Thanks to a pair of free tools that have emerged to take advantage of Apple’s raw data feed of store-by-store availability, we’re getting a much better picture of the company’s supply and distribution problems than is afforded by the availability widget on Apple’s website.

The first is Chris Barnes’s real-time iPhone 3G Store Availability tool, which dips into the data feed every 15 minutes and displays all the information on one page — rather than breaking it up into state-by-state reports as Apple does. That way you can see at a glance that, as of Thursday 6:30 a.m. EDT, for example, the 16GB White iPhone 3G was in stock in 97 of 188 Apple stores in the United States, or 52% of all company shops.

[UPDATE: Apple seems to be having trouble with its data stream. As of Friday 7:00 a.m. EDT, its own widget showed no iPhones available anywhere in the United States. Barnes’ TopMuffin site, using data updated at 3:53 a.m., reported that there are iPhones — at least white ones — in stock in most states.]

The second tool is a series of fever charts published by Sean Harding on his personal blog here. We’ve posted several examples below the fold. When the data are arrayed to show availability over time, some interesting patterns emerge. For one thing, you can clearly see where the iPhone supply nearly flatlined on July 20, when only three Apple stores in the United States had any in stock (see Comic relief: The world is out of iPhones!).

You can also see how supply varies during the day, as stores run out of units one by one, and then spikes in the morning as the stock is replenished. On Wednesday morning, for example, the percentage of Apple stores with iPhones in stock reached 80%, although by the end of the day it was down to just over 50%.

The charts also suggest that the black 8GB model is the most popular and the white 16GB the least — although that assumes that Apple (AAPL) is manufacturing the three varieties in roughly equal numbers.

Below the fold, as promised, Harding’s most recent charts.