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Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach

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Abstract

This paper describes an innovative procedure that is able to simultaneously identify the release history and the source location of a pollutant injection in a groundwater aquifer (simultaneous release function and source location identification, SRSI). The methodology follows a geostatistical approach: it develops starting from a data set and a reliable numerical flow and transport model of the aquifer. Observations can be concentration data detected at a given time in multiple locations or a time series of concentration measurements collected at multiple locations. The methodology requires a preliminary delineation of a probably source area and results in the identification of both the sub-area where the pollutant injection has most likely originated, and in the contaminant release history. Some weak hypotheses have to be defined about the statistical structure of the unknown release function such as the probability density function and correlation structure. Three case studies are discussed concerning two-dimensional, confined aquifers with strongly non-uniform flow fields. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix and the recent step input function procedure has been successfully applied.

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Abbreviations

C(x,t):

Concentration at point x and time t

t :

Time

τ:

Time

x :

Position in the domain

x 0 :

Source location

u :

Velocity tensor

D :

Dispersion tensor

∇:

Nabla operator

F(t):

Concentration of the water injected at the source as function of time t

F 0 :

Constant and known mass rate input function

f(x,t):

Transfer function at position x and time t

m :

Number of observations

n :

Number of unknowns

z :

m × 1 Observations

s :

n × 1 Unknowns

s(t):

Unknown release function

p :

Number of unknown coefficients

h(s) :

m × 1 Vector that describes the transport process

v :

m × 1 Measurement errors

R :

m × m Error covariance matrix

H :

m × n Sensitivity matrix

T :

Sampling time

X :

n × p Matrix, mean of the unknown process

b :

p × 1 Unknown coefficients

Q(θ) :

n × n Matrix, covariance of the unknown process

θ :

Structural parameters of the covariance function

\( \sigma_{s}^{2} \) :

Variance of the unknown release function s(t)

λ s :

Correlation time length of the unknown release function s(t)

Σ :

m × m Dummy matrix

Ξ :

m × m Dummy matrix

σ 2R :

Variance of the measurement error

\( {\hat{\mathbf{s}}} \) n × 1:

Vector of estimated release function

M :

p × n Multipliers

Λ :

n × m Kriging coefficients

V :

n × n Matrix, covariance of the estimate of the errors

\( \tilde{s} \) :

Transformed unknown function

α :

Positive number

h D :

Head level downstream

h U :

Head level upstream

α L :

Longitudinal dispersivity

α T :

Transversal dispersivity

Q in :

Injected flow rate

K :

Hydraulic conductivity

Y :

Logarithm of the hydraulic conductivity

σ 2Y :

Variance of the log-conductivity field

Z :

Normalized log-conductivity

μY :

Mean of the log-conductivity field

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Acknowledgments

We warmly thank Michael Cardiff and Michael Fienen for their valuable review that greatly improved the manuscript.

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Authors and Affiliations

  1. DIATI, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Ilaria Butera

  2. DICATeA, Università degli Studi di Parma, Parco Area delle Scienze, 181/A, 43124, Parma, Italy

    Maria Giovanna Tanda & Andrea Zanini

Authors
  1. Ilaria Butera
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  2. Maria Giovanna Tanda
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  3. Andrea Zanini
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Correspondence to Andrea Zanini.

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Butera, I., Tanda, M.G. & Zanini, A. Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach. Stoch Environ Res Risk Assess 27, 1269–1280 (2013). https://doi.org/10.1007/s00477-012-0662-1

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