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NASA's Interface Region Imaging Spectrograph (IRIS) small explorer missionwill study how the solar atmosphere is energized. IRIS contains an imagingspectrograph that covers the Mg II h&k lines as well as a slit-jaw imagercentered at Mg II k. Understanding the observations requires forward modelingof Mg II h&k line formation from 3D radiation-MHD models.  We compute the vertically emergent h&k intensity from a snapshot of a dynamic3D radiation-MHD model of the solar atmosphere, and investigate whichdiagnostic information about the atmosphere is contained in the synthetic lineprofiles. We find that the Doppler shift of the central line depressioncorrelates strongly with the vertical velocity at optical depth unity, which istypically located less than 200 km below the transition region (TR). Bycombining the Doppler shifts of the h and the k line we can retrieve the signof the velocity gradient just below the TR. The intensity in the central linedepression is anticorrelated with the formation height, especially in subfieldsof a few square Mm. This intensity could thus be used to measure the spatialvariation of the height of the transition region. The intensity in theline-core emission peaks correlates with the temperature at its formationheight, especially for strong emission peaks. The peaks can thus be exploitedas a temperature diagnostic. The wavelength difference between the blue and redpeaks provides a diagnostic of the velocity gradients in the upperchromosphere. The intensity ratio of the blue and red peaks correlates stronglywith the average velocity in the upper chromosphere. We conclude that the Mg IIh&k lines are excellent probes of the very upper chromosphere just below thetransition region, a height regime that is impossible to probe with otherspectral lines.

The formation of IRIS diagnostics II. The formation of the Mg II h&k lines in the solar atmosphere