Determining Cloud Heights and Measurement Precision Using LIDAR Technology

A LiDAR (Light Detection And Ranging) is an instrument that can be used to measure how cloud properties, aerosols, temperatures or ozone concentrations change with height. In this instrument, a powerful laser beam (typically visible or ultraviolet) is fired vertically into the atmosphere in short pulses. The light that is scattered back to Earth is

collected by a telescope and measured by a sensitive detector. The time between the emission of the laser pulse and detection of the scattered light is used to determine the altitude scale for the profile.

Part A

Given:

2. Determine the averaging time for a layer within the cloud that is 50.0 m thick.

1. Height Calculation

d=3.00×108×35.0×10−62d = \frac{3.00 \times 10^8 \times 35.0 \times 10^{-6}}{2}d=23.00×108×35.0×10−6​

d=10.5×1032d = \frac{10.5 \times 10^3}{2}d=210.5×103​

The time to travel 50.0 meters (round trip) is given by:

tlayer=2×thicknessct_{layer} = \frac{2 \times \text{thickness}}{c}tlayer​=c2×thickness​

tlayer=333 nst_{layer} = 333 \, nstlayer​=333ns

So, Emily should average the signals for 333 nanoseconds.

The uncertainty in height (Δd\Delta dΔd) is related to the uncertainty in time (Δt\Delta tΔt) by:

Δd=c×Δt2\Delta d = \frac{c \times \Delta t}{2}Δd=2c×Δt​

Δt=1.003.00×108\Delta t = \frac{1.00}{3.00 \times 10^8}Δt=3.00×1081.00​

Δt=3.33×10−9 s\Delta t = 3.33 \times 10^{-9} \, sΔt=3.33×10−9s

1. The height of the cloud is 5250 meters.

2. Emily should average the signals for 333 nanoseconds to investigate a 50.0 m thick layer within the cloud.