The techniques by which cosmic rays in a given energy range are detected depend critically on the rate of arrival. In the energy spectrum to the left (which you already saw in the section on Ultra-High Energy Cosmic Rays), you see that in the energy range of 1011-1012 eV, the flux of cosmic rays is roughly 1 particle per square meter (one square meter is roughly 10 square feet). This rate is high enough to allow direct detection.
The atmosphere absorbs most of the cosmic rays, as was demonstrated by Hess's original experiments. Radiation detected at ground level are actually secondary particles produced from interactions between primary cosmic rays and the air. To measure the primary cosmic rays directly, the detection equipment must be placed above the atmosphere. This is accomplished usually by carrying the instrument aboard high-altitude balloons flying at above 100,000 feet, on Earth-orbit satellites, or in the future aboard the International Space Station (ISS). An example of a detector scheduled for deployment on the ISS is the Alpha Magnetic Spectrometer (AMS), which is designed to search for nuclear antimatter in cosmic rays.
At above 1015-1016 eV, the flux of cosmic rays drops to below one particle per square meter per year. This rate makes direct measurements impractical, as it would require flying very large detectors in order to collect sufficient number of particles. A different method is required.