Abstraction Techniques for

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