclicking the charts in the legend will reopen them.
11. If necessary, in the Contents pane, collapse the OxygenPoints layer before continuing.
12. Save the project.
In this lesson, you explored the dissolved oxygen measurement data for Monterey Bay by
navigating a local scene and using a histogram and scatterplot. You saw that the largest oxygen
measurements were near the surface, and the smallest measurements were near the middle of the
vertical columns.
Using the histogram chart, you determined that a logarithmic transformation stabilizes the
distribution of dissolved oxygen measurements. The scatterplot then showed a strong
relationship between oxygen levels and depth, and you determined that oxygen on a logarithmic
scale can be accurately approximated with local linear trends based on depth. In the next lesson,
you'll use these findings to interpolate the oxygen measurements using Empirical Bayesian
Kriging 3D.
Interpolate dissolved oxygen using
Empirical Bayesian Kriging 3D
In the previous lesson, you explored the dissolved oxygen measurements in the map and used
charting to better understand the distribution of the oxygen measurements. You also observed
that oxygen levels vary strongly with depth.
In this lesson, you will use these insights to interpolate the oxygen values into a continuous 3D
model that predicts dissolved oxygen levels throughout Monterey Bay. You'll use the Empirical
Bayesian Kriging 3D (EBK3D) geoprocessing tool perform the interpolation and explore the 3D
model in a scene. You will then use cross validation to evaluate if the model accurately predicts
dissolved oxygen.
Interpolate using the geoprocessing tool
In this section, you'll use the EBK3D geoprocessing tool to interpolate the dissolved oxygen
measurements into a continuous model that predicts dissolved oxygen everywhere between the
measured points.
1. If necessary, open your project.
2. On the ribbon, on the Analysis tab, in the Geoprocessing group, click Tools.
3. The Geoprocessing pane opens.
4. In the Geoprocessing pane, in the search box, type Empirical Bayesian Kriging 3D.
5. In the search results, locate and click Empirical Bayesian Kriging 3D.
Note:
Be sure not to choose Empirical Bayesian Kriging, which performs a 2D
interpolation using the same methodology.
EBK3D is available in the Geostatistical Wizard and as a geoprocessing tool, and the
result of the interpolation is a geostatistical layer that shows a horizontal transect at
a given elevation. The current elevation can be changed with a range slider, and the
layer will update to show the interpolated predictions for the new elevation.
1. In the Empirical Bayesian Kriging 3D geoprocessing tool, do the following:
o
For Input features, specify OxygenPoints.
This specifies the feature layer that you want to interpolate.
o
Verify that Elevation field is set to Shape.Z.
A features z-value may be stored in an attribute field or maintained internally
with the feature geometry. In this case, the z-value is maintained with the
geometry in Shape.Z.
o
For Value field, choose Oxygen.
This specifies that you want to interpolate using the attribute field storing the
oxygen measurements.
o
For Output geostatistical layer, delete any text and type Oxygen Prediction
This is all that is required to run the tool, but recall that in the previous lesson, you learned
that the distribution of dissolved oxygen measurements needs a logarithmic
transformation. In the geoprocessing tool, a log empirical transformation applies a
logarithmic transformation before additionally applying a normal score transformation.
Note:
Normal score transformations are beyond the scope of this lesson, but they are flexible,
nonparametric transformations to the normal distribution based on equating empirical
quantiles to corresponding quantiles of the normal distribution. By applying a logarithm
and using an empirical normal score transformation (Log Empirical), the resulting
distribution after the transformation will be very close to a normal distribution and most
optimally suited for EBK3D.
Esto es todo lo que se requiere para ejecutar la herramienta, pero recuerde que en la lección
anterior, aprendió que la distribución de las mediciones de oxígeno disuelto necesita una
transformación logarítmica. En la herramienta de geoprocesamiento, una transformación
empírica de registro aplica una transformación logarítmica antes de aplicar adicionalmente una
transformación de puntuación normal.
Nota:
Las transformaciones de puntaje normal están más allá del alcance de esta lección, pero son
transformaciones no paramétricas flexibles a la distribución normal basadas en la comparación
de los cuantiles empíricos con los cuantiles correspondientes de la distribución normal. Al aplicar
un logaritmo y utilizar una transformación empírica de puntaje normal (Log Empirical), la
distribución resultante después de la transformación estará muy cerca de una distribución normal
y será la más adecuada para EBK3D.
In the Empirical Bayesian Kriging 3D geoprocessing tool, do the following:

Expand Advanced Model Parameters.

For Transformation type, choose Log empirical.
1. After you change the transformation type, the Semivariogram model type
automatically changes to Exponential. This is because the default semivariogram
model is not applicable with a transformation.
Before continuing, verify the following additional settings in Advanced Model
Parameters:
o
Subset size is set to 100.
o
Local model area overlap factor is set to 1.
o
Number of simulated semivariograms is set to 100.
These three parameters are related to the subsetting and simulations that are the
foundation of all empirical Bayesian kriging methods in ArcGIS.
Note:
Empirical Bayesian kriging starts by splitting the input data into local subsets. The
subset size controls the number of points in each subset, and the overlap factor
controls how much the subsets will overlap each other (each point is allowed to be in
multiple subsets). Local kriging models are then simulated in each of these subsets to
capture local effects that may be missed by global methods. These local models are
then merged together to produce the final prediction model.
Learn more about the subsetting and simulation process in empirical Bayesian
kriging
6. Under Advanced Model Parameters, for Order of trend removal, choose First order.
Note:
Previously, you found in the scatterplot that oxygen levels can be accurately
approximated by two local trend lines based on depth. In EBK3D, choosing to remove
a first-order (linear) trend will estimate a vertical linear trend to the oxygen
measurements. Since this vertical trend is calculated locally in subsets, removing the
first-order trend is equivalent to fitting local trend lines in a scatterplot of depth
versus oxygen (the correspondence between vertical trend removal in subsets and
local lines on a scatterplot may not be obvious if you do not have experience with
linear regression). Because you previously showed that this scatterplot can be
accurately approximated with a sequence of straight lines, it is appropriate to remove
the first-order trend.
Note:
The elevation inflation factor defines the ratio of speed of the change of the measured
values vertically versus horizontally. For example, if the values change 10 times
faster vertically than they do horizontally, this value should be 10. This allows the
equations to give proper weights to the measured values in all directions in 3D.
Because you do not know an appropriate elevation inflation factor for the oxygen
measurements, you will leave the parameter empty, and a value will be estimated
when you run the tool. The estimated value can be verified after the tool has run by
viewing tool details.
1. Under Advanced Model Parameters, for Elevation inflation factor, ensure the parameter
is empty.
In this example, the elevation inflation factor is used to correct for the fact that the
oxygen measurements change much more quickly vertically than they do
horizontally. You saw this both in the map and in the scatterplot, and it presents a
problem for 3D interpolation because the kriging equations need to properly weight
each measurement to make predictions at new locations. If the measured values
change faster vertically than horizontally, this means that when making a prediction
at a new location, points that are at approximately the same depth should be
weighted higher than points that are at very different depths, even if the points at the
same depth are comparatively far away from the prediction location.
10. Collapse Advanced Model Parameters and expand Search Neighborhood Parameters.
Note:
The Search neighborhood parameter defines how neighbors will be determined
when making predictions at new locations. To predict a new value, oxygen
measurements near the prediction location (called neighbors) need to be identified,
and it is important to get a variety of neighbors in different directions, especially
when the data forms vertical columns.
11. For Search Neighborhood Parameters, verify and make changes if necessary.
Verify Search neighborhood is set to Standard 3D.
Verify Max neighbors is set to 2.
Verify Min neighbors is set to 1.
Verify Sector Type is set to 12 Sectors (Dodecahedron).
These settings ensure that the search neighborhood will look in 12 different directions
(Sector Type) in 3D and find at least one neighbor (Min neighbors) and at most two
neighbors (Max neighbors) in each of the 12 directions.
12. Before executing the Empirical Bayesian Kriging 3D tool, check that you have
correctly set all necessary tool parameters.
13. Click Run to execute the tool. It may take up to a minute for the tool to execute.
When a geoprocessing tool is run, an entry is added to the project's geoprocessing
history with details on when the tool was run; the settings that were used; whether
the tool completed successfully; and any information, warning, or error messages.
14. In the Geoprocessing pane, after the tool has executed, click View Details to display
the tool details.
The Geoprocessing Messages window appears with a summary of the parameters used
in the tool. In the Messages section at the bottom, notice that an elevation inflation factor
was estimated to be about 12.7. This means that even after removing the vertical trend,
the oxygen values still changed about 12.7 times faster vertically than horizontally.
15. Close the Geoprocessing Messages window.
The Oxygen Prediction geostatistical layer is added to the map and displays as a 2D slice at
the surface of the ocean. The layer is initially entirely red, and a small 3D wireframe box is
drawn around the 3D extent of the layer. If you cannot see this wireframe box on your
screen, turn off the World Ocean Base layer. The geostatistical layer is not yet in the same
vertical exaggeration as the elevation surface and the points, so the wireframe box will not
visually match the 3D extent of the oxygen measurements.
In the next section, you will update the elevation and symbology and use the range
slider to move the 2D slice up and down in 3D to see the predicted oxygen values at
different depths.
Explore the geostatistical layer in 3D
In the previous section, you used EBK3D to create a geostatistical layer predicting
dissolved oxygen levels across Monterey Bay. In this section, you will learn to
explore geostatistical layers in 3D. However, first you need to change some elevation
and symbology settings.
1. In the Contents pane, right-click Oxygen Prediction and choose Properties.
2. On the Elevation tab, for Vertical Exaggeration, type 10.
This sets the vertical exaggeration of the geostatistical layer to match the basemap
and points.
3. Click OK to close the layer property page.
The wireframe box around the geostatistical layer will now extend to the bottom of
the oxygen measurements. Next, you will apply a different color scheme to the
geostatistical layer.
4. In Contents pane, expand the Oxygen Prediction layer.
Geostatistical layers are rendered using filled contours based on a classification
method.
the default color scheme for this data uses red to indicate areas with predicted
oxygen levels above 3.785 micromoles/liter. It appears that all locations at the
surface of the ocean have predicted oxygen levels above this value, so the entire 2D
slice renders in red at the surface.
5. Collapse the Oxygen Prediction layer.
To see variability in the predicted oxygen levels at the surface, you will change the
classification method and increase the number of classes in the Symbology pane.
6. Right-click the Oxygen Prediction layer and choose Symbology.
The Symbology pane opens, displaying available classification options.
7. In the Symbology pane, for Method, choose Equal Intervals. For Classes, type 32.
After changing the method and number of classes, the geostatistical layer updates to
display the predicted oxygen levels using an equal interval color scheme with 32
classes. With the updated color ramp, you can now confirm how oxygen levels vary at
the surface.
8. In the Symbology pane, in the Class Breaks list, scroll down to display the yellow
and orange class breaks associated to the surface oxygen levels.
Notice how these class breaks correspond to dissolved oxygen levels between about 4 and
6 micromoles/liter as observed on the ocean surface.
9. Close the Symbology pane.
The 3D geostatistical layer automatically enables a range slider, located on the right
of the Monterey Bay 3D scene. As you hover over the control, it becomes active and
enables you to change the current depth of the geostatistical layer.
10. On the Range Slider control, point to the slider, click inside the green box, type -100,
and then press Enter.
The slider moves to a depth of 100 meters below the surface, and the geostatistical layer
updates to show the predicted oxygen levels at the new depth.
Note:
It may take several seconds for the layer to update at the new depth. If you find that it takes
too long on your computer, you can reduce the number of classes in the Symbology pane.
This will speed up calculation and not change the basic concepts of these lessons.
By moving to 100 meters below the surface, you'll notice the predicted oxygen levels
have dropped significantly. This should be expected based on what you saw in the
scatterplot previously, and it is reassuring to see that the interpolation model also
predicts that this will happen.
11. Point to the middle of the range slider control and click the Down button.
The layer moves down to a depth of 169 meters and the geostatistical layer updates.
Observe how the dissolved oxygen predictions keep dropping as the geostatistical
layer moves deeper into the ocean.
12. Drag the slider back to the surface of the ocean.
Note:
If you accidentally separate the slider into an interval, the geostatistical layer will
always use the top value of the interval.
13. On the ribbon, click the Range tab, in the tabs Playback group. Click Direction to set the
animation playback direction from top to bottom.
14. On the range slider, click the Play button.
The Oxygen Prediction layer moves down through the ocean and displays the predicted
oxygen levels at 30 different depths. The layer moves under the elevation surface and
basemap as it descends.
Note:
It may take several minutes for the animation to complete because the layer must calculate
and contour itself at every new depth. However, once a depth is calculated, it is cached and
will draw quickly every subsequent time at that same depth.
1. Drag the slider back to the surface elevation (0).
2. Click the Play button again.
Your animation should play quickly this time, allowing you to see how the oxygen
levels change. If you watch closely, you can see the oxygen levels decreasing until
around a depth of 800 meters, and then the oxygen levels begin to slowly rise.
3. Drag the range slider back to the surface elevation (0).
In this section, you learned how to explore geostatistical layers in 3D using the range
slider, and you observed that the predicted oxygen levels visually matched what you
saw in the scatterplot in the first lesson.
In the next section, you will use cross validation to quantitatively assess the accuracy
and reliability of the 3D model. Before you produce a final surface, you should assess
how well the model predicts values at unknown locations. Cross validation and
validation will help you make an informed decision as to which model provides the
best predictions.
Assess the accuracy of the model using cross
validation
You can gain a lot of insight into your model by exploring it in a map or scene, but a more
quantitative and verifiable method is needed to validate the accuracy and reliability of the
predicted dissolved oxygen levels. A common method of validating geostatistical models is via
cross validation.
Note:
Cross validation removes a measured point and then uses all remaining points to predict the
location of the removed point. The measured value at the hidden point is then compared to the
prediction value from cross validation. The difference between these two values is called the
cross validation error and is performed on every input point.
1. In the Contents pane, right-click Oxygen Prediction and choose Cross Validation.
The Cross Validation pane opens and displays various graphical and numerical
diagnostics about the accuracy of the interpolation model. The window is composed
of a graph on the left and summary statistics on the right. The calculated statistics
serve as diagnostics that indicate whether the model and its associated parameter
values are reasonable.
1. here are several things to note in the summary statistics:
o
The Mean and Mean Standardized errors are both close to zero (0.007 and
0.017, respectively), which indicates that the model has very little bias. It does
not tend to predict values that are too large or too small.
o
The Root-Mean-Square value of 0.26 indicates that on average, the predicted
oxygen level differed from the measured value by about one quarter of a
micromole/liter.
o
The Root-Mean-Square-Standardized value of 0.94 is close to the ideal value
of 1, and the Average Standard Error of 0.22 is approximately equal to the
root-mean-square. These indicate that the variability in the predictions is being
estimated properly.
o
The Inside 90/95 Percent Interval values of 90.9 and 95.4 are both close to
the ideal values of 90 and 95, which indicates consistency between the
predicted values and the uncertainty of the predictions.
o
Average CRPS is difficult to interpret literally, but smaller values indicate
higher accuracy and precision. This value of 0.083 will be compared to a
different model in the next lesson.
2. On the right side of the Cross Validation pane, click the Table tab.
1. The table shows individual cross validation results for each input point. These values
are used to generate the graphs on the left side of the window.
2. On the left side of the Cross Validation pane, if necessary, click the Predicted tab.
With cross validation, if your model can accurately predict the oxygen values at the
hidden points, it should be able to accurately predict oxygen levels at new locations
that you haven't measured.
3. Review the graph of predicted versus measured values.
This graph is a scatterplot of the predicted oxygen values from cross validation
versus the measured oxygen values for each point. Since the predicted values should
equal the measured values if the model is accurate, ideally the points will fall along
the gray reference line. A blue regression line is calculated for the points to judge
how closely they follow this ideal line.
Your points are so close to ideal that the regression line (blue) nearly covers up the
reference line (gray), so it is difficult to see.
4. In the graph of predicted versus measured values, focus on the points in the upper
right of the graph.
5. The points in the upper right show that there is more variability around the
regression line for larger oxygen values. This is common for geostatistical data, but
it is interesting to note because it means that the model can more accurately predict
in areas of the ocean with low oxygen levels than it can in areas with high oxygen
levels.
6. On the left side of the Cross Validation pane, click the Error tab.
The measured versus error graph shows the measured oxygen values plotted against
the cross validation errors. The blue regression line is flat, which indicates that the
model is making unbiased predictions for low and high levels of oxygen.
7. he graph shows that the predictions are unbiased for all levels of oxygen, and the
variability of the points around the regression line is largest for the highest
measured values. This means that on average, the model accurately predicts large
oxygen values, but there is a lot of variation in individual predictions in areas of high
oxygen.
8. Close the Cross Validation window.
The cross validation summary statistics and graphs give strong evidence that the
EBK3D model that you created is able to accurately predict dissolved oxygen levels
throughout Monterey Bay with an average error of about one-quarter of a
micromole/liter. This error will generally be larger near the surface, where oxygen
levels are highest.
9. Click Save to save the project.
10.
In this lesson, you used the Empirical Bayesian Kriging 3D tool to interpolate dissolved oxygen
measurements in Monterey Bay. You then learned how to explore geostatistical layers in 3D
using the range slider, and you the demonstrated the accuracy of the model using cross
validation.
In the next lesson, you will interpolate the oxygen measurements again using the Geostatistical
Wizard and learn how to explore geostatistical layers in 2D maps.
Execute 3D interpolation in the
Geostatistical Wizard
In the previous lesson, you used the EBK3D geoprocessing tool to interpolate the dissolved
oxygen measurements throughout Monterey Bay. You learned how to use the range slider to
change the depth of the geostatistical layer, and you validated the accuracy of the model.
In this lesson, you will use the Geostatistical Wizard to interpolate the dissolved oxygen
measurements. The Geostatistical Wizard provides a guided experience that allows you to see the
local kriging models that the EBK3D method uses to make the predictions. By exploring these
local models, you can visualize how the local models change throughout Monterey Bay.
Perform Empirical Bayesian Kriging 3D in the
Geostatistical Wizard
In this section, you will move to a 2D map and run Empirical Bayesian Kriging 3D (EBK3D)
using the Geostatistical Wizard. You will use all default settings and compare the cross
validation results to the advanced model from the previous lesson.
1. Click the Monterey Bay map tab.
The map changes to a 2D map of Monterey Bay. The oxygen measurements are drawn
on the map.
2. If necessary, close the OxygenPoints table.
3. On the ribbon, click the Analysis tab. In the Tools group, click Geostatistical
Wizard.
1. The Geostatistical Wizard opens. The first page of the wizard allows you to choose an
interpolation method on the left and specify input parameters on the right.
Note:
The Geostatistical Wizard is a dynamic set of pages that is designed to guide you
through the process of constructing and evaluating the performance of an
interpolation model. Choices made on one page determine which options will be
available on the following pages and how you interact with the data to develop a
suitable model. The wizard guides you from the point when you choose an
interpolation method all the way to viewing summary measures of the model's
expected performance.
4. From the 3D Interpolation group, choose Empirical Bayesian Kriging 3D.
A. Under Input Dataset, for Source Dataset, choose OxygenPoints.
B. For Data Field, choose Oxygen.
These settings specify that you want to run EBK3D on the Oxygen value field of the
OxygenPoints layer.
5. In the Geostatistical Wizard window, click Next.
The second page of the Geostatistical Wizard opens.
The second page of the Geostatistical Wizard is split into several sections.
o
The General Properties section in the upper right shows all of the parameters
available for EBK3D. You should recognize them from the geoprocessing tool in
the previous lesson.
o
The preview surface in the upper left shows a horizontal slice of predicted
oxygen values at the current depth. The preview surface will update whenever
a parameter is changed in General Properties. This allows you to interactively
change parameters and see how the model responds.
o
The lower left section of the page displays the semivariograms, which are
simulated local models from EBK3D at the current location and depth. The blue
lines in the graph are the simulated semivariograms at the location. The graph
also contains blue crosses (empirical semivariances) that are calculated directly
from the data. In general, the blue crosses should fall toward the middle of the
simulated semivariograms.
o
The Identify Result section in the lower right of the page displays the current
location and predicted value from the preview surface. The location (X and Y)
and depth (Z) can be altered by typing coordinates in the Identify Result
section or by clicking a location in the preview surface.
6. Move your pointer over the preview surface to reveal a depth slider that allows you
to change the current depth.
You can drag the slider to modify depth in much the same manner as the range slider
on the map. You can also type a depth in the box below the slider.
7. Type -500 in the box below the slider and press Enter.
The preview surface now displays the predicted oxygen levels at 500 meters below the surface
of the ocean and the graph updates to show simulated local models from EBK3D at the current
location and depth.
8. In the preview section, drag the slider to several different depths.
At each depth, click around the preview surface and observe how the local semivariograms
change. Some areas will have semivariograms that rise more quickly than others. The faster
these models rise, the faster the oxygen values change at that location.
1. For more information about the local models in EBK, see Analyze Urban Heat Using
Kriging.
9. Drag the slider back to the surface of the ocean when you have finished exploring
the local models.
In the Geostatistical Wizard, you will accept all of the default settings for EBK3D in
order to compare the results with the advanced model results you created in the
previous lesson. You justified using the advanced settings with charting and
exploration, and now you can observe how much better you actually did by using
those advanced options.
10. In the Geostatistical Wizard, click Next.
The Geostatistical Wizard executes and displays cross validation results for the
default EBK3D settings. This page is identical to the Cross Validation window that
you created in the last lesson, but it is integrated into the Geostatistical Wizard.
Measured values appear on the x-axis and predicted values appear along the y-axis.
https://learn.arcgis.com/en/projects/interpolate-3d-oxygen-measurements-in-montereybay/lessons/execute-3d-interpolation-in-the-geostatistical-wizard.htm
https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html
https://learn.arcgis.com/en/projects/analyze-urban-heat-using-kriging/lessons/interpolatetemperature-using-simple-kriging.htm