I am not an expert, but here's an indirect source that includes some about early 20th century usage.

Calculations were precise, including planned factors such as shell and charge, relative positions and elevations of batteries and their targets, measurable factors universal to artillery pieces such as weather conditions (Aerial ballistics), and factors individual to each artillery piece(Internal & external ballistics). Rule of thumb calculations (individual gun registration) were utilized as part of the 'Book'.

The below quote talks about large artillery, not lower echelon mortars. I would be surprised if meteorology was employed to the same extent with the smaller mortars due to difficulties in communication, and also their closer proximity to targets means any weather variations would be much reduced. Calculations had to be precise in order to be effective. The switch from direct fire to indirect fire meant that every shot had to be predictable and reproducible.

Page 121: *"The technical prerequisites were accurate fire control instruments, a precise means of computing fire data, the location of guns and target on a common grid system, and a means of measuring and compensating for the many variables that affected a projectile’s flight. By 1917, the French had worked out the details of indirect fire without adjustment, often called map firing. They had perfected a system of ground survey that could be used to tie the firing batteries and targets together on a common grid system, which the Americans soon adopted. A reconnaissance officer assigned to each battalion, aided by excellent French maps, was responsible for bringing horizontal, vertical, and directional control into each battery position area. A premium was placed on the precise directional orientation of each individual gun. Because of variable factors, including nonstandard guns and powder, atmospheric conditions, and difference in projectiles, artillerymen adopted an empirical method of measuring the sum and direction of nonstandard effects. By firing a weapon of known location and comparing the firing table values achieved in firing, the sum of nonstandard effects could be inferred and expressed as a correction. These corrections, determined and applied in proper ratio, permitted fire without adjustment on other targets. The technique was called registration. To aid in registration, the American field artillery used weather data collected by the French and transmitted it to the field through the Artillery Information Service.(84 Alexander T. Jennette, “Mass Fire in World War,” pt. 1, Field Artillery Journal, May-June 1975, pp. 40–41.)

The AEF’s Artillery Information Service had the responsibility of communicating all target information by daily bulletin to all levels down to battery commanders. The key personnel were the artillery intelligence officers, who were stationed at levels from army artillery through battalion and sometimes the battery. At each level, the artillery intelligence officer unified target information, exchanged this information with other artillery intelligence officers, advised the artillery commander, maintained a plot of enemy locations, disseminated meteorological data, coordinated the observation and adjustment of fire, and supervised sound ranging (the technique of locating targets by sound waves) and flash ranging (the technique of locating targets or adjusting friendly batteries by sighting their fire). He also worked closely with conventional intelligence officers throughout the AEF.( Ibid., pp. 42–43; Manual for the Artillery Orientation Officer . . . (Washington, D.C.: U.S. Government Printing Office, 1917), p. 37. Sound-ranging and flash-ranging organizations were authorized as engineer units.)

I made a post about WWI artillery here

As to the post in question which states

they simply did not have the quality of inputs -- including that of meteorological changes from day to night as well as windage, location, etc -- to deliver accurate fire.

Although this was true in 1914, like most things, artillery certainly changed a lot during the war.

From the British perspective, GHQ acquired a Royal Engineer's Meteorological section after Loos in 1915 and deployed meteorologists across the front to make measurements.

By January of 1916 GHQ published a pamphlet called Close Shooting in the Field and in April of the same year issued Some Notes on Meteorological Conditions which Affect Gunnery which set out how batteries should measure temperature and barometric pressure and should not use local, ground measured wind-speed.

Meteorological section sent out daily telegrams to batteries which gradually increase in the amount of information disseminated and eventually included not just wind speed at various heights but also barometric pressure, temperature and humidity.

The British also utilized a circular sound ranging calibration range where the effect of meteorological conditions could be used to improve the accuracy of sound ranging.

Its hard to overestimate the importance of predicted firing (of which meteor was a crucial factor) to the winning of the war. Although predicted firing had been introduced in the BEF in late 1916 for counter-battery by heavy artillery, it was not until Cambrai that an entirely predicted bombardment could be conducted, the success of which was key to the success of the battle - the role of tanks being overplayed in the popular imagination, and the role of artillery underplayed.