How can air stability be predicted?
It depends on how far in the future you are trying to predict air stability and turbulence. I am not an expert. But, I would look for some indicators.
For instance, the historic Program Charts from Friday and Saturday show a cold front moving through the area of KADS from West to East. The winds were drastically shifting as the front moved through. This would be an indicator that it might not be a good day to fly. Combine this prognostic data with the METARs from the previous 24 hours to your flight, there is cause for concern for a light aircraft. The winds and gust factors in these METARs might have given you as much as a 24 hour warning of what was to come. Then, there is the Aviation Area Forecast Discussion which will give you further guidance. Lastly (and least used), right before the fight, you could have even checked out the Skew-T/Log-P Diagram in order to judge the strength and severity of the instability.
METARs for KADS:
KADS 141352Z 19008G15KT 8SM BKN009 21/19 A2990
KADS 141447Z 19008G16KT 8SM BKN014 22/19 A2990
KADS 141547Z 19010G25KT 10SM BKN022 24/18 A2989
KADS 141647Z 20017G32KT 10SM BKN028 BKN070 25/18 A2987
KADS 141747Z 19016G31KT 10SM BKN033 27/18 A2983
KADS 141847Z 19016G31KT 10SM BKN039 27/17 A2978
KADS 141953Z 19016G30KT 10SM BKN046 BKN055 27/17 A2974
KADS 142053Z 19012G26KT 10SM BKN050 28/17 A2971
KADS 142153Z 19011G20KT 10SM SCT044 OVC055 27/17 A2972
KADS 142253Z 19016G30KT 10SM SKC 26/17 A2971
KADS 142353Z 19012G21KT 10SM SCT120 26/17 A2973
KADS 150047Z 20009G20KT 10SM SKC 25/17 A2976
KADS 150147Z 20009G20KT 13SM SKC 25/17 A2977
KADS 150215Z AUTO 20009G17KT 10SM CLR 25/18 A2980 RMK AO2 T02450175
KADS 150247Z 18008G16KT 10SM SKC 25/17 A2978
KADS 150255Z AUTO 20009KT 10SM CLR 24/18 A2981 RMK AO2 T02420175
KADS 150315Z AUTO 20008KT 10SM CLR 24/18 A2981 RMK AO2 T02410175
KADS 150335Z AUTO 20009G15KT 10SM CLR 24/18 A2982 RMK AO2 T02410175
KADS 150355Z AUTO 21007KT 190V250 10SM CLR 24/18 A2983 RMK AO2 T02400175
KADS 150415Z AUTO 22004KT 10SM CLR 24/18 A2984 RMK AO2 T02360175
KADS 150435Z AUTO 22004KT 10SM CLR 24/18 A2985 RMK AO2 T02350175
KADS 150455Z AUTO 23006KT 10SM CLR 23/17 A2986 RMK AO2 T02330173
KADS 150515Z AUTO 23006KT 10SM CLR 24/17 A2986 RMK AO2 T02380170
KADS 150535Z AUTO 25007KT 230V290 10SM CLR 24/17 A2987 RMK AO2 T02360169
KADS 150555Z AUTO 29017G23KT 10SM CLR 23/15 A2990 RMK AO2 T02330150 10254 20232 402730182
KADS 150615Z AUTO 33018G24KT 10SM CLR 22/07 A2994 RMK AO2 T02150072
KADS 150635Z AUTO 34020G30KT 10SM CLR 18/02 A2999 RMK AO2 T01820024
KADS 150655Z AUTO 35020G27KT 10SM CLR 17/02 A3002 RMK AO2 T01710015
KADS 150715Z AUTO 35015G22KT 10SM CLR 17/01 A3004 RMK AO2 T01650013
KADS 150735Z AUTO 35013G28KT 10SM CLR 16/01 A3006 RMK AO2 T01610005
KADS 150755Z AUTO 35019G25KT 10SM CLR 16/M02 A3008 RMK AO2 T01571018
KADS 150815Z AUTO 35013G18KT 10SM CLR 15/M03 A3010 RMK AO2 T01541034
KADS 150835Z AUTO 35013G22KT 10SM CLR 15/M04 A3011 RMK AO2 T01501045
KADS 150855Z AUTO 35013G20KT 10SM CLR 15/M05 A3013 RMK AO2 T01461051
KADS 150915Z AUTO 35015G24KT 10SM CLR 14/M06 A3014 RMK AO2 T01441065
KADS 150935Z AUTO 35012G19KT 10SM CLR 14/M07 A3014 RMK AO2 T01391070
KADS 151147Z 35010KT 10SM SKC 12/M07 A3020
KADS 151247Z 35012G17KT 10SM SKC 10/M07 A3022
KADS 151347Z 33005KT 10SM SKC 11/M05 A3025
KADS 151447Z 35012G16KT 10SM SKC 13/M06 A3029
KADS 151547Z 36013G20KT 10SM SKC 14/M07 A3030
KADS 151647Z 02010G20KT 10SM SKC 16/M07 A3032
KADS 151747Z 03010G20KT 10SM SKC 17/M08 A3031
KADS 151847Z 34008G15KT 10SM SKC 18/M08 A3029