Spatial Sampling & Interpolation
Summary
TLDRThe video script delves into the intricacies of spatial sampling, a critical process in gathering and analyzing geographical data. It explains the concept of a sample frame and the importance of unbiased sampling where every element has an equal chance of selection. However, due to the complexities of spatial data, biased sampling is sometimes necessary, especially when proximity influences relationships among objects. The script outlines various sampling methods, including random, systematic, stratified, cluster, and transect sampling, each with its advantages and limitations. It also touches on the challenges of implementing random sampling in practice and the trade-offs between representativeness and resource investment. Furthermore, the script introduces spatial interpolation as a technique to estimate values between sampled points, leveraging the spatial autocorrelation found in continuous fields. This method is particularly useful for estimating weather conditions, elevation, and adjusting raster image resolutions. The inverse distance weighting example illustrates how spatial interpolation can be applied effectively.
Takeaways
- 📐 **Spatial Sampling Definition**: Selecting points from within an area, known as the sample frame, to gather data.
- ⚖️ **Bias in Sampling**: A sample is biased if elements have unequal chances of selection, while unbiased sampling gives every element an equal chance.
- 🌐 **Spatial Autocorrelation**: Objects close to each other are more likely to be related, which is important in spatial sampling.
- 🔢 **Random Sampling**: A straightforward method where x and y coordinates are randomly generated within the sample frame.
- 🔄 **Repeated Sampling**: Taking multiple random samples to increase representativeness, but it's more time and resource-intensive.
- 📏 **Systematic Sampling**: Imposing a regular grid on the sample space to ensure evenness, but it may miss features with regular patterns.
- 🤝 **Combined Sampling**: Using a combination of systematic and random sampling to balance structure and randomness.
- 🏪 **Cluster Sampling**: Intensively sampling features within selected clusters, useful for focusing on specific areas.
- 🚶 **Transect Sampling**: Focusing sampling efforts on a specific area of interest, efficient but requires good pre-existing understanding.
- 🌳 **Sample Quantity**: The number of samples needed depends on the spatial homogeneity or heterogeneity of the population.
- 📈 **Spatial Interpolation**: Estimating values between known samples for continuous fields, using patterns observed in the dataset.
- 🔍 **Inverse Distance Weighting**: A spatial interpolation technique that estimates values based on distance from known points, with closer samples weighted more.
Q & A
What is spatial sampling?
-Spatial sampling is the process of selecting points from within an area, known as the sample frame, to gather spatial data for analysis.
Why is it impossible to capture and describe everything about the world at once?
-The world is essentially infinitely complex, making it impossible to capture and describe everything due to the vast amount of information and variables involved.
What are the two main types of sampling that can be applied to spatial data?
-The two main types of sampling are unbiased (where each element has an equal chance of being selected) and biased (where some elements have a greater or lower chance of being selected).
Why might we intentionally design our samples to be biased in spatial sampling?
-In some cases, such as geography, objects that are close to each other are more likely to be related, so a biased sample that focuses on these relationships can be more useful than a completely random one.
What are the advantages of a random sample?
-A random sample is fairly easy to define and implement in theory, providing a good range of possible values in a distribution, and it helps to avoid bias.
What are the potential drawbacks of random sampling?
-Random sampling might result in oversampling of large homogeneous areas or missing smaller elements, leading to an unrepresentative sample of the population.
What is systematic sampling and how does it differ from random sampling?
-Systematic sampling involves imposing a regular grid on the sample space to ensure evenness. It differs from random sampling by introducing a structured bias, which can make the sample more spatially representative but may miss some features with regular patterns.
How can we combine the benefits of systematic and random sampling?
-By defining a regularly spaced grid and then taking random samples within them, we can induce some randomness into the sampling method, which helps to alleviate issues with overlapping periodic features.
What is cluster sampling and when is it beneficial?
-Cluster sampling involves intensive sampling of features in clusters around selected locations. It is beneficial when focusing on certain areas, such as shopping centers for a survey, as it allows for efficient targeting of the desired population.
What is transect sampling and how is it used?
-Transect sampling allows for focusing efforts on a specific area of interest, making it an efficient way to sample a key feature without sampling outside of the focus area. It is commonly used along linear features like roads or rivers.
How does the number of samples required to represent a population relate to the spatial homogeneity of the area?
-The number of samples required is a function of how similar the units of a population are. More homogenous areas require fewer samples, while areas with high spatial heterogeneity need more samples to adequately represent the population.
What is spatial interpolation and why is it used?
-Spatial interpolation is a technique used to estimate values of a continuous field at places where measurements are not available. It is used to fill in gaps between samples, making estimations between weather stations, estimating elevation, and changing the resolution of raster images.
How does inverse distance weighting work in spatial interpolation?
-Inverse distance weighting is a method where values are interpolated based on their distance from known points, with closer samples given more weight than distant ones. The further away an object is, the less weight it has in the interpolation process.
Outlines
📐 Understanding Spatial Sampling
The first paragraph introduces the concept of spatial sampling, which is the process of selecting points within an area known as the sample frame. It discusses the complexity of the world and the need to focus on subsets of data. The narrator explains the importance of unbiased sampling where every element has an equal chance of being selected, contrasting it with biased sampling that is sometimes intentionally designed in spatial contexts. The advantages of random sampling are highlighted, including its ease of implementation, but the potential drawbacks, such as oversampling or missing critical elements, are also noted. The paragraph concludes by mentioning the possibility of repeated sampling to improve representativeness, despite its resource-intensive nature.
🔍 Biased and Systematic Sampling Methods
The second paragraph delves into alternative sampling methods used in geography, focusing on biased and systematic sampling. It contrasts the imperfections of systematic sampling, which may miss regularly patterned features, with the potential adjustments that can be made to compensate. The paragraph explains the concept of a systematic sample, which involves imposing a regular grid on the sample space for evenness, and discusses its suitability for areas with few features and abrupt boundaries. The limitations of systematic sampling for periodic features are also highlighted. The narrator then suggests combining systematic and random sampling to address issues with overlapping periodic features, and introduces stratified random sampling and cluster sampling as additional methods, emphasizing their utility in specific contexts.
🌳 Efficient Sampling Techniques
The third paragraph discusses efficient sampling techniques like cluster sampling and transect sampling. Cluster sampling involves intensive sampling around selected locations, which is beneficial when focusing on specific areas. Transect sampling allows for focused efforts on an area of interest, which is efficient but requires a good understanding of the spatial structure. The paragraph also addresses the question of how many samples are needed, explaining that it depends on the homogeneity of the population. It emphasizes the importance of knowing the study area to determine the best sampling method, balancing effective coverage with the cost of data collection.
🔗 Spatial Interpolation for Data Estimation
The fourth paragraph explores spatial interpolation, a technique used to estimate values between sampled points in a dataset. It explains that interpolation is an 'intelligent guesswork' that makes reasonable estimates of continuous fields where measurements are absent. The narrator distinguishes between linear interpolation in one dimension and spatial interpolation in two or three dimensions. The concept of inverse distance weighting is introduced as a method of spatial interpolation that gives more weight to closer samples, aligning with Tobler's First Law of Geography. The paragraph concludes with a mention of the practical applications of spatial interpolation, such as estimating weather conditions between stations, measuring elevation, and changing the resolution of raster images.
Mindmap
Keywords
💡Spatial Sampling
💡Sample Frame
💡Biased Sample
💡Unbiased Sample
💡Random Sampling
💡Systematic Sampling
💡Stratified Random Sampling
💡Cluster Sampling
💡Transect Sampling
💡Spatial Interpolation
💡Inverse Distance Weighting
Highlights
Spatial sampling involves selecting points from within an area, known as the sample frame, to gather data.
The world is infinitely complex, necessitating the collection of a subset of information or samples to understand it.
Scientific sampling requires each element in the sample frame to have a pre-specified chance of selection to avoid bias.
In some cases, spatial sampling is intentionally designed to be biased to account for the spatial relationships between objects.
Random sampling is theoretically easy to define but can lead to oversampling of large homogeneous areas or missing smaller elements.
Repeated random sampling can lead to a more representative sample but is more time-consuming and resource-intensive.
Systematic sampling involves imposing a regular grid on the sample space to ensure evenness, but may miss features with a regular pattern.
Combining systematic and random sampling can help alleviate issues with overlapping periodic features.
Stratified random sampling involves spacing grids at random intervals to maintain some randomness in the sampling method.
Cluster sampling focuses on intensive sampling of features in clusters around selected locations, useful for targeting specific areas.
Transect sampling allows for focused efforts on specific areas of interest, efficient for linear features like roads or rivers.
The number of samples required depends on the spatial homogeneity of the population; more heterogeneity requires more samples.
Knowledge of the study area is crucial for determining the best sampling method to balance effective coverage with cost.
Spatial interpolation is a technique used to estimate values between known samples, particularly useful for continuous fields.
Inverse distance weighting is a spatial interpolation method that estimates values based on distance from known points.
Spatial interpolation exploits Tobler's First Law of Geography, giving more weight to closer samples.
Continuous fields like temperature, precipitation, and elevation exhibit strong spatial autocorrelation, making spatial interpolation effective.
Spatial interpolation is used for estimating weather conditions between stations, measuring elevation, and changing raster image resolutions.
The choice of sampling method depends on the features being studied and the resources available for data collection and analysis.
Transcripts
all right now i'm going to talk a bit
about spatial sampling
so how do we collect and gather spatial
data
and then um i'll loop back around to
talking a little bit about how we can
exploit a little bit of the special
nature of spatial data
you can think of sampling as the process
of
selecting points from within an area
this area
is also sometimes referred to as the
sample frame
we select some areas from within the
frame but we discard
other right so as i've talked about a
bit already
the world is essentially infinitely
complex there's no way
that we can capture and describe
everything about it all at once so
depending on
the task at hand maybe we focus on just
one subset and collect all the
information we can about it
or maybe the reality or the
area that we're looking at is too
complex and we have to just
stick to looking at a subset so we take
samples
of that area and use that to work with
but how do we choose which points we can
keep and determine
the quality of our data
scientific sampling requires that each
element in a sample frame has
some pre-specified chance of selection
if some elements have either a greater
or lower
chance of being selected then our sample
is said to be biased
and if every element of interest has an
equal chance of being selected then our
sample is said to be
unbiased now biased
isn't necessarily a bad thing in the
context of spatial sampling sometimes we
explicitly design our samples to be
biased
even though again in many of the
hard sciences you want an unbiased
sample
sometimes that's just not a feasible
option in geography
because again objects that are close to
each other are more likely to be related
things that are farther away are more
likely to be
less related in theory
a completely random that is unbiased
sampling process is best with this
each location has an equal chance of
being selected
one of the advantages of a random sample
is that it's
fairly easy to do at least in theory
i'll explain why it's not always
easy in practice but it's easy to define
you create your sample frame that's the
area that you're looking at
and then you just randomly generate x
and y coordinates
within the sample thing typically
speaking this
provides a good range of possible values
in a distribution
however sorry the dog is chewing on a
squeaky toy
however there is a chance that all
samples will be taken from the same type
of elements within a certain population
so for instance we might only sample
from urban areas
and miss forested areas and it's often
difficult to implement this
in practice so if you look at the figure
down here
you can see some of the drawbacks of
random sampling
so all the blue circles are the samples
we take
and with random samples you might end up
by chance
over sampling large elements like a
building or
crop field so these are homogeneous
areas where you don't need a lot of
samples to describe what they are
or you might completely miss smaller
elements so
for instance maybe there's some certain
tree species in an area that you
need to get samples from
if you rely on a random sample maybe
you'll miss all those trees
and then you won't include that in your
abstraction of reality
we have another we have a number of
approaches to limit
the impact of this we can do repeated
sampling
so theoretically if you repeat a random
sample over and over and over again
you'll get a lot more samples and it'll
be more representative of the entire
population
the downside to this is that it's more
time consuming and it requires more
resources
typically speaking collecting data
physically
going out and doing it is fairly
expensive
um you have to pay people to collect the
data or
invest your own time in it it's labor
intensive it's a lot of work
if you've ever done any field work you
know that it's
[Music]
a lot so typically we don't want to do
just random samples you can end up with
a lot of redundancy of labor and things
like that
generally speaking in geography we rely
on biased
systematic sampling methods instead so
this is where we create
some sort of sampling design that trades
a sampling scheme
for randomness so instead of complete
randomness we define some structure
we induce some bias to our sample but we
do that with the intent
of making our sample easier more
spatially representative things like
that
so systematic sampling isn't perfect
either it may miss some features that
have a regular pattern or
cluster but we can make some adjustments
to that
to compensate
a systematic sample is just where some
sort of regular grid is
imposed on the sample space to ensure
evenness so this can be a solid strategy
for areas that contain
only a handful of features with abrupt
boundaries like buildings or something
but it's not ideal for things that
exhibit some degree of periodicity
that is like regular intervals like rows
because you might end up over sampling
or under sampling
the feature if all of your sample points
match
up with the period of whatever
entity you're looking at so for instance
if you
overlay a grid on a road network
it's possible that all of these sample
points might completely miss
the road network it's also possible that
the
samples might mostly fall on the roads
so the purely systematic sample
generally speaking isn't the best option
here
one workaround is you can combine
the benefits of the systematic sample
with the benefits of a random sample
generally speaking the systematic sample
is nice because
it makes your sampling scheme a bit more
organized and regular it's usually
easier to collect
but you get rid of all the randomness
instead you can address this issue
by defining a regularly spaced grid and
then taking
random samples within them so this
induces some randomness
to the sampling method and will
alleviate issues
with overlapping periodic features
however this goes back to the main issue
with
one of the main issues with random
sampling is that it's
time consuming and costly
alternatively another form of stratified
random sampling is you can
rely on the grid method as in your d on
the bottom left
but you can space the grids
at random intervals instead it's
essentially doing the same thing
another option is cluster sampling
so you can do intense sampling of
features in
clusters around a number of selected
locations
this is useful if you know that you want
to focus
on certain areas so for instance
shopping centers
maybe you want to do a survey of
the opinions of shoppers for some
certain thing
right it might make sense to send
canvassers to specific shopping centers
to interview people who pass by
it wouldn't make sense to send one of
your canvassers to a city park to ask
them their opinion on
something if it relates to shopping it
wouldn't be a good idea
to have the surveyors go door-to-door
right you're not necessarily going to be
getting the
target population you're looking for
that would be a waste of resources to go
to a park
or to canada's neighborhood when they
could simply stand outside of the
shopping center and get the target
population they're looking for
so that's one context where cluster
sampling is very beneficial if you
are working with things that are
specifically clustered and you know you
just want to target those things you can
ignore the rest of the sampling area
another option is to just randomly
define
the or you can select the cluster
locations at random
and then intensively sample those
clusters
so this could be beneficial if you're
trying to do a vegetation survey for
instance
you have a large area and you randomly
define
vegetation plots and then you take
samples within those vegetation plots
so again this will this allows you to
use some of the randomness and exploit
some of the advantages
of unbiased sampling while also
exploiting some of the
time saving advantages of biosampling so
you choose a handful of random locations
and then intensively sample them
rather than sporadically sampling a
whole bunch of random
locations this is really efficient time
wise but it might
might not be representative of the
broader population that you're
interested in
another option is transect sampling this
allows you
to focus your efforts only on a specific
area of interest
it's really efficient way to sample just
the key feature that you're looking at
you don't sample outside of the focus
area
but one drawback
is that it requires really good
pre-existing understanding
of the spatial structure of the object
you
or whatever you're studying for maximum
effectiveness
the most common application for this
type of sampling method might be
along linear features like roads or
rivers
so you want to get a stream profile you
just
define transects across the stream
and so you just focus on those specific
areas you don't need to focus
outside of the stream and
uh also because of the
sort of effort and difficulty involved
with like
measuring stream depth you have to have
somebody walk across that stream it
might be easier to just have them walk
in lines across the river rather than
trying to navigate it and
doing random samples at a bunch of
different locations
and then within the transect sample
samples can either be randomly as
randomly spaced stratified or some
combination of the two approaches
so with most of these different types of
sampling methods you can induce some
degree of randomness to make them a
little bit
less biased if you want
how many samples do we need the number
of samples
required to adequately represent a
population is a function
is a function of how similar the units
of a population are
so if you think about the spatially
homogeneous tree farm example
if we have a field where all of the
trees are the same species
and they were planted in the same year
they're all given the same amount of
fertilizer grown under the same light
conditions
there's going to be some small degree of
variability
in tree height so you want to measure
the average height of the trees across
this field
you might need to sample say 30 trees
and go around and measure their height
you can take the average and get a good
idea
of the average tree height on this tree
farm because
it's fairly homogenous they're all
essentially the same
whereas if you want to measure the
average tree height in a natural
landscape with a high degree of spatial
heterogeneity
you're going to need more samples you've
got different tree species
the trees all sprout in different years
especially if it's like an old growth
forest
you've got different soil conditions a
variety of factors that are going to
lead to trees of different heights
spread across the landscape so you're
going to need a lot more samples to
determine the average tree height in
this landscape
than this landscape and
due to spatial heterogeneity because
structure can vary widely across the
landscape
it's important to have a bit of
knowledge about your study area this is
going to help you determine what the
best
sampling method is because the goal is
to maximize returns for minimal effort
need to balance effective coverage with
the cost of collecting the data
and i mean cost not just in money but in
time and
in effort so as is often going to be the
case in this course there's no one
right answer the specific type of
sampling method that you're going to use
will oftentimes depend on the features
that you're looking at and the resources
you have
to conduct whatever analysis you're
working on
so i want to now i'm going to
briefly take a moment to talk about one
of the techniques that we can use
to exploit the special nature of spatial
data
what if we have a data set where we took
some samples
but we want to know what falls between
the samples
we can do something called spatial
interpolation to figure out
what might go this is a really simple
one-dimensional example so you've got a
string of numbers one
two four and five we didn't sample the
middle one
we want to know what's there i think we
can all
assume that it's going to be a three
if you take that to two dimensions
things get a little bit more complicated
but again you can fill in the blanks
using the patterns observed in the data
set
so this is known as spatial
interpolation
and the process of or
the process of filling in blanks in
general is known as interpolation so if
you do it over
one dimension one two three four five
that's known as linear interpolation but
if you do it over two or three
dimensions then we're going to call it
spatial interpolation essentially it's
just
intelligent guesswork where we attempt
to make a reasonable estimate of
values of a continuous field at a place
where we don't have measurements
spatial interpolation only makes sense
for a
continuous field so something
where it varies across space like
temperature or precipitation or
elevation
with categorical data like land cover
it can be a pretty problematic uh thing
to do and it doesn't work very well
the spatial interpolation works really
well with rainfall
temperature pressure most weather
observations in general
so you can use it to make estimations
between
weather stations so canada
has a network of weather stations spread
across the country
some more dense and populated areas some
more sparse especially in the north
but we can use the information from
these weather stations to
estimate the average temperature at all
spaces
at all locations across the country by
interpolating between the values at
weather stations
it can be used to measure or estimate
elevation between measured locations
and it's also used when we change
resolution of raster images
so all spatial interpolation methods
incorporate distance to known samples
and if this sounds familiar that's
because they exploit tobler's first law
of geography
closer samples are going to be given
more weight than
distant ones and a threshold is usually
set to determine the maximum distance to
take samples from
most continuous fields tend to exhibit
very strong
spatial autocorrelation so it's pretty
reasonable to assume
that values that are missing are likely
to be similar
to those that are around them in the
field
so here's just a visual example of how
you might go about doing spatial
interpolation
with elevation data there is a tool
called
inverse distance weighting where
values are interpolated
based on their distance from known
points
where the farther away
the object is the less weight it has
that is it is inversely weighted with
its distance
so you can see a one-dimensional and
two-dimensional example
of inverse distance weighting where on
the left
using it to just interpolate the
values between points on a line and on
the right we're using it to
estimate elevation across space given
a small number of samples
so i will discuss or i'll show an
example
later on in the term of specifically how
to do inverse distance weighting
in arcgis pro but i just wanted to
introduce this concept because it kind
of ties in nicely with what i've already
talked about
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