Transcript Point and Spatial Analysis

Point and Spatial Analysis
• 1. virtually all measurements are “point
values”
– that is to say: they are a sample of a larger
population, methodologically, geographically
and temporally taken to “represent the larger
population”
– A snow course is typically 5 point measures
which are averaged to a single numeric value
for depth, SWE and density.
What is it we really want?
• The total population! We would like to
know exactly how much SWE is on every 1
meter square surface area of the watershed
–
–
–
–
how much energy that spot receives
how much SWE is lost
how much infiltrates
how much becomes surface runoff
• Of course this is impossible so we take what
we assume are representative samples
Why?
• One point sample does not adequately
represent all the complex processes on a
watershed
• variability: snow, precipitation, vegetation,
aspect, soils, impervious areas, management
practices, etc all contribute to variability in
runoff (typically our desired outcome)
• Runoff is the integrator of all processes on
the watershed- the sum of everything
more y
• since runoff is the integrator, and it is
prohibitive to sample the total picture, we
take what we can (points: disintegration)
and try to (by our knowledge of processes
and the physical aspects of our watershed)
put as close a picture as we can of the whole
watershed by expanding our point data to
wider application
How representative?
• This single value, say for SWE is a total of
8.63 sq inches of sample - about 0.06% of a
sq foot. On a 100 sq mile watershed, this is
0.0000000000215% of the total area.
• Given that snowpack is extremely
heterogeneous due to:
– variability in precipitation, redistribution via
wind, etc, ablation, variances in solar radiation,
interception due to vegetation, sublimation, etc.
not much of a sample
• True - snowpack is extremely variable
• True - there are many different processes on
our watershed variable in time and space
• BUT: relationally, the snowpack correlates
very well with streamflow in SNOWMELT
dominated watersheds
• WHY: it is the overwhelmingly dominant
process in many areas
where it falls apart
• ephemeral snowpack areas
• these are the areas of transient snowpacks
that form and melt several times each year,
low elevation watersheds, southern latitudes
such as the southwest, etc. In these areas,
other factors are as important or more so
than the snowmelt factor.
a little better on the pillows
• one hypalon pillow has a surface area of
about 70 sq ft. This then becomes
0.000000025% of the watershed... several
orders of magnitude greater than a snow
course, but still a very small percentage of
the desired outcome.
one sample to represent all?
• How can just one course represent an entire
watershed?
• IT CANT.
• HOWEVER - we cannot physically
measure the entire snowpack or even a
substantial portion of it at any given time.
• SO - WHAT TO DO?
Relational characteristics
• A point measure is always relative to other
points and or variables
• As long as these other points and variables
are reasonably consistent in time and space,
relative to the index measure (the sampled
point) - then the index point is
REPRESENTATIVE of much larger areas.
• Many areas of the snowpack exhibit these
kinds of characteristics.
Relative or Relatives, its always
one or the other
• Over the course of an entire accumulation
and ablation season, many of the same types
of meteorological phenomena occur – not always in the same sequence
– not always in the same magnitude
• however - typically holding close to the
same proportion or relationship to the
indexed value, thus (again, over the course
of a season), various points are stable.
implications
• What this means is the potential to
interpolate point data to a spatial scale.
• more data are necessary than just the
indexed hydroclimatic value to extrapolate
to another point.
• The relationship between the 2 (or more)
points must be clearly understood.
• this relationship is 2 dimensional - time and
space
A relationship with 2 always ends
up hurting one
• The TEMPORAL view
– temporal simply means time
– when an observation is taken, it is like a
snapshot of the current condition.
– a collection of snapshots or observations from a
specific location is called a temporal
distribution or time series.
• The relationship between 2 or more points
differs not only in space but may vary
significantly in time as well
Temporal variability
• This temporal variability adds another kink
into what we all hoped would be a very
simple solution.
• temporal variability in a relational context
makes the system much more complex
because there is not only space to consider,
but the changing relationship with time. Not
impossible, but difficult.
Fortunately
• many variables such as snowpack show
very strong relationships in space and tend
to be consistent in time as well
– can be a static change in time such as when a
low elevation site has melted out (constant
zero)
– things that affect the relationship (temporally)
• abnormal storm patterns, very cool or very warm
late season temperature or, in fine: the extremes of
any type or source.
time - does anybody really know
what time it is?
• variables may have strong relationships at
particular times and not at others
– i.e.: over the course of a season, precipitation or
SWE may have a strong relationship but on an
individual storm or event basis, it may be a
fairly weak relationship thus:
• Time step or scale is a factor of concern that
may or may not be consistent from one
scale to another
longer can be good
• Typically, the larger the time step, the
stronger the relationship:
– annual precipitation correlates stronger than
does daily
– peak SWE correlates stronger than event data
• smaller time steps are subject to all kinds of
meteorological variances that, over a season
tend to average out
STOOPID
• many times, researchers have gone to even
longer time steps and methods to come up
with cyclical or other phenomena
– great care should be exercised when taking a
time step greater than 1 year or a specific
season
– comparing centurial precipitation on a
watershed basis does not make sense, although
I suspect the relationship will be strong:
between any watershed on earth!
larger time steps
• the greater the time step, the smaller the
resolution and of course the less
information can be determined by the
investigator
• time step smoothing has been used (the
practice of replacing a specific observation
with a moving average (3, 5 year) is
common to dampen individual extremes in
climatic variability studies.
smaller time steps
• 1) one cannot resolve smaller time steps
than the most coarse observation available:
(Von Leibig’s law of the minimum)
• this is the typical case- an exception:
– temperature data: relatively well behaved and
can be modeled to a lower scale with some
accuracy (typically due to the longer term and
delayed nature of snowmelt with respect to
temperature and smaller variances in extremes
caution
• When taking temperature to a smaller time
step, there is no guarantee that anomalies
won’t mess the whole thing up
• for most circumstances, it is the extremes
that we are most interested in, not the
normal!
• It is at these levels that a model is most
likely to perform the worst!
time out!
• If you have you have 4 variables: SWE,
snowmelt, temperature and precipitation.
Of these, you get any 3 in an hourly timestep and one in 6 hourly increments - then
you would typically model to the 6 hourly
increment.
• That is the limit of your data!
• Exception: if the variable can be
successfully modeled by the other variables.
Resources
• A small note on resources:
– as the time step for data collection decreases
toward “event data”, the resources required for
collection, processing, quality control and
archival increase exponentially!
– likewise does the resources required to model at
small time steps. One person can run hundreds
of seasonal models. It takes many persons to
run a model at the hourly time step! Do be
careful what you get into!
Space, the final frontier!
• Back to the objective: we want to know all
about each variable on every part of our
watershed
• Scale in space again becomes critical
• In order to effectively interpolate/estimate
other points on our watershed from our
single point of reference, we must know the
relationship between our measured point
and every other single point.
How spatial problems were
handled yesterday
• In the old days, like today! - there wasn’t
much that could be done- limitations in
resources was the single greatest reason
why distributive watershed modeling was
not feasible except on a very limited
research scale. There are very few
extensively instrumented research
watersheds with long term records:
Reynolds Creek, Silver Creek, Niwot
Ridge, etc.
continued
• The choice of scale to work with is critical
and is dependent on the physical
characteristics of the watershed, the
availability of relational data and their scale
(you cannot work at finer scale than the
relational data that are available - you can
always go to a larger scale, but not a finer
scale)
Projecting precipitation data to
the watershed level
• Old Fast and Easy: a simple arithmetic
average of all sites
– advantage: simple and fast, works well in flat
areas with gages that are uniformly distributed
and individual gage catches do not vary widely
from the mean of the total group.
– disadvantage: does not represent
topographically diverse watersheds nor the
processes occurring thereon.
Theissen Method
• The Theissen method was developed in
SLC by an NWS Meteorologist named,
oddly enough, Theissen.
• It attempts to allow for the non-uniform
distribution of gages across a watershed by
providing a weighting factor for each site
based on it relative areal representation of
the watershed
Theissen continued
• The stations are plotted on a map
• The dots (stations) are connected by lines
• perpendicular bisecting lines of these
connecting lines form polygons around each
station.
• These polygons are assumed to be the
relative contributing area of each gage.
• The areas of each are determined and its
percentage of the total is its weight
Theissen: pros and cons
• Non uniform distribution of gages across a
watershed or several watersheds may mean
that any single station may have a much
higher weight than it in reality deserves.
• does not take into account the orography of
complex terrain, no physical context except
that of dividing the watershed
proportionately to each gage
Theissen: more cons than pros
• Thought to be more representative than
simple arithmetic averaging, except again in
the complex terrain. (how do you prove the
assumption of representation except by
catching the entire event?)
• assumes linearity of variables between
stations
• Inflexible - new weighting diagram for
every change in data collection network
Isohyetal method
• This method was widely regarded as the
most accurate of any method used
• Station locations and the amount of
precipitation was plotted on a suitable map
• contours of equal precipitation (isohyets)
are then drawn.
• The average precipitation for an area is
computed by: go to next slide please
isohyets: now you know why GIS
is Big, Really BIG
• weighting the average precipitation between
successive isohyets (usually taken as the
average of the 2 isohyetal values), by the
area between the isohyets, totaling these
products and dividing by the total area.
• This method permits the use and
interpretation of all available data, all
orographic features and storm morphology
isohyets: will the pain ever end?
• Yes Virginia, there is a Santa Claus:
however
• this method is highly dependent on the
individual analyst
• it is time consuming
• is usually done in the past tense- as a
research tool, not generally done in the
present as a modeling or forecasting tool
• linear interpolation between sites yields the
No, the pain continues
• The knowledge to use this method
successfully is not easily transferred from
person to person
• still subjective - who can prove it is better
or worse than the simple arithmetic average
– in theory, of course, it makes sense and the
concepts of orography proven. In any given
circumstance there is a huge potential for
mistakes.
The foreshadower of things to
come
• The true pain comes with the analysis of
each and every watershed and choosing
(again) a scale to work at. Then comes the
data processing, it was not easy nor
convenient. Lots of map work with a
planimeter and bifocals.
• The concepts of the isohyetal method are
used today, but with more modern
processing
back to scales - for just a moment
• For example: if your map or digital
elevation model has an elevation scale of
40’ per interval, then that typically becomes
your smallest potential scale to work at.
Going below that interval gives you no
relevant information about your watershed.
Because the distance between 2 contours
may not be linear, you may not assume a
50/50 split between contour lines.
more scales: practice them every
day
• Horizontal scale: depends on your maps or
DEM’s accuracy - typically a 1 to 24,000
topo map will be accurate in 2 dimensional
space (everything but elevation) to within
1/4 mile. Some DEM’s will have better
spatial resolution. Right now, working at a
100 meter scale is about the lower limit of
functionality and the 1 kilometer scale is far
more common.
A 1 K scale?
• 1 kilometer scale is still relatively crude but
is a quantum leap from a model having a
200 sq K area and 2 areas split by elevation
zones.
• The recent advances in GIS technology and
the digitizing of elevation models (DEM’s
or digital elevation models of 3 dimensional
surfaces) have brought new methods to
modeling of hydroclimatic variables
back up just a moment
• Up to now, if you wanted to include
information about spatial features in a
model, you had to calculate each of the
parameters for each and every block by
hand, a prohibitively expensive
undertaking. Thus, it simply was not done,
except at the expense of poor graduate
students. All models were run on a space
averaged basis and typically on a
temporally averaged basis
complex terrain
• Physical and geographical features of any
watershed can be very complex. These
features can have significant impacts on the
accumulation and ablation of snowpacks
– avalanche runout zones
– windswept ridges and other wind scour features
– cornices and other deposition/accumulation
areas
– aspect and snow accumulation/retention
A great new dawning... gag gag
• With DEM’s, tons of information critical to
spatial relationships has become available!
–
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more precise elevation
aspect (north, south, east ,west and in between)
slope
area (of any give segment)
• All this relational data can be used in
correlation with our single point reference
for example
• Calculating the theoretical energy input
from short-wave radiation for every parcel
for any give day now becomes very easy to
do!
– given this, replicating the seasonal
accumulation and and ablation of a snowpack
becomes much easier. The modeling output
actually LOOKS like what is happening on the
watershed and replicating observation is the
first thing a distributed model should do.
New stuff
• Given the DEM, and the knowledge of the
physical processes of the snowpack
(relational inferences), we can now
extrapolate data from our reference, the
SNOTEL or snow course to other points
with much greater accuracy
– elevational relations: determined from the
correlation of our reference to other stations at
higher/lower elevations with the same aspect
more relations
• Correlation can be made from our reference
site to other locations at different aspects
• correlation can be made from other sites
from similar watersheds in close proximity
about hydroclimatic variables with regard to
aspect and elevation.
• With 4 or 5 stations in close proximity, a
pretty decent snow covered area and
reasonable extent of SWE can be modeled
temporal changes
• given our knowledge of snowmelt and the
dominant heat sources - (short wave) we
can with relative accuracy, calculate the
theoretical difference in energy input
between our point and other points on the
watershed
• Given several points, high and low, we can
model with relative accuracy sensible heat
inputs to the pack instead of using lapse rate
Boundary conditions
• all changes of state depend on accurate
initial and boundary conditions. That is to
say, we must be accurate on our total SWE
and SCA at the point of melt onset in order
to accurately simulate any point in the melt
sequence. If we are not, then we run out of
snow too early or too late (assuming our
melt process is accurate)
Other data
• to a lesser extent, other data are available
that can help in our quest for the total
watershed approach:
– vegetation data: such as forested and non
forested areas.
– forested areas are subject to interception losses
throughout the season. They also typically
occupy the northern and eastern aspects in Utah
geography, which hold snow longer.
veggies
• the vegetation data available are typically
the forested/non forested binary approach:
– they give us little in the way of : species, age,
height, density, canopy area, etc. these other
factors play a major role in our snowpack over
time. How much is intercepted is a function of
canopy area which is a function of species.
Canopy area also limits incoming solar
radiation
more veggies
• stand density: determines how much long
wave is radiated back to the pack from that
which is allowed in from the canopy
• stand species determines whether the
foliage goes to ground level or is attenuated
high above surface level - which, in turn is
relative to the long wave radiation situation.
Vegetation
• Although we have a great deal of point
research on vegetation data and its
relationship with snowpack, we have very
little knowledge of how to apply these data
outside of the area in which they were
observed - thus vegetation data for the time
being, are still a lumped parameter - a sink
variable which accounts for all processes
that we cannot yet accurately model.
So, whats the point
• Often in snow hydrology, we want to know
more than just a seasonal outcome such as
April - July aggregate streamflow. We wish
to know what the monthly hydrograph will
look like or what weekly volumes to expect.
Possibly we want to know daily and hourly
events as well. The operation of dams,
flood control, the extent and duration of
both high and low flows and other variables
Point and counterpoint
• In order to model these parameters within
any semblance of reason, greater knowledge
of the snowpack is required. The total
amount available for melt, melt rates, loss
rates (that water lost to the runoff system
via any of many mechanisms), energy input.
The finer the spatial and temporal scales,
the more potentially accurate the prediction
of these parameters.
Brave new world
• Most of the models in use today use old
(tried and true) but outdated techniques lumped parameter modeling
• because of the relational aspect of
snowpack, most of these models work
relatively well.
• The new modeling age should replace these
older models with physically based GIS
information.
Reality Check Please
• Most of these models are relatively new
• They still depend on assumptions
• They still depend on point data and the
relationships between the points
• Potentially far more accurate that a
single/double area lumped parameter model
• Other data such as point specific soils
information (type, soil moisture/temp) still
lacking and will be costly to gather.
other data
• many other variables in watershed modeling
are still missing: evapotranspiration,
infiltration curves for each point, ground
water recharge, consumptive use,
diversions, storages, lake/reservoir
evaporation, channel losses, all contribute to
the total error in any model.
distributed spatial modeling
• With GIS, we can now realistically model
complex storm events as well as the
subsequent processes of ablation not
possible with previous methods. With the
Isoheyetal and Theissen methods, we could
painfully distribute a storm SWE or precip,
but not the subsequent ablation process.