This is a shell script that runs incremental backups on the btrfs filesystem. I used the instructions on the wiki for the initial setup. It is designed to work with the Ubuntu btrfs configuration. THIS SCRIPT COMES WITH ABSOLUTELY NO WARRANTY. Any loss of data is not my responsibility. However, it does work for me, and I regularly use it.

backup.sh

#!/bin/sh

#Find a date in file name:
#ls | grep -E $datematch

if [ "$(whoami)" != "root" ]; then
    echo Please run this script as root.
    exit
fi

today=$(date +%Y-%m-%d)
datematch='[0-9]{4}-[0-9]{2}-[0-9]{2}'

cd /mnt
#Mount drives
mount /dev/sda3 ./root
mount /dev/sdb ./bu

increment() {
    sync
    # $1 directory to look in
    # $2 subvolume to backup
    # $3 y/n delete old snapshots from internal drive
    local old="$(ls $1 | grep -E $2-$datematch)"
    local new=$2-$today
    echo Backing up $old...
    btrfs sub snap -r $1/$2 $1/$new
    echo Sending $new to external drive...
    if ([ $3 = "y" ] || [ $3 = "Y" ]); then
        #The following two lines make sure that the old subvolume is not deleted
        #if there was an error in the copying.
	    btrfs send -p $1/$old $1/$new | btrfs receive -e bu/ && btrfs sub del $1/$old
	else
	    btrfs send -p $1/$old $1/$new | btrfs receive bu/
    fi
    echo -----------------------------------------------------------------------
}

#User Prompts
read -p 'Do you want to backup home [y/n]? ' bu_home
read -p 'Do you want to backup root [y/n]? ' bu_root
read -p 'Do you want to delete the old snapshots on the internal drive [y/n]? ' del_old

#Backup function calls
if ([ $bu_home = "y" ] || [ $bu_home = "Y" ]); then
    increment root @home $del_old
fi

if ([ $bu_root = "y" ] || [ $bu_root = "Y" ]); then
    increment root @ $del_old
fi

#Unmount drives
umount /mnt/bu
umount /mnt/root
echo Drives unmounted.

Nice