Abstraction Techniques for
Simplification of Environmental
Models
Yakov Pachepsky, USDA

ARS
Origin of Model
Simplification
C. F. Chen and L. S.
Shieh
. A
novel
approach to linear
model simplification. International Journal of Control,
8(6):561

570.
1968
.
The first comprehensive analysis for
environmental modeling
Meisel
, W. S. and D. C.
Collins
.
1973.
Repromodeling
in the Practical Utilization of
Complex Environmental Models
.
IEEE Transactions on Systems, Man, and
Cybernetics SMC

3:
349

358.
The first comprehensive discussion of advantages
of using
simplified models
in environmental modeling:
they
are
less expensive
to use; such savings will permit more thorough
analysis for a given analysis budget;
they
have
fewer input
requirements;
they
are
easier to
transfer and/or
combine
with other models;
they
are
easier to interpret
; it is easier to understand the properties of and
results from a model with a small number of state variables and parameters
than the properties and results of one with more.
Siri
The first summary of model
simplification techniques
Zeigler, B
. Theory
of modeling and
simulation
.
New York, New York: Wiley and Sons, 1976.
The first summary of model simplification
techniques.
Main categories
of the model abstraction
techniques
:
dropping
unimportant
parts of the model,
replacing
some part of the model by a
random variable
,
coarsening
the range of values taken by a variable,
grouping
parts of the model together.
Future Combat System
Most cited
Innis
, G.,
E
.
Rextad
. Simulation
model simplification
techniques.
Simulation
, 41: 7

15, 1983
.
Rextad
, E.,
Innis
, G.S. Model simplification
–
three applications. Ecological
Modelling
, 27: 1

13. 1985
.
Model
simplification techniques suggested
for main
steps of model development
Hypotheses
Formulation
Experiments
System organization
(conservation,
self

organization)
Filtering
(scale selection)
Stochastic features
(random perturbations)
Graph theory
(highly
interactive
subsystems)
Sensitivity

based
(aggregation,
e
limination)
Structure analysis
(modeling artifacts)
Analysis of dimensions
(
unitless
variables)
Metamodeling
Time scales of
subsystems
Analytical
solutions
Interdependencies
among parameters
Linearizations
Direct calculation
of output
moments
Variance
reduction
(correlations)
Linear
systems
(PCA, EOF)
General taxonomies in 1990s
Model abstraction techniques
Model boundary modification
Model be
havior modification
Model form modification
State
Temporal
Function
Entity
Explicit
Derive
d
Hierarchy
of
models
Limited
Input
space
Appro

ximation
Selection
by
influence
Sensitivity
analysis
Causal
influences
Look

up
table
and
interpo

lation
Probabi

lis
tic
input
Metamo

deling
Unit
advance
Event
advance
By
function
By
structure
Behavior
aggrega

tion
Causal
decom

position
Aggregation
of cycles
Numeric
represen

tation
General taxonomy of model abstraction techniques after
Fishwick
(1995),
Caughlin
and
Sisti
(1997)
and
Frantz (2002).
Emphasis on discrete event models
Model simplification:
status around 2000
(
Chwif
,
Barreto
and Paul, 2000)
The
scarcity of research
into simplification in simulation is surprising,
despite
the importance of the subject
.
Proliferation
of complex and large
models created problems requiring
special
technologies
to express
, validate
, solve
and understand the results of
complex models
–
modeling became a young again area.
Model complexity
not only
has an impact
on computer performance,
but
also on
all aspects
of simulation
modeling
, such
as.
managing
a simulation project
, communication time, resource
constraints, etc
.
Model complexity has
two aspects
: (a) related to the user perception/model use
and (b) related to the model structure and to the details of modeling.
It has been realized that:
Model simplification:
status around 2000
Where an extraneous complexity may come from?
Technical factors
Lack
of understanding of the
system
:
complexity comes as crutches.
The
lack of ability to model (or
abstract
)
correctly the
problem
causes building models
"as close to
reality
as
possible”
Unclear
simulation objectives:
this
is one factor that
contributes the
most
to the growth of complex
models
.
Human nature
"
Show off" factor:
A complex model
when shown
to
managers has more
impact
than a simpler
one.
“Better safe than sorry” syndrome.
Include as much as you can.
“Endless possibility
" factor
:
complexity
and size is
not a constraint on building a
simulation
model anymore.
“Structure and function”
Focus on the
system itself and its structure rather
than on the system function and purpose.
Advantages of simple models
Bigelow and Davies (2003)
A significant part of our knowledge of the world is low

resolution.
Both
the strategy

level analysis and the decision support typically require relatively
simple models
Decision makers need
to reason
about their issues and inject their own judgments
and perspectives.
Strategy

level problems usually are characterized by massive uncertainty in many
dimensions. The appropriate way to address such problems is often the
exploratory
analysis
in which one examines issues across the entire domain of plausible initial
states. Simple models are ideal for such analysis.
Simple models require much
smalle
r amounts of the experimental data, much
less
time and efforts for data preparation and post

processing.
Analysts and end users can
quickly comprehend
simple models and their inputs and
outputs.
1. Recognition that the multiplicity of models
is a norm
Heterogeneity of environmental systems is easy to perceive,
but difficult to represent in mathematical terms
Equifinality
Complexity of a model does not necessarily correlate with the
model accuracy
If a complex model is created, the efforts to simplify its code
could be unworthy.
Depends both on system and the model
It may be easier to change the structural units as a part of a model of subsurface flow
and transport.
It is usually much more difficult to change the process descriptions in the model.
Current developments. 1. It is beneficial to use
simple and complex models jointly.
Van Ness, E.H. and M.
Scheffer
. 2005. A strategy to improve the contribution of complex
simulation models to ecological theory. Ecological
Modelling
, 185: 153

164.
Why a complex model
can be hard to understand
Using complex and simple models jointly
via model abstraction
If you cannot beat ‘
em
, join ‘
em
The simple models is
obtained by simplifications
or
developed independently
. This simple model
has to describe the dominant mechanisms
of the full model.
The simple model can be used to explain and
communicate the causes of the phenomenon clearly
The complex model can help to substantiate that
the produced patterns are no artifact of the
Simplifications.
Example of joint use of complex and
simple soil water flow models. A. Problem.
Richards soil water flow model
(coded in HYDRUS) calibration
Failure to
s
imulate soil water fluxes
with the Richards equation
Passive capillary samplers
to measure water fluxes
Time domain
reflectometry
probes
to measure soil water
contents
Richards model was highly accurate;
RMSE = 0.0058 cm
3
cm

3
, R2=0.834
Example of joint use of complex and
simple soil water flow models. B. Solution.
Schematic of the modeling soil water
flow with the MWBUS model.
Soil water flow model (MWBUS)
calibration
MWBUS model was fairly accurate;
0.0072 cm
3
cm

3
,
R
2
=0.74
Successful simulation of soil
water fluxes with the soil water
budget model
The errors in modeling water fluxes appeared
because the best fit with the inverse modeling
for Richards equation model
required
simulation of the substantial surface runoff
during large storm events. No runoff was
observed at the site
The model abstraction from the Richards model
to the MWBUS not only provided a reasonable
estimation of the soil water fluxes as the key
output, but also served as a “sanity check” giving
an indication that the Richards model was
optimized in the wrong domain of its parameter
space.
Current developments. 2. Each research or
engineering field has its own set of model
abstraction/simplification methods
Abstraction of the model structure
Abstraction of parameter determination
Metamodeling
Hierarchy
of models
Limited
input
domain
Scale
change
Upscaling
Aggregation
Discretization
Scaling
Pedotransfer
Model abstraction
Abstraction of the model structure
Abstraction of parameter determination
Metamodeling
Hierarchy
of models
Limited
input
domain
Scale
change
Upscaling
Aggregation
Discretization
Scaling
Pedotransfer
Model abstraction
Categories of model abstraction techniques relevant to flow and transport modeling
in subsurface hydrology (NUREG/CR

6884, available at the WWW)
Examples of process description hierarchies
Single
conti

nuum
Equivalent
matrix and
fracture
continuum
Dual porosity
Matrix
Fracture
Matrix
Fracture
Dual
permeability
Discrete
fractures
without
matrix
Discrete
fractures
with
matrix
Water
budget
Relative
permeability
Pressure head
Complexity
Model abstraction
a
b
c
d
e
f
g
Single
conti

nuum
Equivalent
matrix and
fracture
continuum
Dual porosity
Matrix
Fracture
Matrix
Fracture
Dual
permeability
Discrete
fractures
without
matrix
Discrete
fractures
with
matrix
Water
budget
Relative
permeability
Pressure head
Complexity
Model abstraction
a
b
c
d
e
f
g
Hierarchy of models to simulate water flow and solute transport in structured soils or in unsaturated fractured rock
( modified from Altman et al., 1996)
Hierarchy of models for soil water content accounting in watershed modeling ( modified from
Bai
et al., 2009
)
Why we may want to use a simpler model?
The base model includes a complex description of processes that
cannot be
observed well
, but still needs to be calibrated
The base model
magnifies uncertainty
in the initial distributions, the parameters,
and the invoked boundary conditions (forcing)
The base model produces
inexplicable results
in terms of the key output.
The base model requires an
unacceptable amount of resources
for the computations,
data preprocessing, or data post

processing (e.g., the base model is not suited to be
a part of an operational modeling system
The base model lacks
transparency
to make the model and its results explicable
and believable to users of the key output.
The base model may need abstraction for one or more of the following reasons
(NUREG/CR

6884, available at the WWW)
The model simplification has to be systematic
and comprehensive
The decision to perform the model abstraction is made by reviewing the
modeling context
and includes consideration of the key output and base model
NUREG/CR 7026, available at WWW
Neuman
and Wierenga (2003),
What is (are) the question(s)
that the base and abstracted
models are to address?
Potential or existing problem in which
modeling is one of the solution instrument.
Potential or existing causes of problem,
Issues needing resolution.
Criteria to decide on efficiency of the
resolution.
The key model output has to be provided
with the spatial and temporal scale at
which it is evaluated.
Acceptable accuracy and uncertainty of
the model output have to be established.
Performance measures t should describe
simple and clear ideas about the
correspondence between the data and
simulations.
What kind of data is available
to calibrate and test the base
and the abstracted models?
The essential condition is to have the
database as broad as possible and to
include the data from public and private
sources, cover both quantitative and
qualitative (expert) information, and
encompass both site

specific and generic
information
It is imperative to have statistics of all
available model inputs and measurable
model outputs. And especially model
parameters typical for the site. The latter
can be inferred from the ensemble
of
pedotransfer
functions
Additional information to
insure that the abstracted
models include descriptions
of essential flow and
transport processes for
given site.
This information may be
of lower quality compared with the
necessary part of the database. However,
one has to be sure that some small

scale
internal heterogeneities will not have a
dominant effect on flow and/or transport at
the scale of interest. It is easy to
become right for a wrong reason without the
information on possible effects of
processes that are not included in the
model. To become wrong for a right reason
is much more responsible way in this case.
Emerging topics in model abstraction.
1. Evaluation of models which is
not
based on space

and

time

aggregated average measures of error
The repertoire of available metrics
has been small and mainly based
on space

and

time

aggregated average measures of performance error, e.g.
the well

known Nash

Sutcliffe efficiency. This
is not enough for the multimedia
environmental modeling.
Metrics are needed
• for spatial and temporal analysis of landscape structure and flow path connectivity
• suitable for probabilistic/ensemble information
• for functional similarity
• that explicitly quantify the information, relevant in a hydrological context,
embedded in the data and in our hydrological models
• for optimality, such as Maximum Entropy Production (MEP) and
Maximum Energy Dissipation (MED)
Uwe
Ehret
(2011)
Beyond the
equifinality

patterns
Information theory measures to quantify
patterns
Symbolic coding of time series (Lange, 1999).
ACCBACBCAABC….
A
B
C
Ymin
Ymax
Observations
1
2
3
4
5
6
7
8
9
10
11
12
Probabilities of joint and individual occurrence of symbols
and transitions from one group of symbols to another
Bioinformatics methods
Eight hydrological models of increasing
complexity applied to simulate streamflow
Data and hydrologic modeling results from T. Wagener, Penn State
Nash

Sutcliffe efficiency
Mean information gain
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
a
b
c
d
e
f
g
h
Example of Guadalupe River, TX
Mean Information Gain
0.0
0.2
0.4
0.6
0.8
1.0
Fluctuation Complexity
0.0
0.5
1.0
1.5
2.0
a
b
c
d
e
f
g
h
Measured streamflow
Rainfall
a b c d e f g h
Complexity increases
Emerging topics in model abstraction. 2.
Monitoring for model discrimination.
ARS

NRC tracer experiment site, Beltsville, MD
MCP
Groundwater
well
Soil tensiometers
Soil tensiometers
Runoff flume
tensiometers
Sprinklers
flume
tensiomete
rs
MCP
Runoff collector
Runoff collector
Multiplexer
Sprinclers
flume
tensiometers
Models of different complexity for subsurface structural units
Where to put the next wells for the best discrimination between models?
Maximize the total weight of evidence

the sum
of information in favor of choosing model 1
and information in favor of choosing model 2
The sum of the expected information in favor of choosing each of the models is
It has to be maximized to find the next best location for model discrimination.
The probability density of model “r” being correct is
Military Intelligence Hall of Fame
Kullback
, S. 1959. Information theory and statistics. Wiley.
Ensemble modeling with pedotransfer functions to define
σ
Y
The next observation well locations suggested
from data of each of 5 wells
Selected research avenues
Model abstraction in multimedia environmental models
–
abstraction of media
models, abstraction with the multimedia model needs in mind.
Analysis of the modeling context for model abstraction with database

supported model population
Ensemble modeling and model abstraction
Model abstraction to improve monitoring
Model abstraction as a component of modeling project
“
Variety is charming, and not at all alarming
”
Old English song
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