Lead Investigator:

Mark Hansen, Deborah Estrin, Miodrag Potkonjak

Overview

Using wireless in situ sensing systems, application scientists are tackling environmental that require measurements of many parameters and in many locations. We are developing algorithmic techniques for iterative deployment as well as system tools to help design and deploy such sensing systems. Although we are focusing in particular upon soil monitoring deployments, we hope that our tools and techniques will be applicable to a larger class of networked sensing systems.

Approach

Deployment results are uncertain, and choosing sensing locations can be a difficult problem. Some prior information and domain expertise may be available, but because the surprising results of a deployment cannot be anticipated it is difficult to know just where sensors should be placed in an environment. An iterative approach to deployment is then a natural fit. By using an iterative deployment methodology a few sensors can be placed, and the resulting data can be used to learn about other potentially good deployment locations. In this way, a deployment can be grown and refined into a large-scale sensing system. As more data is collected, the ability to choose quality sensing locations should increase. Maximizing the quality of sensing locations allows more area to be covered with a fixed sensing budget.

Sensor placement in soil monitoring applications is particularly difficult due to the heterogeneous nature of soil. A natural response to soil heterogeneity is to deploy many sensors. However, in soil monitoring, the cost of instrumenting a site is high. This cost is paid primarily in terms of time: once disturbed the soil needs time to resettle, which can take upwards of three months. While the soil is settling the data from the sensors is considered unreliable in that the data does not reflect the state of uninstrumented soil. In addition, the density of deployed sensors may be fundamentally limitted. Soil moisture sensors often use the dialectric effect, and their readings can be affected by other nearby soil moisture sensors.

In contrast to the difficulty and cost of installing sensors in the soil, meteorological sensors are much easier to deploy. Because above-ground phenomenon affects conditions below ground it is possible to use meteorological measurements to infer what is happening below ground. Thus, we are developing placement algorithms that use portable, and noninvasive, sensing arrays (which we refer to as auditioning arrays) to make measurements at potential in-situ deployment sites in order to gain insight quickly into below-ground processes. The difficulty and delay associated with in-situ sensors is in contrast to the ease and rapidity that sensor data can be collected from a site using an auditioning array. Auditioning arrays leverage models that relate above-ground meteorological conditions to below-ground soil parameters. The use of auditioning arrays to audition potential deployment sites becomes an “inner loop” to of the iterative deployment process, creating a deployment within a deployment. We are developing algorithms and tools to enable this iterative deployment methodology, and we have evidence that auditioning can yield useful information about below-ground processes.

Systems/Experiments

To demonstrate the usefulness of auditioning arrays to infer below-ground conditions, we use AMARSS data that collected both the above-ground and the below-ground conditions to create a model of the temperature at 2 cm from meteorological measurements. Each of the ten AMARSS sites has been measuring the following for over two years: (a) Above-Ground Barometric pressure,  Air temperature, Relative humidity,  Photosynthetically active radiation (PAR) ; and (b) Below-Ground Soil CO2 concentration sensors at 2 cm, 8 cm, and 16 cm, Soil temperature at 2 cm, 8 cm, and 16 cm,  Soil moisture at 2 cm, 8 cm, and 16 cm.

The top half of figure 1 shows the soil temperature at 2 cm for one of the AMARSS sites. A quick rise in temperature in the mid-morning is followed by spikes in the temperature during the middle of the day, and finally a rapid decrease in temperature as the sun sets. Cooling continues until the next morning. The spikes in the temperature during midday are caused by variations in direct sunlight. The bottom half shows the PAR during the same period. Spikes in the light level are also evident during midday due to variations in shading. Although the light sensor is not on the ground a similar spike pattern is evident, although the temperature spikes are lagged slightly. Because temperature is a diffusion phenomenon, the temperature at 2 cm below the ground will be a function of time-shifted above-ground inputs. We assume that temperature at 2 cm is only impacted by the air temperature and the incident radiation.

Although it is possible to try to model the diffusion process, this is difficult because of unknown environmental parameters: leaf litter composition, leaf litter thickness, leaf litter moisture content, and soil composition. An automated approach to fitting was applied, and our knowledge of the physical process was leveraged by our choice of input variables. We use multivariate adaptive polynomial spline regression (polymars in the statistics package R) to perform the regression. As input we use the number of hours since midnight (ranging from 0 to 23), air temperature, radiation, and several delayed version of both, with the most delayed being two hours. The fitted model was trained on 2/3 of the data, and tested on the last 1/3 . Polymars uses the input data, adds knots to them, and uses pairwise interactions as well. Rather than try to provide a modeling technique with data that had been delayed appropriately (which would require knowing the impact of the leaf litter and soil composition) we leave it to the modeling procedure to choose the proper variables. Regression was done using two different sets of delayed curves. The first had data delayed in 5 minute intervals, the second had data delayed in 10 minute intervals. After training, the two models both use similar interaction terms, implying that the model is stable. Only results from the data set lagged in 10 minute intervals is discussed.

Figure 2 is a histogram of the residuals of the fit, and figure 3 is a Q-Q plot comparing the distribution of residuals to the normal distribution. Although the residuals are strongly unimodal the residuals also display heavy tails, indicated by the divergence from the Q-Q line. Figures 4 shows the portion of the temperature data where training stops and prediction begins (marked by the gray vertical line on the left side of the plot). The sudden change a little further on is caused by the hours since midnight wrapping around from the 23rd hour (11 pm) to 0th hour (12 am). Although the amplitude of the temperature is off, the spikes during the day occur at the correct times (indicated by the three vertical black lines on the right side of the plot).

Illustration 2: Histogram for the residuals of the fit.

Illustration 3: Normal Q-Q plot of the residuals of the fit.

Illustration 4: True (black) and predicted (cyan) temperature at 2cm depth using polymars

An advantage of this model is the possibility of parameter interpretability. Unlike neural networks, the effect that each term has on the model is easily understood, and we can try to ascribe the choice of parameters to known phenomenon. Figure 5 is an interaction plot showing the effect of the air temperature two hours in the past (predictor 14), and the light levels 10 minutes in the past (predictor 17), on he current soil temperature (response). From the plot, when the air temperature was high two hours ago then the light level tend to have little effect on the response. This is because if the air was hot two hours in the past then that heat has had time to diffuse into the soil. This damps the effect of fluctuating light levels in the middle of the day, the air temperature two hours ago is then a good predictor of current response of the soil temperature.

Illustration 5: Interaction plot of air temperature 2 hours ago vs. light levels 10 minutes ago

Accomplishments

In order to begin exploring iterative design methodologies we have augmented the existing AMARSS transect, originally consisting of 10 sites, with another 11 sites. Unlike the original 10, these new sites are connected wireless, providing data and feedback in real time. All 11 sites are equipped with a soil moisture sensor at a depth of 8 cm. Five of the eleven sites are monitoring soil temperature at 2 cm, 8 cm, and 16 cm, while the remaining are monitoring soil temperature at 2 cm, and 8 cm. (See TEOS section for further description of the scientific motivation for the AMARSS array)

Future Directions

We are currently developing placement algorithms that take into account phenomenon specific properties, as well as utilizing auditioning arrays. We plan to develop tools that will enable a user to design and deploy using available models and data, and to simulate the performance of a design under simulated and historic data sets. We also plan to build tools that will help a user in the field during deployment, so that when unforeseen obstacles arise the experimental design can be altered to accommodate the obstacle.

People

Faculty:

• Mark Hansen, Statistics, UCLA
• Deborah Estrin, Computer Science, UCLA
• Miodrag Potkonjak, Computer Science, UCLA

Staff:

• Eric Graham, CENS, UCLA

Graduate students:

• Tom Schoellhammer, UCLA