The weather ATC transmissions to aircraft are based on the local routine and special reports (not to be confused with METAR/SPECI), which are displayed in the ATS unit, and are ultimately covered by Annex 3, where no minimum mean is specified to start reporting a variation, and where "significant" variations are defined:
- Wind speed: 10 knots above mean, or 5 knots above mean if noise abatement is in effect
- Direction: when it's ≥ 60° (details below).
ICAO Doc 4444
Starting from Doc 4444, which is complementary to SARPs Annex 2 and directed mainly at ATC personnel (§ 2.1):
188.8.131.52.2 Prior to take-off aircraft shall be advised of:
[...] any significant changes in the surface wind direction and speed, the air temperature, and the visibility or RVR value(s) given in accordance with 184.108.40.206.1 [...]
Note.— The meteorological information listed above is to follow the criteria used for meteorological local routine and special reports, in accordance with Chapter 11, 220.127.116.11.2 to 18.104.22.168.3.
Likewise for landing (22.214.171.124.3), so let's check 126.96.36.199.2 and .3:
188.8.131.52.2 Meteorological information concerning the meteorological conditions at aerodromes, to be transmitted to aircraft by the ATS unit concerned, in accordance with Annex 11, Chapter 4 and this document, Chapter 6, Sections 6.4 and 6.6 and Chapter 7, Section 7.4.1, shall be extracted by the ATS unit concerned from the following meteorological messages, provided by the appropriate meteorological office, supplemented for arriving and departing aircraft, as appropriate, by information from displays relating to meteorological sensors (in particular, those related to the surface wind and runway visual range) located in the ATS units:
a) local meteorological routine and special reports [...]
184.108.40.206.3 The meteorological information referred to in 220.127.116.11.2 shall be extracted, as appropriate, from meteorological reports providing information on the following elements: [...]
Note. — Provisions relating to meteorological information to be provided in accordance with 18.104.22.168.3 are contained in Annex 3 — Meteorological Service for International Air Navigation, Chapter 4 and Appendix 3.
The local routine and special reports displayed to the controller are used, and are handled by Annex 3 Chapter 4, so let's go there:
4. OBSERVING AND REPORTING OF METEOROLOGICAL ELEMENTS [...]
4.1 Surface wind [...]
4.1.5 Reporting [...]
22.214.171.124 In local routine and special reports and in METAR and SPECI: [...]
c) variations from the mean wind speed (gusts) during the past 10 minutes shall be reported when the maximum wind speed exceeds the mean speed by:
2.5 m/s (5 kt) or more in local routine and special reports when noise abatement procedures are applied in accordance with paragraph 7.2.6 of the PANS-ATM (Doc 4444); or
5 m/s (10 kt) or more otherwise [...]
If you're still unsure about the term "significant", Annex 3 says:
Table A3-1. Template for the local routine (MET REPORT) and local special (SPECIAL) reports [...]
Significant speed variations (C)4
With the footnote saying:
4. To be included in accordance with 126.96.36.199 c).
188.8.131.52 c) is already quoted above.
Likewise for the direction:
b) variations from the mean wind direction during the past 10 minutes shall be reported as follows, if the total variation is 60° or more:
when the total variation is 60° or more and less than 180° and the wind speed is 1.5 m/s (3 kt) or more, such directional variations shall be reported as the two extreme directions between which the surface wind has varied;
when the total variation is 60° or more and less than 180° and the wind speed is less than 1.5 m/s (3 kt), the wind direction shall be reported as variable with no mean wind direction; or
when the total variation is 180° or more, the wind direction shall be reported as variable with no mean wind direction;
(All bold emphasis added.)