For the last two days and for the coming 24 hours (at least), a stationary front has stretched from East Texas to the Upper Ohio Valley, separating cooler air to the north from warm, humid air to the south. This front is responsible for the swath of tornados, severe thunderstorms and flooding rains that have plagued that region.
While most storm systems move rapidly from west to east, some stall out, their trailing front creating a clash zone between the air masses. When this happens, secondary storms and their precipitation train above the same swath of geography, producing the unrelenting rain we have seen this week. Once the soil is saturated, runoff rapidly fills and then floods the rivers and streams, spilling across floodplains and often taking out bridges and riverside structures.
Unfortunately, this flooding often does not peak until the storm system has finally moved on to the east. As the swollen tributaries empty into larger streams and rivers, the latter continue to rise long after the skies have cleared.