Natural springs’ protection and probabilistic risk assessment under uncertain conditions Emanuela Bianchi Janetti, Monica Riva, Alberto Guadagnini This document and its content is copyright of Emanuela Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Bianchi Janetti, 2020. All rights reserved.

1. Pilot site characterization 2. Conceptual models

SECT. 1 SECT. 1 CREMONA aquifer is a heavily exploited site Facies volumetric We parameterize the conductivity field following two different conceptual schemes: in the alluvial plain (Northern Italy), its 1 fraction2 3 4 5 Composite Medium Overlapping Continuum CM n f n f 10% Kk= OC_ A OC_ G Iij, natural high-quality water springs are the ji a) SECT. 2 Class 1 K= I k Kk= 15% A’ 195 Class 2 j i, j i ii Class 3 37% Prescribed flow Class 4 .) Class 5 i=1 i=1

SECT. 2 main supply to agriculture and a key 95 Prescribed a.s.l 40 head -5 Indicator function

B’ B’ flow (m a. s. l.) environmental driver. 5% (m

33% z z

-105 Prescribed low hydraulic conductivity lithotypes Section A’A’ borehols The analysis of available sedimentological 30 -205 00 10000 10 20000 20 y local (m) 30000 30 40000 40

Sondrio (m) b) c)

C’ C’ y

Hydrometric level station information allows identifying a set of 5 main local (km) Serio river y

20 Prescribed

Lecco Clay and silt 37% Prescribed Varese Como Meteorological station Class 1 head

Bergamo head (km) Monza .) Brescia Well geomaterials (facies/classes) which constitute Class 2 y

Monza Sand 5% head

head Prescribed

Class 3 a.s.l

Milano Geological stratigraphy 10 Prescribed Class 4 (m a. s. l.) No flow

Gravel 33% z Lodi the geological makeup of the system. (m river Mantova Spring Class 5 Pavia Cremona z 5 km Compact conglomerates 15% 0 a) A’ b) Section B’B’ Section C’C’ FACIES 1 FACIES 2 FACIES 3 FACIES 4 FACIES 5 Fractured conglomerates 10% 0 10 20 0 10 20 0 5 10 15 20 25 0 5 10 15 20 25 x local (km) x local (km) x local(m) (km) xxlocal(m) (km) x (m) x (m) 20 km x (km) x (km) x (km) x (km) x (km) 3. Groundwater flow modeling 4. Uncertain parameters

GEOLOGICAL HYDRAULIC LOG- Uncertain parameters are associated with (i) 5 hydraulic conductivities AQUIFER CONDUCTIVITY Three-dimensional groundwater flow We analyze the impact of ARCHITECTURE FIELDS Sample pdf OC_A A’ and (ii) 2 selected boundary conditions Elevation (m asl) Sample pdf OC_G 1 3 2 the uncertainty in the model under steady state regime. 4 Short Lower Upper 5 conceptual model and Parameter Description Unit 195 Composite medium 6 pdf The flow domain size is 23 km (E-W name bound bound 40 ] 8 7 model parameters on 95 9 asl 12 direction) × 48 km (N-S direction) × Clay and silt conductivity Facies 10 p k 10-8 10-5 m/s 11 14 15 z [m z [m -5 1 1 13 model outputs (hydraulic conductivity 16 475 m (depth). Each cell has dimension 17 -105 COMPOSITE COMPOSITE 18 MEDIUM (CM) MEDIUM Fine and silty sand 30 19 20 heads at 39 target wells) by -7 -4 21 22 -205 100 m × 200 m × 5 m. p2 k2 10 10 m/s 0 Overlapping 10 20 continuum 30 40 ln k 23 24 195 OC_G y [km] Gaussian pdf OC_A conductivity 25 (Arithmetic mean) CM 26 27 way of three GSA 28

] 95 Gaussian pdf OC_G Gravel, sand and gravel asl The diverse averaging strategies -4 -2 (km) 30 p3 k3 10 10 m/s 20 29 methodologies: (a) -5 conductivity y z [m z [m 31 Neumann BC significantly affect the spatial distribution Prescribed flow -105 Compact conglomerate derivative-based, (Morris) -6 -3 32 p4 k4 10 10 m/s -205 of Y. The domain is (on average) more conductivity 33 0 Overlapping 10 20 continuum 30 40 10 Dirichlet BC (b) variance-based 195 y [km] 34 36 (Geometric mean)CM pdf permeable and less heterogeneous when Fractured conglomerate 35 Prescribed head ] -3 -1 37 95 p k 10 10 m/s (Sobol’) (c) moment asl 5 5 the arithmetic rather than the geometric conductivity 38

-5 39 z [m z [m

B.C. based (AMAM indices, Total flow rate from 3 0 -105 mean operator is employed. p6 p6 4.83 14.47 m /s

OVERLAPPING OVERLAPPING northern boundary

CONTINUA (OC) CONTINUA Dell’Oca et al., 2017). -205 0 10 20 30 40 p7 p7 River stage 0.0 3.0 m A’ y [km] Y = lnK 0 10 20 x (km) 5. Global Sensitivity Analysis 6. Probabilistic Risk Assessment

Composite medium Overlapping Continuum_A What is the probability of spring discharge reduction due to increasing exploitation of the aquifer? Morris Indices [1] Sobol Indices [2] AMAM Indices [3] Morris Indices [1] Sobol Indices [2] AMAM Indices [3] We evaluate this probability, stemming from the combination of the various

sources of uncertainty illustrated above, through a Fault Tree Analyses. well well SF

k1 INCREASING

k2 PUMPING RATE k k1 3 k1 k4 k2 OR k2 Q1 Q2 > Q1 k3 k5 k3 k Active spring observation 4 p6 k4

observation Depleted spring p7 k5 k5 K1 ID ID p6 K < K ID ID p6 2 1 AND p7 YA p7 WELL WELL T * (m)  * S S AMAE AMAV AMA (m)  p p pi pi pi pi pi i i YB hhTR, j j Our results show that: (i) hydraulic head for all conceptual models are significantly affected by the uncertainty of k and/or k ,(ii) impact of k and/or k is negligible and (iii) impact of BCs depends on 3 5 2 4 V pp1 ,..., s T the model. S = SSSSSp= p + p, p + p , p , p +..... + p ,..., p References i i i j i j k i N pp1 ,..., s Vf  j j, k We find that the sensitivity measures considered convey different yet complementary information. The [1] Morris, M.D., 1991. Factorial sampling plans for preliminary computational experiments. Technometrics 33, 161-174. ; [2] Sobol, I. M., 2001. Global 1 sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simulat. 55(1–3), 271-280. ; [3] Dell’Oca, A., Riva, choice of the conceptual model employed to characterize the lithological reconstruction of the aquifer AMAMp=− M f M [ f | p i ]  dp i M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydrol. Earth Syst. Sci. 21, 6219-6234.; [4] ip i Mf   Bianchi Janetti, E., Guadagnini, L., Riva, M., Guadagnini, A., 2019. Global sensitivity analyses of multiple conceptual models with uncertain parameters affects the degree of influence that uncertain parameters can have on modeling results. pi driving groundwater flow in a regional-scale sedimentary aquifer, J. Hydrol., 574, 544-556.