Though I am in no - let's say - tactical situation of knowledge and information to exchange fire with experts on the topic, I can look at this from an atmospheric persepctive and add my commentary. Indeed, the variables of temperature and pressure are on the cards already for inclusion in the simulation model. I was motivated as yourself to wonder, once I had a basic model working, how these factors affected gunnery during battles in atmospherically different locations such as Barents Sea or North Atlantic and, for example, the South China Sea. That, and whether these factors were considered significant enough to be incorporated in the gunnery calculations or computers of the day. I honestly do not know anything about that last statement.
What I can say, and it is already confirmed in the posts above, is that pressure and temperature will certainly have an effect on the range a shell travels, all other factors aside. When you ask...
and the incremental decrease with altitude would mantain the same pattern normal air pressure does ?
...you are referring to the lapse rates of temperature, pressure, and as a product of these, density. The answer is they most certainly do not follow a simple "one fits all" pattern, but they are predictable to a great extent. They are in fact closely related to the altimetry "problems" of true versus indicated altitudes that pilots (and airline Operations Engineering departments, I hasten to add) have when flying in regions where the temperature differs widely from ISA conditions.
Please pardon me if this is all known stuff here, but the post also serves me as a reference in what I was thinking on a particular date in relation to my gun model progress. The problem is generally broken down into two related subjects; Indicated Altitude and Density Altitude. The first of these does not really concern us, but it helps to understand what is happening to air pressure in regions of different sea level ambient temperatures;
In ISA conditions, a gain of 1,000 ft entails a drop of pressure of approximately 3607 Pascals. In warmer temperatures (let's say, ISA +20º C), that drop of 3607 pascals does not occur until you have gained about 1,075 ft, and in colder temperatures (ISA -20º C) a gain of 935 ft is enough to cause that same pressure change. In essense, what is happening is that the higher temperature is vertically expanding the pressure gradient, and vice versa.
Now it is plainly obvious that air pressure is going to affect its density, simply by cramming more kg's worth of air molecules into a cubic metre. But it is not the full story. The very temperature that causes the expanding temperature gradient itself also affects the density, albeit to a smaller measure than the pressure. As expected, higher temperatures will tend to reduce the density. The best way to think of it is that temperature "fine tunes" the density that is predominantly set by the air pressure. Pilots generally use a rule of thumb here;
Each degree of difference of temperature from an ISA value for a given Pressure Altitude is equivalent to a change of 120 feet in Density Altitude. For example, at a pressure altitude of 8,000 ft, the ISA temperature would be about -1º C, but the real outside air temperature is 21º C. So; 8,000 + 22 x 120 = 10,640 ft. The density of the air would be equivalent to the ISA value for 10,640 ft, or 0.902 kg / m³, and not 0.963 kg/m³, as it would normally be at ISA at 8,000 ft.
It is rough, yes, as it assumes a constant gradient, and is certainly not what I am going to do in the gun model. But it does give an idea of what is happening. It also becomes obvious that it will affect the range of a shell, bearing in mind that density is one of the main variables in the dynamic pressure calculation, which in turn is a component of the drag calculation.
It will be exciting to see the results in the model. Sorry, I prattled on a bit as I got somewhat carried away in a subject that interests me!
Humidity reduces air density, and is calculable. As far as wind is concerned, it will obviously affect the trajectory of a shell, both in range and azimuth, much the same way it affects an aircraft's ground track and ground speed. The important thing here would be wind directions and strengths at different altitudes, as even that is not constant, and a shell goes through them in short order.
And that is definitely IT, from me, now.