MD11 CREW GOT A SERIES OF WINDSHEAR ALERTS ON ROTATION AT ONT.

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ON TKOF FROM ONTARIO; WITH HVY SMOKE IN AREA AND HIGH WINDS FROM FIRES; UPON ROTATION GOT TAILWIND SHEAR ALERT FOLLOWED IN APPROX 5 SECONDS BY HEADWIND SHEAR. FOLLOWED WINDSHEAR ALERT GUIDANCE SYS FLT DIRECTOR AND ESCAPED WINDSHEAR APPROX 1500 FT AGL. FILED RPT WITH ACR; BUT MISSED THE FLT OPS MANUAL ESCAPE MANEUVER REQUIREMENT TO LAND AT NEAREST SUITABLE ARPT. PROCEEDED TO ZZZ ARPT. NEVER EXCEEDED ENG OR AIRFRAME PARAMETERS DURING ESCAPE MANEUVER; SO NO DAMAGE WAS EXPECTED. SUPPLEMENTAL INFO FROM ACN 597984: FIRES WERE BURNING OUT OF CTL NEARBY AND SANTA ANA. AT ROTATION I HEARD AN AUDIBLE WARNING; BUT COULD NOT DETERMINE WHAT IT WAS SINCE MY ATTN WAS FOCUSED UPON ROTATING ACFT. ALMOST IMMEDIATELY I HEARD ANOTHER WARNING. THIS TIME I WAS ABLE TO OBSERVE AN INCREASING PERFORMANCE WINDSHEAR ALERT. WE CONTINUED THE SID; AND NOTIFIED ATC OF THE WINDSHEAR ALERT. AFTER THE EVENT; I HAD BEEN INFORMED THAT IN THE EMER PROC SECTION; WE WERE ALSO REQUIRED TO LAND AS SOON AS POSSIBLE. SINCE NO EMER WAS DECLARED; I NEGLECTED TO REFER TO THIS SECTION.