D4.5 A package of calibration procedures linked to SWAT through a generic platform to perform calibration, validation, and uncertainty analysis

enviroGRIDS – FP7 European project
Building Capacity for a Black Sea Catchment
Observation and Assessment System supporting
Sustainable Development

A package of calibration procedures linked to SWAT through
a generic platform to perform calibration, validation, and
uncertainty analysis

Creator K.C. Abbaspour, (Eawag)
Creation date 31.03.2012

Date of last revisions 20.05.2012
Subject A software package for calibration of SWAT
Status Finalized
Type Software package
Description A package of different calibration methods linked
to SWAT
Contributors K.C. Abbaspour, Eawag
Rights Public
Identifier EnviroGRIDS_D4.5
Language English
Relation EnviroGRIDS_D4.2, D4.3, D4.6, D4.7,D4.8

SWAT-CUP
SWAT-CUP (SWAT Calibration Uncertainty Procedures) is a package of software
designed for calibration, validation, sensitivity analysis, and uncertainty analysis of a
SWAT model. Details of the software is explained in the following pages which are the
manual of the software.
The software can be downloaded from :
http://www.eawag.ch/forschung/siam/software/swat/index

1


DISCLAIMER

This report documents SWAT-CUP, a computer program for calibration of SWAT
models. SWAT-CUP4 is a public domain program, and as such may be used and copied
freely. The program links SUFI2, PSO, GLUE, ParaSol, and MCMC procedures to
SWAT. It enables sensitivity analysis, calibration, validation, and uncertainty analysis
of SWAT models. SWAT-CUP4 has been tested for all procedures prior to release.
However, no warranty is given that the program is completely error-free. If you
encounter problems with the code, find errors, or have suggestions for improvement,
please contact Karim C. Abbaspour (abbaspour@eawag.ch) or Raghvan Srinivasan
(r-srinivasan@tamu.edu).

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New Implementations 2011
version 4.3.2

New features in this version are:
- Parallel processing (licensed)
- Visualization of the watershed outlets using the Bing map
- Formulation of multi-objective objective functions through extraction of variables
from .rch, .hru, and .sub files
- Extraction and visualization of the 95ppu for variables from .rch, .hru, and .sub files
when there are no observations
- Temperature data in tmp1.tmp is also allowed to be calibrated as well as the rainfall
data
- In SUFI2, a threshold for the objective function can now be given so as to separate the
behavioral solutions from the non-behavioral ones. The 95ppu as well as all other
statistics are also calculated for these behavioral solutions.
- Input file formats have been changed to make the files more self-explanatory.

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New Implementations 2010
version 3.1.1

1- Parameters of all soil layers can now be calibrated (see pages 32-34)
2- Next to landuse, texture, subbasin, and hydrologic unit, slope can also be used to
parameterize the SWAT model
3- Management parameters can all be calibrated including each rotation and operation
4- All crop parameters can be explicitly calibrated
5- Rainfall in the file pcp.pcp can be calibrated for input uncertainty
6- At the end of the file *.gw, 20 auxiliary parameters can be specified as R1,
R2, ...,R20, which can be used by other programs linked to SWAT. This is useful for
users that link their own routines to SWAT and want to calibrate the parameters of their
program along with the SWAT parameters.
7- Swat_EditLog.txt file lists the actual value of all the parameters that have been
changed
8- GLUE, ParaSol, and MCMC now use the same *_extract_rch.def file as SUFI2 and
can all accept missing observation data.

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Content Page

Food for thought in calibration and application of watershed models 8

SUFI-2 20
Conceptual basis of the SUFI-2 uncertainty analysis routine 21

Step-by-step running of SWAT-SUFI2 30

Parameterization in SWAT-CUP 40

Objective function definition 44

Sensitivity Analysis 47

Parallel Processing 51

The sequence of program execution 52

File definition 53

Latin hypercube Sampling 55

Validation in SUFI2 56

PSO 57

Introduction 58
The algorithm 59

GLUE 66

Introduction to GLUE 67

Coupling GLUE to SWAT-CUP 69

Step-by-step procedure to run GLUE in SWAT-CUP 70

Validation 72

File Definition 73

ParaSol 74

Introduction to ParaSol 75

Coupling ParaSol to SWAT-CUP 76

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Step-by-step procedure to run ParaSol in SWAT-CUP 77

Validation 79

File Definition 80

Appendix - ParaSol in more detail 81

MCMC 94

Introduction to MCMC 95

Step-by-step running of MCMC 97

References 102

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Food for thought in calibration and application of watershed
models
Calibration and uncertainty analysis of distributed watershed models is beset with a few
serious issues that deserve the attention and careful consideration of researchers. These
are: 1) Parameterization of watershed models. 2) Definition of what is a “calibrated
watershed model” and what are the limits of its use. 3) Conditionality of a calibrated
watershed model. 4) Calibration of highly managed watersheds where natural processes
play a secondary role, and 5) uncertainty and non-uniqueness problems. These issues
are briefly discussed here.

1) Model Parameterization

Should a soil unit appearing in various locations in a watershed, under different
landuses and/or climate zones, have the same or different parameters? Probably it
should have different parameters. The same argument could be made with all other
distributed parameters. How far should one go with this differentiation? On the one
hand we could have thousands of parameters to calibrate, and on other we may not have
enough spatial resolution in the model to see the difference between different regions.
This balance is not easy to determine and the choice of parameterization will affect the
calibration results. Detailed information on spatial parameters is indispensable for
building a correct watershed model. A combination of measured data and spatial
analysis techniques using pedotransfer functions, geostatistical analysis, and remote
sensing data would be the way forward.

2) When is a watershed model calibrated?

If a watershed model is calibrated using discharge data at the watershed outlet, can the
model be called calibrated for that watershed? If we add water quality to the data and
recalibrate, the hydrologic parameters obtained based on discharge alone will change. Is
the new model now calibrated for that watershed? What if we add discharge data from
stations inside the watershed? Will the new model give correct loads from various
landuses in the watershed? Perhaps not, unless we include the loads in the calibration

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process (see Abbaspour et al., 2007). Hence, an important question arises as to: “for
what purpose can we use a calibrated watershed model?” For example: What are the
requirements of a calibrated watershed model if we want to do landuse change analysis?
Or, climate change analysis? Or, analysis of upstream/downstream relations in water
allocation and distribution? Can any single calibrated watershed model address all these
issues? Can we have several calibrated models for the same watershed where each
model is applicable to a certain objective? Note that these models will most likely have
different parameters representing different processes (see Abbaspour et al. 1999).

3) Conditionality of calibrated watershed models

Conditionality is an important issue with calibrated models. This is related to the
previous question on the limitation on the use of a calibrated model. Calibrated
parameters are conditioned on the choice of objective function, the type, and numbers of
data points and the procedure used for calibration, among other factors. In a previous
study (Abbaspour et al. 1999), we investigated the consequences of using different
variables and combination of variables from among pressure head, water content, and
cumulative outflow on the estimation of hydraulic parameters by inverse modeling. The
inverse study combined a global optimization procedure with a numerical solution of
the one-dimensional variably saturated Richards flow equation. We analyzed multi-step
drainage experiments with controlled boundary conditions in large lysimeters.
Estimated hydraulic parameters based on different objective functions were all different
from each other; however, a significant test of simulation results based on these
parameters revealed that most of the parameter sets produced similar simulation results.
Notwithstanding the significance test, ranking of the performances of the fitted
parameters revealed that they were highly conditional with respect to the variables used
in the objective function and the type of objective function itself. Mathematically, we
could express a calibrated model M as:

M  M ( p, g , w, b, v, m,....)

where  is a vector of parameters, p is a calibration procedure, g is the objective
function type , w is a vector of weights in the objective function, b is the boundary

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conditions, v is the variables used in the objective function, m is the number of observed
v’s, etc. Therefore, a calibrated model is conditioned on the procedure used for
calibration, on the objective function, on the weights used in the objective function, on
the initial and boundary conditions, on the type and length of measured data used in the
calibration, etc. Such a model can clearly not be applied for just any scenario analysis.

4) Calibration of highly managed watersheds

In highly managed watersheds, natural processes play a secondary role. If detailed
management data is not available, then modeling these watersheds will not be possible.
Examples of managements are dams and reservoirs, water transfers, and irrigation from
deep wells. In Figure 1a the effect of Aswan dam on downstream discharge before and
after its operation is shown. It is clear that without the knowledge of dam’s operation, it
would not be possible to model downstream processes. Figure 1b shows the effect of
wetland on discharge upstream, in the middle, and downstream of Niger Inland Delta.

a b

Figure 1. a) Effect of Aswan dam on down stream discharge before and after its operation
in 1967. b) The influence of Niger Inland Delta on the through flow at upstream, within,
and downstream of the wetland. (After Schuol et al., 2008a,b)

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In Figure 2 the effect of irrigation on actual ET and soil moisture is illustrated in
Esfahan, Iran. Esfahan is a region of high irrigation with a negative water balance for
almost half of the year.

marf

60 100 with irrigation
(a) 90 without irrigation (b)
Actual ET (mm month )

50
-1

80
Soil water (mm) 70
40
60
30 50
40
20 30
10 20
10
0 0

l
ug
l

n
ug
n

pr
n

ov
ar

ct
ay

ec
pr
n

ov
ar

ct
ay

b

p
ec
b

p

Ju
Ju

Ju
Ja
Ju
Ja

Fe

Se
Fe

Se

O
M
O
M

A
A

A

D
M
A

D

N
M

N

Month
Figure 2. Illustration Month differences in predicted actual ET (a) and soil moisture (b) with
of the
and without considering irrigation in Esfahan province, Iran. The variables are monthly
averages for the period of 1990-2002. (After Faramarzi et Without irrigation
With irrigation al., 2008)

In the study of water resources in Iran, Faramarzi et al., (2008) produced a “water
management map” (Figure 3) in order to explain the calibration results of a hydrologic
model of the country.

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Figure 3. Water management map of Iran showing some of man’s activities during
1990-2002. The map shows locations of dams, reservoir, water transfers and
groundwater harvest (background shows provincial-based population). After Faramarzi
et al., (2008).
5) Uncertainty issues

Another issue with calibration of watershed models is that of uncertainty in the
predictions. Watershed models suffer from large model uncertainties. These can be
divided into: conceptual model uncertainty, input uncertainty, and parameter uncertainty.
The conceptual model uncertainty (or structural uncertainty) could be of the following
situations: a) Model uncertainties due to simplifications in the conceptual model, b)
Model uncertainties due to processes occurring in the watershed but not included in the
model, c) Model uncertainties due to processes that are included in the model, but their
occurrences in the watershed are unknown to the modeler, and d) Model uncertainties
due to processes unknown to the modeler and not included in the model either!

Input uncertainty is as a result of errors in input data such as rainfall, and more
importantly, extension of point data to large areas in distributed models. Parameter
uncertainty is usually caused as a result of inherent non-uniqueness of parameters in
inverse modeling. Parameters represent processes. The fact that processes can
compensate for each other gives rise to many sets of parameters that produce the same
output signal. A short explanation of uncertainty issues is offered below.

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5.1) Conceptual model uncertainty

a) Model uncertainties due to simplifications in the conceptual model. For example, the
assumptions in the universal soil loss equation for estimating sediment loss, or the
assumptions in calculating flow velocity in a river. Figures 4a and 4b show some
graphical illustrations.

Fig. 4a. A simplified
conceptual model of Fig. 4b. A natural process near the source of
hydrology in a watershed Yellow River in China playing havoc with river
where revap is ignored loading based on the USLE!

b) Model uncertainties due to processes occurring in the watershed but not included in
the model. For example, wind erosion (Fig. 5a), erosions caused by landslides (Fig. 5b),
and the “second-storm effect” effecting the mobilization of particulates from soil
surface (see Abbaspour et al., 2007).

a b

Figure 5. Natural processes not included in most watershed models but with a large impact
on hydrology and water quality of a watershed, albeit for a short period

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c) Model uncertainties due to processes that are included in the model, but their
occurrences in the watershed are unknown to the modeler or unaccountable; for
example, various forms of reservoirs, water transfer, irrigation, or farm management
affecting water quality, etc. (Fig. 6, 7).

Fig. 6. Agricultural management practices such as water withdrawal and animal husbandry
can affect water quantity and quality. These, may not always be known to the modeller.

Fig. 7. Water control and water diversions may change the flow in ways that are unknown
to the modeller and, hence, can not be accounted for in the model.

d) Model uncertainties due to processes unknown to the modeler and not included in the
model either! These include dumping of waste material and chemicals in the rivers, or
processes that may last for a number of years and drastically change the hydrology or
water quality such as large-scale constructions of roads, dams, bridges, tunnels, etc.
Figure 8 shows some situations that could add substantial “conceptual model error” to
our analysis.

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Fig. 8 Large construction projects such as roads, dams, tunnels, bridges, etc. can change river
flow and water quality for a number of years. This may not be known or accountable by the
modeller or the model

Fig. 8 continued

5.2) Input Uncertainty

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In addition to model uncertainty, there are uncertainties due to errors in input variables
such as rainfall and temperature, as point measurements are used in distributed models.
It is quite difficult to account for input uncertainty. Some researchers propose treating
inputs as random variable, which allows fitting them to get better simulations. As model
outputs are very sensitive to input data, especially rainfall, care must be taken in such
approaches. In mountainous regions, input uncertainty could be very large.

5.3) Parameter non-uniqueness

A single valued parameter results in a single model signal in direct modeling. In an
inverse application, an observed signal, however, could be more-less reproduced with
thousands of different parameter sets. This non-uniqueness is an inherent property of
inverse modeling (IM). IM, has in recent years become a very popular method for
calibration (e.g., Beven and Binley, 1992, 2001; Abbaspour et al., 1997, 2007; Duan et
al., 2003; Gupta et al., 1998). IM is concerned with the problem of making inferences
about physical systems from measured output variables of the model (e.g., river
discharge, sediment concentration). This is attractive because direct measurement of
parameters describing the physical system is time consuming, costly, tedious, and often
has limited applicability. Because nearly all measurements are subject to some
uncertainty, the inferences are usually statistical in nature.

GW_DELAY CH_N2 CN2 REVAPMN Sol_AWC g
3.46 0.0098 50 0.8 0.11 0.010
0.34 0.131 20 2.4 0.2 3 0.011

250

Obs 0.01 0.011

200
Discharge (m3/s)

150

100

50

0
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129

Time
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Figure 9. Example of parameter non-uniqueness showing two similar discharge signals
based on quite different parameter values

Furthermore, because one can only measure a limited number of (noisy) data and
because physical systems are usually modelled by continuum equations, no
hydrological inverse problem is really uniquely solvable. In other words, if there is a
single model that fits the measurements there will be many of them. An example is
shown in Figure 9 where two very different parameter sets produce signals similar to
the observed discharge. Our goal in inverse modelling is then to characterize the set of
models, mainly through assigning distributions (uncertainties) to the parameters, which
fit the data and satisfy our presumptions as well as other prior information.

The Swiss cheese effect

The non-uniqueness problem can also be looked at from the point of view of objective
function. Plotting the objective-function response surface for two by two combinations
of parameters could be quite revealing. As an example, see Figure 10 where the inverse
of an objective function is plotted against two parameters, hence, local minima are
shown as peaks. Size and distribution of these peaks resembles the mysterious holes in a
block of Swiss Emmentaler cheese where the size of each hole represents the local
uncertainty. Our experience shows that each calibration method converges to one such
peak (see the papers by Yang et al., 2008, Schuol et al., 2008a, and Faramarzi et al.,
2008). Yang et al., (2008) compared Generalized Likelihood Uncertainty Estimation
(GLUE) (Beven and Binley, 1992), Parameter Solution (ParaSol) (Van Griensven and
Meixner, 2003a), Sequential Uncertainty Fitting (SUFI2) (Abbaspour et al., 2004; 2007),
and Markov chain Monte Carlo (MCMC) (e.g., Kuczera and Parent, 1998; Marshall et
al., 2004; Vrugt et al., 2003; Yang et al., 2007) methods in an application to a watershed
in China. They found that these different optimization programs each found a different
solution at different locations in the parameter spaces with more less the same discharge
results. Table 1 has a summary of the comparison.

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To limit the non-uniqueness, the objective function should be made as comprehensive
as possible by including different fluxes and loads (see Abbaspour et al., 2007). The
downside of this is that a lot of data should be measured for calibration. The use of
remote sensing data, when it becomes available, could be extremely useful. In fact we
believe that the next big jump in watershed modeling will be made as a result of
advances in remote sensing data availability.

Figure 10. A multidimensional objective function is “multimodal” meaning that there are
many areas of good solutions with different uncertainties much like the mysterious holes in a
slice of Swiss cheese.

Further errors could also exist in the very measurements we use to calibrate the model.
These errors could be very large, for example, in sediment data and grab samples if used
for calibration. Another uncertainty worth mentioning is that of “modeler uncertainty”!
It has been shown before that the experience of modelers could make a big difference in

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model calibration. We hope that packages like SWAT-CUP can help decrease modeler
uncertainty by removing some probable sources of modeling and calibration errors.

On a final note, it is highly desirable to separate quantitatively the effect of different
uncertainties on model outputs, but this is very difficult to do. The combined effect,
however, should always be quantified on model out puts.

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Table 1. Summary statistics comparing different calibration uncertainty procedures.

Criterion GLUE ParaSol SUFI-2 Bayesian inference with cont.
autoregr. error model
MCMC IS
Goal function Nash-Sutcliffe Nash-Sutcliffe Nash-Sutcliffe post. prob. density post. prob.
density
a__CN2.mgt -16.8 (-29.6, -9.8)1 -21.0 (-21.9, -20.1) -26.9 (-30.0, -7.2) -14.2 (-16.8, -11.6) -19.60
v__ESCO.hru 0.76 (0.02, 0.97) 0.67 (0.65, 0.69) 0.82 (0.43, 1.0) 0.74 (0.63, 0.75) 0.62
v__EPCO.hru 0.22 (0.04, 0.90) 0.16 (0.13, 0.20) 1 (0.34, 1.0) 0.94 (0.39, 0.98) 0.27
r__SOL_K.sol -0.16 (-0.36, 0.78) -0.37 (-0.41, -0.34) -0.1 (-0.58, 0.34) -0.29 (-0.31, 0.78) 0.01
a__SOL_AWC.sol 0.11 (0.01, 0.15) 0.07 (0.08, 0.08) 0.07 (0.05, 0.15) 0.12 (0.1, 0.13) 0.05
v__ALPHA_BF.gw 0.12 (0.06, 0.97) 0.12 (0.08, 0.13) 0.51 (0.23, 0.74) 0.14 (0.11, 0.15) 0.91
v__GW_DELAY.gw 159.58 (9.7, 289.3) 107.7 (91.2,115.2) 190.07 (100.2, 300) 25.5 (17.8, 33.3) 33.15
r__SLSUBBSN.hru -0.45 (-0.56, 0.46) -0.59 (-0.60, -0.58) -0.52 (-0.60, 0.03) -0.55 ( -0.56, 0.15) 0.58
a__CH_K2.rte 78.19 (6.0, 144.8) 35.70 (27.72,37.67) 83.95 (69.4, 150.0) 78.3 (68.0, 86.2) 147.23
a__OV_N.hru 0.05 (0.00, 0.20) 0.11 (0.07, 0.10) 0.06 (0.00, 0.11) 0.12 (0.00, 0.19) 0.08
2
σdry - - - 0.93 (0.81, 1.10) 0.87
2
σwet - - - 2.81 (2.4, 3.9) 2.30
2
τdry - - - 38.13 (29.5, 53.8) 28.47
2
τwet - - - 3.42 (2.4, 8.0) 0.92
NS for cal (val) 0.80 (0.78) 0.82 (0.81) 0.80 (0.75) 0.77 (0.77) 0.64 (0.71)
R2 for cal (val) 0.80 (0.84) 0.82 (0.85) 0.81 (0.81) 0.78 (0.81) 0.70 (0.72)
LogPDF for cal -1989 (-926) -2049 (-1043) -2426 (-1095) -1521 (-866) -1650 (-801)
(val)
3
p-factor for cal 79% (69%) 18% (20%) 84% (82%) 85% (84%) -
(val)
4
d-factor for cal 0.65 (0.51) 0.08 (0.07) 1.03 (0.82) 1.47 (1.19) -
(val)
Uncertainty All sources of Parameter All sources of Parameter Parameter
described by uncertainty uncertainty only uncertainty uncertainty only uncertainty
parameter only
uncertainty
Difficulty of very easy easy easy more complicated more
implement. complicated
Number of runs 10000 7500 1500 + 1500 5000 + 20’000 + 100’000
20’000
1
c(a, b) for each parameter means: c is the best parameter estimate, (a,b) is the 95% parameter
uncertainty range except SUFI-2 (in SUFI-2, this interval denotes the final parameter
distribution).
2
the σdry, σwet, τdry, and τwet used to calculate the Calculate the logarithm of the posterior
probability density function (PDF) are from the best of MCMC.
3
p-factor means the percentage of observations covered by the 95PPU
4
d-factor means relative width of 95% probability band
(After Yang et al., 2008).

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SUFI2
Sequential Uncertainty Fitting

version 2

Discharge Calibration

700
measured data bracketed by the 95PPU = 91%

600 d-factor = 1.0

500
Daily discharge (m3 s-1)

400

300

200

100

0
01.01.91 01.07.91 01.01.92 01.07.92 01.01.93 01.07.93 01.01.94 01.07.94 01.01.95 01.07.95 01.01.96
Date

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Conceptual basis of the SUFI-2 uncertainty analysis routine
In SUFI-2, parameter uncertainty accounts for all sources of uncertainties such as
uncertainty in driving variables (e.g., rainfall), conceptual model, parameters, and
measured data. The degree to which all uncertainties are accounted for is quantified by a
measure referred to as the P-factor, which is the percentage of measured data bracketed
by the 95% prediction uncertainty (95PPU). As all the processes and model inputs such
as rainfall and temperature distributions are correctly manifested in the model output
(which is measured with some error) - the degree to which we cannot account for the
measurements - the model is in error; hence uncertain in its prediction. Therefore, the
percentage of data captured (bracketed) by the prediction uncertainty is a good measure
to assess the strength of our uncertainty analysis. The 95PPU is calculated at the 2.5%
and 97.5% levels of the cumulative distribution of an output variable obtained through
Latin hypercube sampling, disallowing 5% of the very bad simulations. As all forms of
uncertainties are reflected in the measured variables (e.g., discharge), the parameter
uncertainties generating the 95PPU account for all uncertainties. Breaking down the
total uncertainty into its various components is highly interesting, but quite difficult to
do, and as far as the author is aware, no reliable procedure yet exists.

Another measure quantifying the strength of a calibration/uncertainty analysis is the R-
factor, which is the average thickness of the 95PPU band divided by the standard
deviation of the measured data. SUFI-2, hence seeks to bracket most of the measured
data with the smallest possible uncertainty band. The concept behind the uncertainty
analysis of the SUFI-2 algorithm is depicted graphically in Figure 11. This Figure
illustrates that a single parameter value (shown by a point) leads to a single model
response (Fig. 11a), while propagation of the uncertainty in a parameter (shown by a
line) leads to the 95PPU illustrated by the shaded region in Figure 11b. As parameter
uncertainty increases, the output uncertainty also increases (not necessarily linearly)
(Fig. 11c). Hence, SUFI-2 starts by assuming a large parameter uncertainty (within a
physically meaningful range), so that the measured data initially falls within the 95PPU,
then decreases this uncertainty in steps while monitoring the P-factor and the R-factor.
In each step, previous parameter ranges are updated by calculating the sensitivity
matrix (equivalent to Jacobian), and equivalent of a Hessian matrix, followed by the

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calculation of covariance matrix, 95% confidence intervals of the parameters, and
correlation matrix. Parameters are then updated in such a way that the new ranges are
always smaller than the previous ranges, and are centered around the best simulation
(for more detail see Abbaspour et al., 2004, 2007).

The goodness of fit and the degree to
which the calibrated model accounts for
the uncertainties are assessed by the
above two measures. Theoretically, the
value for P-factor ranges between 0 and
100%, while that of R-factor ranges
between 0 and infinity. A P-factor of 1
and R-factor of zero is a simulation that
exactly corresponds to measured data.
The degree to which we are away from Figure 11. A conceptual illustration of
the relationship between parameter
these numbers can be used to judge the
uncertainty and prediction uncertainty
strength of our calibration. A larger P-
factor can be achieved at the expense of
a larger R-factor.
Hence, often a balance must be reached between the two. When acceptable values of R-
factor and P-factor are reached, then the parameter uncertainties are the desired
parameter ranges. Further goodness of fit can be quantified by the R2 and/or Nash-
Sutcliff (NS) coefficient between the observations and the final “best” simulation. It
should be noted that we do not seek the “best simulation” as in such a stochastic
procedure the “best solution” is actually the final parameter ranges.

If initially we set parameter ranges equal to the maximum physically meaningful ranges
and still cannot find a 95PPU that brackets any or most of the data, for example, if the
situation in Figure 11d occurs, then the problem is not one of parameter calibration and
the conceptual model must be re-examined.

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SUFI-2 as an optimization algorithm

A short step-by-step description of SUFI-2 algorithm is as follows:
Step 1. In the first step an objective function is defined. The literature shows many
different ways of formulating an objective function (e.g., Legates and McCabe, 1999;
Gupta et al., 1998). Each formulation may lead to a different result; hence, the final
parameter ranges are always conditioned on the form of the objective function. To
overcome this problem, some studies (e.g., Yapo et al., 1998) combine different types of
functions (e.g., based on root mean square error, absolute difference, logarithm of
differences, R2, Chi square, Nash-Sutcliffe, etc.) to yield a “multi-criteria” formulation.
The use of a “multi-objective” formulation (Duan et al. 2003; Gupta et al., 1998) where
different variables are included in the objective function is also important to reduce the
non-uniqueness problem. The objective functions included in SUFI-2 are described later
in the manual.

Step 2. The second step establishes physically meaningful absolute minimum and
maximum ranges for the parameters being optimized. There is no theoretical basis for
excluding any one particular distribution. However, because of the lack of information,
we assume that all parameters are uniformly distributed within a region bounded by
minimum and maximum values. Because the absolute parameter ranges play a
constraining role, they should be as large as possible, yet physically meaningful:
bj: bj,abs_min  bj  bj,abs_max j = 1.... m, (1)
where bj is the j-th parameter and m is the number of parameters to be estimated.

Step 3. This step involves an optional, yet highly recommended “absolute sensitivity
analysis” for all parameters in the early stages of calibration. We maintain that no
automated optimization routine can replace the insight from physical understanding and
knowledge of the effects of parameters on the system response. The sensitivity analysis
is carried out by keeping all parameters constant to realistic values, while varying each
parameter within the range assigned in step one. Plotting results of these simulations
along with the observations on the same graph gives insight into the effects of
parameter changes on observed signals.

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Step 4. Initial uncertainty ranges are next assigned to parameters for the first round of
Latin hypercube sampling, i.e,
bj: [bj,min  bj  bj,max] j = 1, m (2)
In general, the above ranges are smaller than the absolute ranges, are subjective, and
depend upon experience. The sensitivity analysis in step 3 can provide a valuable guide
for selecting appropriate ranges. Although important, these initial estimates are not
crucial as they are updated and allowed to change within the absolute ranges.

Step 5. Latin Hypercube (McKay et al., 1979) sampling is carried out next; leading to n
parameter combinations, where n is the number of desired simulations. This number
should be relatively large (approximately 500-1000). The simulation program is then
run n times and the simulated output variable(s) of interest, corresponding to the
measurements, are saved.
Step 6. As a first step in assessing the simulations, the objective function, g, is
calculated.

Step 7: In this step a series of measures is calculated to evaluate each sampling round.
First, the sensitivity matrix, J, of g(b) is computed using:
 gi
J ij  n
i = 1,..., C2 , j = 1,..., m, (3)
bj
n
where C2 is the number of rows in the sensitivity matrix (equal to all possible
combinations of two simulations), and j is the number of columns (number of
parameters). Next, equivalent of a Hessian matrix, H, is calculated by following the
Gauss-Newton method and neglecting the higher-order derivatives as:

H  J TJ (4)
Based on the Cramer-Rao theorem (Press et al., 1992) an estimate of the lower bound of
the parameter covariance matrix, C, is calculated from:

2
 
C  sg JT J
1
, (5)

24


2
where s g is the variance of the objective function values resulting from the n runs. The

estimated standard deviation and 95% confidence interval of a parameter bj is calculated
from the diagonal elements of C (Press et al., 1992) from:

s j  C jj (6)

b j ,lower  b*  t  ,0.025s j
j (7)

b j ,upper  b*  t  ,0.025s j ,
j (8)

where b*j is the parameter b for one of the best solutions (i.e., parameters which produce

the smallest value of the objective function), and  is the degrees of freedom (n – m).
Parameter correlations can then be assessed using the diagonal and off-diagonal terms
of the covariance matrix as follows:
C ij
rij  (9)
C ii C jj

It is important to note that the correlation matrix r quantifies the change in the objective
function as a result of a change in parameter i, relative to changes in the other
parameters j. As all parameters are allowed to change, the correlation between any two
parameters is quite small. This is expected because in SUFI-2 sets of parameters are
drawn contrary to procedures that keep all parameters constant while changes only one.
Parameter sensitivities were calculated by calculating the following multiple
regression system, which regresses the Latin hypercube generated parameters against
the objective function values:
m
g    i bi (10)
i 1

A t-test is then used to identify the relative significance of each parameter bi. We
emphasize that the measures of sensitivity given by [10] are different from the
sensitivities calculated in step 3. The sensitivities given by [10] are estimates of the
average changes in the objective function resulting from changes in each parameter,
while all other parameters are changing. Therefore, [10] gives relative sensitivities
based on linear approximations and, hence, only provides partial information about the
sensitivity of the objective function to model parameters. Furthermore, the relative

25


sensitivities of different parameters, as indicated by the t-test, depend on the ranges of
the parameters. Therefore, the ranking of sensitive parameters may changes in every
iteration.

Step 8. In this step measures assessing the uncertainties are calculated. Because SUFI-2
is a stochastic procedure, statistics such as percent error, R2, and Nash-Sutcliffe, which
compare two signals, are not applicable. Instead, we calculate the 95% prediction
uncertainties (95PPU) for all the variable(s) in the objective function. As previously
mentioned, this is calculated by the 2.5th (XL) and 97.5th (XU) percentiles of the
cumulative distribution of every simulated point. The goodness of fit is, therefore,
assessed by the uncertainty measures calculated from the percentage of measured data
bracketed by the 95PPU band, and the average distance d between the upper and the
lower 95PPU (or the degree of uncertainty) determined from:
1 k
dX   ( X U  X L )l ,
k l 1
(11)

where k is the number of observed data points. The best outcome is that 100% of the
measurements are bracketed by the 95PPU, and d is close to zero. However, because
of measurement errors and model uncertainties, the ideal values will generally not be
achieved. A reasonable measure for d , based on our experience, is calculated by the R-
factor expressed as:
dX
R-factor  , (12)
X
where X is the standard deviation of the measured variable X. A value of less than 1 is
a desirable measure for the R-factor.

Step 9: Because parameter uncertainties are initially large, the value of d tends to be
quite large during the first sampling round. Hence, further sampling rounds are needed
with updated parameter ranges calculated from:

26


 (b j ,lower  b j ,min ) (b j ,max  b j ,upper ) 
bj ,min  b j ,lower  Max
 , 

 2 2 

 (b j ,lower  b j ,min ) (b j ,max  b j ,upper ) 
bj ,max  b j ,upper  Max
 , ,

 2 2 
(13)

where b indicate updated values. Parameters of the best simulation is used to calculate
bj,lower and bj,upper. The above criteria, while producing narrower parameter ranges for
subsequent iterations, ensure that the updated parameter ranges are always centered on
the best estimates. In the formulation of 13, the uncertainty in the sensitive parameters
reduces faster than those of the insensitive parameters due to the inclusion of the
confidence interval, which is larger for less sensitive parameters.

27


SWAT-CUP4
Automated model calibration requires that the uncertain model parameters are
systematically changed, the model is run, and the required outputs (corresponding to
measured data) are extracted from the model output files. The main function of an
interface is to provide a link between the input/output of a calibration program and the
model. The simplest way of handling the file exchange is through text file formats.
SWAT-CUP is an interface that was developed for SWAT. Using this generic
interface, any calibration/uncertainty or sensitivity program can easily be linked to
SWAT. A schematic of the linkage between SWAT and SUFI2 is illustrated in Figure
12.

A step by step operation of SWAT-SUFI2 is given below.

28


SUFI2_LH_sample.exe par_inf.sf2

par_val.sf2 SUFI2_new_pars.exe

BACKUP SWAT_Edit.exe SUFI2_swEdit.def

Modified SWAT
inputs

swat2005.exe

SWAT
outputs

observed.sf2
SUFI2_extract_rch.def SUFI2_extract_rch.exe

*.out SUFI2_goal_fn.exe goal.sf2

SUFI2_95ppu.exe

Is
calibration no
criteria
satisfied?

yes

stop

Figure 12. Showing the link between SWAT (orange), iSWAT (green), and SUFI2 (yellow)
The entire algorithm is run by two batch files: SUFI2_pre.bat and SUFI2_post.bat

29


Step-by-step running of SWAT-SUFI2
1- Read the theory and application of SWAT-SUFI2 at the beginning of this manual and
in the following papers:
- Thur watershed paper (Abbaspour et al., 2007)
- The application to the landfills in Switzerland (Abbaspour et al., 2004)
- The continental application in Africa (Schuol et al, 2008a,b)
- The country-based application to Iran (Faramarzi et al., 2008)
- The comparison of different programs (Yang et al., 2008)
Start
Click to start
2. Install the SWAT-CUP and start the
program

3. For a new project:
a) Locate a “TxtInOut” directory. Any
file with “TxtInOut” in the name string
would be accepted

b) Select a program from the list
provided (SUFI2, GLUE, ParaSol,
MCMC, PSO).

30


c) Give a name to the project. Note the default addition to the name provided in the
window to the right of “Project Name” window.

The program creates the desired project directory and copies there all TxtInOut files. It
also creates a directory called “Backup” and copies all SWAT file there. The
parameters in the files in the Backup directory serve as the default parameters and do
not changed.

4. Under the Calibration Inputs edit
the following files:

- Par_inf.txt file - contains input
parameters to be optimized. This file
needs to be edited by the user. Examples
show the formats. Edit this to your
needs.
Parameterization is explained below.

- SUFI2_swEdit.def - contains the
beginning and the ending simulations.

- File.cio - This is a SWAT file. It is put
here for convenience. What you need from
this file are the simulation years and the

31


number of warm-up period (NYSKIP) to
correctly provide SWAT-CUP with
beginning and end year of simulation (not
including warm-up period).

- Absolute_SWAT_Values.txt - All
parameters to be fitted should be in this file
plus their absolute min and max ranges.
Currently most, but not all parameters are
included in this file. Simply add to it the
parameters that don’t exist in the format
that is shown.

5. Under Observation are three files that
contain the observed variables. Observed
variables correspond to the variables in
output.rch, output.hru, and output.sub files.
Variables from different files can now be
included to form a multi-objective
objective function. Simply only edit the
file(s) that applies to your project and do
not worry about the ones that don’t. The
format should be exactly as shown in the
examples that are included in the program.
You may have missing data here that can
be expressed as shown in the example files.
The first column has sequential numbers
from the beginning of simulation time
period (in the example here days 4 and 5
are missing). Second column has an
arbitrary format. Here, it is showing the

32


variable name, month, and year. Third
column is the variable value.

6. Under Extraction you will find two
types of files .txt and .def corresponding
again to SWAT output files output.rch,
output.hru, and output.sub. If you have
observations corresponding to variables in
these files, then you need to extract the
corresponding simulated values from these
files.
.txt files simply contain the names of the
files that extracted values should be written
to, and .def files define which variables
need to be extracted from which subbasins.
These files are relatively self-explanatory.
Here again only edit the needed files.

7. Next, Objective Function is defined. In
this step the file observed.txt should be
edited. This file contains all the
information in observed_rch.txt,
observed_hru.txt, observed_sub.txt files,
plus some extra information for the
calculation of objective function.
Similarly, the Var_file_name.txt contains
the names of all the variables that should
be included in the in the objective function.
These names are similar to the names in
the var_file_*.txt in the Extraction section.

33


8. The No Observation section is designed
for the extraction and visualization of
uncertainties in the variables for which we
have no observations, but would like to see
how they are simulated such as various
nutrient loads, or soil moisture, etc.
The .txt and .def files are the same as the
Extraction section. The file
95ppu_No_Obs.def is a file used for the
calculation of the 95ppu in the extracted
variables with no observation. All these
files are self explanatory as they appear in
the examples provided.

9. The section Executable Files plays the
role of engine in SWAT-CUP. The four
batch files indicate what should or should
not be run.

SUFI2_pre.bat - this batch file runs the
pre-processing procedures, which now
SUFI2_pre.bat
include running the Latin hypercube
SUFI2_LH_sample.exe
sampling program. This batch file usually
does not need to be edited.

SUFI2_run.bat - this program executes SUFI2_run.bat
sufi2_execute.exe
SUFI2_execute.exe program, which runs
the SWAT_Edit.exe, extraction batch files,
as well as SWAT2009.exe.

34


SUFI2_post.bat
SUFI2_post.bat - runs the post-
SUFI2_goal_fn.exe
processing batch file, which runs the SUFI2_new_pars.exe
SUFI2_95ppu.exe
programs for objective function SUFI2_95ppu_beh.exe
calculation, new parameter calculation,
95ppu_NO_Obs.exe
95ppu calculation, 95ppu for behavioral
simulations, and 95ppu for the variables
with no observations.

SUFI2_Extract.bat
SUFI2_Extract.bat - This batch file
SUFI2_extract_rch.exe
should contain the names of all the SUFI2_extract_hru.exe
SUFI2_extract_sub.exe
extract programs with or without
extract_hru_No_Obs.exe
observations. extract_rch_No_Obs.exe
extract_sub_No_Obs.exe
Currently 6 programs can be supported:

This file must be edited and the programs that are not desired to run should be
“remarked” as shown below:
SUFI2_Extract.bat
SUFI2_extract_rch.exe

rem SUFI2_extract_hru.exe
rem SUFI2_extract_sub.exe

rem extract_hru_No_Obs.exe
rem extract_rch_No_Obs.exe
rem extract_sub_No_Obs.exe

10. Next, after editing all the input files,
the programs in the Calibration are
executed. In this section three steps are
performed:

35


Sufi2_pre.bat - This command runs the
Sufi2_pre.bat file. This file must be run
before the start of every new iteration.

SUFI2_run.bat - This command executes
the run batch file. This file is described
above in 9.

SUFI2_post.bat - After all simulations are
finished, this command executes the post
processing batch file described above in 9.

11. Calibration Outputs

95ppu plot - This command shows the
95ppu of all variables. Also shown are
observations and best simulation of the
current iteration.

95ppu-No_Observed plot - This
command shows the 95ppu of all
variables with no observations

Dotty Plots - This command show the dotty plots of all parameters. These are plots of
parameter values vs objective function. The main purpose of these graphs are to show
the distribution of the sampling points as well as to give an idea of parameter sensitivity.

Best_Par.txt - This command shows the best parameters (giving the best value of
objective function) of the current iteration.

Best_Sim.txt - This command shows the best simulated values.

36


Goal.txt - This command shows the value of all parameter sets as well as the value of
the objective function in the last column.
New_Pars.txt - This file shows the suggested values of the new parameters to be used
in the next iteration. These values can be copied and pasted in the Par_inf.txt file for
the next iteration. The new parameters should be checked for possible unreasonable
values (e.g., negative hydraulic conductivity,..). These parameter values should be
manually corrected.

Summary_Stat - This file has the statistics comparing observed data with the
simulation band through p-factor and r-factor and the best simulation of the current
iteration by using R2, NS, bR2, MSE, and SSQR. For definition of these functions see
the section on objective functions. Also shown is the objective function (goal function)
type, best simulation number of the current iteration, and the best value of the objective
function for the current run.
If behavioral solutions exist, then the p-factor and r-factor for these solutions are also
calculated. As shown in the following Table the effect of using behavioral solutions is
to obtain smaller p-factor and r-factor, or a smaller prediction uncertainty.

37


Goal_type= br2 (type 6) Best_sim_no= 12 Best_goal = 2.793585e-
001

Variable p-factor r-factor R2 NS br2 MSE SSQR
q_31 0.71 0.94 0.55 0.36 0.38 2004.1
534.2
q_43 0.70 0.96 0.33 0.00 0.18 4263.8
792.8
.....

---- Results for behavioral parameters ---
Behavioral threshold= 0.2
Number of behavioral simulations = 35

Variable p_factor r-factor R2 NS br2 MSE
SSQR
q_31 0.65 0.82 0.55 0.36 0.38 2004.1
534.2
q_43 0.62 0.78 0.33 0.00 0.18 4263.8
792.8
.....

12. Sensitivity analysis - This section of
the program performs sensitivity analysis.
Two types of sensitivity analysis are
allowed. Global Sensitivity and One-at-a-
time sensitivity analysis.
Global sensitivity analysis can be
performed after an iteration.
One-at-a-time sensitivity should be
performed for one parameter at a time only.
The procedure is explained in the next
section.

13. Maps - Maps section refers to the
visualization of the outlets. The Bing map is
started and the location of outlets is projected
on the map using their Lat, Long coordinate.

38


Both text and dbf files are accepted. The
programs looks for a file called outlets.txt
or outlets.dbf. The program converts these
into outlets.xml file. If there is one such
file in the swatcup project directory, then
remove or rename it and locate the outlets
file for the visualization.

14. Iterations History - All iterations can be
saved in the iteration history and the progress to
convergence studied.

15. After a complete iteration, review the suggested new parameters in the new_pars.txt,
copy them to par_inf.txt and make a new iteration.

39


Parameterization in SWAT-CUP

In SWAT, the HRU is the smallest unit of spatial disaggregation. As a watershed is
divided into HRUs based on elevation, soil, and landuse, a distributed parameter such as
hydraulic conductivity can potentially be defined for each HRU. An analyst is, hence,
confronted with the difficult task of collecting or estimating a large number of input
parameters, which are usually not available. An alternative approach for the estimation
of distributed parameters is by calibrating a single global modification term that can
scale the initial estimates by a multiplicative, or an additive term. This leads to the
proposed parameter identifiers.
An important consideration for applying parameter identifiers is that the changes
made to the parameters should have physical meanings and should reflect physical
factors such as soil, landuse, elevation, etc. Therefore, the following scheme is
suggested:

x__<parname>.<ext>__<hydrogrp>__<soltext>__<landuse>__<subbsn>__<slope>
Where
x__ = Code to indicate the type of change to be applied to the parameter:
v__ means the existing parameter value is to be replaced by the
given value,
a__ means the given value is added to the existing parameter value,
and
r__ means the existing parameter value is multiplied by (1+ a given
value).

Note: that there are always two underscores
<parname> = SWAT parameter name (see the file ).
<ext> = SWAT file extension code for the file containing the parameter
(see the file Absolute_SWAT_Values.txt)
<hydrogrp> = (optional) soil hydrological group (‘A’,’B’,’C’ or ‘D’)
<soltext> = (optional) soil texture
<landuse> = (optional) name of the landuse category
<subbsn> = (optional) subbasin number(s)

40


<slope> = (optional) slope
Any combination of the above factors can be used to describe a parameter identifier. If
the parameters are used globally, the identifiers <hydrogrp>, <soltext>, <landuse>,
<subbsn>, and <slope> can be omitted.

Note: the two underscores for every previous specifications must be kept, i.e., to
specify only the subbasin we must write v__USLE_C.crp________2

The presented encoding scheme allows the user to make distributed parameters
dependent on important influential factors such as: hydrological group, soil texture,
landuse, and slope. The parameters can be kept regionally constant to modify a prior
spatial pattern, or be changed globally. This gives the analyst larger freedom in
selecting the complexity of a distributed parameter scheme. By using this flexibility, a
calibration process can be started with a small number of parameters that only modify a
given spatial pattern, with more complexity and regional resolution added in a stepwise
learning process.

Specification of Soil Parameters
Parameter identifiers Description
r__SOL_K(1).sol K of Layer 1 of all HRUs
r__SOL_K(1,2,4-6).sol K of Layer 1,2,4,5, and 6 of all HRUs
r__SOL_K().sol K of All layers and all HRUs
r__SOL_K(1).sol__D K of layer 1 of HRUs with hydrologic group D

r__SOL_K(1).sol____FSL K of layer 1 of HRUs with soil texture FSL
r__SOL_K(1).sol____FSL__PAST K of layer 1 of HRUs with soil texture FSL and
landuse PAST
r__SOL_K(1).sol____FSL__PAST__1-3 K of layer 1 of subbasin 1,2, and 3 with HRUs
containing soil texture FSL and landuse PAST

41


Specification of Management Parameters
v__HEAT_UNITS{rotation no,operation no}.mgt Management parameters that
are subject to operation/rotation
must have both specified
v__CNOP{[],1}.mgt This changes an operation's
parameters in all rotations
v__CNOP{2,1,plant_id=33}.mgt Changes CNOP for rotation 2,
operation 1, and plant 33 only
v__CNOP{[],1,plant_id=33}.mgt Similar to above, but for all
rotations
v__CNOP{[],1,plant_id=33}.000010001.mgt With this command you can
only modify one file
r__manure_kg{9,1}.mgt In these three examples,
rotation 9, operation 1, and the
r__manure_kg{9,1,PLANT_ID=12}.mgt
rest are filters where , means
r__manure_kg{9,1,PLANT_ID=12,HUSC=0.15}.mgt AND

Specification of Crop Parameters
v__T_OPT{30}.CROP.DAT Parameter T_OPT for crop number 30 in
the crop.dat file
v__PLTNFR(1){3}.CROP.DAT Nitrogen uptake parameter #1 for crop
number 3 in crop.dat file

Specification of Pesticide Parameters
v__WSOL{1}.pest.dat This changes parameter WSOL for
pesticide number 1 in pest.dat file

Specification of Precipitation Parameters
v__precipitation(1){1977300}.pcp1.pcp (1) means column number 1 in the pcp
file

42


{1977300} specifies year and day
v__precipitation(1-3){1977300}.pcp1.pcp (1-3) means column 1, 2, and3
{1977300} specifies year and day
v__precipitation( ){1977300,1977301}.pcp ( ) means all columns (all stations)
{1977300,1977301} means 1977 days
300 and 301
v__precipitation( ){1977001- ( ) means all columns
1977361,1978001-1978365,1979003}.pcp from day 1 to day 361 of 1977, and from
day 1 to day 365 of 1978, and day 3 of
1979

Specification of slope Parameters
v__SOL_K(1).sol______________0-10 K of layer 1 for HRUs with slope 0-10

43


Objective Function Definition
In observed.sf2 file,
Obj_Fn_Type(1=mult,2=sum,3=r2,4=chi2,5=NS,6=br2,7=ssrq)= indicates the type
of objective functions. Seven types of objective functions can be used:

- 1=mult A multiplicative form of the square error:

 Q  Qs i  S  S s i  N  N s i
2 2 2
m m m
g i
* i
* i
* ....
nQ nS nN

Sometimes the denominator is divided by 1000 to keep g small.

2=sum A summation form of the square error:
n1 n2 n3
g  w1  Qm  Qs i  w2  S m  S s i  w3  N m  N s i  .....
2 2 2

i 1 i 1 i 1

where weights w’s could be calculated as:

i) wi  1
ni  i
2

where  i is variance of the ith measured variable (see Abbaspour, et al., 2001), or
2

Qm Qm
ii) w1  1, w2  , w3 
Sm Nm
where bars indicate averages (see Abbaspour et al., 1999). Note that choice of weighs
can affect the outcome of an optimization exercise (see Abbaspour, et al., 1997).

3=r2 Coefficient of determination R2 calculated as:
2
 
 Qm ,i  Qm Qs ,i  Qs 
R2   
i

 Qm,i  Qm   Qs,i  Qs 
2 2

i i

If there is more than one variable, then the objective function is defined as:
g   wi Ri2
i

4=Chi2 Chi-squared  2 calculated as:

44


 Q m  Qs i
2

2  i
Q
2

If there is more than one variable, then the objective function is calculate as:
g   wi  i2
i

5=NS Nash-Sutcliffe (1970) coefficient calculated as:

 Qm  Q s i
2

NS  1  i

 Qm,i  Qm 
2

i

If there is more than one variable, then the objective function is defined as:
g   wi NS i
i

6=br2 Coefficient of determination R2 multiplied by the coefficient of the regression
line, bR2. This function allows accounting for the discrepancy in the magnitude of two
signals (depicted by b) as well as their dynamics (depicted by R2). The objective
function is expressed as:
 b R2
 if b 1
   1
b R

2
if b 1

in case of multiple variables, g is defined as:
g   wii
i

7=ssqr The SSQR method aims at the fitting of the frequency distributions of the
observed and the simulated series. After independent ranking of the measured and the
simulated values, new pairs are formed and the SSQR is calculated as

 Q  (2)
SSQR   Q j , simulated
2
j , measured
j 1, n

where j represents the rank.

45


As opposed to the SSQ method, the time of occurrence of a given value of the variable
is not accounted for in the SSQR method (van Griensven and Bauwens, 2003).

NOTE: After an iteration, one can change the type of objective
function and run SUFI2_Post.bat alone to see the effect of different
objective functions, without having to run SWAT again. This is quite
informative as it shows how the choice of objective function affects the
inverse solution.

46


Sensitivity Analysis
1- Global Sensitivity analysis
Parameter sensitivities are determined by calculating the following multiple regression
system, which regresses the Latin hypercube generated parameters against the objective
function values (in file goal.sf2):
m
g    i bi
i 1

A t-test is then used to identify the relative significance of each parameter bi. The
sensitivities given above are estimates of the average changes in the objective function
resulting from changes in each parameter, while all other parameters are changing. This
gives relative sensitivities based on linear approximations and, hence, only provides
partial information about the sensitivity of the objective function to model parameters.

t-stat provides a measure of sensitivity (larger in absolute values are more sensitive)
p-values determined the significance of the sensitivity. A values close to zero has more
significance. In the above example, the most sensitive parameters are CN2 followed by
ESCO and GW_DELAY.

47


2- One-at-a-time sensitivity analysis
One-at-a-time sensitivity shows the sensitivity of a variable to the changes in a
parameter if all other parameters are kept constant at some value. The problem here is
that we never know what the value of those other constant parameters should be. This is
an important consideration as the sensitivity of one parameter depends on the value of
other parameters.

P1

y1

y2

x1 x2
P2

The above example illustrates this point. If value of parameter P1 is kept constant at y1,
then small changes is parameter P2 make significant changes in the objective function
and indicate that P2 is quite a sensitive parameter. While if the values of parameter P1 is
kept constant at y2 value, then changes in parameters P2 around x2 will give the
impression that P2 is not a sensitive parameter. Therefore, the values of the fixed
parameters make a difference to the sensitivity of a parameter.

To perform the one-at-a-time sensitivity analysis:
1- Do as shown in the following Figure. Set the number of parameters in the Par_:inf.txt
file to 1, and perform a minimum of 3 simulations.

48


2- Then set the values of file SUFI2_swEdit.def as follows:

3- Finally perform the simulation by running under Calibration -----> SUFI2_pre.bat
and then SUFI2_run.bat.
4- Now, the three simulation can be visualized for each variable by executing one-at-a-
time command under Sensitivity analysis as shown below:

The dashed line is the observation and the discharge signal for FLOW_OUT_1 is
plotted for three values of CN2 within the specified range. Clearly, CN2 needs to have
larger values.
NOTE: The users must be aware that the parameters in the SWAT files in the main
project directory are always changing. Once you perform an iteration, then the
parameter values in those files are the values of the last run (last parameter set) of the

49


last iteration. To perform the one-at-a-time sensitivity analysis, one should set the
values of the parameters that are kept constant to some reasonable values. These
reasonable values could, for example, be the best simulation (simulation with the best
objective function value) of the last iteration.

To set the parameters to the best value of the last iteration,
1- Note the number of the best simulation in the Summary_Stat.txt file
2- In the SUFI2_swEdit.txt set the starting and ending simulation values to the number
of the best simulation.
3- Under Calibration, run SUFI2_run.bat
This command will replace the parameter values and set them to the best values of the
last iteration. If there is no need to run SWAT here, then the program can be stopped
when SWAT run begins.

50


Parallel Processing

Parallel processing is a licensed product. Its function is to speed up the calibration
process by parallelizing the runs in SUFI2. A procedure is being worked out for PSO
also. The speed of the parallel processing depends on the characteristics of the computer.
New laptops now have at least 4 CPUs. The parallel processing module can utilize all 4
CPUs are so a 1000 run iteration can be divided into 4 simultaneous runs of 250 each
per CPU. The speedup will not be 4 times because of program and Windows overheads;
but the run with parallel processing will be substantially faster than a single run
submission.

Now a days it is possible to build quite inexpensively a computer with 48 to 64 CPUs
and more than 24 GB of RAM. Most SWAT models of any detail could be run on such
machines without the need for cloud or grid computing.

Currently, 20 simulations are allowed to be made without the need for a license. To
activate parallel processing, simply click the Parallel Processing button on the
command bar. A new set of command icons appear. Press Parallel Processing icon
again. This will show the number of parallel processes that can be submitted to the
computer in use. If the size of the project is large and there is not enough memory, then
smaller number of parallel processes than the number of CPUs may be possible. The
Calibration icon here works as before.

A paper submitted to Environmental Modelling and Software (Rouholahnejad, et al.,
2011) could be consulted for more details.

51


The sequence of program execution
The sequence of program execution and input/outputs are shown in Figure 13. In the
following, each input and output file is described in detail.

INPUT FILES OUTPUT FILES

- SUFI2.INtrk.txt ECHOecho_LH_sample.txt
- SUFI2.INpar_inf.txt SUFI2_LH_sample.exe SUFI2.INpar_val.txt
SUFI2.INstr.txt

- SUFI2.INtrk.txt Echoecho_make_par.txt
- SUFI2.INpar_inf.txt SUFI2_make_input.exe
model.in
- SUFI2.INpar_val.txt

- model.in New SWAT parameter files
- Absolute_SWAT_Values.txt SWAT_Edit.exe
Swat_EditLog.txt
- BACKUP file
SUFI2_Run.bat
SWAT2009.exe SWAT output files

- SUFI2_Extract_*.def
- output.* Echoecho_extract_*.txt
- SUFI2.INvar_file_*.txt SUFI2_Extract_*.exe SUFI2.OUTfiles listed in
- SUFI2.INtrk.txt var_file_*.txt
- SUFI2.INobserved_*.txt

- extract_*_No_Obs.def SUFI2.OUTfiles listed in
- output.* SUFI2_Extract_*_No_obs.exe var_file_*_No_obs.txt
- SUFI2.INvar_file_*_No_obs.txt
- SUFI2.INtrk.txt
Echoecho_goal_fn.txt
SUFI2.OUT*.*
- Echoecho_goal_fn.txt
SUFI2.OUTgoal.txt
- SUFI2.INpar_inf.txt
SUFI2.OUTbest_sim.txt
- SUFI2.INobserved.txt SUFI2_goal_fn.exe
SUFI2.OUTbest_par.txt
- SUFI2.INpar_val..txt
SUFI2.OUTbeh_pars.txt
- SUFI2.INvar_file_name.txt
SUFI2.OUTno_beh_sims.txt
- Files listed in var_file_names.txt
SUFI2.OUTbest_sim_nr.txt
- SUFI2.OUT*.*
- SUFI2.INpar_val.sf2
Echoecho_95ppu.txt SUFI2_Post.bat
- SUFI2.INpar_inf.txt
SUFI2.OUT95ppu.txt
- Files liste in var_file_rch.txt
SUFI2_95ppu.exe SUFI2.OUTsummary_stat.txt
- SUFI2.INobserved.txt
SUFI2.OUTbest_sim.txt
- SUFI2.INvar_file_rch.txt SUFI2.OUTbest_par.txt

- 95ppu_No_Obs.def
- SUFI2.INpar_inf.txt SUFI2.OUT95ppu_No_Obs.txt
95ppu_No_Obs.exe
SUFI2.OUT95ppu_g_No_Obs.txt

SUFI2.INobserved.txt
SUFI2.OUTgoal.txt Echonew_pars_all.txt
SUFI2.OUTbest_par.txt SUFI2_new_pars.exe SUFI2.OUTnew_pars.txt

Figure 13. Sequence of program execution and input/output files in SUFI2

52


FILE DEFINITION
Parameter in Observed.txt

- var_weight= is the weight of each variable, i.e., discharge, sediment concentration etc.
This weight could be chosen such that contribution of each variable to the objective
function is equal as explained above. In file Echoecho_goal_fn.sf2 at the last line
contribution of each variable to the objective function is given. Based on this one can
adjust the weights as desired and run the SUFI2_Post.bat again.

- var_Threshold= is a threshold where a signal is divided into two parts. We refer to
this as a “multi-component” assignment (see Abbaspour et al., 2004). Values smaller
than the threshold and values larger than the threshold are treated as two variables. This
is to ensure that, for example, base flow has the same values as the peak flows. If you
choose option 2 for objective function, i.e., mean square error, then base flow my not
have much effect on the optimization, hence, peak flow will dominate the processes.
With this option they can be given the same weight. This option is most effective for
option 2 of objective function and is not defined for R2 and bR2.

250

200

150
Discharge

100

50
Threshold=35
0
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141
Time

In case multi-component assignment is used, all objective functions above are divided
into a lower and an upper part. To not use this option, simply set var-threshold to a
negative number (say -1 for a variable that is always positive) and the weights for upper
and lower thresholds to 1.

53


- wt_below_threshold and wt_above_threshold are the weights for the two components.In
file Echoecho_goal_fn.sf2 at the last line contribution of each variable for lower and
upper section of the variable is given. Based on this one can adjust the weights as
desired and run the SUFI2_Post.bat again. See the definition of objective functions and
weights above.

- pcnt_Error= is the percentage of error in the measurement. This is used in the
calculation of the percentage of data bracketed by the 95% prediction uncertainty

- no_obs= this indicated the number of observed data for each variable.

The above format is repeated for every variable in the objective function.

54


Latin Hypercube Sampling

SUFI2_pre.bat

The batch file SUFI2_pre.bat runs the SUFI2_LH_sample.exe program, which
generates Latin hypercube samples. These samples are stored in par_val.sf2 file.
This program uses Latin hypercube sampling to sample from the parameter intervals
given in par_inf.sf2 file. The sampled parameters are given in par_val.sf2 file, while the
structure of the sampled data is written to str.sf2 just for information. If the number of
simulations is 3, then the following happens:
1) Parameters (say 2) are divided into the indicated number of simulations (say 3)

1 2 3

1 2 3

2) Parameter segments are randomized
2 1 3
3 2 1

3) A random sample is taken in every segment
2 1 3
3 2 1

Every vertical combination is then a parameter set.

55


Validation in SUFI2

To perform validation in SUFI2, edit the files observed_rch.txt, observed_hru.txt,
obsrved_sub.txt, and observed.txt as necessary for the validation period. Also, the
extraction files and the file.cio to reflect the validation period. Then simply use the
calibrated parameter ranges to make one complete iteration without changing the
parameters further.

56


PSO
Particle Swarm Optimization

57


1. Introduction

Particle swarm optimization (PSO) is a population based stochastic optimization
technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social
behavior of bird flocking or fish schooling.

PSO shares many similarities with evolutionary computation techniques such as Genetic
Algorithms (GA). The system is initialized with a population of random solutions and
searches for optima by updating generations. However, unlike GA, PSO has no
evolution operators such as crossover and mutation. In PSO, the potential solutions,
called particles, fly through the problem space by following the current optimum
particles. The detailed information will be given in following sections.

Compared to GA, the advantages of PSO are that PSO is easy to implement and there
are few parameters to adjust. PSO has been successfully applied in many areas: function
optimization, artificial neural network training, fuzzy system control, and other areas
where GA can be applied.

The remaining of the report includes six sections:

Background: artificial life.

The Algorithm

Comparisons between Genetic algorithm and PSO

Artificial neural network and PSO

PSO parameter control

Online resources of PSO

2. Background: Artificial life

The term "Artificial Life" (ALife) is used to describe research into human-made
systems that possess some of the essential properties of life. ALife includes two-folded
research topic: (http://www.alife.org)

1. ALife studies how computational techniques can help when studying biological
phenomena

58


2. ALife studies how biological techniques can help out with computational problems

The focus of this report is on the second topic. Actually, there are already lots of
computational techniques inspired by biological systems. For example, artificial neural
network is a simplified model of human brain; genetic algorithm is inspired by the
human evolution.

Here we discuss another type of biological system - social system, more specifically, the
collective behaviors of simple individuals interacting with their environment and each
other. Someone called it as swarm intelligence. All of the simulations utilized local
processes, such as those modeled by cellular automata, and might underlie the
unpredictable group dynamics of social behavior.

Some popular examples are floys and boids. Both of the simulations were created to
interpret the movement of organisms in a bird flock or fish school. These simulations
are normally used in computer animation or computer aided design.

There are two popular swarm inspired methods in computational intelligence areas: Ant
colony optimization (ACO) and particle swarm optimization (PSO). ACO was inspired
by the behaviors of ants and has many successful applications in discrete optimization
problems. (http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html)

The particle swarm concept originated as a simulation of simplified social system. The
original intent was to graphically simulate the choreography of bird of a bird block or
fish school. However, it was found that particle swarm model can be used as an
optimizer. (http://www.engr.iupui.edu/~shi/Coference/psopap4.html)

3. The algorithm

As stated before, PSO simulates the behaviors of bird flocking. Suppose the following
scenario: a group of birds are randomly searching food in an area. There is only one
piece of food in the area being searched. All the birds do not know where the food is.
But they know how far the food is in each iteration. So what's the best strategy to find
the food? The effective one is to follow the bird which is nearest to the food.

59


PSO learns from the scenario and uses it to solve the optimization problems. In
PSO, each single solution is a "bird" in the search space. We call it "particle". All of
particles have fitness values which are evaluated by the fitness function to be optimized,
and have velocities which direct the flying of the particles. The particles fly through the
problem space by following the current optimum particles.

PSO is initialized with a group of random particles (solutions) and then searches
for optima by updating generations. In every iteration, each particle is updated by
following two "best" values. The first one is the best solution (fitness) it has achieved so
far. (The fitness value is also stored.) This value is called pbest. Another "best" value
that is tracked by the particle swarm optimizer is the best value, obtained so far by any
particle in the population. This best value is a global best and called gbest. When a
particle takes part of the population as its topological neighbors, the best value is a local
best and is called lbest.

After finding the two best values, the particle updates its velocity and positions
with following equation (a) and (b).

v[ ] = v[ ] + c1 * rand() * (pbest[ ] - present[ ]) + c2 * rand() * (gbest[ ] - present[ ])
(a)

present[] = persent[] + v[ ] (b)

v[ ] is the particle velocity, persent[ ] is the current particle (solution). pbest[ ] and
gbest[ ] are defined as stated before. rand () is a random number between (0,1). c1, c2
are learning factors. usually c1 = c2 = 2.

The pseudo code of the procedure is as follows

For each particle

Initialize particle

END

Do

For each particle

Calculate fitness value

If the fitness value is better than the best fitness value (pBest) in history

60


set current value as the new pBest

End

Choose the particle with the best fitness value of all the particles as the gBest

For each particle

Calculate particle velocity according equation (a)

Update particle position according equation (b)

End

While maximum iterations or minimum error criteria is not attained

Particles' velocities on each dimension are clamped to a maximum velocity Vmax. If the
sum of accelerations would cause the velocity on that dimension to exceed Vmax,
which is a parameter specified by the user. Then the velocity on that dimension is
limited to Vmax.

4. Comparisons between Genetic Algorithm and PSO

Most of evolutionary techniques have the following procedure:

1. Random generation of an initial population

2. Reckoning of a fitness value for each subject. It will directly depend on the distance
to the optimum.

3. Reproduction of the population based on fitness values.

4. If requirements are met, then stop. Otherwise go back to 2.

From the procedure, we can learn that PSO shares many common points with GA. Both
algorithms start with a group of a randomly generated population, both have fitness
values to evaluate the population. Both update the population and search for the
optimum with random techniques. Both systems do not guarantee success.

However, PSO does not have genetic operators like crossover and mutation. Particles
update themselves with the internal velocity. They also have memory, which is
important to the algorithm.

61


Compared with genetic algorithms (GAs), the information sharing mechanism in PSO is
significantly different. In GAs, chromosomes share information with each other. So the
whole population moves like a one group towards an optimal area. In PSO, only gBest
(or lBest) gives out the information to others. It is a one-way information sharing
mechanism. The evolution only looks for the best solution. Compared with GA, all the
particles tend to converge to the best solution quickly even in the local version in most
cases.

5. Artificial neural network and PSO

An artificial neural network (ANN) is an analysis paradigm that is a simple model of the
brain and the back-propagation algorithm is the one of the most popular method to train
the artificial neural network. Recently there have been significant research efforts to
apply evolutionary computation (EC) techniques for the purposes of evolving one or
more aspects of artificial neural networks.

Evolutionary computation methodologies have been applied to three main
attributes of neural networks: network connection weights, network architecture
(network topology, transfer function), and network learning algorithms.

Most of the work involving the evolution of ANN has focused on the network
weights and topological structure. Usually the weights and/or topological structure are
encoded as a chromosome in GA. The selection of fitness function depends on the
research goals. For a classification problem, the rate of mis-classified patterns can be
viewed as the fitness value.

The advantage of the EC is that EC can be used in cases with non-differentiable
PE transfer functions and no gradient information available. The disadvantages are 1.
The performance is not competitive in some problems. 2. representation of the weights
is difficult and the genetic operators have to be carefully selected or developed.

There are several papers reported using PSO to replace the back-propagation
learning algorithm in ANN in the past several years. It showed PSO is a promising
method to train ANN. It is faster and gets better results in most cases. It also avoids
some of the problems GA met.

62


Here we show a simple example of evolving ANN with PSO. The problem is a
benchmark function of classification problem: iris data set. Measurements of four
attributes of iris flowers are provided in each data set record: sepal length, sepal width,
petal length, and petal width. Fifty sets of measurements are present for each of three
varieties of iris flowers, for a total of 150 records, or patterns.

A 3-layer ANN is used to do the classification. There are 4 inputs and 3 outputs.
So the input layer has 4 neurons and the output layer has 3 neurons. One can evolve the
number of hidden neurons. However, for demonstration only, here we suppose the
hidden layer has 6 neurons. We can evolve other parameters in the feed-forward
network. Here we only evolve the network weights. So the particle will be a group of
weights, there are 4*6+6*3 = 42 weights, so the particle consists of 42 real numbers.
The range of weights can be set to [-100, 100] (this is just a example, in real cases, one
might try different ranges). After encoding the particles, we need to determine the
fitness function. For the classification problem, we feed all the patterns to the network
whose weights is determined by the particle, get the outputs and compare it the standard
outputs. Then we record the number of misclassified patterns as the fitness value of that
particle. Now we can apply PSO to train the ANN to get lower number of misclassified
patterns as possible. There are not many parameters in PSO need to be adjusted. We
only need to adjust the number of hidden layers and the range of the weights to get
better results in different trials.

6. PSO parameter control

There are not too many parameters needing to be tuned in PSO. Here is a list of the
parameters and their typical values.

The number of particles: the typical range is 20 - 40. Actually for most of the problems
10 particles is large enough to get good results. For some difficult or special problems,
one can try 100 or 200 particles as well.

Dimension of particles: It is determined by the problem to be optimized.

Range of particles: It is also determined by the problem to be optimized, you can
specify different ranges for different dimension of particles.

63


Vmax: it determines the maximum change one particle can take during one iteration.
Usually we set the range of the particle as the Vmax for example, the particle (x1, x2, x3)

X1 belongs [-10, 10], then Vmax = 20

Learning factors: c1 and c2 usually equal to 2. However, other settings were also used
in different papers. But usually c1 equals to c2 and ranges from [0, 4]

The stop condition: the maximum number of iterations the PSO execute and the
minimum error requirement. For example, for ANN training in previous section, we can
set the minimum error requirement is one misclassified pattern. The maximum number
of iterations is set to 2000. This stop condition depends on the problem to be optimized.

7. Online Resources of PSO

The development of PSO is still ongoing. And there are still many unknown areas in
PSO research such as the mathematical validation of particle swarm theory.

One can find much information from the internet. Following are some information you
can get online:

http://www.particleswarm.net lots of information about Particle Swarms and,
particularly, Particle Swarm Optimization. Lots of Particle Swarm Links.

http://icdweb.cc.purdue.edu/~hux/PSO.shtml lists an updated bibliography of particle
swarm optimization and some online paper links

http://www.researchindex.com/ you can search particle swarm related papers and
references.

References:

http://www.engr.iupui.edu/~eberhart/

http://users.erols.com/cathyk/jimk.html

http://www.alife.org

http://www.aridolan.com

http://www.red3d.com/cwr/boids/

64


http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html

http://www.engr.iupui.edu/~shi/Coference/psopap4.html

Kennedy, J. and Eberhart, R. C. Particle swarm optimization. Proc. IEEE int'l conf. on
neural networks Vol. IV, pp. 1942-1948. IEEE service center, Piscataway, NJ, 1995.

Eberhart, R. C. and Kennedy, J. A new optimizer using particle swarm theory.
Proceedings of the sixth international symposium on micro machine and human science
pp. 39-43. IEEE service center, Piscataway, NJ, Nagoya, Japan, 1995.

Eberhart, R. C. and Shi, Y. Particle swarm optimization: developments, applications
and resources. Proc. congress on evolutionary computation 2001 IEEE service center,
Piscataway, NJ., Seoul, Korea., 2001.

Eberhart, R. C. and Shi, Y. Evolving artificial neural networks. Proc. 1998 Int'l Conf. on
neural networks and brain pp. PL5-PL13. Beijing, P. R. China, 1998.

Eberhart, R. C. and Shi, Y. Comparison between genetic algorithms and particle swarm
optimization. Evolutionary programming vii: proc. 7th ann. conf. on evolutionary conf.,
Springer-Verlag, Berlin, San Diego, CA., 1998.

Shi, Y. and Eberhart, R. C. Parameter selection in particle swarm optimization.
Evolutionary Programming VII: Proc. EP 98 pp. 591-600. Springer-Verlag, New York,
1998.

Shi, Y. and Eberhart, R. C. A modified particle swarm optimizer. Proceedings of the
IEEE International Conference on Evolutionary Computation pp. 69-73. IEEE Press,
Piscataway, NJ, 1998

Source of this article is:

http://www.swarmintelligence.org/

65


GLUE
Generalized Likelihood Uncertainty Estimation

66


Introduction to the Program GLUE

A short summary of the GLUE (Beven and Binley, 1992) concept is given below. For
more information the readers are referred to the GLUE literature and the Internet.
The Generalized Likelihood Uncertainty Estimation (GLUE) (Beven and
Binley, 1992) was introduced partly to allow for the possible non-uniqueness (or
equifinality) of parameter sets during the estimation of model parameters in over-
parameterized models. The procedure is simple and requires few assumptions
when used in practical applications. GLUE assumes that, in the case of large over-
parameterized models, there is no unique set of parameters, which optimizes
goodness-of fit-criteria. The technique is based on the estimation of the weights or
probabilities associated with different parameter sets, based on the use of a
subjective likelihood measure to derive a posterior probability function, which is
subsequently used to derive the predictive probability of the output variables. In
Romanowicz et al., (1994) a statistically motivated, more formal equivalent of
GLUE is developed, where the likelihood function is explicitly derived based on the
error between the observed outputs and those simulated by the model. This formal
approach is equivalent to a Bayesian statistical estimation: it requires assumptions
about the statistical structure of the errors. GLUE is usually applied by directly
likelihood weighting the outputs of multiple model realizations (deterministic or
stochastic, defined by sets of parameter values within one or more model
structures) to form a predictive distribution of a variable of interest. Prediction
uncertainties are then related to variation in model outputs, without necessarily
adding an additional explicit error component. There is thus an interesting
question as to whether an appropriate choice of likelihood measure can produce
similar results from the two approaches.
There are a number of possible measures of model performance that can be
used in this kind of analysis. The only formal requirements for use in a GLUE
analysis are that the likelihood measure should increase monotonously with
increasing performance and be zero for models considered as unacceptable or
non-behavioral. Application-oriented measures are easily used in this framework.
Measures based on formal statistical assumptions, when applied to all model

67


realizations (rather than simply in the region of an “optimal” model) should give
results similar to a Bayesian approach when used within a GLUE framework
(Romanowicz et al., 1994), but the assumptions made (additive Gaussian errors in
the simplest cases) are not always easily justified in the case of nonlinear
environmental models with poorly known boundary conditions.

A GLUE analysis consists of the following three steps:
1) After the definition of the “generalized likelihood measure” L( ) , a large number of
parameter sets are randomly sampled from the prior distribution and each parameter set
is assessed as either “behavioral” or “non-behavioral” through a comparison of the
“likelihood measure” with the given threshold value.
2) Each behavioral parameter is given a “likelihood weight” according to:
L( i )
wi  N
(1)
 L(
k 1
k )

where N is the number of behavioral parameter sets.
3) Finally, the prediction uncertainty is described as prediction quantile from the
cumulative distribution realized from the weighted behavioral parameter sets.
In literature, the most frequently used likelihood measure for GLUE is the Nash-
Sutcliffe coefficient (NS), which is also used in the GLUE06 program:
n

( y
ti 1
M
ti (θ)  y ti ) 2
NS  1  n
(2)
( y
ti 1
ti  y) 2

where n is the number of the observed data points, and y ti and ytM (θ) represents the
i

observation and model simulation with parameter θ at time ti, respectively, and y is the
average value of the observations.

68


Coupling of GLUE to SWAT-CUP

SWAT-CUP is an interface to facilitate the coupling between external system analysis
tools and SWAT model. The following diagram illustrates the GLUE-SWAT-CUP links.

Glue06.def Glue06.exe

model.in

SWAT inputs SWAT_Edit.exe backup dir

SWAT2009.exe

GLUE_95ppu.exe
SWAT outputs

glue_extract_rch.def GLUE_extract_rch.exe

model.out exit
if max simulations reached

Figure 14. Interface of GLUE and SWAT-CUP.

69


Step-by-step procedure to run GLUE in SWAT-CUP

1) Follow the initial steps as in SUFI-2,
but choose a GLUE project type

2) Edit the files in “Calibration Input”

3) Edit the command file under “Execution
Files” if necessary

4) Execute the program by running
Glue06.exe and then Glue_95ppu.exe.

5) Examine the output in the “Calibration
Output”. For Glue a large number of
simulations (>5000) is usually required.
Convergence may need to be confirmed by
making a run of a larger number of
simulations and comparing the objective
functions, the dotty plots, and the 95PPU.
Further processing can be done on GLUE
outputs as required by the user.

In Figure 15, the execution order and each input and output file of GLUE is listed. The
entries are self explanatory.

model.in
GLUE.OUTmodelpara.out
GLUE.OUTmodelres.out
GLUE.OUTmodelpara.beh
GLUE.OUTmodelquant.out 70
GLUE.OUTmodelres.beh


glue06.def
GLUE.INglue.inf GLUE06.exe
GLUE.INglue_obs.dat
GLUE.INglue_par.def

model.in
Absolute_SWAT_Values.txt New SWAT parameter files
SWAT_Edit.exe
BACKUP Swat_EditLog.txt

glue_run.cmd

GLUE_Extract_rch.def
SWAT reach output file Echoecho_extract_rch.txt
GLUE.INglue.inf GLUE_extract_rch.exe model.out
GLUE.INglue_obs.dat

GLUE.INvar_file_rch.in
Echoecho_95ppu.txt
GLUE.INglue.inf
GLUE.OUTbest_sim.out
GLUE.INglue_obs.dat GLUE_95ppu.exe Files listed in var_file_rch.in
GLUE.OUT95ppu.out
GLUE.OUTsummary_stat.out
GLUE.OUTmodelres.beh

GLUE.INglue.inf
GLUE.OUTmodelpara.beh Echoecho_validate.txt
GLUE.INGLUE_obs.dat GLUE_Validate.exe GLUE.OUTmodelres.beh
model.out model.in

Figure 15. Sequence of program execution and input/output files in GLUE

Outputs of Glue are in the following files:

71


modelpara.beh Contains the behavioural parameter sets as well as the
value of the objective function

modelpara.out Contains all parameter sets as wll as the value of the
objective function
modelquant.out Contains the 95% prediction uncertainty (95PPU) of
output variables

modelres.beh Contains model simulation for behavioural parameters

modelres.out Contains all model simulations

VALIDATION

After calibration, validation can be performed by using the “Validate” option from the
menu. Before executing validation, however, the GLUE_obs.dat file must be edited to
contain validation data, GLUE_Extract_rch.def must be edited to extract validation data,
and SWAT’s File.cio and climate files (pcp.pcp etc.) must cover the validation period.
The validation program uses the good parameters only to run SWAT.

Input files of GLUE are described below. They are for most parts self explanatory.

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File Definition

glue06.def
Line parameter value Remark
1 // comment
2 MaxSimulation 10000 The larger, the better!
3 ParDefFile glue_par.def parameter definition file
4 ObjfunThresh 0.3 Threshold value given by the user
to separate the behavioural
parameters from the non-
behavioural parameters
5 Percentile 0.025 The percentile used to
calculate the quantiles of
behavioural model results in
line 14
6 ModelInFile model.in output of glue06.exe, and the
input of SWAT_Edit.exe
7 ModelOutFile model.out output of
GLUE_extract_rch.exe and
input of glue06.exe
8 ModelCmd glue_run.cmd Bach file executed during
GLUE run
9 ModelObjfunFile F glue_obs.dat If the first parameter is “F”,
then the second parameter is
the observed data filename
and Nash-Sutcliffe is the
objective function.

If the first parameter is “T”,
then the second parameter is
the objective function
filename that must be
calculated and provided by
the user
10 ModelParaSet modelpara.out The output filename for all
sampled parameter sets
11 ModelBehParaset modelpara.beh The output filename for the
behavioural parameter sets
12 ModelResult T modelres.out The output filename for all
the model results
13 ModelBehResult modelres.beh The output filename for the
behavioural model results
14 ModelResQaunt T modelquant.out The output filename for the
quantiles of behavioural
model results

73


ParaSol
Parameter Solution

74


Introduction to the Program ParaSol
A short summary of the ParaSol (Van Griensven and Meixner, 2006) concept is given
below. For more information the readers are referred to the APPENDIX, the literature
and the Internet.
The ParaSol method aggregates objective functions (OF’s) into a global
optimization criterion (GOC), minimizes these OF’s or a GOC using the Shuffle
Complex (SCE-UA) algorithm and performs uncertainty analysis with a choice between
2 statistical concepts. The SCE algorithm is a global search algorithm for the
minimization of a single function for up to 16 parameters (Duan et al., 1992). It
combines the direct search method of the simplex procedure with the concept of a
controlled random search of Nelder and Mead (1965), a systematic evolution of points
in the direction of global improvement, competitive evolution (Holland, 1975) and the
concept of complex shuffling. In a first step (zero-loop), SCE-UA selects an initial
‘population’ by random sampling throughout the feasible parameters space for p
parameters to be optimized (delineated by given parameter ranges). The population is
portioned into several “complexes” that consist of 2p+1 points. Each complex evolves
independently using the simplex algorithm. The complexes are periodically shuffled to
form new complexes in order to share information between the complexes.
SCE-UA has been widely used in watershed model calibration and other areas of
hydrology such as soil erosion, subsurface hydrology, remote sensing and land surface
modeling (Duan, 2003). It was generally found to be robust, effective and efficient
(Duan, 2003). The SCE-UA has also been applied with success on SWAT for the
hydrologic parameters (Eckardt and Arnold, 2001) and hydrologic and water quality
parameters (van Griensven and Bauwens, 2006). The procedure of ParaSol is:
1) After the optimization of the modified SCE-UA, the simulations performed are
divided into ‘good’ simulations and ‘not good’ simulations by a threshold in this way
similar to the GLUE methodology, and accordingly, ‘good’ parameter sets and ‘not
good’ parameter set. Unlike GLUE, the threshold value can be defined by either the 2-
statistics where the selected simulations correspond to the confidence region (CR) or
Bayesian statistics that are able to point out the high probability density region (HPD)
for the parameters or the model outputs.

75


2) The prediction uncertainty is hence constructed equally from the ‘good’ simulations.
The Objective function used in ParaSol is Sum of the squares of the residuals (SSQ):
n
SSQ   ( y tM (θ)  y ti ) 2
i
(3)
ti 1

Coupling ParaSol to SWAT-CUP

The dataflow between program ParaSol and SWAT-CUP is as shown below.

ParaSol.in ParaSol.exe

model.in

SWAT inputs SWAT_Edit.exe backup dir

SWAT2005.exe
ParaSol_95ppu.exe
SWAT outputs

ParaSol_extract_rch.def ParaSol_extract_rch.exe

model.out exit
if max simulation reached

Figure 16. Interface of ParaSol and SWAT-CUP.

76


Step-by-step procedure to run ParaSol in SWAT-CUP

1) Choose ParaSol program type.

2) Edit the input files in “Calibration Files”

3) Execute ParaSol2.exe under “Calibrate”

4) Examine the output in “Calibration
Outputs”. ParaSol also requires a large
number of runs (>5000)

Outputs of ParaSol are in the following files in Para_Sol.OUT:

95ppu.out Contains the 95% prediction uncertainty of good parameter
ParaSol.out Detailed outputs
Bestpar.out File with the best parameter set
Scepar.out File with all parameter sets used in SCE-UA optimization
Sceobjf.out File with all objective functions calculated during the SCE-UA
optimization
Scegoc.out File with all objective functions (standardized) and the global
optimization criterion (GOC) calculated during the SCE-UA
optimization
goodpar.out File with “good” parameters according to ParaSol
scepargoc.out File with all parameters and GOC values during SCE runs

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summary_stat.out Summary statistics of all variables


model.in
Para_Sol.OUTbestpar.out
Para_Sol.OUTcum_result.out
Para_Sol.INParaSol.in Para_Sol.OUTgoodpar.out
Para_Sol.INParaSol_obs.dat ParaSol2.exe Para_Sol.OUTParaSol.out
Para_Sol.INParaSol_par.def Para_Sol.OUTscegoc.out
Para_Sol.OUTsceobjf.out
Para_Sol.OUTscepar.out
Para_Sol.OUTscepargoc.out

model.in New SWAT parameter files
SWAT_Edit.exe

programbatch.bat

ParaSol_Extract_rch.def
ParaSol_extract_rch.exe model.out
Para_Sol.INParaSol_obs.dat

Para_Sol.INvar_file_rch.in
Echoecho_95ppu.txt
Para_Sol.INParaSol_obs.dat
Para_Sol.OUTbest_sim.out
model.out ParaSol_95ppu.exe Files listed in var_file_rch.in
Para_Sol.INparasol.in
Para_Sol.OUT95ppu.out
Para_Sol.OUTgoodpar.out
Para_Sol.OUTsummary_stat.out
Para_Sol.OUTcum_result.out
Para_Sol.OUTParaSol_goal.out
Para_Sol.INParaSol_par.def
Para_Sol.OUTscepargoc.out

Para_Sol.INparasol.in
Para_Sol.INParaSol_par.def Echoecho_validate.txt
Para_Sol.INParaSol_obs.dat ParaSol_Validate.exe Para_Sol.OUTcum_result.out
Para_Sol.OUTgoodpar.out model.in
model.out

Figure 17. Sequence of program execution and input/output files in ParaSol-SWAT-
CUP

VALIDATION

78


After calibration, validation can be performed by using the “Validate” option from the
menu. Before executing validation, however, the ParaSol_obs.dat file must be edited to
contain validation data, ParaSol_Extract_rch.def must be edited to extract validation
data, and SWAT’s File.cio and climate files (pcp.pcp etc.) must cover the validation
period. The validation program uses the good parameters only to run SWAT.

Input files of ParaSol are described below. They are for most parts self explanatory.
Read more details about the procedure in the Appendix below.

File Definition

79


ParaSol.in

10 ! Number of parameter to be optimized

1000 ! MAXN max no. of trials allowed before optimization is terminated
3 ! KSTOP maximum number of shuffling loops in which the criterion value

0.01 ! PCENTO percentage by which the criterion value must change...

10 ! NGS number of complexes in the initial population

1677 ! ISEED initial random seed
5 ! NPG number of points in each complex

3 ! IPS number of points in a sub-complex
5 !NSPLnumber of evolution steps allowed for each complex before comp

1 ! ISTEP1=run optimization + parameter uncertainty
2=rerun model with good parameter sets (see chapter 9)
1 ! ISTAT Statistical method for ParaSol (1=Chi-squared; 2=Bayesian)
3 !IPROB iprob, when iprob=1 90% probability ; iprob=2 95% probability;
iprob=3 97.5% probability , iprob=4 99% probability; iprob=5 99.9 % probability
0 IFLAG Flag indicating whether the objective functions are to be calculated by ParaSol or
read from “modelof.out”
i=0: objective functions are calculated by LH-OAT based on model.out and data.obs files
i>0: i objective functions are read by LH-OAT in the modelof.out file

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APPENDIX

ParaSol: optimization and uncertainty analysis tool

Ann van Griensven and Tom Meixner

Department of Environmental Sciences
University of California, Riverside
Riverside, CA92521, USA

Phone: 1-909-787-2356
E-mails: ann@biomath.ugent.be
tmeixner@hwr.arizona.edu

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ParaSol files:

File description
ParaSol.exe Executable for windows
ParaSol.f Fortran codes for ParaSol.exe
ParaSol.in Input file for ParaSol.exe
Simple_model.exe Executable for example model in windows
Simple_model.f Fortran codes for Simple_model.exe
Batchprogram.bat Batch file that call simple_model.exe
Input4. Rainfall inputs for simple_model.exe
Model.in Input file for simple_model.exe (EAWAG
protocol)
Model.out Output file of simple_model.exe
(EAWAG protocol)

Copyrights and terms of use

The users of the programs contained in this diskette can copy and use these programs
freely, without seeking authors' permission.
The authors request all users make appropriate references to the use of these programs.
The authors disclaim any responsibility resulting from use of these programs.

Introduction

PS-SG is a tool that performs an optimization and uncertainty analysis for model
outputs. In incorporates two methods: ParaSol (Parameter Solutions) that allows for the
optimization of model parameters based on SCE-UA algorithm (Duan et al., 1992) and
uses the simulations to assess confidence ranges on parameters and outputs (van
Griensven and Meixner, 2003a).

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Description of the ParaSol method
(van Griensven and Meixner, 2003a)

The ParaSol method aggregates objective functions (OF’s) into a global optimization
criterion (GOC), minimizes these OF’s or a GOC using the SCE-UA algorithm and
performs uncertainty analysis with a choice between 2 statistical concepts.

The Shuffled complex evolution (SCE) algorithm
The SCE algorithm is a global search algorithm for the minimization of a single
function for up to 16 parameters [Duan et al., 1992]. It combines the direct search
method of the simplex procedure with the concept of a controlled random search of
Nelder and Mead [1965], a systematic evolution of points in the direction of global
improvement, competitive evolution [Holland, 1975] and the concept of complex
shuffling. In a first step (zero-loop), SCE-UA selects an initial ‘population’ by random
sampling throughout the feasible parameters space for p parameters to be optimized
(delineated by given parameter ranges). The population is portioned into several
“complexes” that consist of 2p+1 points. Each complex evolves independently using the
simplex algorithm. The complexes are periodically shuffled to form new complexes in
order to share information between the complexes.
SCE-UA has been widely used in watershed model calibration and other areas of
hydrology such as soil erosion, subsurface hydrology, remote sensing and land surface
modeling (Duan, 2003). It was generally found to be robust, effective and efficient
(Duan, 2003). The SCE-UA has also been applied with success on SWAT for the
hydrologic parameters (Eckardt and Arnold, 2001) and hydrologic and water quality
parameters (van Griensven and Bauwens, 2003).

Objective functions to be used

83


Within an optimization algorithm it is necessary to select a function that must be
minimized or optimized that replaces the expert perception of curve-fitting during the
manual calibration. There are a wide array of possible error functions to choose from
and many reasons to pick one versus another (for some discussions on this topic see
[Legates and McCabe, 1999; Gupta et al., 1998]). The types of objective functions
selected for ParaSol are limited to the following due to the statistical assumptions made
in determining the error bounds in ParaSol.

Sum of the squares of the residuals (SSQ): similar to the Mean Square Error method
(MSE) it aims at matching a simulated series to a measured time series.

SSQ   x  xi , simulated  (1)
2
i , measured
i 1, n
with n the number of pairs of measured (xmeasured)
and simulated (xsimulated) variables
The sum of the squares of the difference of the measured and simulated values after
ranking (SSQR): The SSQR method aims at the fitting of the frequency distributions of
the observed and the simulated series.
After independent ranking of the measured and the simulated values, new pairs are
formed and the SSQR is calculated as

 x  (2)
SSQR   x j , simulated
2
j , measured
j 1, n

where j represents the rank.
As opposed to the SSQ method, the time of occurrence of a given value of the variable
is not accounted for in the SSQR method (van Griensven and Bauwens, 2003).

Multi-objective optimization

Since the SCE-UA minimizes a single function, it cannot be applied directly for multi-
objective optimization. Although there are several methods available in literature to
aggregate objective functions to a global optimization criterion (Madsen, 2003; van
Griensven and Bauwens, 2003), they do not foresee further application of uncertainty
analysis.

84


A statistically based aggregation method is found within the Bayesian theory (1763).
By assuming that the residuals have a normal distribution N(0, σ2), the variance is
estimated as

SSQMIN
2  (3)
nobs

with SSQMIN the sum of the squares at the optimum and nobs the number of observations
(Box and Tiao, 1973):. The probability of a residual for a given parameter set depends
on a specific time series of data and can then be calculated as:

1   yt , sim  yt ,obs 2 
p( | yt ,obs )  exp   (4)
2 2
 2 2 
 
or
  yt , sim  yt ,obs 2 
p( | yt ,obs )  exp   (5)
 2 2 
 

for a time series (1..T) this gives

1 T   yt ,sim  yt ,obs 2 
p( | Yobs )   exp  
 2 
(6)
2
T
t 1  2 2 
 
or
  y
t , sim  y t ,obs  
T 2 

p( | Yobs )  exp  t 1  (7)
 2 2 
 

For a certain time series Yobs the probability of the parameter set θ p(θ|Yobs) is thus
proportional to
 SSQ1  (8)
p( | Yobs )  exp  2
 2 * 1 

where SSQ1 are the sum of the squares of the residuals with corresponding variance σ 1
for a certain time series. For 2 objectives, a Bayesian multiplication gives:

85


 SSQ1   SSQ2 
p( | Yobs)  C1 * exp 2
* exp  2
(9)
 2 *1   2 * 2 
Applying equation (3), (9) can be written as:
 SSQ1 * nobs1   SSQ2 * nobs2  (10)
p( | Yobs )  C 2 * exp   * exp  

 SSQ1, min  
 SSQ2, min 

In accordance to (10), it is true that:

ln p( | Yobs )  C 3 
SSQ2 * nobs 2 SSQ2 * nobs 2 (11)

SSQ2 min SSQ2, min

We can thus optimize or maximize the probability of (11) by minimizing a Global
Optimization Criterion (GOC) that is set to the equation:
SSQ1 * nobs1 SSQ2 * nobs 2 (12)
GOC  
SSQ1, min SSQ2, min

With equation (11), the probability can be related to the GOC according to:
p( | Yobs )  exp  GOC (13)
The sum of the squares of the residuals get thus weights that are equal to the number
of observations divided by the minimum. The minima of the individual objective
functions (SSQ or SSQR) are however initially not known. After each loop in the SCE-
UA optimization, an update is performed for these minima of the objective functions
using the newly gathered information within the loop and in consequence, the GOC
values are recalculated.
The main advantage of using equation 12 to calculate the GOC is that it allows for a
global uncertainty analysis considering all objective functions as described below.

Uncertainty analysis method
The uncertainty analysis divides the simulations that have been performed by the SCE-
UA optimization into ‘good’ simulations and ‘not good’ simulations and in this way is
similar to the GLUE methodology [Beven and Binley, 1992]. The simulations gathered
by SCE-UA are very valuable as the algorithm samples over the entire parameter space
with a focus of solutions near the optimum/optima. To increase the usefulness of the
SCE-UA samples for uncertainty analysis, some adaptations were made to the original
SCE-UA algorithm, to prevent being trapped in a localized minimum and to allow for a

86


better exploration of the full parameter range and prevent the algorithm from focusing
on a very narrow set of solutions. The most important modifications are:
1. After each loop, the m worst results are replaced by random sampling this
change prevents the method from collapsing around a local minimum (where m
is equal to the number of complexes). Similarly, Vrugt et al. (2003) solved this
problem of collapsing in the minimum by introducing randomness. Here
however, the randomness was introduced for the replacement of the best results.
2. When parameter values are under or over the parameter range defined by SCE-
UA, they get a value equal to the minimum bound or maximum bound instead of
a random sampled value .
The ParaSol Algorithm uses two techniques to divide the sample population of SCE-
UA into “good” and “bad” simulations. Both techniques are based on a threshold value
for the objective function (or global optimization criterion) to select the ‘good’
simulations by considering all the simulations that give an objective function below this
threshold. The threshold value can be defined by 2-statistics where the selected
simulations correspond to the confidence region (CR) or Bayesian statistics that are able
point out the high probability density region (HPD) for the parameters or the model
outputs (figure 1).

2-method
For a single objective calibration for the SSQ, the SCE-UA will find a parameter set
Ө* consisting of the p free parameters (ө*1, ө*2,… ө*p), that corresponds to the
minimum of the sum the square SSQ. According to 2 statistics (Bard, 1974), we can
define a threshold “c” for “good’ parameter set using equation
 2 p ,0.95
c  OF ( *) * (1  ) (14)
n p

whereby the χ2p,0.95 gets a higher value for more free parameters p .
For multi-objective calibration, the selections are made using the GOC of equation
(12) that normalizes the sum of the squares for n, equal to the sum of nobs1 and nobs2,
observation. A threshold for the GOC is calculated by:

87


 2 p ,0.95 (15)
c  GOC( *) * (1  )
nobs1  nobs 2  p

thus all simulations with GOC < Xgocmin + are deemed acceptable

Bayesian method

According to the Bayesian theorem, the probability p(θ|Yobs) of a parameter set θ is
proportional to equation (11).
After normalizing the probabilities (to ensure that the integral over the entire
parameter space is equal to 1) a cumulative distributions can be made and hence a 95%
confidence regions can be defined. As the parameters sets were not sampled randomly
but were more densely sampled near the optimum during SCE-UA optimisation, it is
necessary to avoid having the densely sampled regions dominate the results. This
problem is prevented by determining a weight for each parameter set θi by the following
calculations:
1. Dividing the p parameter range in m intervals
2. For each interval k of the parameter j, the sampling density nsamp(k,j) is calculated
by summing the times that the interval was sampled for a parameter j.
A weight for a parameter set θi is than estimated by
1. Determine the interval k (between 1 and m) of the parameter θi
2. Consider the number of samples within that interval = nsamp(k,j)
3. The weight is than calculated as
1/ p
 p  (16)

W (i )   nsamp(k , j )
 j 1i 
 

The “c” threshold is determined by the following process:
a. Sort parameter sets and GOC values according to decreasing probabilities
b. Multiply probabilities by weights
c. Normalize the weighted probabilities by division using PT with
T
PT  W (i ) *p( I | Yobs ) (17)
i 1

88


d. Sum normalized weighted probabilities starting from rank 1 till the sum gets higher
than the cumulative probability limit (95% or 97.5%). The GOC corresponding to or
closest to the probability limit defines the “c” threshold.

sce sampling Xi-squared CR Bayesian HPD

200

150
Smax

100

50 Figure 2: Confidence region CR for the χ2-
statistics and high probability density (HPD)
0 region for the Bayesian statistics for a 2-
0.0 0.2 0.4 0.6 0.8 1.0
parameter test model
k

Using ParaSol

It uses an input file “ParaSol.in”. It operates by communicating to the model through
input and output files. Input of the model is printed in “model.in” that containes the new
parameter values. There are 2 options to communicate with the output:
1. “modelof.out” with the objective functions OR
2. “model.out” with the output values and “data.obs” with the observed values.
For option 2, the model will calculate objective functions based on equation 1.
ParaSol.exe is programmed to run a batchfile “programbatch.bat”, containing the
necessary commands for the execution of the following:
1. reading the parameters listed in “model.in” and changing the model input files
for these parameters values.
2. running the program
3. reading output of the program and printing the objective function(s) into a
“modelof.out” file in the right format (if iflag>0)

The ParaSOl package contains an example for the application (simple_model.exe) that
is a contains a model with 2 parameters ec [0,200] and ek [0,1], having an optimum at

89


the parameter set (100,0.3). simple_model.exe performs the 3 previously mentioned
tasks and is called from the in the “programbatch.bat” file.

For running PS-SG on another applications “otherapplication.exe”, it is thus necessary:

1. To create the appropriate ParaSol.in file, listing all parameters (up to 100) and
ranges to be considered and indicating the number of objective functions to
consider (up to 40)
2. Having a program “changeinputs.exe” that changes the input files for
“otherapplication.exe” according to the values in “ParaSol.in”
3. Having a program “makeobjf.exe” that will read the outputs of
“otherapplication.exe”, calculates the objective functions and writes these to the
file “modelof.out” (or writes the model.out file with simulations according to
the EAWAG format in case of iflag=0).
4. Put the commands “changeinputs.exe”, “otherapplication.exe” and
“makeobjf.exe” (if iflag>0) in the “programbatch.dat” file.

Input file formats
Formats for the model.in file (see also example)
Each input (parameter) has one line with parameter name (maximum 40 digits) and the
parameter value (free format).

Formats for the modelof.out file (see also example)
1 line with the objective functions in column (free format)

90


Formats for ParaSol.in

Control parameters
Each control parameter uses one line with free format

MAXN 20000 max no. of trials allowed before optimization is terminated
KSTOP 5 maximum number of shuffling loops in which the criterion value
PCENTO 0.01 percentage by which the criterion value must change...
NGS 10 number of complexes in the initial population
ISEED 1677 initial random seed
NPG 5 number of points in each complex
NPS 8 number of points in a sub-complex
NSPL 5 number of evolution steps allowed for each complex before
comp
ISTEP 1 1=run optimization + parameter uncertainty
2=rerun model with good parameter sets (see chapter 9)
ISTAT 1 Statistical method for ParaSol (1=Xi-squared; 2=Bayesian)
IPROB 3 iprob, when iprob=1 90% probability ; iprob=2 95% probability;
iprob=3 97.5% probability , iprob=4 99% probability; iprob=5
99.9 % probability
IFLAG 0 Flag indicating whether the objective functions are to be
calculated by ParaSol or read from “modelof.out”
i=0: objective functions are calculated by LH-OAT based on
model.out and data.obs files
i>0: i objective functions are read by LH-OAT in the
modelof.out file

91


CHANGEPAR
This section follows the previous section. Each parameter has one row, containing
lower limit, upper limit, and the parameter name (up to 250 digits), all in free format.

Output files

File name Description
ParaSol.out Detailed outputs.
Bestpar.out File with the best parameter set
Scepar.out File with all parameter sets used in SCE-UA
optimization
Sceobj.out File with all objective functions calculated during the
SCE-UA optimization
Scegoc.out File with all objective functions (standardized) and
the GOC calculated during the SCE-UA optimization
goodpar.out File with “good” parameters according to ParaSol
scepargoc.out File with all parameters and goc values during sce
runs.

Rerun the model with good parameter sets

This option only makes sense if you have your model output according to the EAWAG

protocol. If you put ISTEP=2 in the ParaSol.in file, the model will rerun all the good

parameter sets (in goodpar.out) and calculate the minimum and maximum bounds for

the model output (in model.out). These mimimum and maximum values will we printed

in the files modelminval.out and modelmaxval.out respectively.

92


93


MCMC
Markov Chain Monte Carlo

94


95


Introduction to MCMC
MCMC generates samples from a random walk which adapts to the posterior
distribution (Kuczera and Parent, 1998). The simplest technique from this class is the
Metropolis-Hasting algorithm (Gelman et al. 1995), which is applied in this study. A
sequence (Markov Chain) of parameter sets representing the posterior distribution is
constructed as follows:
1) An initial starting point in the parameter space is chosen.
2) A candidate for the next point is proposed by adding a random realization from a
symmetrical jump distribution, f jump , to the coordinates of the previous point of the

sequence:
 k*1   k  rand ( f jump ) (13)

3) The acceptance of the candidate points depends on the ratio r:
f Θpost Y (θ* 1 y meas )
k
r (14)
f Θpost Y (θ k y meas )

If r >= 1, then the candidate point is accepted as a new point with probability r. If the
candidate point is rejected, the previous point is used as the next point of the sequence.
In order to avoid long burn-in periods (or even lack of convergence to the posterior
distribution) the chain is started at a numerical approximation to the maximum of the
posterior distribution calculated with the aid of the shuffled complex global
optimization algorithm (Duan et al., 1992).

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Step-by-step running of MCMC

The MCMC in SWAT-CUP is based on the procedures developed by Peter Reichert in the UNCSIM package. For more detail we refer the reader
to http://www.uncsim.eawag.ch/. To run MCMC the following input files must be created:

mcmc.def
Model External
External_ModelInFile mcmc.in //parameter file generated internally
External_ModelOutFile mcmc.out //simulation file created internally
External_ModelExecFile mcmc_run.bat //batch file to start mcmc

ParDefFile mcmc_par.def //paerrameter definition file to be prepared by user
PriorDistFile mcmc_prior.def //parameter priors to be prepared by user
LikeliDefFile mcmc_obs.dat //observation file to be prepared by user
JumpDistFile mcmc_jump.def //jump distribution file to be prepared by user
SampSize 100 //number of run to be made by mcmc

ResValFile mcmc_best.out //best solution
ResidValFile mcmc_resid.out //residual of best solution
PostMarkovChainParSampFile mcmc_parsamp.out //Markov Chain of parameters
PostMarkovChainParQuantFile mcmc_parquant.out /quantiles of parameter distribution
PostMarkovChainResSampFile mcmc_ressamp.out //Markov Chain of result
PostMarkovChainResQuantFile mcmc_resquant.out //quantile of Markov Chain residuals
PostMarkovChainPdfSampFile mcmc_pdfsamp.out //Markov Chain of pdf of posterior

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mcmc_par.def
Name Value Minimum Maximum Scale UncRange Increment ActSens ActEstim Unit Description
r__CN2.mgt -0.37213 -0.8 0.2 0.3 0.03 0.03 T T 0.2
r__ALPHA_BF.gw -0.32866 -0.85 0.2 0.325 0.0325 0.0325 T T 0.2
r__GW_DELAY.gw 0.404144 -0.2 0.9 0.35 0.035 0.035 T T 0.9
r__CH_N2.rte -0.14402 -0.8 0.8 1 0.1 0.1 T T 0.8
v__CH_K2.rte 6.205686 1 10 5.5 0.55 0.55 T T 10
........ ........ ........ ........ ........ ........ ........ ........ ........ ........
........ ........ ........ ........ ........ ........ ........ ........ ........ ........
Lamda1 0.5 0 1 1 0.1 0.1 F F
Lamda2 0 0 10 1 0.1 0.1 F F
Std_Dev_Out 1 0.1 10 1 0.1 0.1 F F

Value - initial estimate of parameter value
Minimum - minimum parameter value
Maximum - maximum parameter value
Scale -
UncRange -
Increment - parameter increment for step changes in Value within Mimimum-Maximum
ActSens -
ActEstim -
Unit -
Description -

98


mcmc_obs.dat
ResCode Dat Transformation Par_1 Par_2 Dist Mean Std_Dev
1 21.41 BoxCox Lamda1 Lamda2 Normal 0 Std_Dev_Out
...... 16.261 BoxCox Lamda1 Lamda2 Normal 0 Std_Dev_Out

ResCode - label of measured data points
Dat - data value
Transformation - transformation to be performed on the data, i.e., Box Cox
transformation
Par_1 - the first parameter of the transformation
Par_2 - the second parameter of the transformation
Dist - distribution of the data point
Mean - mean of the distribution of the data point
Std_Dev - standard deviation of the distribution of the data pint

mcmc_prior.def
Name Dist Par_1 Par_2
r__CN2.mgt Uniform -0.8 0.2
r__ALPHA_BF.gw Uniform -0.85 0.2
r__GW_DELAY.gw Uniform -0.2 0.9
r__CH_N2.rte Uniform -0.8 0.8
v__CH_K2.rte Uniform 1 10
r__SOL_AWC.sol Uniform -0.2 0.6
......... ......... ......... .........
......... ......... ......... .........

Dist - parameter distribution
Par_1 - first moment of the distribution
Par_2 - second moment of the distribution

99


Prepare the mcmc_jump.def file according to the following format. A short run maybe
necessary first, in order to generate reasonable numbers.

mcmc_jump.def
Name Dist Par_1 Par_2
r__CN2.mgt Normal 0 0.003
r__ALPHA_BF.gw Normal 0 0.00325
r__GW_DELAY.gw Normal 0 0.0035
r__CH_N2.rte Normal 0 0.01
v__CH_K2.rte Normal 0 0.055
r__SOL_AWC.sol Normal 0 0.002

Name - parameter name
Dist - parameter distribution
Par_1 - first moment of the distribution
Par_2 - second moment of distribution

The jump distributions are quite important to convergence and require some initial trial
and error runs to specify.

mcmc_run.bat
SWAT_Edit.exe //program to insert generated parameters in swat input files
swat2005.exe //swat program either swat2000 or swat2005
MCMC_extract_rch.exe //program to extract the desired outputs from swat output
files

7- Run the program executing mcmc_start.bat

Note: Please ignore the following error during the run:

100



mcmc.def model.in
MCMC.INmcmc_par.def MCMC.OUTmcmc_parquant.out
MCMC.INmcmc_obs.dat MCMC.OUTmcmc_parsamp.out
uncsimb.exe MCMC.OUTmcmcpdfsamp.out
MCMC.INmcmc_prior.def
MCMCmcmc_jump.def MCMC.OUTmcmc_resquant.out
MCMC.OUTmcmc_ressamp.out

model.in New SWAT parameter files
SWAT_Edit.exe

mcmc_run.bat

MCMC_Extract_rch.def
MCMC_extract_rch.exe
MCMC.INParaSol_obs.dat model.out

Figure 18. Sequence of program execution and input/output files in MCMC-SWAT-
CUP

101


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D4.5 A package of calibration procedures linked to SWAT through a generic platform to perform calibration, validation, and uncertainty analysis

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