Scalable surrogate models facilitate computationally tractable emulation of computer models (or simulators) when large ensembles of runs are available. Gaussian Process (GP) models are commonly used for computer model emulation; however they cannot scale to truly large datasets. Dense functional output such as spatial or time-series data adds an additional layer of complexity that must be handled carefully for fast emulation. In this work we develop a highly scalable emulator for functional data motivated by Kennedy and O’Hagan (2001) and Higdon et al. (2008), but built upon Local Approximate Gaussian Process (Gramacy, 2016). We apply our emulator to model calibration using global GP lengthscale parameter estimates to scale the input space, which dramatically increases the speed of MCMC. We show that our fast approximation based emulator can be a suitable alternative to the methods in Higdon et al. (2008) for functional response at a fraction of the computational cost.