'somewhat independently' is correct and usable in written English.
You could use it to indicate that something is not completely independently, but is still partially independent. For example: She was able to live somewhat independently with the help of visiting carers.
While related, they operate somewhat independently, almost as backups for each other.
But Mr. Haqqani operates somewhat independently of those leaders inside Afghanistan.
Researchers are finding evidence that different synapses of the same neuron act somewhat independently.
The designer must create separate implementations of the different architectures, optimizing each of them somewhat independently.
Pepsi already operates much like a holding company, with its Tropicana, Frito-Lay and soft-drink divisions acting somewhat independently.
The interface is geomorphological change, an interface both are aware of but study somewhat independently and differently.
The Times, in my opinion, did take a reputational risk in doing business with WikiLeaks, though it has inoculated itself somewhat by reporting independently on the organization.
The school was built through a program in Britain that channels private philanthropy into schools that are technically public but run independently, somewhat like charter schools in the States.
This notion of Algorithmic Information Theory was invented independently somewhat later separately by Kolmogorov (1965) and Chaitin (1969).
In the case of uncorrupted signals, the main criterion for a dictionary to be recoverable is that its coherence scales well with the average sparsity level S of the signals (S μ 2≲1, [29]) and that all atoms are somewhat equally and independently used.
Although such perceptions are subjectively influenced by disease processes, they are thought to exist somewhat universally and independently of particular life events and circumstances.
