Could you please tell us exactly what you have in mind?

Golf-Sierra

when we takeoff from high elevation airports such as at 3800amsl,it is often that the cabin rate descends on climb,why is this so

No different to flying along at 3800ft unpressurised and then setting up normal pressurisation.

Although it will vary between aircraft, due to design pressure differential, there will be a pressurisation schedule for the aircraft such that, for a given pressure height outside the aircraft, X, the cabin altitude will be Y.

As the aircraft climbs from SL/descends from cruise while pressurised, the cabin will climb/descend at a lesser rate according to the pressurisation schedule.

Now, if we start off somewhere other than SL or cruise - unpressurised - and then set up pressurisation, the cabin altitude first will change from the outside pressure equivalent to whatever the schedule calls for at that outside pressure.

Hence, if you takeoff from an above SL aerodrome, but lower than the maximum FL at which the pressurisation can maintain SL cabin altitude, you would expect to see the cabin descend to/towards SL as the initial setup and then climb per the schedule as the aircraft climbs.

There are plenty of atmospheric calculators on the net (the equations you can find in the appropriate textbooks) for you to play with. You can find one example here.

In regards to a real time adventure, I would note that the typical cabin pressure, when at 35,000 descending to an airport elevation of 14,300, the system has difficulty adjusting that quickly, and on the tarmack, perhaps it was that not enough time was let to stabilize, or the crew just wasnt used to this pressure differential, at that experience, it was a bit of a shocker when the front door was opened.

In regards to a real time adventure

Pressurisation schedule monitoring and pilot control is a standard requirement. It should only be a problem requiring extra pilot management if the

(a) system is not operating correctly or if the

(b) aircraft is descending much more rapidly than normal or to an high aerodrome (in which case, the crew should have reset the rate demand to address the problem)

Three end situations -

(a) the aircraft is still pressurised at landing.

The situation arises if the pressurisation system is mishandled. If the aerodrome is above SL then the controller demands must be adjusted to meet the landing diff limit requirements (typically no diff or, for some aircraft, there may be a small residual diff permitted for landing).

Depending on the aircraft, if it lands pressurised, one would normally expect automatic cabin pressurisation dump on touchdown - the occupants would detect that readily via the eardrums.

If the aircraft, for some reason, were still slightly pressurised at the gate, then the doors ought not to be able to be opened. If the crew noticed this and dumped pressure, again the ears would tell the story.

(b) aircraft on schedule at landing - normal situation

(c) aircraft catches the cabin on descent - aircraft becomes unpressurised ahead of schedule expectation and either the crew adjusts aircraft rate of descent or eardrums are uncomfortable

For reference...

The negative pressure relief valves on the cargo doors on, say, a B747-400, crack open at 0.2~0.4psi. On the 767, it is 0.3~0.5. The 737NG is a little higher with 1.0psi.

A couple of years ago I was called out to a B757.
During the descent into a sea level airport, at about 8000ft the crew had heard a bang, felt pressure in their ears, looked up and saw the cabin was at the same altitude as the aircraft and followed it down to the ground.
They thought that the bang had been a failure, and they had a hole in the fuselage. After much inspecting and checking and finding nothing, I decided to pressurise the aircraft. Looking up at the pressure control panel the cabin rate of descent knob was set at min! The aircraft had overtaken the cabin in the descent, the bang was the safety valves opening.
Rate knob reset to the pip, and aircraft departed.