Grounding wire is typically gray or green. If green, then 10 AWG is
in Home Depot, Lowes, or any electrical supply company. But that
ground wire is their responsibility. You don't pay anything for them
to fix their ground wire. However verify or install an 8+' earthing
rod before they fix their wire. That 8 foot electrode (or network of
electrodes) should make a 'less than 10 foot' connection to NID as well
as to breaker box and cable TV. You provide a preferred earthing
electrode that already earths AC breaker box.

Sometimes a telco lineman can detect failures with a tester. Problem
that would not be apparent on your phone (during dry days) can
sometimes appear as leakage to earth on his tester. Business office
will recite reams of rules such as who pays that $99. But a lineman is
typically good about finding a problem even when noise does not exist
today. Good as long as he gets details from you and not from the
business office. Generally, a lineman will inspect your wire back to
the CO even if reason for noise is not apparent. Some problems can
only be located by inspection.

However some telcos are now instituting cost controls. If a lineman
gets the call too late in his day, he may simply declare the wire good
without inspecting. Executives give him hell for doing overtime to
complete a job. Therefore he may sign off on the job early. This
problem created when business school trained managers (who never worked
as linemen) know better.

Sounds like water is dripping into a splice somewhere back towards
the CO. All wires should enter a junction box by dropping down below,
then rising up from beneath. If not, then even a taped wire will
conduct water 'hum destructively' into a splice. Verify that every
wire into that NID comes up from below. Verify that no tapes over
wires are exposed to the weather.

wrote:
Thanks to all who replied. I did do as you say, on the first day. The
hum was the same when plugged into the NID. I called the telco while
outside in the drizzle, and still plugged into that NID jack. The
customer rep told me that someone would arrive the next day, and if
they plugged into the outside jack and there was no hum, I'd get
charged $99 for the visit. I said that the problem might be gone the
next day, which was forecasted to be dry and sunny - so I told her not
to send anybody.

That decision saved me the $99. By 11am the next day, the hum was gone.
But the day after that was rainy again, and the hum was back. I
disconnected and reconnected the ground, which had no effect
whatsoever. Next, I fiddled with the wires inside the NID. Then the
phone was clear. A half hour later, the hum was back. I removed the
plug and sprayed electronic cleaner into the jack. (Note that wasps had
made a nest inside, since abandoned - but there could be some fine
organic material all over.) The noise came and went with no rhyme or
reason on that day, but was gone the following day.

There have been some slight rains since, with no hum. I guess I have to
wait for bad rains, and try to schedule a visit while it is still in
the rain period. It's a crap shoot.

In the meantime, where could I get the exact same grey wire that the
telco uses for ground?
I don't want to one day have them show up and charge me a small fortune
to redo it. Thanks.