"No dust without water" is a famous quote by Prof Grant McTainsh, also known as "Doctor Dust".
What he meant to say is that dust storms often occur on dried-up river beds and lake floors. This process is very clearly visible in Australia, especially in the center of the continent: Lake Eyre. This is a so-called ephemeral lake, which means that it does not always contain water. In fact, only once every so many years there is a thin (up to 50cm) layer of water on the lake. This water flows in from the north from rivers that drain into the lake, and originates from summer rains that fall in Queensland. These rivers carry fine-grained sediments in suspension, and this mud is finally washed into the lake. With 3-4m evaporation in the center of the continent, the water is gone within a few months and the freshly deposited sediments are waiting to be picked up by winds. Occasionally, these dust storms are so spectacular that they make the frontlines of the news. For an example of this, see the frontpage of "The Australian" below, the spectacular photo was taken by Karen Brook
In this video, you can see the initiation of such a dust cycle; the dried-up lake floor of Lake Eyre fills up with water flowing in from the north. The movie ends when the lake is covered with water but anyone who knows the extreme heat and dryness in these parts of Australia can imagine that this water evaporates very quickly! Once the water has evaporated, the muds will be picked up by the winds again.
In March this year, tropical cyclone "Debbie" caused a lot of damage by >160mph winds and dropped a LOT of rain on Queensland. This waters have flown into Lake Eyre already and chances are that in a few months there will be large dust storms again!
In the satellite image (copyright: NASA) one can clearly see dust plumes being blown out of the rims of Lake Eyre as well as from channels that feed into the lake.