Harrie-Jan Hendricks Franssen

Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.

Soil moisture and soil properties estimation in the Community Land Model with synthetic brightness temperature observations

The Community Land Model (CLM) includes a large variety of parameterizations, also for flow in the unsaturated zone and soil properties. Soil properties introduce uncertainties into land surface model predictions. In this paper, soil moisture and soil properties are updated for the coupled CLM and Community Microwave Emission Model (CMEM) by the Local Ensemble Transform Kalman Filter (LETKF) and the state augmentation method. Soil properties are estimated through the update of soil textural properties and soil organic matter density. These variables are used in CLM for predicting the soil moisture retention characteristic and the unsaturated hydraulic conductivity, and the soil texture is used in CMEM to calculate the soil dielectric constant. The following scenarios were evaluated for the joint state and parameter estimation with help of synthetic L-band brightness temperature data assimilation: (i) the impact of joint state and parameter estimation; (ii) updating of soil properties in CLM alone, CMEM alone or both CLM and CMEM; (iii) updating of soil properties without soil moisture update; (iv) the observation localization of LETKF. The results show that the characterization of soil properties through the update of textural properties and soil organic matter density can strongly improve with assimilation of brightness temperature data. The optimized soil properties also improve the characterization of soil moisture, soil temperature, actual evapotranspiration, sensible heat flux, and soil heat flux. The best results are obtained if the soil properties are updated only. The coupled CLM and CMEM model is helpful for the parameter estimation. If soil properties are biased, assimilation of soil moisture data with only state updates increases the root mean square error for evapotranspiration, sensible heat flux, and soil heat flux.

Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review

More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a simulation model. Existing approaches can be used to simultaneously update several model states and model parameters if applicable. In other words, the basic principles for multivariate data assimilation are already available. We argue that a better understanding of the measurement errors for different observation types, improved estimates of observation bias and improved multiscale assimilation methods for data which scale nonlinearly is important to properly weight them in multiscale multivariate data assimilation. In this context, improved cross-validation of different data types, and increased ground truth verification of remote sensing products are required.

Joint simulation of transmissivity and storativity fields conditional to steady-state and transient hydraulic head data

Abstract The self-calibrated method has been extended for the generation of equally likely realizations of transmissivity and storativity conditional to transmissivity and storativity data and to steady-state and transient hydraulic head data. Conditioning to transmissivity and storativity data is achieved by means of standard geostatistical co-simulation algorithms, whereas conditioning to hydraulic head data, given its non-linear relation to transmissivity and storativity, is achieved through non-linear optimization, similar to standard inverse algorithms. The algorithm is demonstrated in a synthetic study based on data from the WIPP site in New Mexico. Seven alternative scenarios are investigated, generating 100 realizations for each of them. The differences among the scenarios range from the number of conditioning data, to their spatial configuration, to the pumping strategies at the pumping wells. In all scenarios, the self-calibrated algorithm is able to generate transmissivity–storativity realization couples conditional to all the sample data. For the specific case studied here the results are not surprising. Of the piezometric head data, the steady-state values are the most consequential for transmissivity characterization. Conditioning to transient head data only introduces local adjustments on the transmissivity fields and serves to improve the characterization of the storativity fields.

Monitoring and Modeling the Terrestrial System from Pores to Catchments: The Transregional Collaborative Research Center on Patterns in the Soil–Vegetation–Atmosphere System

AbstractMost activities of humankind take place in the transition zone between four compartments of the terrestrial system: the unconfined aquifer, including the unsaturated zone; surface water; vegetation; and atmosphere. The mass, momentum, and heat energy fluxes between these compartments drive their mutual state evolution. Improved understanding of the processes that drive these fluxes is important for climate projections, weather prediction, flood forecasting, water and soil resources management, agriculture, and water quality control. The different transport mechanisms and flow rates within the compartments result in complex patterns on different temporal and spatial scales that make predictions of the terrestrial system challenging for scientists and policy makers. The Transregional Collaborative Research Centre 32 (TR32) was formed in 2007 to integrate monitoring with modeling and data assimilation in order to develop a holistic view of the terrestrial system. TR32 is a long-term research program ...

Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling

[1] The ensemble Kalman filter (EnKF) is coupled with upscaling to build an aquifer model at a coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had been taken for the purpose of inverse modeling. Building an aquifer model at the support scale of observations is most often impractical since this would imply numerical models with many millions of cells. If, in addition, an uncertainty analysis is required involving some kind of Monte Carlo approach, the task becomes impossible. For this reason, a methodology has been developed that will use the conductivity data at the scale at which they were collected to build a model at a (much) coarser scale suitable for the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (1) Generate an ensemble of realizations of conductivities conditioned to the conductivity data at the same scale at which conductivities were collected. (2) Upscale each realization onto a coarse discretization; on these coarse realizations, conductivities will become tensorial in nature with arbitrary orientations of their principal components. (3) Apply the EnKF to the ensemble of coarse conductivity upscaled realizations in order to condition the realizations to the measured piezometric head data. The proposed approach addresses the problem of how to deal with tensorial parameters, at a coarse scale, in ensemble Kalman filtering while maintaining the conditioning to the fine-scale hydraulic conductivity measurements. We demonstrate our approach in the framework of a synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities, piezometric heads, or both is analyzed.

Joint assimilation of piezometric heads and groundwater temperatures for improved modeling of river-aquifer interactions

The ensemble Kalman filter (EnKF) is increasingly used to improve the real-time prediction of groundwater states and the estimation of uncertain hydraulic subsurface parameters through assimilation of measurement data like groundwater levels and concentration data. At the interface between surface water and groundwater, measured groundwater temperature data can provide an additional source of information for subsurface characterizations with EnKF. Additionally, an improved prediction of the temperature field itself is often desirable for groundwater management. In this work, we investigate the worth of a joint assimilation of hydraulic and thermal observation data on the state and parameter estimation with EnKF for two different model setups: (i) a simple synthetic model of a river-aquifer system where the parameters and simulation conditions were perfectly known and (ii) a model of the Limmat aquifer in Zurich (Switzerland) where an exhaustive set of real-world observations of groundwater levels (87) and temperatures (22) was available for assimilation (year 2007) and verification (year 2011). Results for the synthetic case suggest that a joint assimilation of piezometric heads and groundwater temperatures together with updating of uncertain hydraulic parameters gives the best estimation of states and hydraulic properties of the model. For the real-world case, the prediction of groundwater temperatures could also be improved through data assimilation with EnKF. For the validation period, it was found that parameter fields updated with piezometric heads reduced RMSEs of states significantly (heads −49%, temperature −15%), but an additional conditioning of parameters on groundwater temperatures only influenced the characterization of the temperature field.

Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. By comparison with a more standard implementation of the EnKF, the NS-EnKF gives better results with regard to histogram preservation, uncertainty assessment, and transport predictions.

Real-time management of an urban groundwater well field threatened by pollution.

We present an optimal real-time control approach for the management of drinking water well fields. The methodology is applied to the Hardhof field in the city of Zurich, Switzerland, which is threatened by diffuse pollution. The risk of attracting pollutants is higher if the pumping rate is increased and can be reduced by increasing artificial recharge (AR) or by adaptive allocation of the AR. The method was first tested in offline simulations with a three-dimensional finite element variably saturated subsurface flow model for the period January 2004-August 2005. The simulations revealed that (1) optimal control results were more effective than the historical control results and (2) the spatial distribution of AR should be different from the historical one. Next, the methodology was extended to a real-time control method based on the Ensemble Kalman Filter method, using 87 online groundwater head measurements, and tested at the site. The real-time control of the well field resulted in a decrease of the electrical conductivity of the water at critical measurement points which indicates a reduced inflow of water originating from contaminated sites. It can be concluded that the simulation and the application confirm the feasibility of the real-time control concept.

Integrating hydrological modelling, data assimilation and cloud computing for real-time management of water resources

Online data acquisition, data assimilation and integrated hydrological modelling have become more and more important in hydrological science. In this study, we explore cloud computing for integrating field data acquisition and stochastic, physically-based hydrological modelling in a data assimilation and optimisation framework as a service to water resources management. For this purpose, we developed an ensemble Kalman filter-based data assimilation system for the fully-coupled, physically-based hydrological model HydroGeoSphere, which is able to run in a cloud computing environment. A synthetic data assimilation experiment based on the widely used tilted V-catchment problem showed that the computational overhead for the application of the data assimilation platform in a cloud computing environment is minimal, which makes it well-suited for practical water management problems. Advantages of the cloud-based implementation comprise the independence from computational infrastructure and the straightforward integration of cloud-based observation databases with the modelling and data assimilation platform. A cloud-based real-time modelling and data assimilation framework is established.Can be connected to a cloud-based data acquisition and monitoring module.HydroGeoSphere is used as the hydrological forward model.The tiltedV-catchment problem is used as a benchmark for the system.