PRIOR TO NOTIFYING ATC; A CRJ100 CREW EXECUTED A MISSED APCH FOLLOWING A WINDSHEAR INDICATION AND APCHING DETERIORATING WX.

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WE WERE BEING VECTORED TO THE ILS RWY 36R AT HSV. THERE WAS A SIGNIFICANT AREA OF WX TO THE W OF HSV. CURRENT CONDITIONS WERE RPTED TO US BY HSV APCH 320 DEGS AT 17 KTS; 16 SCATTERED; 44 BROKEN; 2 1/2 MI RAIN. AT 3000 FT AND ON A 050 DEG HDG; WE WERE CLRED FOR THE ILS RWY 36R APCH. WE WERE PAINTING A LEVEL 3 AREA OF PRECIP OVER THE FINAL; HSV APCH SAID THEY SHOWED IT AS A LEVEL 2 AREA. WE CONTACTED TWR OUTSIDE THE MARKER AT 180 KTS; AND WITH OUR FLAPS AT 20 DEGS WE BEGAN OUR DSCNT. AT ABOUT 2500 FT MSL; THE AIRSPD INCREASED TO 205 KTS. OUR TREND VECTOR SHOWED A 40 KT INCREASE. OUR PITCH WENT FROM 3 DEGS TO ABOUT 7 DEGS AND WE WERE NOW 1 DOT ABOVE THE GS. I DISCONNECTED THE AUTOPLT; REDUCED THE PWR; AND INCREASED THE PITCH TO AVOID EXCEEDING THE FLAP 20 DEG SPD. I ANNOUNCED TO THE FO THAT I WAS DISCONTINUING THE APCH AND I WAS GOING TO TURN OUT TO THE SE TO BETTER WX. DURING THIS THE TWR WAS GIVING US OUR CLRNC TO LAND AND THE CURRENT WX ON THE FIELD. AS SOON AS THE FO HAD A CHANCE TO TELL THE TWR OUR INTENTIONS; I HAD ALREADY BEGUN OUR TURN OFF THE APCH. I ALSO CLBED THROUGH OUR PREVIOUS ALT OF 3000 FT; WHICH WAS ALSO THE MISSED APCH ALT. I CLBED AS HIGH AS 3500 FT. I BELIEVED I GAINED MOST OF THE ALT DUE TO THE INCREASING PERFORMANCE WINDSHEAR. I HAD MOST OF THE PWR BACK AND A PITCH DOWN ATTITUDE. I DID NOT WANT TO BE TOO AGGRESSIVE IN PITCHING OVER OR REDUCING THE PWR TO IDLE IN THE CURRENT CONDITIONS AND THAT CLOSE TO THE GND. THE TWR CTLR SEEMED UPSET THAT WE TURNED OFF THE APCH AND GAINED ALT WITHOUT TELLING HIM FIRST. THE FO RPTED THAT WE WERE TURNING TO THE SE AS SOON AS HE HAD A CHANCE. I UNDERSTAND HIS POS; BUT I FEEL IF I WOULD'VE CONTINUED THE APCH; WHILE WE HAD A CHANCE TO REQUEST A TURN OUT TO THE SE; WE WOULD'VE FLOWN INTO WORSENING WX; AND PUT OUR FLT INTO A WORSE SIT. I SHOULD NOT HAVE ACCEPTED THE APCH CLRNC. I PUT TOO MUCH FAITH IN APCH CTL RADAR. FROM WHAT MY RADAR WAS SHOWING; IT WAS WORSE. THE CURRENT CONDITIONS ON THE FIELD HAD A LOT TO DO WITH MY DECISION AS WELL. THE WX WAS ACTUALLY S OF THE FIELD; SO THIS DIDN'T TELL THE WHOLE STORY. HOWEVER; NEXT TIME I WILL TELL THE CTLR OUR INTENTIONS RATHER THAN ACTING AND WAITING TO COMMUNICATE WITH THE CTLR.