We investigate the carrier-envelope phase and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above-threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750,nm is varied in a range between $0.7 times 10^{14}$ and $unit[5.5 times 10^{14}]{W/cm^2}$. Our measurements reveal a prominent maximum in the carrier-envelope phase-dependent asymmetry at photoelectron energies of 2,$U_mathrm{P}$ ($U_mathrm{P}$ being the ponderomotive potential), that is persistent over the entire intensity range. Further local maxima are observed at 0.3 and 0.8,$U_mathrm{P}$. The experimental results are in good agreement with theoretical results obtained by solving the three-dimensional time-dependent Schr{o}dinger equation (3D TDSE). We show that for few-cycle pulses, the carrier-envelope phase-dependent asymmetry amplitude provides a reliable measure for the peak intensity on target. Moreover, the measured asymmetry amplitude exhibits an intensity-dependent interference structure at low photoelectron energy, which could be used to benchmark model potentials for complex atoms.
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