Niagara Falls, From The American Side, painted in 1867 by American landscape artist Frederic Church, is a real showstopper.

As an adult, I've stood in front of this huge painting in the Scottish National Gallery in Edinburgh, just as I did as a wee girl of nine looking at the real thing from the Canadian side, and marvelled at its sheer scale and potency.

Church was a member of the Hudson River School, a group of American artists who started the country's great tradition of landscape painting knowing that a highly finished painting was the one thing which would guarantee critical as well as commercial acclaim. This one did, with knobs on.

Church was 40 and at the peak of his powers when he received a commission to paint a large work for the Exposition Universelle in Paris of 1867. Ever the showman (he was described as "Barnumesque" by one critic of the day), he decided to return to a theme, Niagara Falls, for which he was well known, having painted it several times to great acclaim in the late 1850s.

He was also a compulsive sketcher in oil paint, and many on-the-spot studies made from 1856 to 1859 from both sides of the falls are on show in this quieter exhibition of work by the man often referred to as the American Turner.

These sketches include a hybrid study made in 1858 called Niagara From The American Side, which shows how Church was using the relatively new science of photography to help him in his work. Almost in the way artists now use apps as tools, he painted over a small (32.7cm x 29.5cm) albumen print which he may have bought as a souvenir on his 1856 visit.

Church is clearly exploring the possibilities of tonal values, perspective and experimenting with a vivid turquoise which would find its way, a decade later, into the much-loved painting which is in the collection of the Scottish National Gallery. This gigantic painting, now temporarily situated at the bottom of a stairwell leading up to the gallery known as the Impressionist Room, provides a grand welcome to the 25 smaller oil sketches by Church on show from today.

This painting of Niagara was never shown in Paris, but when it was exhibited in London in 1868, it created a sensation. It was duly acquired by a Scots-American businessman, John S Kennedy, who gifted it to the gallery in Edinburgh in 1868. Astonishingly, it remains the only major work by Church in a European public collection – perhaps the reason why he so well known on this side of the Atlantic.

Frederic Church, born to a wealthy jeweller father in Hartford, Connecticut, was a precocious talent from an early age. "He had the finest eye for drawing in the world" reckoned his mentor, the great American landscape artist Thomas Cole and, in keeping for the 19th-century passion for the plein-air oil sketch, Church was a prolific and accomplished exponent of this art. His output was constant from the late 1840s until his death in 1900.

Michael Clarke, director of the National Gallery of Scotland, likens Church's place in the art firmament of his day to being a bit like the way we now view Sir David Attenborough's wildlife documentaries.

"His large paintings were intended to knock you out," Clarke says. "It was a bit like him saying, 'you wanna see the Arctic – I'm your man!' America was very bound up with its own landscape at the time. There were moral overtones to it and of course there was a desire within Church's land to be free from Europe."

One of the most enduring images of the Civil War was his 1861 oil sketch, Our Banner In The Sky. Depicting a blood-orange night scene in which the Union Flag is embodied by a flash of greenish star-spangled sky against a livid striped sunset, this natural stars-and-stripes is attached to a lone spindly tree. The sketch affirmed Church's support for the northern cause and reinforced his deep religious beliefs. A print of this image sold in its thousands and this exhibition offers the opportunity to view the original in all its glory.

Clarke also alludes to the private sorrow of Church, the family man, who escaped to Jamaica in 1865 with his wife Isabel, following the death from diphtheria of their two eldest children. "He came to Jamaica to grieve," he explains, "and the four sketches from Jamaica on show are stunning."

Seeing Church within the historical context of an era when America was asserting its independence against the backdrop of a rapidly changing world in which old orders were being challenged, is key to viewing this vital body of work with a fresh pair of eyes.

Through American Eyes: Frederic Church And The Landscape Oil Sketch, Scottish National Gallery, The Mound, Edinburgh (0131 624 6200, until September 8