A "Crash Course" to Spatial Interpolation

Summary

In this video, Anastasios Dardis from Ezra Canada explores spatial interpolation in ArcGIS Pro, a technique for estimating values at unsampled locations using geocoded sample points. He explains two main methods: deterministic, which uses mathematical formulas, and geostatistical, employing statistical models with spatial autocorrelation. The tutorial covers popular models like IDW and Kriging, discussing their applications, advantages, and limitations. Dardis also guides viewers through the iterative process of selecting a model, setting parameters, and validating results using cross-validation, ultimately helping users apply spatial interpolation effectively.

Takeaways

• 🌐 Spatial interpolation is a technique used to estimate values at unknown points or areas based on geocoded sample points with known values.
• 📈 It is more efficient and cost-effective to use spatial interpolation to map unknown values at unsampled locations rather than extracting samples at every location.
• 🔍 Spatial interpolation applies Tobler's First Law of Geography, which states that everything is related to everything else, but near things are more related than distant things.
• 💧 It is widely used in various disciplines such as hydrology, soil, agriculture, weather, climate, atmosphere, land use, and topography.
• 🛠️ There are two types of spatial interpolation techniques: deterministic (mathematics-based formulas) and geostatistical (statistical models with spatial autocorrelation).
• 📊 Deterministic methods like IDW provide smooth interpolated surfaces and are easier to understand and process, while geostatistical methods like Kriging are more complex but consider distance and variation between data points.
• 📉 IDW is efficient for large datasets and good for high spatial density, but it may not be suitable for small datasets or areas with abrupt changes.
• 🔍 Kriging is excellent for smaller datasets, identifies interpolation errors, and considers spatial autocorrelation, but it can be computationally intensive and requires knowledge of geostatistics.
• 🔄 The process of spatial interpolation is iterative and includes visualizing data, exploring for outliers or skewness, selecting a model, checking its accuracy, and comparing multiple models if necessary.
• 📊 Decision trees developed by ESRI can guide the selection of the most appropriate spatial interpolation model based on various factors such as the type of information required, method complexity, and desired level of smoothness.
• 📈 A semi-variogram is used in geostatistical methods to visualize spatial autocorrelation and help determine parameters such as the sill, range, and nugget effect.

Q & A

What is spatial interpolation?

Spatial interpolation is a technique that uses geocoded sample points with known values to estimate values at unknown points or areas. It's more efficient and cost-effective than extracting samples at every location.

Why is spatial interpolation important?

Spatial interpolation is important because it allows for the prediction of values at unsampled locations, which can be costly or impractical to directly measure. It's widely used across various disciplines such as hydrology, soil science, agriculture, weather, and climate.

What is Tobler's First Law of Geography, and how does it relate to spatial interpolation?

Tobler's First Law of Geography states that 'everything is related to everything else, but near things are more related than distant things.' This law is fundamental to spatial interpolation as it suggests that the value at an unknown location can be estimated based on the values of nearby locations.

What are the two types of techniques used in spatial interpolation?

The two types of techniques used in spatial interpolation are deterministic and geostatistical. Deterministic methods use mathematical formulas, while geostatistical methods use statistical models that consider spatial autocorrelation.

What is the difference between deterministic and geostatistical methods?

Deterministic methods, like Inverse Distance Weighting (IDW), assign values based on surrounding measured values, and they are smooth and simple to understand. Geostatistical methods, like Kriging, consider distance and variation between known data points, predict with accuracy, and identify interpolation errors, but they are more complex and computationally intensive.

What are the advantages and disadvantages of IDW?

IDW is efficient for large datasets, easy to understand, and good for high spatial density. However, it is not suitable for small datasets, assumes similar values for closer points (not good for abrupt changes), and does not consider spatial autocorrelation.

What are the advantages and disadvantages of Kriging?

Kriging considers distance and variation between data points, is prediction-based, and identifies interpolation errors. It is excellent for smaller datasets. However, it can be complex, requires knowledge of geostatistics, and cannot identify absolute min or max values outside the current range.

What is the role of cross-validation in spatial interpolation?

Cross-validation is used to check the accuracy of the spatial interpolation model by comparing the predicted values with the actual values. It helps to fine-tune the model parameters and select the best-performing model.

How does the semi-variogram help in spatial interpolation?

The semi-variogram visualizes spatial autocorrelation and helps in determining the model parameters such as the sill, range, and nugget. It aids in understanding the spatial structure of the data and in fitting the best semi-variogram model to predict values at unsampled locations.

What are the key parameters to consider when performing spatial interpolation?

Key parameters include lag size, lag tolerance, direction, angle tolerance, bandwidth, and the type of semi-variogram model (e.g., spherical, Gaussian, exponential). These parameters influence how spatial autocorrelation is measured and how values at unknown locations are predicted.

What tools are available in ArcGIS Pro for spatial interpolation?

ArcGIS Pro offers the Interpolation toolset in the Spatial Analyst toolbox for deterministic methods, the Interpolation toolset in the Geostatistical Analyst toolbox for geostatistical methods, and the Geostatistical Wizard for an interactive approach to spatial interpolation.

Outlines

00:00

🌏 Introduction to Spatial Interpolation in ArcGIS Pro

Anastasios Dardis introduces himself as a higher education developer at Ezra Canada and presents the topic of spatial interpolation in ArcGIS Pro. Spatial interpolation is a technique that estimates values at unknown points or areas using geocoded sample points. It is more efficient and cost-effective than extracting samples at every location. The method is based on Tobler's First Law of Geography, which states that everything is related, especially nearby things. Spatial interpolation is widely used in various disciplines such as hydrology, soil science, agriculture, weather, climate, atmosphere, land use, and topography. The video will discuss two types of techniques: deterministic, which uses mathematical formulas, and geostatistical, which uses statistical models with spatial autocorrelation. Deterministic methods are smoother and simpler, while geostatistical methods provide more accuracy but are more complex.

05:02

📊 Spatial Interpolation Techniques and Models

The script explains the differences between deterministic and geostatistical methods in spatial interpolation. Deterministic methods, like Inverse Distance Weighting (IDW), Natural Neighbor, Trend, and Spline, assign values based on surrounding measures, are efficient for large datasets, and are aesthetically smooth. Geostatistical methods, such as Kriging, Co-kriging, Empirical Bayesian Kriging (EBK), and others, consider distance and variation, are excellent for smaller datasets, and can identify interpolation errors. The script also mentions that IDW is not suitable for datasets with abrupt changes and does not account for spatial autocorrelation. Kriging, on the other hand, is more complex but can predict and provide accuracy measures. The tutorial will cover IDW and Kriging in detail.

10:05

🛠️ Steps and Considerations for Spatial Interpolation

The script outlines the multi-step process of spatial interpolation, which includes visualizing data for patterns or trends, exploring data for outliers or skewness, selecting a spatial interpolation model, filling in required parameters, and checking model accuracy through cross-validation. It emphasizes the importance of understanding data, using decision trees to choose the most appropriate model, and iteratively refining parameters. The tutorial also discusses the concept of semi-variograms, which are used to visualize spatial autocorrelation in geostatistical methods. The script explains how to interpret semi-variograms, including the sill, range, and nugget effect, and how these are influenced by parameters like lag size and tolerance.

15:07

📚 Conclusion and Additional Resources

The script concludes by emphasizing the importance of understanding spatial interpolation and the steps involved in the process. It mentions that the tutorial will cover how to apply the concepts learned, perform cross-validation, and identify the best model to use. The video encourages viewers to access additional resources, subscribe to the higher education listserv for updates, and follow on social media for more educational content related to ArcGIS software. The resource finder page is highlighted as a place to find a range of tutorials from ArcGIS Pro to ArcGIS Enterprise.

Keywords

💡Spatial Interpolation

Spatial interpolation is a technique used in Geographic Information Systems (GIS) to estimate values at unknown points based on known sample points. It is crucial for efficiently mapping areas where direct measurement is impractical or costly. In the video, spatial interpolation is the central theme, with a focus on how it applies Tobler's First Law of Geography, which states that 'everything is related to everything else, but near things are more related than distant things.'

💡Geocoded Sample Points

Geocoded sample points are specific locations that have been assigned geographic coordinates and associated values. These points are used as a basis for spatial interpolation to estimate values at other locations. The script mentions using these points to estimate ozone levels across California, illustrating how spatial interpolation can be applied in a real-world context.

💡Deterministic Methods

Deterministic methods in spatial interpolation use mathematical formulas to assign values to unknown locations based on surrounding known values. These methods are highlighted in the video as being simpler and more efficient for large datasets. An example given is the Inverse Distance Weighting (IDW), which is one of the deterministic techniques discussed.

💡Geostatistical Methods

Geostatistical methods incorporate statistical models that account for spatial autocorrelation to predict values at unknown locations. The video explains that these methods are more complex than deterministic ones but offer greater accuracy, especially for smaller datasets. Kriging is mentioned as a geostatistical method that considers both distance and variation between data points.

💡Tobler's First Law of Geography

Tobler's First Law of Geography is a fundamental concept in geography that spatial interpolation relies on. It suggests that the properties of objects are related to the properties of surrounding objects, with closer objects being more related. The video uses this law to justify why spatial interpolation is effective, as it assumes that nearby locations will have similar values.

💡Cross-validation

Cross-validation is a statistical method used to evaluate the accuracy of spatial interpolation models by comparing the predicted values with actual values. The video emphasizes the importance of cross-validation in ensuring that the chosen interpolation model performs well. It is part of the iterative process of refining the model to achieve the best results.

💡Semi-variogram

A semi-variogram is a graphical representation used in geostatistics to measure spatial autocorrelation. It helps in understanding how the variation in data is related to the distance between sample points. The video describes how to interpret a semi-variogram and its components like the sill, range, and nugget, which are crucial for selecting appropriate parameters in kriging.

💡Lag Size

Lag size refers to the distance interval used in spatial analysis to measure the degree of spatial autocorrelation. The video explains how to determine an appropriate lag size, which is essential for creating a semi-variogram and, subsequently, for selecting the right parameters in spatial interpolation models.

💡Anisotropy

Anisotropy is a property of spatial data where the statistical properties vary with direction. The video mentions that if anisotropy is present in the data, it can influence the choice of direction for spatial interpolation, which can affect the model's accuracy.

💡Spatial Analyst Toolbox

The Spatial Analyst Toolbox in ArcGIS Pro is a collection of tools used for spatial analysis, including spatial interpolation. The video mentions this toolbox as one of the resources for executing deterministic spatial interpolation methods.

💡Geostatistical Analyst Toolbox

The Geostatistical Analyst Toolbox is another set of tools in ArcGIS Pro, specifically designed for geostatistical methods of spatial interpolation. The video contrasts this toolbox with the Spatial Analyst Toolbox, noting that it is used for more complex, statistically-based interpolation techniques.

Highlights

Spatial interpolation is a technique that estimates values at unknown points using geocoded sample points.

Spatial interpolation is more efficient than extracting samples at every location.

It applies Tobler's First Law of Geography, which states that near things are more related than distant things.

Spatial interpolation is widely used in hydrology, soil, agriculture, weather, climate, atmosphere, land use, and topography.

There are two types of spatial interpolation techniques: deterministic and geostatistical.

Deterministic methods use mathematics-based formulas, while geostatistical methods use statistical models with spatial autocorrelation.

Deterministic methods are smooth, whereas geostatistical methods are less so.

Inverse Distance Weighting (IDW) is a popular deterministic method, efficient for large data sets.

Kriging is a geostatistical method that considers distance and variation between known data points.

Kriging identifies interpolation errors, demonstrating the model's performance.

Spatial interpolation is a multi-step and iterative process involving data visualization, exploration, model selection, and validation.

ESRI provides decision trees to help select the most appropriate spatial interpolation model.

Parameters for spatial interpolation models need to be defined through an iterative process of experimentation.

A semi-variogram is used to visualize spatial autocorrelation in geostatistical methods.

The nugget effect is an estimate of error affected by volume sampling and should be minimized.

Lag size, tolerance, and direction are important components in fitting the semi-variogram model.

Cross-validation is used to assess the accuracy of the spatial interpolation model.

ArcGIS Pro offers toolsets for both deterministic and geostatistical spatial interpolation methods.

The Geostatistical Wizard in ArcGIS Pro provides an interactive interface for spatial interpolation.

The resource includes three tutorials for understanding, applying, and validating spatial interpolation models.

Transcripts

hello everyone

my name is anastasios dardis and i'm a

higher education developer at the

education

and research group at ezra canada

in this video you will learn spatial

interpolation in arcgis pro

so what is spatial interpolation

well spatial interpolation is a

technique that uses geocoded sample

points with values to estimate values at

unknown point slash areas the reason

this gis

method exists is it because it is more

efficient to map

unknown values at unsampled locations

than it is to extract samples at every

location

additionally extracting samples at every

location can be quite expensive

to predict values at unknown points

spatial interpolation uses either

deterministic

or geostatistical methods which will be

discussed in the next

slide at its core

spatial interpolation applies tobler's

first law of geography

to identify unknown values at unsampled

areas

for review tobler's first law states

that everything is related to everything

else

but near things are more related than

distant things

thus we could say that spatial

interpolation is widely used across

disciplines

the most popular use cases are in the

fields of hydrology

soil agricultural weather and climate

atmosphere land use and topography

here we can see an image of sample

points in california

collecting ozone levels and then the

next image is interpolating those valves

to display

all of california

in spatial interpolation there are two

types of techniques

deterministic and geostatistical

the differences are the following

backend

deterministic uses mathematics-based

formulas

whereas geostatistical use statistical

models with spatial autocorrelation

what it actually does is that in

deterministic is it assigns

values of locations based on surrounding

measure values

whereas geostatistical predicts and

provides accuracy

as for aesthetics deterministic are

smooth whereas geostatistical are less

so

and both sides have a wide range of

tools to execute

deterministic has inverse distance

weighting or known as idw

natural neighbor trend radial basis

and spline in contrast geostatistical

has

cragging co-creating empirical base

intriguing

or known as ebk ebk regression

ebk 3d and air interpolation

and lastly deterministic are more simple

to understand

and process whereas geostatistical are

not

the next slide shows the concepts

disadvantages

and disadvantages of the most popular

spatial interpolation model

for the sake of time we will go through

idw and kriging

as they will be used in the tutorial

natural neighbor

spline and trend won't be used however

you will have access to this powerpoint

as reference when downloading the

resource from our

higher education page idw

increases its distance decay weight when

a sample location is

relatively close to unknown location

idw is one of the most popular as it is

efficient for large data sets

it's easy to understand and it's good

for high spatial density

however it is not good for small data

sets it assumes that closer points have

similar values

which is not good for abrupt changes

such as mountains and peaks

and is not based on spatial

autocorrelation

on the other hand krigging is somewhat

similar to idw

except it considers distance and the

degree of variation

between known data points

unlike idw trigging is prediction based

has a wide range of methods it's

excellence for smaller data sets

and most importantly it identifies

interpolation errors which demonstrates

the model's performance

the downside of krigging is that it can

be complex

and requires background knowledge of

geostatistics when modeling

it cannot identify values of the

absolute min or max

meaning that values that are higher or

lower than the current range

and lastly kragen can be computationally

intensive

indicating slower processing times

both idw and krigging are thoroughly

discussed in the tutorial in terms of

how they work

now for those of you that are not

familiar with spatial interpolation

it is a multi-step and iterative process

first you visualize the data on the map

and see if there are

any patterns or trends with the data

second

you explore the data and see if there

are any outliers or skewness

if outliers exist you may need to remove

it

if the data is skewed you would have to

perform some data transformation

ignoring these refinement steps could

result in accurate models

next you pick your spatial interpolation

model

fill in required parameters and check

the model's accuracy

by looking at a preview of it and

diagnostic statistics via cross

validation

which is the fifth step ideally

it is best to have at least two models

that way you can compare each of the

model and select the best performing one

now the big question is which model do

you pick

fortunately at esri they have developed

decision trees

as guidance to pinpoint the most

appropriate models

each decision tree asks you a question

and it provides the result

these are what type of information does

your decision require

which method requires measurement or

model spatial

autocorrelation what output type do you

care most

what is the level of assumptions and how

complex do you want your model to be

what type of interpolation you want

what level smoothes do you want would

you like to have

uncertainty of the predicted values and

how fast do you want to interpolate your

model

these are questions you should ask

before starting the interpolation

process

so let's say you've selected your

spatial interpolation models

there are several required parameters

you will have to fill in

unfortunately there is no silver bullet

to properly define the parameters

instead it is an iterative process of

experimentation based on a set of clues

these clues are mining and understanding

your data

checking the model decision tree

checklist

understanding this in my variogram and

deciding the lag size

direction type of model and whether to

combine

multiple models into one that is if it

is applicable

you'll only interpret the semi-varigram

whenever you've decided to use kriging

code kriging or empirical beige

intriguing as your spatial interpolation

model

a semi-varigram is essentially what

visualizes spatial autocorrelation

in case you're not familiar with spatial

autocorrelation

it is a measure of similarity between

nearby observations

in a semi-varigram you have to look at

when the model flattens out

or in other words when spatial

autocorrelation

ceases to exist by identifying three

components

the first is the sill which is the

maximum value or semi-variance

the second is the range which is the

maximum distance reached

and the third is a nugget the nugget is

the value at which the semi-varigram is

virtually close to the y

value here is an image of what it would

look like

the nugget effect is an estimate of

error affected by volume sampling

if the nugget is relatively high from

zero it implies of a large nugget effect

which is something to avoid having in

the model if possible

if you do have a large nugget effect

then there could be measurement

inaccuracies

regards the predictions at unsampled

locations

or spatial sources of variation at

distances smaller than the sampling

interval

in other words it is unpredictable over

very short distances

that is why it is colloquially phrased

as a nugget effect

when gold miners come across a gold

nugget in soils with very low

concentrations of gold

the best way to reduce the nugget effect

is to increase the number of samples

especially at closer intervals

the sill range and nugget are impacted

by several model parameters

the first is lag size that defines the

increment distance intervals

to measure spatial autocorrelation

determining a lag size cannot be too

large as it would skip

short range spatial autocorrelation

neither too small

as it may not represent enough

information

the rule of thumb is to take half of the

largest distance among all points

divided by the number of lags

for example the largest distance between

two sample points

is a hundred kilometers and you want to

set the number of lags to ten

the lag size would be set to five

kilometers another way is to execute

average nearest neighbor tool in arcgis

pro and take the observed mean distance

if your sample happens to be clustered

then go for a smaller number than the

observed mean distance value

next which is not required but may

improve the model's performance

is lag tolerance this is the tolerance

range between lags

usually at half the lag size which

captures extra sample points

increase the lag tolerance only if the

semi-varigram seems to be erratic

another important component is the

direction

this is only used when you see a

directional pattern or influence in the

data

hence the term anisotropy if

anisotropy exists in the data then set

the angle tolerance which is

conceptually

similar to electron tolerance and the

bandwidth

which is the maximum search width to

include other sample points

the next is fitting the calculated semi

variances across the log distance

which is then used to predict data

values at unsampled locations

in arcgis pro there are many such as k

bessel

j bessel hall effect pentospherical and

tetrospherical

however the most popular ones are

spherical

gaussian and exponential given their

simplicity and robustness

lastly is combining multiple fitting

models into one

this is only to be used if you have

other variables that would influence the

phenomena

such as elevation for temperature or

biomass here are two images of what the

parameters would look like if you were

to do this on paper

and on the map

in the final step of modeling you would

assess

the the blue line are known as a

semi-varigram model

the question is does the semi-varigram

model pass through the center of the

cloud of bin values

which are the red dots does it pass as

closely as possible to the average

values which are the blue crosses

and does it pass as closely as possible

through the middle of the local

polynomials displayed as green lines

if the answer is yes to all of them then

you can assess the final part of

modeling via cross validation

cross validation contains the the

statistic diagnostics

these include asking the whether the

regression line displayed as blue

is closely aligned with the reference

gray line

are the points closely lined with a

normal qq plot line

is the mean prediction error close to

zero

is the root mean square as small as

possible

and is the average standard error

similar to the root mean square

if you're using ebk based methods

further questions you need to ask is

whether the 90

interval is close to 90 the 95 percent

interval is close to 95

and the average continuous rank

probability score

is as small as possible if most of your

results are within these guidelines

then the model likely perform well and

can be exported

in arcgis pro there are several tool

sets that can be used to execute spatial

interpolation models

the first is the interpolation toolset

located in the spatial analyst toolbox

this is more mathematical based on value

and distance and is not interactive

the other is the interpolation toolset

located in the geostatistical analyst

toolbox

this one is strictly for the

geostatistical methods

and finally the geostatistical wizard

which has the

most of the spatial interpolation

methods this graphical user interface

is powerful as it is interactive and

provides previews of the interpolated

surface before exporting

you will use this one in this tutorial

finally when you download the resource

it will consider a set of three

tutorials

see how it is structured in the folder

part one is to have a deeper

understanding of spatial interpolation

which is an expansion of the video you

are watching now

and i highly recommend you to go through

this one first

part two is applying of what you've

learned in part one

by probably using the inverse distance

weighting

krigging and empirical bayesian creating

to spatially interpolate air temperature

in the province of new brunswick

and part three is to perform

cross validation and validation to

identify which model

is best to use

thank you for watching the spatial

interpolation resource

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student you can still follow us on

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at gis ajd lastly

if you'd like to learn more check out

our higher education

resource finder page and there you will

find a range of tutorials from arcgis

pro

to arcgis enterprise