Let's say that your initial four-hour window and any data that has gone through a scaling process is 'good.'
Let's say our good data ends at time T, and we have a new 4-hour window of data that ends at time T+10.
The only difference between the data in our new window and good data is the scaling factor. Every minute that the new window has in common with good data can generate a vote for scaling factor we need to make the new data 'good': scaling factor = (good value) / (new value).
Normally I'd use the median of votes for something like this, but because the data is so coarse, you're at risk for there being 'cliffs' in the data, and in particular the median might be next to a significantly larger or smaller number. For that reason, I suggest generating a scaling factor off the votes by eliminating the k outliers in both directions, then taking the average of the remaining votes.
If you want even more votes, you can get them off non-adjacent 4-hour blocks (though obviously with limited returns).
--- Example ---
Say in the initial window, the peak searches is 1000. That means the scaling factor for that window is 0.10, which will result in the peak searches Google displays to us being 100.
In the next window we have a new peak of 2000. Now, these peaks are invisible to us, but what we do see is that each of the points that exist in both windows have half the value in the new window vs the old window. Since votes (described above) are (good value) / (new value), we have a bunch of votes close to 2.0 (close not exact due to coarseness and rounding).
So we multiply each of our 10 new values by 2.0 to convert them to the good scale. A value of zero is unchanged since no searches is no searches whatever the scale.
