Traditional irrigation timers typically support optional rain sensors
that open the circuit to irrigation valve solenoids while rain falls,
but generally do not account for rainfall amounts,
much less rain that falls while irrigation is not happening.
A number of irrigation controllers and weather stations for consumers are Internet-aware,
and several irrigation controller companies apply smart metering
based on local weather information, e.g. from NOAA.
At least 3 companies will supplement that with information
from websites collecting data from personal weather stations:
Orbit b-hyve, RainMachine and rachio.
Of these, RainMachine may obtain data from e.g.
Acurite weather stations via Weather Underground AKA Wunderground.

IBM recently acquired Wunderground
and disabled access to that API for new consumers.
RainMachine released beta firmware to obtain Wunderground PWS (but not forecast) data.
Meanwhile, b-hyve and rachio use aerisweather.com,
which in turn collects PWS data via pwsweather.com and NOAA's Citizen Weather Observation Program (CWOP):
https://www.aerisweather.com/support/kb/api/what-data-sources-are-used-for-the-api/
https://support.rachio.com/en_us/rachio-weather-intelligence-B153wIJKD
Weather Underground (PWS) & Rachio

While Acurite works with Wunderground but not pwsweather.com,
other PWS brands may communicate to pwsweather.com (but not Wunderground).
There was a mechanism for transferring Wunderground PWS data to pwsweather.com,
allowing rachio and b-hyve controllers to refine their smart irrigation calculations
with very local Acurite PWS data:   http://beta.wufyi.com

All 3 of these irrigation controller suppliers employ Wi-Fi,
which may lack signal strength at typical controller installation locations.
Thick wires (gauge numbers below 18) are problematic.

rachio - most expensive and best support,
              but control only by smartphone
RainMachine - less expensive, decent support, smartphone and simple local controls;
                        Mini-8 fits existing timer housing
                        and uses existing 24VAC power,
                        detects rain sensor switch...
                        perhaps better Wi-Fi implementation;
                        can be initialized near access point
                        before installation at irrigation wiring.
                        https://support.rainmachine.com/hc/en-us/articles/228019028-WiFi-Range
b-hyve - least expensive @ $92.50, smartphone and elaborate local controls;
              should be within 30 ft of WiFi access point.
              Power cord with plug
              Support, code and app documentation are concerns.