A320 Captain describes difficulties encountered during the LDA DME 19 approach to DCA. The approach occurred late at night in reduced visibility and was the first time for this reporter. Reporter believes that simulator training should be required prior to flying the actual approach.

Narrative

Late night arrival; we were first cleared for the visual to Runway 19. It was too hazy and dark for us to pick up the river in time. We were vectored around to the LDA approach. We quickly reviewed and briefed the approach and commenced the approach. The visibility was poor; though legal; for the approach. It was very difficult to see the visual landmarks and do the circling part of the approach. We were very aware of avoiding the prohibited areas and may have inadvertently strayed too far west. It was VERY difficult to see our exact position as it was after midnight on a very dark night with haze. I had never done this approach in my 30+ years of flying and we were both very fatigued. We made every effort to fly the approach correctly but this was; by far; the most difficult approach I have ever flown in my 5 years on the Airbus. I do not feel that the Commercial Chart pages and depictions are adequate for a night approach by someone unfamiliar with the airport and the extremely difficult approaches; especially at night and in reduced visibility. This approach should be a simulator training approach instead of a very simple NDB!