Overview

This project is focused designing a scaled up soil pylon deployment in the context of a real problem at the Palmdale, CA water reuse experimental site.  Wireless sensor networking technology is being coupled with soil geospatial parameter characterization and data assimilation efforts to develop a network design strategy based wireless technology, environmental media, and economic constraints.  The objectives of this project are:

• Create algorithms based on soil geospatial properties which optimize the placement of subsurface sensors to maximize information return for a given budget
• Develop and test a closed-loop feedback control algorithm using coupled sensor network data to calibrate process models, then using these models to forecast and prescribe control measures for avoiding the problem of excess nitrate penetration through soil to groundwater
• Explore the use of data assimilation methods for designing and maximizing the information content (and uncertainty) of sensor networks in complex environmental systems

Approach

Palmdale Soil Geostatistics and Network Design – Past work reported on the geostatistics of the soil hydraulic conductivity at the Palmdale site.  Over the past year, the geostatistics for the site have been used to identify optimal sensor locations given a budget (maximum number of sensors).  Two approaches have been developed focusing on (1) zones of maximum hydraulic conductivity and (2) hydraulic conductivity transitions between relatively low and high values.  The former case characterizes zones of maximum and fastest vertical penetration of water and nitrate.  The latter case is being investigated as a potential focal point for horizontal flow feeding into vertical flow to accelerate vertical flow and transport processes near the transition zones.

 

Soil Flow and Transport Model Parameter Sensitivity Analysis – The deterministic models for moisture, heat and nitrate propagation have been developed for the pylon and parameter estimation schemes have been implemented to enable near real-time model calibration.  Seven parameters, Cin(input nitrate concentration), λ(decay rate), Dm(molecular diffusion coefficient), α(soil dispersivity), Ks(saturated hydraulic conductivity), q(application rate), Co(initial nitrate concentration in soils) were analyzed in a sensitivity analysis. The uncertainty of the parameters was characterized by assigning a uniform distribution to q and Co, normal distribution to Cin, λ, Dm, and α, with 200 replicates. The replicates of Ks are selected from measurement data from Palmdale. The effects of individual parameters on the nitrate concentration are mapped in scatter plots. Scatter plots show the relationships between model input parameters and output of the simulation model (nitrate concentration in soils). For example, input and output can have linear or nonlinear relationships or no relationship so that the points are randomly spread over the plot.

 

Data Assimilation - This is the newest effort in the Contam project portfolio.  The approach is to implement a stochastic unsaturated flow and transport model in conjunction with the Ensemble Kalman Filter (EnKF) to form the basis of a real-time algorithm for ongoing state and parameter estimation at the Palmdale site.  The geostatistical techniques are used to create a best-estimate of the hydraulic conductivity distribution at the Palmdale experimental field site.  The EnKF uses a Monte Carlo approach to describe how the conditional probability density of the state evolves over time (between measurements) and how it changes when new measurements are included, by propagating individual realizations drawn from a small population (or ensemble).  Realizations are simply predictions from the physical model under different sets of parameter and forcing inputs.  The combined data and simulation tools developed will be used to optimally design and bound forecasts gathered from the Palmdale sensor network-trained simulation models.

Systems/Experiments

Pamdale Soil Geostatistics and Network Design - The EPS is a circular plot roughtly 400 M in diameter.  An aerial view of the sample collection locations is shown in the figure at right.  Overall, 119 soil samples have been collected at four or five depths from 28 borehole locations between summer 2003 and spring 2005.  Sampling depths were generally 1, 3, 5, 7 and 9 ft below ground surface (bgs).  Occational deviations from these depths were necessary when excessively dry soil conditions prevented sample collection at a particular depth.

Figure 1.  Overview of the Palmdale experimental pivot site with sampling locations (black dots), initial pylon locations (red squares), and Stargate base station (larger blue circle).

Previous reports have described the geostatistics in terms of histograms, kriging maps, kriging error (variance) maps.  During the past year work with the Palmdale geostatistics has been directed at the sensor network design problem. 

Figure 2. Optimal sensor network design superimposed on kriging map for hydraulic conductivity (Ks); first approach optimally spaces

Algorithms have been created which, given a budgeted number of pylons, use the kriging maps to identify the optimal placement of these pylons in terms of providing adequate coverage in critical soil zones. 

Soil Flow and Transport Model Parameter Sensitivity Analysis - The nitrate transport is simulated with one-dimensional model for sensitivity analysis in Matlab. The reclaimed water is sprinkled for 6 hours and the scatterplots are examined with nitrate concentration at the surface 1 hour after the water stops.  The most prominent parameter turns out to be decay rate. Inversely proportional relationship between nitrate concentration and decay rate is noticeable (Figure 1 (a)). The close pattern becomes more well-defined when the time goes on assuming that the decay rate is constant. This means that the nitrate concentration in soils can be highly reduced by decay component such as nitrate uptake by plant root or microbial decomposition of nitrate in soils.

Nitrate concentration in the reclaimed water and initial concentration in soils have proportional relationship with the amount of nitrate in soils (Figure 1 (b) and (c)). This is somewhat expected because higher input and higher initial condition supplies more nitrate in soils. The application rate which is the steering wheel in our irrigation control system does not have much impact on the output (Figure 1 (d)). It is hard to see the direct pattern between application rate and nitrate concentration, that is, nitrate concentration reacts slowly to the rate of change of the reclaimed water input. This makes our irrigation system not easy to control.

Figure 3. Scatterplots of (a) decay rate (λ), (b) initial nitrate concentration in soils (Co), (c) nitrate concentration in the reclaimed water (Cin), and (d) application rate (q) at 7 hours.

The scatterplots of other parameters (Dm(molecular diffusion coefficient), α(soil dispersivity), Ks(saturated hydraulic conductivity)) showed that the individual points are randomly spread over the plot, which means nitrate concentration is insensitive to these parameters.

Data Assimilation Effort.  The first phase of the data assimilation project has been the selection and implementation of a flow and transport model.  For our application we need a robust and fast-running code for simulating highly-nonlinear unsaturated flow processes under a variety of parameter sets.  To meet this objective we chose the Hydrus-1D model, which is an extremely well-tested Fortran code capable of simulating moisture, heat, and contaminant flow and transport through the unsaturated zone.  The governing equations for volumetric soil moisture content (), soil temperature (T), and contaminant concentration (C) are given respectively by:

which represent the moisture, energy, and contaminant mass budgets throughout the soil column.  Hydrus-1D efficiently solves these equations using robust numerical techniques.  Further, this “off-the-shelf” model has source code that can easily be modified for the purposes of our project.  Initial test runs for various scenarios provided with the model have shown it is performing as expected on our platform.

Hydrus-1D has been modified to accept a more realistic evaporative boundary conditions, and parameterized using soil properties characteristic of the Palmdale site were used to study flow in the unsaturated zone which is highly sensitive to the saturated hydraulic conductivity (Ks).  In addition to its sensitivity, hydraulic conductivity is a highly uncertain parameter, known to vary over orders of magnitude in the field.  To begin to characterize the uncertainty in flow realizations under uncertainty in this parameter we did several perturbation runs using values between 50-200% of the nominal value shown in Table 1. Results from these preliminary simulations are shown in Figures 4 and 5.  Figure 4 shows the time series of the ensemble of surface soil moisture realizations over the course of the first day of the simulation.

Figure 4.  (left) Ensemble of surface soil moisture realizations as a function of time during the first day of the simulation; (right)  ensemble of soil moisture profiles at the end of the simulation (7 days).

Figure 4 (right) shows the ensemble of soil moisture profiles at the end of the simulation.  Both plots show the relatively large impact of uncertainty in the saturated hydraulic conductivity on the evolution of the soil moisture profiles.  For the surface soil moisture, significant differences emerge within a day after the first irrigation event.  The differences in conductivity manifest in different penetration depths of the wetting fronts which lead to significant variability at depth in the soil. 

Accomplishments

The following are the major accomplishments in this area:

• Development of geostatistics-based soil sensor network design strategies for optimal placement of sensors under budget constraints
• Completion of a process-based modeling framework and feedback-control algorithm to close the loop on irrigation and nitrate management in the Palmdale test bed
• Initiation of work on developing robust data assimilation strategies