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Estimators of outer scales of atmospheric turbulence usually fit the phasescreen snapshots derived from local wave front sensors to a Zernike basis, andthen compare the spectrum of expansion coefficients in this basis with anarrowing associated with decreasing outer scales.  This manuscript discusses aspects that arise if the Zernike basis isexchanged for a Karhunen-Loeve basis of statistically independent modes. Dataacquisition turns out to be more demanding because sensing the tip-tilt mode isrequired. The data reduction methodology is replaced by fitting of varianceratios of an entire (long exposure) data set. Statistical testing of hypotheseson outer scale models can be applied to a set of modes - supposing other noiseoriginating from detector readout and the optical train can be disentangled.

Modal Decomposition of the von-K\'arm\'an Covariance of Atmospheric Turbulence in the Circular Entrance Pupil