A dragon with a full wingspan of 20000 km (folded to fit into a 10000 km resting area) and surface area of 44 million sqkm will have a terrible impact on the environment.
In the first days of her awakening, as she shifts, freeing herself from the encumbrance of all the cities and forests and so forth that are littering her back, widespread but relatively shallow quakes will be felt all around the perimeter. It will be quite a ride for those residing on her back! Cities will be thrown down, forests toppled, hills broken and everything will begin a terrific slide towards the edges of the Beast. Initially, small tsunamis will race across the Indian, Pacific and Arctic Oceans and the Black and Red Seas as well, as the earth of India, Arabia, northern Siberia and Eastern Asia begins to slough off. With a coastline of 63000 km, she might slough off a 1 km wide by say 100m deep ring of rubbish. This will dump 6300 cukm of rock, earth and debris into the coastal waters. I don't know the equations to model a tsunami of this size, but can imagine that most coastal areas will be considerably dampened!
These next weeks to months will be very exciting for everyone on the planet. As the dragon lifts herself up, the mountains and earth upon her back and wings will begin a catastrophic and precipitous slide down her flanks and the dorsal surfaces of her wings. Since she's been sleeping for, like, forever, she's got quite a bit of accretion on her back. This larger slide will be composed of about 2,199,517,610 cukm of rubble --- mountain chains, accreted bedrock, soil, destroyed infrastructure and natural debris. Perhaps a quarter or third of this volume will in fact make it to her periphery in time to rain down upon the churning ocean waters below.
At this point in time, she's lifting up the edges of her wings and beginning to raise her own voluminous body. Ocean water will begin to rush into the verges, creating a muddy slurry all around her perimeter.
As she stands, her hundred km thick body will begin to rise up, lifting and rippling the underlying 50km of continental plate beneath her, much like the way, when you get out of bed in the morning, the sheets become crumpled and rippled. Contrary forces --- the release of pressure upon the mantle will cause the crust to uplift; the increased pressure of the remaining weight of the upper 50 km of the accretion plate, plus her own weight, will press down through her legs, depressing the continental plate and the underlying mantle, thinning it and perhaps causing widespread localised vulcanism running from (what were) central India and central Siberia. Massive outgassing will blow hot volcanic plumes in all directions; inflowing oceanic water will spill down over a 100km high precipice forming a vast waterfall that will empty the ocean into a 6,600,000,000 cukm chasm. All the oceans waters only amount to about 1,400,000,000 cukm of water. This new Eosphoratic Ocean will be a deep, steamy, stormy and utterly unaccessible seafood gumbo to everyone with the possible exception of any vessels that survive, Land of the Lost style, the drop over the precipice. Elsewhere it's been said that the noise of the Gibraltar Cataract would have deafened local wildlife. This waterfall will certainly deafen anyone close by!
Having stablised her stance on the shifting surface of the underlying continental plate, the areas surrounding what was Asia will suffer massive earth quakes, as her movements cause the plate to depress and rise. Broad chasms will evolve at the plate boundaries, allowing for magma to rise; and as plates catastrophically collide, vast earthquake swarms will overwhelm even the most distant lands. The heat generated from these motions may raise the overall temperature by many degrees, a process called Dragon-Made Global Warming. During this phase, the remaining unstable crust materials on her back will continue to slide off. Much, of course, will land relatively harmlessly in the mud surrounding the Eosphoratic Ocean, but quite a bit will rain down into the Ocean itself. As mountains with weights of up to 161,932,476,090,000 kg rain down into the water from a height of about 250 km, great fountains of water and rock will be cast up into the atmosphere. Other geological features will be cast high into the atmosphere, even into space, as she shakes out her wings and seeks to rid her body of all irritants. These low velocity meteors, hundreds of which will be mountain sized or larger, and many millions of which will be smaller, will eventually be stopped by Earth's gravity and return to the surface causing widespread chaos as the meteor shower ensues.
If anyone is left on the surface of the planet, after all the teratsunamis, petaquakes and Global Warming, two catastrophes will ensue. The first is the gradual collapse of the Eosphoratic Precipice itself. All the weight of the damaged and unstable continental crust surrounding the Ocean will cause a massive weakening. Gravity will begin the process of destroying the newly formed Ocean by causing the 200 km high walls of the chasm to collapse inward.
But that's not even the worst of it! The second and final catastrophe to befall Earth's climate will be the flight of the Dragon. Every dragon wants to fly. Tis instinct. If you've ever been privileged to watch a dragon take off, as I have, or at least have watched a bird take off, say from a branch, you know there are two components to achieving flight: one is the wing lift & body crouch; two is the leap with the legs and downthrust with the wings.
Our dragon will now crouch down, settling like a great duck in the boiling waters of the Eosphoratic Ocean, tensing her body to prepare for her leap. Furthermore, she will rapidly raise her nearly 44 million sqkm wingspread well above the height of the atmosphere. It's only about 500 km thick --- each of her wings is about 10000 km long, a 20000 km wingspread all unfurled! She's a big girl. Raising those wings will create a vacuum generating updraft over the Ocean, causing hurricane force winds to blow towards her. This will cause destruction of any remaining structures through hypercane force derechos ripping across the surface of the planet at all levels of the atmosphere. The result will be a massive accumulation of air and water vapour over the Ocean and a severe partial vacuum area over the antipodes. The storms surrounding her body will be amazing!
And then - - - she flies!
Her powerful legs will spring into action. Causing her 16 146 000 000 000 kg weight to gracefully leap into the air, she'll punch the full strength of her legs down onto the already stressed, cracked, and heaving continental plate. The exertion will be too much for the solid crust to handle. Her 10000 km long body will simply press the crust down into the mantle below. The mantle is only about 2700 km deep, and she's gonna be using all that in order to take off. She's going to cause localised solidification of the mantle as incredible pressures compress crust into all layers of mantle. Her toes may even touch the outer core!
At the same time, she'll bring her wings down. Anyone left alive on the planet will be able to see as the outer edges enter the atmosphere and light up infrared as the friction interactions with all that piled up air cause her wings to heat up.
Her rapidly descending wings will now cause all the pent up air to be explosively expelled from around her body. If Smaug's wings were a hurricane, this girl's wings simply blow much of the remaining atmosphere out into space. The relatively gentle hypercane force winds that were generated by their lift will now be increased by orders of magnitude as she forces them downward.
As her body leaps up, up and away from the ravaged Earth, first, as her forelimbs rise up from the surface, the northern half the Asiatic plate will crack due to the release of massive pressure and undulating mantle waves will, due to dvorakian forces, cause the fractured portions to roll and tilt precariously even as her full weight further depresses the southern half. The release of pressure in the north will cause the viscoelastic mantle to liquefy into gargantuan gouts of molten magma while the remaining portion of solid plate screams and groans as its relative cool is pressed deep into the liquid core. And then, her hind limbs too shall rise up from the surface: the northern half of the Asiatic plate will collapse back down onto the raging mantle and the sudden release of pressure on the core and deep mantle will cause a fountain of molten material to spew from the very centre of the planet! She will be lifted up and as she rockets peacefully into space and on to her journey, she'll leave the Greatest Show On Earth's last act and curtain call for the few survivors.
The sudden departure of an Asia sized ettadragon will instantly remove all remaining pressure on the mantle and underlying core beneath where she was. The Eosphoratic Ocean, now long vapourised and blown away by her thunderous wingstroke won't even help hold down the final cataclysm. Now, the remainder of the planet will suffer gravitational shocks as it struggles to attain homeastasis: the planet was round(ish) and now it's not, but it wants to be again. Resulting shockwaves will pulverise and melt the crust. Whatever water remains will boil. Air will sear. The exposed core and mantle will create a wonderful geyser of gaseous iron and molten rock which will shoot up into space.
The shocks and violence of this partial core ejection will cause the remaining mantle and crust to collapse. Quite apart from the remaining mountainous meteors that are still raining down on the ravaged surface, the liquefying core and mantle matter will now begin to rain back down. Most of the surface by this time will already be molten. And what isn't will be very hot, shaken, cracked, splintered and smithereened. Atmospheric temperature might be as high as 200 degrees centigrade and winds will still be raging.
There won't be an environment left to have an impact on.