INFLUENCED
avalanche (rain)
erosion (rain)
landslide (rain)
sunshine/blue skies (lack of precipitation/wind/rain)
dust devil (wind/drought)
dust storm (wind/drought)
flash flood (rain)
rainbow (precipitation)
sandstorm (wind/drought)
Avalanches are usually influenced not by rain or weather at all but by weight. Of course, if the avalance is of snow, then it could be influenced by weather especially if you kept snowing and snowing and snowing.

But if it were an avalance of rocks, for example, i think it would be influenced by weight.
Also, I agree with Syl that a tsunami is influenced more by tectonic forces than by weather. From Wikipedia:
A tsunami (IPA: /(t)sʊˈnɑːmi/) is a series of waves created when a body of water, such as an ocean, is rapidly displaced. Earthquakes, mass movements above or below water, volcanic eruptions and other underwater explosions, landslides, large meteorite impacts comet impacts and testing with nuclear weapons at sea all have the potential to generate a tsunami.
Of course, you could always create a storm underwater to replace the ocean, thus causing a tsunami. hehehehe.

Many waters cannot quench love, neither can floods drown it. There is no fear in love; for perfect love cast out fear.