CAPT OF A GULFSTREAM 1; TURBOPROP; G159; OVERSHOT ASSIGNED ALT DUE TO SEVERE TURB. SUBSEQUENTLY CAUSED ACFT TO CLB OFF ASSIGNED ALT RESULTING IN ATC APPROVING A HIGHER ASSIGNED ALT.

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NO CONFLICTS THAT I WAS AWARE OF. DEPARTING AUSTIN MUELLER FOR DALLAS LOVE. I CALLED AUSTIN CLRNC FOR MY CLRNC AND WAS CLRED AS FILED. DURING THE DELIVERY OF THE CLRNC THE ATC SPECIALIST TOLD ME THERE HAD BEEN RPTS OF MODERATE TURB ALONG THE FLT PLAN RTE BTWN FL190 AND FL200. THIS WAS BECAUSE OF TSTMS ENRTE. DURING CLBOUT RADAR INDICATED A TSTM LINE OFF TO THE L WHICH WAS ON OUR COURSE. I REQUESTED A DEV TO THE R TO A HDG OF 060 DEGS TO CLR THE LINE. HOUSTON APPROVED. AS WE WERE APCHING FL190 HOUSTON ASSIGNED FINAL ALT OF FL200. I HAD FILED FOR FL210 FOR E DIRECTION. MY RATE OF CLB AT THIS TIME WAS 2500 FPM. I STARTED LOWERING NOSE OF ACFT FOR A GRADUAL CAPTURE OF ASSIGNED ALT. AT FL195 THE ACFT ENCOUNTERED MODERATE TURB WHICH CAUSED AN OVERSHOOT OF ASSIGNED ALT OF ABOUT 400 FT. CTR CALLED TO TELL US THAT HE INDICATED OUR DEV. I SAID 'ROGER' AND INITIATED A CORRECTION BACK TO ASSIGNED ALT. I ALSO REQUESTED L TURN DIRECT TO CEDAR LAKE BECAUSE RADAR INDICATED A CLRING OF STORMS IN THAT DIRECTION. ALMOST IMMEDIATELY THE ACFT ENCOUNTERED SEVERE TURB WITH AN UPDRAFT THAT CAUSED ALT GAIN TO FL210. CTR AGAIN CALLED ABOUT DEV. I INFORMED HIM IT WAS REALLY ROUGH RIGHT HERE. HE ASKED IF I WOULD LIKE HIGHER. I SAID 'YES.' WE WERE THEN CLRED HIGHER AND GOT OUT OF THE SEVERE TURB. WE EXPERIENCED LIGHT TO MODERATE TURB THE REST OF THE FLT TO DALLAS. NO CONFLICTS WERE NOTED.