The June 2004 edition of the Communications of the ACM magazine has an article on Habitat Monitoring with Sensor Networks (Mote Sensing). Mote Sensing uses a network of tiny embedded devices that work together to provide detailed real-time data that can then uploaded and analyzed in a larger database. Scientists on Great Duck Island, Maine are using these devices to monitor burrows for an elusive nesting bird.

The workhorse behind the system is an application called TinyDB. It allows a central data warehouse to collect real-time data on a detailed scale. A basic hardware kit can be had for less than $1000, so I just might own one soon. I'm thinking that I should put some sensors in the woods behind my house along with my laptop and cell phone and start recording some soil temperatures.

Why soil temperatures? I'm always interested in problems that have an applied math component, and soil temperature utilizes the heat equation, which is u_t = Du_xx. The t in the equation is time and the x in the equation is depth. There is a special function A * e^iwt which solves this problem (anything not an x or a t is a constant and of scientific interest). Yeah, it's a sine or cosine wave, who'd a thunk it? The solution is of the form u(x,t) = A U(x) e^iwt where D U'' = iwU. Solving for U we get that U(x) = A e^-1(w/2D)1/2 so: u(x,t) = A U(x) e^{i(wt-(w/2d)1/2x)}. Sorry, I know it's a lot of math and I leaving out HUGE details - like - what is a derivative? I learned about this equation and others from this book (The author is was one of my favorite profs in college and I partly owe my ability to earn a good living to his patience).

The solution of the 1D heat equation implies that soil under the surface is out of phase with the surface temperature by p = (w / 2D)^1/2x. For me, it makes sense to think of it as the speed that the heat travels through the soil. The speed is sure to vary with moisture, time of year, ground-cover, etc. By putting several of these devices at different depths, I could get interesting real-time data about how specific constants of my nearby soil (w and D) vary during the year. If I had enough patience and a big enough data warehouse, I could get a detailed view of how the soil properties vary over time. I'd say that would be a pretty fun adventure for an amateur scientist and would benefit my not-so-amateur pursuits in the area of data warehousing.