unformatted write of allocatable data structure

This is confusing, because it seems to work with the Intel compiler (2015) when the write is done in the same program before the read.

The compile fails with G95 giving the error message

         write(1)TestData
                 1
Error: Data transfer element at (1) cannot have ALLOCATABLE components

Here is the example code. Invoke with "test" to write first and "test 1" to attempt to read the old file, which fails. Why?

      implicit none
      
      integer::i
      character(len=1)::buf
      logical::WriteFileFirst=.false.
      
      type TestType
         real*8,dimension(:),allocatable::a
      end type TestType
       
      type(TestType),dimension(:),allocatable::TestData
      
      call getarg(1,buf)
      if(buf.ne."")then
         write(*,*)'using old file'
      else
         WriteFileFirst=.true.
         write(*,*)'Writing file first'
      endif
       
      allocate(TestData(3))
      do i=1,3
         allocate(TestData(i)%a(2))
      enddo
      
      if(WriteFileFirst)then
         do i=1,3
            TestData(i)%a(1)=3
            TestData(i)%a(2)=4
         enddo
         
         open(1,file='TestData',form='unformatted')
         write(1)TestData
         close(1)
      endif
      
      open(1,file='TestData',form='unformatted')
      read(1)TestData
      close(1)
      write(*,*)'TestData(1)=',TestData(1)
      end