Urban Water Journal, 2018VOL. 15, NO. 3, 269–275
https://doi.org/10.1080/1573062X.2018.1439975

On the use of global sensitivity analysis for the numerical analysis of permeable
pavements
Giuseppe Brunettia, Jirka Šimůnekb, Michele Turcoc and Patrizia Piroca

Department of Civil Engineering, Architecture, Land and Environment and Mathematic, University of Brescia, Brescia, Italy; bDepartment ofEnvironmental Sciences, University of California, Riverside, CA, USA; cDepartment of Civil Engineering, University of Calabria, Rende, Italy

ABSTRACTThe aim of this study is to investigate the use of different global sensitivity analysis techniques in
conjunction with a mechanistic model in the numerical analysis of a permeable pavement installed at
the University of Calabria. The Morris method and the variance-based E-FAST procedure are applied toinvestigate the influence of soil hydraulic parameters on the pavement’s behavior. The analysis reveals that
the Morris method represents a reliable computationally cheap alternative to variance-based proceduresfor screening important factors and provides the first inspection of the model. The study is completed by a
combined GSA-GLUE uncertainty analysis used to evaluate the model accuracy.

ARTICLE HISTORY

Received 18 August 2017
Accepted 8 February 2018
KEYWORDS

Urban drainage; permeable
pavement; infiltration;
sensitivity analysis; modeling

Abbreviations: LID: low-impact development; GSA: global sensitivity analysis; E-FAST: extended Fourier
amplitude sensitivity test; GLUE: generalized likelihood uncertainty estimation; NSE: Nash-Sutcliffe
efficiency; SM: screening methods; OAT: one-factor-at-a-time

Introduction
The low-impact development (LID) approach aims to restore thenatural hydrological cycle of urban catchments by increasing
their evapotranspiration and infiltration capacity. Several studies have confirmed the quantitative and qualitative benefits of
LIDs on the hydrological cycle (Brattebo and Booth 2003, Davis
2008, Brunetti et al. 2016b). Even though the benefits of LID are
significant, widespread adoption at the catchment scale is rather
limited. One of the key limiting factors is availability and knowledge of reliable modeling tools among practitioners. This issue
is exacerbated by the complexity of various physical processes
involved in LIDs (e.g. infiltration, evapotranspiration, root water
uptake, solute transport, heat transport, etc.), which requires a
combination of high expertise and modeling accuracy. In thisview, mechanistic models have proven to be reliable and accurate tools for the numerical analysis of LIDs, as already demonstrated in several studies (e.g. Hilten et al. 2008, Li and Babcock
2015, Brunetti et al. 2016b).
While mechanistic models can offer both accuracy and modeling flexibility, their calibration and computational cost represent a significant limitation in their widespread adoption. In a
recent study, Brunetti et al. (2017) proposed the use of a Gaussian
emulator to calibrate a two-dimensional mechanistic model of astormwater filter. This study has demonstrated how the surrogate
model can drastically reduce the computational cost while maintaining relatively high accuracy. A reasonable alternative would
be to reduce the dimensionality of the optimization problem
by fixing unimportant factors. This is usually accomplished by

CONTACT Giuseppe Brunetti

giusep.bru@gmail.com© 2018 Informa UK Limited, trading as Taylor & Francis Grouprunning a preliminary sensitivity analysis. Thus far, few studies
have investigated the use of a statistically rigorous sensitivity
analysis. Recently, Brunetti et al. (2016a) used global sensitivity
analysis (GSA) to investigate the influence of soil hydraulic properties on the hydraulic behavior of a permeable pavement using
the HYDRUS-1D mechanistic model (Šimůnek et al. 2016). The
analysis revealed that the wear layer had the highest influenceon the hydraulic response of the pavement. However, the GSA
required between 90,000 and 110,000 model runs, thus leading
to a significant computational cost. In another study, Turco et al.
(2017) combined the two-dimensional HYDRUS-1D model with
the Morris method (Morris 1991) to screen most important soil
hydraulic factors. While results were promising, more research isneeded in this direction to test and compare alternative sensitivity
analysis techniques and to evaluate their use in combination withmechanistic modeling.
The aim of this study is to investigate the use of different
sensitivity analysis techniques in conjunction with a mechanistic model in the numerical analysis of a permeable pavement
installed at the University of Calabria (Italy). The problem isaddressed in the following way. First, the HYDRUS-1D model isselected to describe the variably saturated hydraulic behavior of
the pavement. Next, the Morris method and the extended Fourier
amplitude sensitivity test (E-FAST) (Saltelli et al. 1999) are appliedand compared to screen the influence of soil hydraulic properties on the likelihood function. Finally, the E-FAST is coupledwith the generalized likelihood uncertainty estimation (GLUE)(Beven and Binley 1992) to carry out an uncertainty analysis ofsoil hydraulic parameters and to investigate the accuracy of the270 ﻿G. BRUNETTI ET AL.

model in reproducing the hydraulic behavior of the permeable
pavement. It must be emphasized that the use of the GSA-GLUE
approach for the mechanistic modeling of LIDs represents a novel
application in this field. Furthermore, the comparison between avariance-based sensitivity analysis (i.e. E-FAST) and a screening
method (SM) (i.e. the Morris method) could provide important
information to urban hydrologists regarding their statistical accuracy and computational efficiency.

Methods
Case study description
The University of Calabria is located in the south of Italy,
in the vicinity of Cosenza (39°18′ N 16°15′ E). The climate is
Mediterranean with a mean annual temperature of 15.5°C andan average annual precipitation of 881.2 mm. The permeable
pavement has an area of approximately 154 m2, an averageslope of 2% and a total depth of the profile of 0.98 m. Figure
1 shows a schematic of the permeable pavement, consistingof five layers. The surface wear layer consists of a porous concrete block characterized by high permeability. The bedding
layer is composed of a mixture of sand, glass sand and zeolite toimprove the pollutant removal efficiency of the pavement. Baseand sub-base layers were constructed by following the stone
gradations suggested by the Interlocking Concrete Pavement
Institute. In particular, the ASTM No57 stone gradation, used forthe base layer, is characterized by a porosity of about 30–35%.
The ASTM No2 stone gradation is used in the sub-base layer
for its stability and a high volumetric porosity of about 40%. A
highly permeable geotextile separates the bedding layer fromthe underlining base layer. An impervious membrane is placedat the bottom of the profile to prevent water from percolating
into deeper horizons. Baseflow is collected in a horizontal drain,
which consists of a perforated PVC pipe, and is conducted to amanhole for quantity and quality measurements.
A weather station located directly at the site measures precipitation, wind velocity and direction, air humidity, air temperature,atmospheric pressure and global solar radiation. Rain data aremeasured by a tipping bucket rain gauge with a resolution of
0.254 mm and an acquisition frequency of 1 min. Climatic data
are acquired with a frequency of 5 min. Data are processed andstored in an SQL database. Baseflow is measured by a flux meter,
composed of a PVC pipe with a sharp-crested weir and a pressuretransducer, which was previously calibrated in the laboratory.
One month-long data-set, which starts on 15 January 2014
and ends on 15 February 2014, is selected for further analysis.
The data-set is the same as that used in Brunetti et al. (2016a)
and it includes precipitation, climatic data and baseflow. Climatic
data are used to calculate hourly reference evapotranspiration
using the well-established Penman-Monteith equation (Allen etal. 1998). An albedo of 0.25 is used (Brunetti et al. 2016a). Total precipitation and total reference evapotranspiration for the selectedperiod are 274 mm and 43 mm, respectively. The precipitation andsubsurface outflow time series are downsampled to a temporal
resolution of 15 min, which is considered a balanced resolution
for a monthly numerical simulation. The measured subsurface
outflow from the pavement is used to calculate the likelihood
values and thus to carry out both the sensitivity and uncertainty
analyses. It is worth noting that no surface runoff was observed
during the selected period.

Modeling theory
Water flow
The variably-saturated water flow in the permeable pavement
is simulated using the HYDRUS-1D model (Šimůnek et al. 2016).
The one-dimensional Richards equation describes the unsaturated water flow:
)]
[
(
𝜕
𝜕𝜃
𝜕h
=
+1
K (h)
𝜕t
𝜕z
𝜕z
where θ is the volumetric water content [−], h is the soil waterpressure head [L], K(h) is the unsaturated hydraulic conductivity[LT−1], t is time [T] and z is the soil depth [L]. The soil hydraulicproperties are described by the van Genuchten–Mualem relations (van Genuchten 1980):{
𝜃s −𝜃r+ 𝜃r if h ≤ 0(1+(𝛼|h|)n )m𝜃=𝜃s
ifh > 0Se =

𝜃 − 𝜃r𝜃s − 𝜃r��2⎧
1⎪ Ks SeL (1 − (1 − Sem )m
K =⎨
⎪ Ks
⎩

m=1−

Figure 1. A schematic of the permeable pavement (Brunetti et al. 2016a).

if h ≤ 0
if h > 01nwhere θr [−] is the residual water content, θs [−] is the saturated
water content, Ks [LT−1] is the saturated hydraulic conductivity, n[−] and α [L−1] are two shape parameters, L represents the tortuosity and pore connectivity, and is usually assumed to be 0.5
for many soils, and Se is the effective saturation [−]. The residual
water contents are assumed to be 0.045 and 0.03 for the wear
and bedding layers, respectively, and set to 0.0 for both the base

URBAN WATER JOURNAL﻿ and sub-base layers. The same hydraulic properties are used forthe bedding and protection layers, respectively. Despite all these
considerations, the model still involves 16 unknown parameters(θsi, αi, ni, and Ksi for four soil layers).

Numerical domain and boundary conditions
The vertical domain is discretized into 197 finite elements,
refined at the top to accommodate larger pressure head gradients that are likely to occur in the wear layer. An atmosphericboundary condition is applied at the pavement surface using:(a) precipitation and potential evaporation fluxes, (b) a prescribed zero pressure head (i.e. full saturation) during pondingand (c) equilibrium between the pavement surface pressure
head and the atmospheric water vapor pressure when theatmospheric evaporative demand cannot be met by the wear
layer. The threshold pressured head, which is set to −1000 cm,
divides the evaporation process from the pavement surface
into two stages: (1) a constant-rate stage when actual evaporation (equal to potential evaporation) is limited only by the
supply of energy to the surface and (2) the falling-rate stage
when actual evaporation (smaller than potential evaporation)is controlled by water flow towards the pavement surface. Since
no vegetation was present on the surface of the pavement, thereference evapotranspiration ET0 is fully assigned to potential
evaporation.
A seepage face boundary condition is specified at the bottom of the protection layer. A seepage face boundary acts as a
zero-pressure head boundary when the bottom boundary nodeis saturated and as a no-flux boundary when it is unsaturated. The
initial conditions are specified in terms of the soil water pressure
head and assumed to increase linearly with depth, from −90 cm
at the top of the flow domain (z = 0) to −0.5 cm at the bottom(z = −98). The influence of the initial condition on the model’s output is assumed to be limited to the first few days of the simulated
period and thus does not affect the likelihood.
HYDRUS-1D uses an adaptive time stepping strategy, which
automatically adjusts the time step depending on the numerical solution, thus leading to increased computational efficiency.
Simulated results are printed with a time-frequency of 15 min tofacilitate the comparison with previously downsampled measured data. The mass balance error is calculated for each model
run, and simulations affected by mass balance errors above 2%
are discarded from the following analysis.

Likelihood function
The Nash-Sutcliffe efficiency (NSE) index is used to measure theagreement between the simulated and modeled hydrographs,
and as the likelihood function in the following sensitivity anduncertainty analysis:
�
� ∑T
obs
− Qj mod )2
j=1 (Qj
NSE = 1 − ∑T
obs
obs 2
− Qmean)j=1 (Qj
where Qjobs is the jth measured value, Qjmod is the jth simulated
value, Qmeanobs is the mean value of observed data and T is thenumber of measured values.

271

Sensitivity analysis
Morris method
The Morris method (Morris 1991) belongs to the class of screening methods (SM). SMs aim to provide qualitative sensitivity
measures for different factors using a relatively small number ofmodel evaluations. In general, the Morris method is a one-factor-at-a-time (OAT) local method, since it computes the elementary effect by changing only one factor at a time. However, it canbe viewed as a global method, since it averages several elementary effects computed at different points in the parameter space.
In this study, the modified version of the Morris method proposed by Campolongo et al. (2007) is used to investigate theinfluence of soil hydraulic properties on the pavement response.
Two sensitivity measures, σ and μ*, are calculated in the Morris
method. While the former summarizes the interaction effect, thelatter reflects the overall importance of a particular parameter.
For a detailed description of the method refer to Morris (1991)
and Campolongo et al. (2007). To interpret the results by simultaneously taking into account both sensitivity measures, Morrissuggested using their graphical representation in the (μ*-σ) plane.
Considering the intent of the present analysis, which was targeted
to investigate the efficiency of the method, the sample size was
set to 100, for a total of 1700 numerical simulations.

Extended Fourier amplitude sensitivity testing (E-FAST)
The E-FAST method (Saltelli et al. 1999) belongs to the class ofglobal variance decomposition methods. It does not require any
particular assumptions on the model structure, and it provides
quantitative sensitivity measures for each factor. In particular,
two sensitivity indices are calculated for each parameter, i.e. themain effect Si and the total effect STi. While Si measures how theith factor contributes to the output’s variance without taking
into account the interactions with other parameters, STi quantifies the higher-order effects and thus the parameter interactions. A significant difference between STi and Si indicates animportant role of an interaction for the parameter considered.
STi = 0 is a condition necessary and sufficient for a factor to be
non-influential. In such a case, this parameter can be fixed at
any value within its range of uncertainty without affecting theoutput unconditional variance. For a detailed description of the
E-FAST method, please refer to Saltelli et al. (1999).
The E-FAST analysis requires q∙N simulations, where q is thenumber of parameters and N is the sample size. In this study, N
is set to 3000 for a total of 48,000 model executions. It is evident
that the E-FAST method is more computationally demanding thanthe Morris method. As a result, it provides quantitative sensitivity
measures.

Uncertainty analysis
GSA-GLUE approach
The methodology used to carry out uncertainty analysis consistsof a combination of the GLUE method (Beven and Binley 1992)
with the E-FAST variance-based sensitivity analysis. The GLUE
analysis has been used extensively in the literature for the uncertainty assessment of various hydrological models (Beven andFreer 2001; Montanari 2005). For a detailed description of the

272 ﻿G. BRUNETTI ET AL.

GLUE implementation, please refer to Beven and Binley (1992).
The GSA-GLUE approach was first proposed by Ratto et al. (2001).
This statistical approach is rather intuitive and straightforward
to implement. The sample generated for the variance-based
sensitivity analysis is also used in the GLUE framework. In thisway, the same sets of model runs provide the statistical base forthe calculation of uncertainty bounds. In this study, the sample
generated for the E-FAST analysis has been used to carry out the
GLUE uncertainty estimation. The confidence intervals at 5% and
95% of significance have been calculated for each soil hydraulicparameter. One of the most critical aspects of the GLUE analysis
is the choice of the threshold likelihood value used to identify
the so-called behavioral solutions. As pointed out by Freni et al.
(2008), the threshold value strongly influences the calculated
uncertainty bounds. Therefore, care should be taken in selecting
the appropriate value. In this study, three values of the thresholdlikelihood values are investigated: 0.0, 0.1 and 0.2.

Results and discussion
Sensitivity analysis
Results of the sensitivity analysis carried out with the Morris
method (left plot) and the E-FAST procedure (right plot) are
reported in Figure 2. On first inspection, it is evident how bothmethods identified a modeling scenario characterized by thehigh parameter interaction, similar to that reported in Brunetti
et al. (2016a). The results of the Morris analysis show that eachfactor with a high value of μ* also has a high value of the standard deviation σ, indicating that none of the parameters has apurely linear effect. This is also evident from the scatter plot μ*-σ,
where all points are located around the diagonal. A more careful inspection reveals the presence of two groups of factors: thefirst one includes the shape parameters α and the second one
all remaining factors. However, it must be emphasized that thegroup separation is rather limited. Since all soil hydraulic parameters exhibited significant values of μ* and σ, it is not possible
to fix these factors and thus reduce the dimensionality of the
problem without affecting the quality of the fit.
Findings of the Morris method are, in general, confirmed by
the results of the E-FAST analysis. The main effect Si and the total
effect STi for each factor are reported in the right plot of Figure 2. In

particular, grey and black bars indicate the total and main effects,
respectively. It is evident that all parameters exhibit a significant
STi and only a limited or negligible Si. Differences in STi-Si indicate
strong interaction effects between factors and a high nonlinearity of the model. Similarly as for the Morris method, the shapeparameters α are the most influential, although their ranking isslightly different, with α4 being slightly more sensitive than α2. The
saturated hydraulic conductivities of the wear and base layers are
the less sensitive parameters, although their total effects were still
significant. Since the condition STi = 0 is never encountered, themodel cannot be further simplified.
It is worth noting that the two sensitivity analyses reach similar
results and conclusions. Both highlight strong parameter interactions and the nonlinearity of the model, as well as identifying
the shape parameters α as the most influential factors. The maindifference between the two methods is the computational cost,with the Morris method being computationally cheaper than the
E-FAST approach. As a result of this analysis, a number of conclusions can be drawn:• Both the Morris method and the E-FAST analysis indicatethat the model response is mainly driven by parameter interactions, underlining the high nonlinearity of themodel.
• The shape parameters α have the highest influence on themodel’s output in both sensitivity analyses.
• All soil hydraulic parameters exhibit a substantial total
effect ST, and thus it is not possible to reduce the dimensionality of the problem by fixing some parameters.
• Results of the Morris method and the E-FAST analysis are ingood agreement, indicating that the former can represent
a computationally cheaper alternative to global variancedecomposition methods when the main goal of the analysis is to screen important factors.

Uncertainty analysis
The sample generated for the E-FAST analysis is used next tocarry out the GLUE uncertainty assessment of soil hydraulicparameters. Figure 3 shows cumulative probability distributions of analyzed soil hydraulic parameters obtained for three

Figure 2. Scatter plots of the Morris sensitivity measures (left plot) and a bar chart of the E-FAST sensitivity indices (right plot) for various soil hydraulic parameters.

URBAN WATER JOURNAL﻿ 273

Figure 3. Cumulative likelihood distributions of soil hydraulic parameters calculated using the GSA-GLUE analysis for three different values of the GLUE threshold (i.e. NSE> 0, NSE > 0.1, NSE > 0.2). Dashed blue lines indicate the 5% and 95% confidence intervals.

different values of the NSE GLUE threshold. It is evident how
factors exhibit significantly different behaviors. The cumulative
distribution for Ks1 is approximately linear and insensitive to the
GLUE threshold, indicating a significant parameter uncertainty
and a general lack of identifiability. This confirms the findingsof the sensitivity analysis, which highlighted the limited influence of Ks1 on the likelihood function. This behavior could
indicate that the information content of measured variables
related to subsurface outflow is not sufficient to identify Ks1
and that other types of measurements are needed to reduceparameter uncertainty. On the other hand, the influence of thesaturated hydraulic conductivity of the wear layer of a strongly
unsaturated system, such as the pavement, is expected to behydraulically limited unless surface pressure heads approach
saturation (e.g. surface runoff ), a situation that never occurred
during the observed period. A similar behavior is encountered

for the saturated hydraulic conductivity Ks3, which together with
Ks1 exhibits the lowest total effect ST in the sensitivity analysis.
Conversely, Ks2 is appreciably sensitive to the GLUE threshold,although parameter uncertainty remains high. These results arein agreement with a recent study by Turco et al. (2017), who analyzed the hydraulic behavior of a permeable pavement at thelaboratory scale. Turco et al. (2017) used the Morris method toinvestigate the influence of four soil hydraulic parameters on
subsurface outflow and water contents in the bedding layer.
Their results confirmed that Ks1 had a low impact on outflow,
while Ks2 exhibited a significant influence on it. Furthermore,similarly to our study, the shape parameter α was the most influential parameter.
Cumulative likelihood distributions of the shape parameters
ni are always almost linear and insensitive to the GLUE threshold.
Only n1 shows an appreciable influence for n1<3.4. On the other274 ﻿G. BRUNETTI ET AL.

Figure 4. A comparison of measured (red line) and modeled (grey area) outflow from the pavement. The grey area represents the uncertainty band.

hand, the shape parameters αi are highly sensitive to the GLUE
threshold. The cumulative likelihood distribution for α1 indicatesa leptokurtic and positively skewed posterior parameter distribution. While the 5% percentile is insensitive to the GLUE threshold, the 95% percentile changes significantly. In particular, the
95% confidence limit changes from 0.27 to 0.2, thus reducing
the parameter uncertainty. This indicates that the model tends togive a more accurate reproduction of the measured hydrographfor low values of α1. Again, these results agree with what was
found by the earlier GSA, when α1 was among the most sensitive
parameters. In general, the analysis reveals that selected observations allow estimates of the shape parameter of the wear layer tobe found with good confidence. A similar situation is observed for
α2, while some differences are evident for α3 and α4. In particular,
the shape parameter of the base layer, α3, exhibits a multimodal
behavior, with two substantial increases around 0.05 and 0.3.
Interestingly, the sensitivity of the saturated water content of thebase layer, θs3, is significant and well matches results of the E-FAST
analysis, which ranked θs3 as the fifth most influential parameter.
The cumulative probability distributions obtained using the
GSA-GLUE approach are used to calculate confidence intervals
and to evaluate the accuracy of the model in reproducing thehydrograph. In particular, the behavioral sample obtained withthe threshold value NSE>0.2 is used. Figure 4 compares the measured hydrograph (red line in Figure 4) with the modeled uncertainty bands (grey area in Figure 4). The uncertainty bands are
obtained by sampling solutions (i.e. set of soil hydraulic parameters) with NSE>0.2. More specifically, behavioral solutions are
passed to HYDRUS, which is then executed, and for each numerical simulation, subsurface outflow is stored. Measured outflow
lies only partially in the uncertainty bands, thus indicating thepoor accuracy of the proposed model in reproducing the hydraulic behavior of the pavement. The results confirm the tendencyof the model to overestimate the hydrograph, similarly to thereport by Brunetti et al. (2016a) for the same pavement modeledusing the unimodal van Genuchten function for the soil hydraulic properties. The analysis suggests a general inadequacy ofthis formulation in describing the water flow in the pavement.
However, it must be emphasized that other possible sources of
uncertainty (i.e. measurement errors, input uncertainty, etc.) were

not accounted for in the present study and thus a more comprehensive uncertainty analysis is recommended to clearly separate
the effects of model input and structural errors.

Conclusions
The main aim of this study was to investigate and compare theuse of global sensitivity analysis techniques for the numericalanalysis of the hydraulic behavior of permeable pavements. The
Morris method and the variance-based E-FAST analysis wereused in conjunction with the HYDRUS-1D mechanistic model
to investigate the influence of soil hydraulic parameters on theability of the model to reproduce measured outflow from thepavement. Both methods reached similar conclusions, indicating strong parameter interactions and the nonlinearity ofthe model. Interestingly, the analysis revealed that the Morris
method represents a reliable, computationally cheap alternative
to variance-based GSAs, such as E-FAST. It can be used prior tomodel calibration to screen important and unimportant factors
and to provide the first inspection of the model’s behavior at areasonable computational cost. On the other hand, the E-FAST
approach must be chosen when the modeler’s aim is to obtain
quantitative sensitivity measures. Furthermore, at the same
computational cost, the combined GSA-GLUE analysis allows
one to estimate the parameter uncertainty and to evaluate theaccuracy of the model in reproducing the hydraulic behaviorof the pavement. However, since the choice of the likelihood
threshold strongly influences the estimation of the model predictive uncertainty, leading to wider posterior parameter distributions, the use of the formal Bayesian analysis is suggested.
An interesting future development could be to test the use of
the Hamiltonian Monte Carlo algorithm combined with theno-u-turn-sampler (Hoffman and Gelman 2011), which guarantees high computational efficiency compared to the traditional
Monte Carlo Markov chain algorithm.
Overall, the GLUE uncertainty analysis presented in this study
targeted a modeling situation characterized by high parameter
uncertainty. As previously stated, further measurements areneeded to constrain the model and reduce uncertainty. The
type of measurement can be chosen using a model-based

URBAN WATER JOURNAL﻿ optimal Bayesian experimental design approach. Synthetic
modeling scenarios can be used in conjunction with Bayesian
techniques (i.e. GSA-GLUE) to quantify the model predictive
uncertainty when different types of data are used. The set ofdata that minimizes the model uncertainty for the variable ofinterest (e.g. subsurface outflow) can be adopted in a following
experimental test. While this and other studies report promising results, there are still other open questions that need to beaddressed in the future: in particular, how to reduce parameter uncertainty, how to maximize the information content of
measurements and how the uncertainty in LID modeling propagates at the catchment scale. However, by combining accurate
modeling tools, reliable measurements and modern statisticaltechniques, it is possible to answer these questions and boost
the adoption of LIDs.

Nomenclature
t
z
h
Se
m
θr
θs
α
n
Ks
L
σ
μ*
S
ST

time [T]pavement depth [L]pressure head [L]effective saturation [−]retention curve shape parameter [−]residual water content [−]saturated water content [−]retention curve shape parameter [L−1]retention curve shape parameter [−]saturated hydraulic conductivity [LT−1]
tortuosity [−]Morris sensitivity measure of the parameter’s interaction [−]Morris sensitivity measure of the parameter’s main effect [−]E-FAST sensitivity measure of the parameter’s main effect [−]E-FAST sensitivity measure of the parameter’s total effect [−]SubscriptsiJ

layer number (1–4)
data ID

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
The study was co-funded by the Italian National Operative Project (PON)– Research and Competitiveness for the convergence regions 2007/2013-I
Axis ‘Support to structural changes’ operative objective 4.1.1.1. ‘Scientifictechnological generators of transformation processes of the productive
system and creation of new sectors’ Action II: ‘Interventions to support
industrial research’.

ORCID
Giuseppe Brunetti

http://orcid.org/0000-0001-7943-8088

275

References
Allen, R. G., L. S. Pereira, D. Raes, and M. Smith. 1998. FAO Irrigation andDrainage Paper No. 56: Crop Evapotranspiration. Rome: Fao. doi:10.1016/j.
eja.2010.12.001.
Beven, K., and A. Binley. 1992. “The Future of Distributed Models: Model
Calibration and Uncertainty Prediction.” Hydrological Processes 6 (3): 279–
298. doi:10.1002/hyp.3360060305.
Beven, K., and J. Freer. 2001. “Equifinality, Data Assimilation, and Uncertainty
Estimation in Mechanistic Modelling of Complex Environmental Systems
Using the GLUE Methodology.” Journal of Hydrology 249 (1–4): 11–29.
doi:10.1016/S0022-1694(01)00421-8.
Brattebo, B. O., and D. B. Booth. 2003. “Long-Term Stormwater Quantity andQuality Performance of Permeable Pavement Systems.” Water Research 37(18): 4369–4376. doi:10.1016/S0043-1354(03)00410-X.
Brunetti, G., J. Šimůnek, and P. Piro. 2016a. “A Comprehensive Analysis of the
Variably Saturated Hydraulic Behavior of a Green Roof in a Mediterranean
Climate.” Vadose Zone Journal 15 (9). doi:10.2136/vzj2016.04.0032.
Brunetti, G., J. Šimůnek, and P. Piro. 2016b. “A Comprehensive Numerical
Analysis of the Hydraulic Behavior of a Permeable Pavement.” Journal of
Hydrology 540: 1146–1161. doi:10.1016/j.jhydrol.2016.07.030.
Brunetti, G., J. Šimůnek, M. Turco, and P. Piro. 2017. “On the Use of SurrogateBased Modeling for the Numerical Analysis of Low Impact Development
Techniques.” Journal of Hydrology 548: 263–277. doi:10.1016/j.
jhydrol.2017.03.013.
Campolongo, F., J. Cariboni, and A. Saltelli. 2007. “An Effective Screening
Design for Sensitivity Analysis of Large Models.” Environmental Modelling& Software 22 (10): 1509–1518. doi:10.1016/j.envsoft.2006.10.004.
Davis, A. P. 2008. “Field Performance of Bioretention: Hydrology Impacts.”
Journal of Hydrologic Engineering 13 (2): 90–95. doi:10.1061/(ASCE)10840699(2008) 13:2(90).
Freni, G., G. Mannina, and G. Viviani. 2008. “Uncertainty in Urban Stormwater
Quality Modelling: The Effect of Acceptability Threshold in the GLUE
Methodology.” Water Research 42 (8–9): 2061–2072. doi:10.1016/j.
watres.2007.12.014.
van Genuchten, M. T. 1980. “A Closed-Form Equation for Predicting theHydraulic Conductivity of Unsaturated Soils1.”Soil Science Society of America
Journal 44 (5): 892–898. doi:10.2136/sssaj1980.03615995004400050002x.
Hilten, R. N., T. M. Lawrence, and E. W. Tollner. 2008. “Modeling Stormwater
Runoff from Green Roofs with HYDRUS-1D.” Journal of Hydrology 358 (3–4): 288–293. doi:10.1016/j.jhydrol.2008.06.010.
Hoffman, M. D., and A. Gelman. 2011. “The No-U-Turn Sampler: Adaptively
Setting Path Lengths in Hamiltonian Monte Carlo.” http://arxiv.org/
abs/1111.4246.
Li, Y., and R. W. Babcock. 2015. “Modeling Hydrologic Performance of a Green
Roof System with HYDRUS-2D.” Journal of Environmental Engineering 141(11): 4015036. doi:10.1061/(ASCE)EE.1943-7870.0000976.
Montanari, A. 2005. “Large Sample Behaviors of the Generalized Likelihood
Uncertainty Estimation (GLUE) in Assessing the Uncertainty of RainfallRunoff Simulations.” Water Resources Research 41 (8): 1–13. doi:10.1029/
2004WR003826.
Morris, M. D. 1991. “Factorial Sampling Plans for Preliminary Computational
Experiments.” Technometrics 33 (2): 161–174. doi:10.2307/1269043.
Ratto, M., S. Tarantola, and A. Saltelli. 2001. “Sensitivity Analysis in Model
Calibration: GSA-GLUE Approach.” Computer Physics Communications 136(3): 212–224. doi:10.1016/S0010-4655(01)00159-X.
Saltelli, A., S. Tarantola, and K. P. S. Chan. 1999. “A Quantitative ModelIndependent Method for Global Sensitivity Analysis of Model Output.”
Technometrics 41 (1): 39–56. doi:10.2307/1270993.
Šimůnek, J., M. T. van Genuchten, and M. Šejna. 2016. “Recent Developments
and Applications of the HYDRUS Computer Software Packages.” Vadose
Zone Journal 15 (7): 25. doi:10.2136/vzj2016.04.0033.
Turco, M., R. Kodešová, G. Brunetti, A. Nikodem, M. Fér, and P. Piro. 2017.
“Unsaturated Hydraulic Behaviour of a Permeable Pavement: Laboratory
Investigation and Numerical Analysis by Using the HYDRUS-2D Model.”Journal of Hydrology 554: 780–791. doi:10.1016/j.jhydrol.2017.10.005.