EXPERT RESPONSE
802.11 signal strength can certainly be affected by physical obstacles. I have never read anything regarding the impact of sandstorms, but it stands to reason that sand in the air between transmitter and receiver would cause some attenuation.
Strong winds also frequently impact radio transmission systems –- not through signal attenuation, but by knocking directional antennas out of alignment or causing other physical damage to base stations.
According to my colleague Craig Mathias, heat won't directly affect RF propagation, but it could affect the electronics used if temperatures rose to, say 70+ degrees C. Some mil-spec products are designed to handle higher temperatures.
In your case, you can try to determine the impact of these weather conditions by taking performance measurements at regular intervals. Ping can be helpful –- for example, run a batch file hourly to send a fixed number of pings (ping –n) and write the average to a file. But it may be more useful to run something that measures application throughput, like using FTP to copy a few files (perhaps several large images) from a Web site and average their throughput. Alternatively, a number of Web sites let you measure your connection speed interactively. You can view this list of international speed test sitess.
But the reason that I suggest batch-mode tests at regular intervals is that you'll end up with a larger set of samples that you can review or plot with a spreadsheet program. That will help you establish a baseline -- what your performance usually is -- and differentiate it from anomalies caused by weather -- what your performance is during or following a storm.
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