[ADSM-L] V6.1.4.1 internal database backup

I'm seeing error messages in db2diag.log when DB2 attempts an internal
online database backup that the disk is out of space. The system is AIX
6.1 and the filesystem is / and I believe the system is trying to back
up to somewhere under /home/tsminst1/sqllib/.

2010-11-29-07.04.08.664788-300 E744475749A451     LEVEL: Info
PID     : 12452072             TID  : 40361       PROC : db2sysc 0
INSTANCE: tsminst1             NODE : 000         DB   : TSMDB1
APPHDL  : 0-46592              APPID: *LOCAL.tsminst1.101129120415
AUTHID  : TSMINST1
EDUID   : 40361                EDUNAME: db2agent (TSMDB1) 0
FUNCTION: DB2 UDB, database utilities, sqlubSetupJobControl, probe:1508
MESSAGE : Starting an online db backup.

2010-11-29-07.07.10.119813-300 E744476201A816     LEVEL: Error (OS)
PID     : 12452072             TID  : 28134       PROC : db2sysc 0
INSTANCE: tsminst1             NODE : 000
EDUID   : 28134                EDUNAME: db2med.40361.0 (TSMDB1) 0
FUNCTION: DB2 UDB, oper system services, sqlowrite, probe:70
MESSAGE : ZRC=0x850F000C=-2062614516=SQLO_DISK "Disk full."
         DIA8312C Disk was full.
CALLED  : OS, -, write
OSERR   : ENOSPC (28) "No space left on device"
DA

How does the the DB2 internal database backup tie in with TSM and the
integrity of the database? Does the instance filesystem have to be as
big as the total size of the database?

Any information will be appreciated. Thank you.