Field Sampling Methods, Error, and Limitations in Remote Sensing

1
Field Sampling Methods, Error, and Limitations in
Remote Sensing
Our ability to asses the accuracy of remote
sensing products is largely determined by our
ability to validate remote sensing estimates with
accurate ground measurements.
2
Outline

• Field sampling methods
• Quadrat sampling
• Plotless density estimators
• Estimating error
• Pilot study
• How many plots?
• Measuring LAI or biomass
• Destructive sampling
• Allometric relationships
• Gap fraction sensors
• Relating ground data to RS data
• Regression
• Error Propagation into Land Surface Models

3
Field Sampling Methods

• Questions
• How many? Density (/per unit area)
• What kind? Identification
• Characteristics? Size, shape, cover, etc..

4
Field Sampling Methods

• Quadrats plot of a fixed size in which density
  of objects can be measured. Ancillary information
  such as type of objects, size and shape can be
  measured as well.The plots are usually circular
  or square in shape but can be other shapes as
  well. The main goal is that we want to know the
  number of objects per unit area (density).

5
Field Sampling Methods

• Considerations in Quadrat Sampling
• What shape should the quadrats be?
• Choice for the shape of a quadrat is generally
  associated with the ease of implementation and
  has minimal impact on the results of the
  sampling. For example, it may be easier to
  delineate a circular plot in low lying vegetation
  using a center post than walking out the
  boundaries of a square plot.
• What is the difference between a square plot
  with X m2 area and a circular plot with X m2
  area?

6
Field Sampling Methods

• Considerations in Quadrat Sampling
• 2. What Size should the quadrats be?
• The size of the quadrats in relation to the size
  of the objects measured is a critical
  consideration. Choosing quadrat sizes that are
  too small with regards to the size of the objects
  being measured will negatively affect the
  sampling precision and accuracy while choosing
  quadrat sizes that are too large will result in
  excess work.

7
Field Sampling Methods

• Considerations in Quadrat Sampling
• 3. How should I distribute the quadrats over the
  area of interest?

Stratified random
regular
subjective
random
8
Field Sampling Methods

• Considerations in Quadrat Sampling
• 4. How many quadrats should I place in the area
  of interest?
• The number of quadrats along with their size are
  the most important of the considerations. In
  terms of experimental design, each quadrat (plot)
  is treated as a replicate. The more replicates
  the better in terms of increasing the precision
  of estimates. We will return to this topic later
  in the lecture

9
Field Sampling Methods

• Plotless Density Estimators (PDE)
• Plotless density estimators (PDE) were developed
  in order to overcome the limitations of fixed
  plot sampling strategies as well as reduce the
  amount of man-hours necessary for sampling. There
  are no fixed plots to delineate. In contrast to
  quadrat techniques which measure the number of
  organisms per unit area, PDEs attempt to
  estimate the mean area per organism, the inverse
  of density. This allows for the use of spacing
  between organisms to be used in determining mean
  area per organism. Consequently, density can be
  calculated given the mean distance between
  organisms (Cottam and Curtis 1956).

10
Field Sampling Methods

• Plotless Density Estimators (PDE)
• The mean distance between organisms is determined
  either by measuring the distance from n random
  points to the rth closest organism (closest
  individual methods) or by measuring the distance
  from one organism to its rth closest neighbor
  (nearest neighbor methods). In addition to
  density estimates, ancillary data such as the
  type, size, shape, etc..of organisms can be
  recorded.

11
Field Sampling Methods
Example Closest Individual Methods (Point
Center Quarter)
Mean area per organism (mean distance to
nearest r individuals)2
Density unit area / mean area per organism
12
Field Sampling Methods
Example Closest Individual Methods (Variable
Area Transect)
Distances measured while walking transect r 3
x
Randomly located sample point along transect
x
Density nr 1/ (w ? xi )
Where n number of sample points. r number of
distances between organisms measured at each
sample point. W width of transect. Xi
distance between organisms
13
Field Sampling Methods

• Comparison of Quadrat Vs. PDEs

• Quadrats
• Designed for more intensive measurements over
  smaller spatial extent
• Can be made permanent so you can revisit
  location (good for change detection?)
• results are dependent on the size of quadrat in
  relation to organism size and spatial
  distribution of organisms.
• PDE
• Suitable for less intensive measurements over
  larger spatial extent (RS) Measurements are quick
  and you can cover a lot of area.
• Assume random distribution of organisms (error
  in estimates increase as distribution becomes
  less random)

14
Estimating Error

• Question How much error is in my estimates and
  how can I reduce the error?

Precision, sensitivity, or amount of information
of a sample is measured as the reciprocal of the
sample variance of a mean   I 1 /
s2y n / s2 (1)   Where I
precision s2y the sample variance of a mean
s2 the sample variance n number of
samples   From equation 1 it is apparent that as
sample number increases in the numerator,
precision increases. Similarly, the sample
variance (s2 ) in the denominator is inversely
proportional to the sample size and decreases as
sample number increases.
15
Estimating Error

• Accuracy is associated with the concepts of bias
  or systematic error in measurement and is
  influenced by the procedure of taking
  measurements or the instrument of measure itself.
  While precision increases with larger sample
  sizes accuracy does not necessarily follow in
  suit.

16

Estimating Error
Question How many samples (quadrats or PDE
samples) should I measure to achieve a certain
level of error? required sample size at a given
sample error level is determined by n ( s t
/ e )2 (2)  where n sample size s
standard deviation of samples t t value for a
two-tailed test with n-1 degrees of freedom at
the 95 confidence level. e acceptable
error in terms of a percent of the mean  How do
you know what the standard deviation is when you
have not sampled yet? Pilot Study go out
and determine how variable the system is
beforehand.
17
Estimating Error

• Question If Ive already sampled an area, can I
  determine the error associated with my estimate
  of the mean?
• Equation 2 can be rearranged to solve for the
  estimated error level (e) at a given sample size
    e s t / (n)1/2

18
Measuring LAI or Biomass

• Remote sensing estimates are only as good as the
  ground measurements they are related to

Question How can we quantify the LAI or biomass
within a given area? How good are these
estimates?
19
Measuring LAI or Biomass

• Destructive Sampling
• In short-stature ecosystems (e.g. agricultural
  crops, grasslands, shrublands) direct estimates
  of leaf area can be obtained using area
  harvesting. Area harvesting involves the
  destructive sampling of vegetation within plots
  located within a vegetation community. The
  widespread utility of this method is limited,
  however, by the labor-intensive nature of these
  types of measurements as well as the number of
  plots needed to capture the spatial heterogeneity
  of a particular ecosystem.

20
Measuring LAI or Biomass

• Allometric Methods
• Allometry relates the size of one structure in an
  organism to the size or amount of another
  structure in the same organism.
• Example the diameter of a trunk of a tree is
  related to the amount of leaf area or biomass in
  the tree. Trunk or stem diameters are relatively
  easy to measure while leaf area is not.

21
Measuring LAI or Biomass
22
Measuring LAI or Biomass

• Developing allometric equations related to leaf
  area and biomass for a particular site requires
  destructive sampling.
• Consequently, investigators commonly use
  published allometric equations for specific plant
  communities. Unfortunately, allometric
  coefficients vary between sites and species due
  to a number of environmental variables. As a
  result, the use of generalized equations can lead
  to significant errors in vegetation parameter
  estimations. Grier et al. (1984), cited in Gower
  et al. (1999) found that generalized allometric
  equations produced errors in biomass estimates
  ranging from 8 to 93 as compared with
  site-specific equations.

23
Measuring LAI or Biomass

• Indirect techniques Gap Fraction Sensors
• Indirect methods of estimating LAI include canopy
  gap fraction measurements which are based on an
  interactive relationship between canopy structure
  and radiation interception. These optical
  techniques measure the gap fraction, i.e. the
  proportion of transmitted light which is not
  blocked by foliage in a band of azimuthal
  directions. Leaf area is then estimated using
  canopy models with the gap fraction as an input
  parameter.

24
Measuring LAI or Biomass
Extinction coefficient
Fraction of incident beam radiation from a
specific zenith angle that penetrates the canopy
Solve for this
Assumes random distribution of leaves and no
light interception by woody elements! This is
often not the case.
25
Measuring LAI or Biomass

• Indirect techniques Gap Fraction Sensors
• It is estimated that violating the random foliage
  distribution assumption can lead to errors in LAI
  estimation in excess of 100 (Fassnacht et al.,
  1994).

26
Measuring LAI or Biomass

• A comparison of direct (area harvest and
  allometry) and indirect (gap fraction) estimates
  of LAI across a wide variety of ecosystems showed
  that the two methods compare to within 25-30 for
  most canopy types (Gower et al., 1999).
• This is badSo in terms of taking ground
  measurements of LAI or Biomass for forests, there
  is lots of potential error

27
Relating Ground Data to Remote Sensing Data

• Question Given the potential error in ground
  measurements, how can we validate remote sensing
  products?
• Well, good question. Im not certain I have the
  answer but we can re-evaluate what we currently
  do now.

28
Relating Ground Data to Remote Sensing Data

• Linear Regression
• Linear regression assumes that we know the
  independent variable (ie. we dont take into
  account error in our estimate of the independent
  variable). This is problematic in that we often
  treat ground measurements as independent
  variables and RS data as dependent variables. Our
  uncertainty levels for ground based measurements
  are often much greater than the uncertainty
  levels from RS data.

29
Error Propagation into Land Surface Models

• Given the increased reliance of land-surface
  biophysical and biogeochemical models on remote
  sensing inputs, a logical question is How
  sensitive are these models to errors in estimates
  of LAI and NDVI? There are surprisingly few
  studies that address this question explicitly
  despite the importance of this type of analysis
  in assessing the accuracy of model predicted
  estimates of biospheric function.

30
Error Propagation into Land Surface Models

• The sensitivity of a coupled biosphere-atmosphere
  model (NCAR CCM2 - BATS land surface
  parameterization) to global changes in LAI was
  examined by Chase et al. (1996). A global
  decrease in LAI of 20.8 resulted in a 12.1
  increase in sensible heat flux and a 4.8
  decrease in latent heat flux in the months of
  January and July.
• In a similar study, Bounoua et al. (2000)
  examined the sensitivity of a coupled
  biosphere-atmosphere model (SIB2-CSU GCM) to
  maximum and minimum distributions of NDVI
  determined from an eight year period of satellite
  records. They showed that a 0.1 absolute increase
  in NDVI (approximately 17 relative difference)
  resulted in a 46 increase in FPAR, a 42
  increase in gross photosynthetic CO2 uptake, and
  a 1.8K cooling in the northern latitudes during
  the growing season.

31
Error Propagation into Land Surface Models

• Asner (2000) explicitly examined the effects of
  potential remote sensing error on the CASA model.
  After determining a plausible range of NDVI
  values from a perturbation analysis, he showed
  that annually estimated values of NPP from the
  CASA model showed significant sensitivity to
  NDVI, with errors of up to 30 in modeled NPP
  values due to plausible errors in NDVI
  estimation. Similar results were reported by
  Kaufman and Holben (1993) who showed that NDVI
  errors of only 5 caused by instrument
  calibration resulted in errors up to 30 in
  annual NPP estimation.