Goodall's Wikipedia entry is here. A web site devoted to his family includes this biographical information.
Although he painted a variety of subjects, Goodall is best considered an Orientalist, one of a group of (mostly) European 19th century artists who traveled North Africa and the Near East, painting scenes of the exotic for their pre-television / pre-internet audiences.
To put it another way, Orientalist painters were reporters of a kind. That, combined with their typically academic training, accounts for that fact that most Orientalist paintings (regardless of artist) are hard-edged and detail-filled.
Many Orientalists needed little excuse of paint exotic beauties, clothed or (so much the better) partly so. The lady pictured here appears to be a fair-skinned Greek in what logically would be a Turkish setting, but more likely she was an Englishwoman.
Presumably during the annual rise of the Nile in Egypt.
The color work is nice on this, one of Goodall's better Orientalist paintings.
Not strictly Orientalist, but informed by Goodall's travels in Egypt.
Lawrence Alma-Tadema was a master of painting marble and Northern Europeans in Classical scenes. Goodall was not so good at this.
Now for some examples of Goodall's non-Orientalist work.
She was his second wife.
A Biblical scene with an Englishwoman posing -- an offshoot of Orientalism.