Why upgrading only to 16.04 when you could upgrade to latest 16.10 (WB.16.10.0002)? See here.
Pay attention that such old software version (15.13.0008) will require the BootROM to be updated too...this will happen automatically (and will causes a double reboot, the very first to update the BootROM image, the second to update the Software).
Moreover to upgrade to 16.10 HPE suggests to first update to 16.08 as interim:
"Software Release WB.16.10.0002
UPGRADE NOTE: HPE recommends that you update to this software from one of the three previous releases (WB.16.08 xxxx - WB.16.10.xxxx). If your switch is running an earlier version of software, incremental updates are recommended. Please follow 'Best Practices for Software Upgrade' section of the HPE ArubaOS-Switch Basic Operations Guide Version 16.08 for guidelines about configuration compatibility during upgrade.
IMPORTANT: This software includes an update to BootROM WB.16.03. If your switch has an older version of BootROM, the BootROM will be updated with this software. Do not interrupt power to the switch during this important update!"
The same happens to upgrade to 16.08...HPE suggest to step into 16.06 first...and to upgrade to 16.06 HPE, again, suggest an interim upgrade to 16.03 first...the loop continues...and to arrive on 16.03 is suggested to upgrade to 15.18 first (which is "near" to your current very old 15.13), 15.18 seems to not require an interim release before it.
Be prepared to perform these jumps 15.13 --> 15.18 --> 16.03 --> 16.06 --> 16.08 --> 16.10 and almost each jump (excluding probably latest three) will force a BootROM automatic update (dual reboot).
Reference here. Read carefully each Release Notes of any software version you plan to use.
