Petros Gaganis

A Bayesian Approach to the quantification of the effect of model error on the predictions of groundwater models

Errors arising from the imperfect mathematical representation of the structure of a hydrologic system (model error) are not random but systematic. Their effect on model predictions varies in space and time and differs for the flow and solute transport components of a groundwater model. Such errors do not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. A Bayesian approach is presented for quantifying model error in the presence of parameter uncertainty. Insight gained in updating the prior information on the model parameters is used to assess the correctness of the model structure, which is defined relative to the accuracy required of the model predictions. Model error is evaluated for each measurement of the dependent variable through an examination of the correctness of the model structure for different accuracy levels. The effect of model error on each dependent variable, which is quantified as a function of location and time, represents a measure of the reliability of the model in terms of each model prediction. This method can be used in identifying possible causes of model error and in discriminating among models in terms of the correctness of the model structure. It also offers an improved description of the uncertainties associated with a modeling exercise that may be useful in risk assessments and decision analyses.

Deconstructing vulnerability and adaptation in a coastal river basin ecosystem: a participatory analysis of flood risk in Nadi, Fiji Islands

Despite the growing discussion on vulnerability and adaptation in urban areas, there is limited research on how smaller towns and cities in Small Island Developing States are being affected by and responding to climate change impacts. This study uses fuzzy cognitive mapping (FCM), field visits and semi-structured interviews with 40 stakeholders across 6 different stakeholder groups in the Nadi River Basin, Fiji Islands to identify, analyse and deconstruct climate change vulnerability and adaptation options to manage increasing flood risks. The research evidence suggests that vulnerability to floods in the basin is on the rise due to a complex mesh of three intersecting factors. Firstly, non-climatic pressures such as development, drainage, social change, agriculture, tourism growth and deforestation combine, juxtapose and interact in a rather unique way with global climate variability (interdependent systems) to increase the stress on the river and coastal ecosystems. Secondly, the most vulnerable or at-risk populations like the farmers, squatter households and in particular women within the community have weak coping capacity due to a combination of demographic and social characteristics. Thirdly, vulnerability is on the rise due to climate factors as well as the flurry of unplanned development, redevelopment and degradation of catchment resources. The research findings have implications for adaptation policies. In particular, the basin stakeholders should integrate climate change within sectorial planning processes, actively engage the vulnerable groups, promote knowledge, awareness and social learning, and invest in adaptive management across all levels of decision-making. Structural policy changes to land-use planning and insurance financing schemes are also necessary to address growing risks. These have the potential to enhance local capacities of communities to adapt to climate-induced floods and improve ecosystem integrity for resilience building.

Vulnerability assessment of water resources and adaptive management approach for Lesvos Island, Greece

In the Aegean Islands, the continued availability of freshwater resources is of fundamental concern. This study analyzes the freshwater system for the Island of Lesvos by simultaneously conceptualizing various issues surrounding it using vulnerability assessment as a quantitative tool. The endpoint approach to vulnerability assessment was applied by developing a numerical expression based on a set of 25 quantitative and qualitative indicators; the indicators were identified as proxies to reflect the various conspicuous and inconspicuous issues surrounding water resources of the Island. In addition, concurrent visualization of the indicators was carried out by plotting radar charts. The assessment indicated that the Lesvian hydrogeological system has significant vulnerabilities emanating from both natural and anthropogenic pressures in addition to a poor adaptive capacity to counter perturbations; this was corroborated by the composite water vulnerability index which was calculated to be 0.69. Based on the analysis of the assessment results, the priority management targets and existing management optimization tools, the authors propose a quantitative framework that could aid the development of an effective methodology for addressing problems in water resource management; this approach couples adaptive water management with vulnerability assessment. The proposed methodology may represent a tool for identification of better solutions to water management–decision problems and/or provide important insights during decision making in similar environments.

Efficient Simulation of (Log)Normal Random Fields for Hydrogeological Applications

Two methods for generating representative realizations from Gaussian and lognormal random field models are studied in this paper, with term representative implying realizations efficiently spanning the range of possible attribute values corresponding to the multivariate (log)normal probability distribution. The first method, already established in the geostatistical literature, is multivariate Latin hypercube sampling, a form of stratified random sampling aiming at marginal stratification of simulated values for each variable involved under the constraint of reproducing a known covariance matrix. The second method, scarcely known in the geostatistical literature, is stratified likelihood sampling, in which representative realizations are generated by exploring in a systematic way the structure of the multivariate distribution function itself. The two sampling methods are employed for generating unconditional realizations of saturated hydraulic conductivity in a hydrogeological context via a synthetic case study involving physically-based simulation of flow and transport in a heterogeneous porous medium; their performance is evaluated for different sample sizes (number of realizations) in terms of the reproduction of ensemble statistics of hydraulic conductivity and solute concentration computed from a very large ensemble set generated via simple random sampling. The results show that both Latin hypercube and stratified likelihood sampling are more efficient than simple random sampling, in that overall they can reproduce to a similar extent statistics of the conductivity and concentration fields, yet with smaller sampling variability than the simple random sampling.

Attenuation capacity of a coastal aquifer under managed recharge by reclaimed wastewater

Managed Aquifer Recharge (MAR) is becoming an increasingly attractive water management option, especially in semiarid areas. Nevertheless, field studies on the fate and transport of priority substances, heavy metals and pharmaceutical products within the recharged aquifer are rare. Based on the above, the objective of this project is to study the hydrological conditions of the coastal aquifer of Ezousa (Cyprus) and its ability to attenuate pollutants. The Ezousa riverbed is a locally important aquifer used for a MAR project where treated effluent from the Paphos Waste Water Treatment Plant is recharged into the aquifer through a number of artificial ponds along the riverbed. Additionally, groundwater is pumped for irrigation purposes from wells located nearby. The hydrological conditions of the area are unique due to the construction of the Kannaviou dam in 2005 that reduced natural recharge of the Ezousa aquifer significantly, inducing the saltwater intrusion phenomenon. A three-dimensional finite element model of the area was constructed using the FEFLOW software to simulate the groundwater flow conditions and transport of Phosphorous and cooper in the subsurface from the recharge process. The model was calibrated using hydraulic head and chemical data for the time period of 2002-2011. The groundwater model was coupled with a geochemical model PHREEQC attempting to evaluate nitrate and Copper processes. Inverse modeling calculation was used to determine sets of moles transfers of phases that are attributed to the water composition change in groundwater between the mixture of natural groundwater and reclaimed wastewater and the final water composition.

Seasonal and spatial variation of arsenic in groundwater in a rhyolithic volcanic area of Lesvos Island, Greece

A survey conducted in water wells located in the rhyolithic volcanic area of Mandamados, Lesvos Island, Greece, indicated that significant seasonal variation of arsenic concentration in groundwater exists mainly in wells near the coastal zone. However, there were differences among those coastal wells with regard to the processes and factors responsible for the observed seasonal variability of the element, although they are all located in a small homogeneous area. These processes and factors include (a) a higher rate of silicate weathering and ion exchange during the dry period followed by the dilution by the recharge water during the wet period, (b) enhanced desorption promoted by higher pH in summer and subsequent dilution of As by rainwater infiltration during the wet period, and (c) reductive dissolution of Mn during the wet period and by desorption under high pH values during the dry period. On the other hand, in wells located in higher-relief regions, the concentration of As in groundwater followed a fairly constant pattern throughout the year, which is probably related to the faster flow of groundwater in this part of the area due to a higher hydraulic gradient. In general, seasonal variation of As in groundwater in the study area was found to be related to geology, recharge rate, topography—distance from coast, and well depth.

Assessing the efficiency of a coastal Managed Aquifer Recharge (MAR) system in Cyprus

Managed Aquifer Recharge (MAR) is becoming an attractive water management option, with more than 223 sites operating in European countries. The quality of the produced water, available for drinking or irrigation processes is strongly depended on the aquifers hydrogeochemical characteristics and on the MAR system design and operation. The objective of this project is the assessment of the operation efficiency of a MAR system in Cyprus. The coupling of alternative methodologies is used such as water quality monitoring, micro-scale sediment sorption experiments, simulation of groundwater flow and phosphate and copper transport in the subsurface using the FEFLOW model and evaluation of the observed change in the chemical composition of water due to mixing using the geochemical model PHREEQC. The above methodology is tested in the Ezousa MAR project in Cyprus, where treated effluent from the Paphos Waste Water Treatment Plant, is recharged into the aquifer through five sets of artificial ponds along the riverbed. Additionally, groundwater is pumped for irrigation purposes from wells located nearby. A slight attenuation of nutrients is observed, whereas copper in groundwater is overcoming the EPA standards. The FEFLOW simulations reveal no effective mixing in some intermediate infiltration ponds, which is validated by the inverse modeling simulation of the PHREEQC model. Based on the results, better control of the infiltration capacity of some of the ponds and increased travel times are some suggestions that could improve the efficiency of the system.

Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation.

Model calibration/parameter estimation techniques and conceptual model error

In a modeling exercise, errors in the model structure cannot be avoided because they arise from our limited capability to exactly describe mathematically the complexity of a physical system. The effect of model error on model predictions is not random but systematic, therefore, it does not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. The effect of model error varies in both space and time. It is also different for the flow and the solute transport components of a groundwater model and may have a significant impact on parameter estimation, uncertainty analyses and risk assessments. Structural errors may result in a misleading evaluation of prediction uncertainty associated with parameter error because model sensitivity to uncertain parameters may be quite different than that of the correct model. A substantial model error may significantly degrade the usefulness of model calibration and the reliability of model predictions because parameter estimates are forced to compensate for the existing structural errors. Incorrect uncertainty analyses and estimated parameters that have little value in predictive modeling could potentially lead to an engineering design failure or to a selection of a management strategy that involves unnecessary expenditures. A complementary to classical inverse methods model calibration procedure is presented for assessing the uncertainty in parameter estimates associated with model error. This procedure is based on the concept of a per-datum calibration for capturing the spatial and temporal behavior of model error. A set of per-datum parameter estimates obtained by this new method defines a posterior parameter space that may be translated into a probabilistic description of model predictions. The resulted prediction uncertainty represents a reflection on model predictions of available information regarding the dependent variables and measures the level of confidence in model performance.