GIS and Models

8/6/2019 GIS and Models

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GIS AND MODELS

!!!! From theory to practice:

loose-coupling, tight-coupling, integration between GIS and models

GIS is

- input, storage, analysis and visualization of spatial data

- data

- people

This is a ~10ha watershed

it's dry, sandy and cultivated

Which areas are prone to erosion?

Where is it worth building terraces?

What crops will grow well in a dry year?

Is agroforestry feasible?

H ow many animals can graze here? What practices would reduce ET deficit?

H ow many families can it support?

What data is necessary for such decisions?

H ow uncertain are predictions with limited data? Can we substitute/ guess missing data?


2/17

TOWARD BUILDIN G MODELS WITH GIS

DATA DATA DATA DATA DATA

!!!! there is N EVER enough data

- budget constraints on sampling

- data from other sources is inaccessible, outdated, oddly projected, aggregated

e.g., zinc concentration in soils scatterred points

e.g., elevation contour lines

e.g., demographic data census polygons

e.g., runoff very new stations/ gauges at " arbitrary" locations

e.g., climate/ weather data at very old stations at " arbitrary" locations

e.g., rare plants/ animal observations on paper field notes


3/17

INTERPOLATION:

WH AT WE NEED WITH IN COMPLETE DATA

! interpolation: the ' art & science' of intelligently guessing attribute values

based on neighbouring ones where no data is available

! appropriate methods of interpolation ALWAYS depend on

the nature of the data statistical considerations

both (match or mismatch)

! how to consider the nature of the data

TERRAIN (elevation) characteristics

(spatial attrbutes)

elevation potential energy, temperature, soil, vegetation, viewshed

slope flow(s), erodibility, relectance aspect irradiance, evapotransipration

profile curvature flow acceleration, erosion, cultivation

upstream elements flow accumulation, watershed


4/17

METH ODS OF IN TERPOLATION

! GLOBAL methods:

regression using surrogate information (e.g., soil depth ~ distance from ridge)

classification using external information (e.g., zinc concentration ~ flood frequency)

trend surfaces (e.g., precipitation ~ slope position)

! LOCAL methods:

proximity (Voronoi, Thiessen) polygons (e.g., climate station data)

pycnophylactic methods (e.g., population)

distance-weighted averaging (e.g., elevation)

thin-plate splines (e.g., soil moisture, global climate)

! DETERMINISTIC

! GLOBAL methods:

global measures of spatial association (e.g., Moran, Geary, Getis, autocorrelation)

random simulation (e.g., noise, error) hierarchical partitioning (e.g., quadtrees and wavelets)

! LOCAL methods:

geostatistics (e.g., homogeneous covariance structure)

geostatistical simulation (e.g., sequential simulation) autoregressive methods (e.g., SAR, CAR, MA)

local indexes of spatial association (LISA)

! STATISTICAL (stochastic ~ data dependent parameters)


5/17

SAMPLING

! imagine a small watershed

contour lines barely visible (may even cross, nudge)

numbers are barely visible

take your own sample!

! sampling strategies

random

regular

stratified

transect

clustered

convenience


6/17

GLOBAL IN TERPOLATION OF ELEVATION

sample (~ 1000 points, ~ 10% !!!)(range: 1420-1489 m)

1st order 2nd order 3rd order

interpolation using global trend surfaces:

z=a+bx+cy+dx2+ey2+fxy+

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7/17

LOCAL IN TERPOLATION OF ELEVATION

TIN

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D-2 smoothed D-2


8/17

CH ECKIN G IN TERPOLATION

! RMS (root mean square) error

sum and/ or max-value... requires ~ equal number of test-sites for measurement

! cross-validation

a proportion of points predict the remaining points...

(tests the " stability" of the interpolation like the bootstrap/ resampling)

! analytical computation possible only with some stochastic methods (such as kriging)

! checking derivatives of interpolated surface


9/17

BASIC PRIN CIPLES OF STOCH ASTIC IN TERPOLATION

!the impactof neighbours

the value at location-s is a function of its neighbours: z(s)=a+q(s)+wi the " trick" is how to determine the weights (wi)

and

if we want ONE " likely" output or many of them...(e.g., the likelihood of zinc concentration above critical threshold)

distancedistance

weightweightlinear

spherical

exponential shapes of the weight vs. distance functions

which determine the decreasing correlation

between neighbouring values

there are fairly strict mathematical conditions on the

spatial autocorrelation function

built on these geostatisticalfoundations 'kriging'

has become popular as the BLUP (best linear

unbiased predictor)


10/17

(NON -SPATIAL) ATTRIBUTE OPERATIONS

!towrd building models, consider what to do once you have the values...

ARITH METIC/ NUMERICAL operations

" CALCULATOR" (+/ - sin cos log) ... ! numerical output (as per number representation)

MEASUREMENT LEVEL/ DATA TYPE operations

NOMIN AL, ORDINAL, IN TERVAL...!

take care of information available (problems?)

UNIVARIATE STATISTICAL operations

MIN, MAX, AVERAGE, VARIAN CE... ! the art of summaries

MULTIVARIATE STATISTICAL operations

CLASSIFICATION, PCA... ! many variables, but still non-spatial

TRUE/ FALSE, AND, OR, XOR, NOT...! binary output (after logical " if" )

LOGICAL operations


11/17

NON-SPATIAL ATTRIBUTE OPERATIONS IN IDRISI


12/17

A SIMPLE SOIL SUITABILITY MODEL:

BASIC FORMULATION

! Areas are suitable for cropping if there are enough nutrients, enough moisture and there is

no high erosion hazard..."

! S = f(nutrients, moisture, erosion)

nutrientsnutrients: reclassifyfrom soil classes [N ote: gross spatial averaging]

erosionerosion: reclassifyfrom slope [N ote: limited sensitivity]]

moisturemoisture: accumulatefrom elevation and aspect [N ote: truly spatial component]


13/17


NUTRIENTS


nutrientsnutrients: reclassifyfrom soil classes [N ote: gross spatial averaging]

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14/17


MOISTURE


moisturemoisture: accumulatefrom elevation and aspect [N ote: truly spatial component]

accumulation is far from trivial; it is a function of neighbourhaccumulation is far from trivial; it is a function of neighbourhood size and redistributionood size and redistribution

ln(a/ tan())


15/17


EROSION


erosionerosion: reclassifyfrom slope [Note: limited sensitivity]]

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16/17

SOIL SUITABILITY MODEL PREDICTIONS

! simple Boolean (binary): if no limitation value is greater than 2

! semi-continuous suitability...


17/17

A NOTE ON ERROR PROPAGATION

CATEGO RICAL NUMERICAL

RASTER

VECTOR

LAYERS

va riab les ...

LATTICES

POINTS

GEOSTAT

REGULAR

!everything is related to everything..." : there is usually high cross-correlation between data sets errors CAN be concentrated and carried over (warning for logical operations!)

nobody likes to make BIG mistakes (on average? or locally?)

choosing the APPROPRIATE statistical framework can be difficult

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