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We present constraints on the structure of the chromosphere from observationsof the Ca II H line profile near and off the solar limb. We obtained a data setof the Ca II H line in a field of view extending 20" across the limb. Weanalyzed the spectra for the properties of off-limb spectra. We used tracers ofthe Doppler shifts, such as the location of the absorption core, the ratio ofthe two emission peaks H2V and H2R, and intensity images at a fixed wavelength.The average off-limb profiles show a smooth variation with increasing limbdistance. The line width increases up to a height of about 2 Mm above the limb.The profile shape is fairly symmetric with nearly identical H2V and H2Rintensities; at a height of 5 Mm, it changes into a single Gaussian withoutemission peaks. We find that all off-limb spectra show large Doppler shiftsthat fluctuate on the smallest resolved spatial scales. The variation is moreprominent in cuts parallel to the solar limb than on those perpendicular to it.As far as individual structures can be unequivocally identified at our spatialresolution, we find a specific relation between intensity enhancements andDoppler shifts: elongated brightenings are often flanked all along theirextension by velocities in opposite directions. The average off-limb spectra ofCa II H present a good opportunity to test static chromospheric atmospheremodels because they lack the photospheric contribution that is present indisk-center spectra. We suggest that the observed relation between intensityenhancements and Doppler shifts could be caused by waves propagating along thesurfaces of flux tubes: an intrinsic twist of the flux tubes or a wavepropagation inclined to the tube axis would cause a helical shape of theDoppler excursion, visible as opposite velocity at the sides of the flux tube.

Spectroscopy at the solar limb: I. Average off-limb profiles and Doppler shifts of Ca II H