One cannot definitively determine the three most important events of natural phenomena in American history because no objective criteria define "most important.” We clearly want events (probably "natural disasters") after 1776 that affected vast areas and caused great change in American thought.
So where do we go? Well, I will start with one that did not kill many people or cause much damage anywhere near its location. On 7 February 1812 occurred the strongest earthquake in American history (outside Alaska), measuring fully 8.0 in the Richter scale--in New Madrid, Missouri. It concluded a series of four 7.0+-magnitude earthquakes in Arkansas and Missouri that winter. People as far away as Boston felt this earthquake. The winter quakes altered the course of the Mississippi River and caused much liquefaction and geologic instability throughout the upper Mississippi Delta. This event leads to the question, "what if it happened again today?” The impact on the American economy probably would rank alongside Hurricane Katrina but with devastation dispersed across a truly enormous region. How would Saint Louis survive? How would it affect navigation and trade along the Mississippi River, which has served our nation well as the principal artery of commerce into the heartland? We cannot answer those questions definitively, but we can point to the history. The New Madrid Seismic Zone remains active, and it will happen again.
My second event is even more mysterious that the first. Giant swarms of locusts devastated the northern Great Plains states during the 1870s, devouring crops and even eating shirts off people's backs. The repeated summer swarms imperiled agriculture and homesteading throughout the Plains. You do not hear much about locusts any more because they diminished rapidly after the 1870s and apparently went extinct in 1902. (Congress thankfully had not passed the Endangered Species Act. But how might the course of American history changed if the locust plagued us still today--under Congressional protection?) Why and how did a species once so numerous that it reduced Nebraska repeatedly to dust suddenly go extinct? Moreover, what impact did its extinction have on the evolution of the American environment? We might never know the answers.
For my final selection (in chronological order...nothing special here), I choose the 1927 Mississippi Delta flood. This event left vast swaths of western Mississippi, lowland Arkansas, and Louisiana under several feet of water for months on end. The Government had attempted to channel the Mississippi River into ever-higher levees for decades. This flood-mitigation strategy led to a prosperous Delta agriculture that attracted a large African-American farm-worker population. This flood directly altered the course of millions of lives, aided the political rise of Herbert Hoover from Secretary of Commerce to President, and dramatically changed American river-engineering policy. This was no ordinary flood but the greatest flood in American history; the Mississippi River flowed at places more than one hundred miles wide (except a few high spots). Because of the great scope of devastation, it also gave rise to the first federally led (and terribly botched) relief efforts in American history.
Honorable mention: the great pandemic influenza of 1918-1921. Although it started in Kansas, midway between Garden City and Liberal, it spread around the world and did most of its killing outside the United States. The dead number well into the tens of millions, perhaps more than one hundred million. We also could name any of the hurricanes that scourged various parts of the American South until 1928, many of which killed hundreds if not thousands. The Johnstown flood (1889), the San Francisco earthquake (1906), the Great Chicago Fire (1871), and the Year without a Summer (1816) also come to mind. We also might choose some more recent events, most notoriously Hurricane Katrina, but history is best viewed and evaluated in hindsight rather than as it happens.
Sorry for being so long-winded. In review, they are:
(1) 1811/1812 ARKANSAS/MISSOURI EARTHQUAKES
(2) 1870s ROCKY MOUNTAIN LOCUST SWARM and subsequent extincton
(3) 1927 MISSISSIPPI RIVER FLOOD (one-seventh of Arkansas under water!)