Durante l'intervento saranno illustrate le problematiche legate alla gestione dei dati, alla messa in opera del modello, alla sua calibrazione e validazione ed al suo utilizzo. In particolare si analizzeranno i risultati della modellazione per la stima della disponibilità di risorse idriche per l'isola. Il modello per il territorio sardo è composto da 109 bacini, suddivisi in 1363 sottobacini, ognuno caratterizzato da una grande varietà di suoli, di coperture vegetazionali e regioni geo-morfologiche. Il modello è stato calibrato e validato con dati di portata in 27 sezioni di controllo ubicate nei bacini idrografici dell'isola.

1. Pierluigi Cau
Energy and Environment Program
Center for Advanced Studies, Research
and Development in Sardinia
plcau@crs4.it
CRS4
Sardegna Ricerche, 09010 Pula CA, Italy
http://www.crs4.it
Sensitivity Analysis, Calibration,
Validation e Uncertainty Analysis

2. SA, Calibration and Validation
Sensitivity, calibration and uncertainty analysis of a complex
watershed model such as SWAT is beset with a few complex
issues that need to be accounted for, such as:
1) Model parameterization: quality of data and resolution,
parameterization and choices done to set up a watershed
model
2) Definition of what is a “calibrated watershed model” and
what are the limits of its use
3) Uncertainty
4) Non uniqueness of a solution (many calibrated model
may exist)

3. Model parameterization
A soil /land cover unit appearing in different locations in a
watershed, under different land management and/or climate
zones, should have different parameters. This may also be
due to small and large scale heterogeneity.
When calibrating a model, such spatial and temporal
differentiation can be brought as far as one decides.
Naturally there is a practical limit.
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.

4. What is a calibrated model
Calibration depends mostly on the calibration target
(values used to calibrate a model).
If a watershed model is calibrated using discharge data at the
watershed outlet, when we add water quality to the data and
recalibrate, the hydrologic parameters obtained based on
discharge alone will change.
This process can go as far as one wants.

5. Uncertainties
Another issue with watershed models is that uncertainty in the
predictions can be due to:
1. conceptual model uncertainty,
2. input uncertainty (meteo-climatological forcing, etc.),
3. parameter uncertainty.
The conceptual model uncertainty (or structural uncertainty)
could be the result 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,
d) Model uncertainties due to processes unknown to the modeler and
not included in the model

6. Data uncertainties within SWAT
• Land Use/Land Cover:
- one land use /land cover is used throughout the simulation
- course resolution map and parameterization
• Soil:
- course resolution map and parameterization
• Climate date (precipitation, temperature, wind, solar
radiation, etc.)
- distribution of climate gages
- error in the measures and missing values
• Land and water resources management practices
……..

7. Data quality / Model Calibration
Model calibration consists of changing values of model
parameters in an attempt to match field conditions within some
acceptable criteria
This requires that field conditions at a site be properly
characterized
Data uncertainty must be evaluated
Lack of proper site characterization may result in a model that is
calibrated to a set of conditions which are not representative of
actual field conditions

8. Model Calibration in Hydrology
Model calibration is complex due to:
§
inadequate description of processes and interactions
§
scarcity of appropriate field data
o
small and large scale heterogeneity
o
lack of detailed information about the geometry of the
system
o
inadequate knowledge of water exploitation scenarios
o
others
§
variability of boundary conditions
§
low quality of control data
Calibration must take into account all sources of uncertainty. Errors must
be incorporated into the modeling process.
The degree of the uncertainty in model based decision needs to be
quantified.

9. Sensitivity analysis (I)
Sensitivity is a measure of the effect of change in one factor on
another factor.
Sensitivity analysis is potentially useful in all phases of the modeling
process:
1. model formulation,
2. model calibration
3. and model validation.
The sensitivity of model parameters should be recognized as a
special case of the above general definition.
Parametric sensitivity is a vital part of most optimization techniques.
However, other facets of sensitivity need to be recognized.

10. Sensitivity analysis (II)
The time-dependent nature of sensitivity should be considered in the
formulation of hydrologic models.
A variety of simplified hydrologic models are used to demonstrate the
potential of sensitivity in all phases of the modeling process.
The failure to recognize and exploit the potential of sensitivity analysis may
result in the inadequacy of model formulation.

11. The objective function
No objective function characterizes in an exhaustive manner a
model performance.
The model performance depends:
1. model structure,
2. objective function used in calibration,
3. data quality and calibration data length
4. model complexity
Some models are calibrated at an annual / monthly time-scale; this
may not guarantee good simulation performance on a monthly / daily
time step.
An equation to be optimized given certain constraints and with
variables that need to be minimized or maximized in the calibration
process

12. The objective function
The Nash-Sutcliffe objective function:
1
Q1,i is the observed sample for time i, and Q2,i is the corresponding
simulated value.
The Nash-Sutcliffe index ranges between - and 1, with a perfect match
(KNS = 1) when Q1,i = Q2,i for all i
2
1
1
,1
2
,2
1
,1
)(
)(
1
QQ
QQ
K N
i
i
i
N
i
i
N S

13. Other objective functions
The EQM and Correlation:
2)
3)

14. Some situations
In highly managed watersheds, natural processes may play a secondary role

15. Some situations

16. Calibration plot