Why A waterfall is a scrolling spectrogram: the horizontal axis is frequency, just like a spectrum analyzer or panadapter, and each new line of data is painted at the top (or bottom) and scrolls, so the vertical axis represents time. Signal strength is not a height but a color or brightness, so a strong signal shows as a bright or hot-colored vertical streak. That is why it is called a waterfall, the display flows downward as time passes.
Watch out The choice with frequency horizontal and signal strength vertical describes an ordinary spectrum scope or panadapter trace, which shows amplitude versus frequency at one instant with no time history.
Waterfalls fall down: time runs vertically, frequency across, strength = color.