Tasks of parameter identification and uncertainty quantification for inverse problems are ubiquitous in environmental and hydrological sciences. The curse of dimensionality often makes these problems ill-posed and can lead to ambiguity in parameter combinations. This effect is aggravated if model parameters are not physically interpretable or not restrictable by field measurements. Active subspaces (AS) – related to proper orthogonal decomposition – enable linear dimension reduction and have been previously applied to hydrological models. AS is a gradient-based method aiming to identify directions in the parameter space, in which the scalar model output changes more, on average, than in other directions. We use a lumped parameter model to simulate karst system spring discharge of the well-studied Milandre catchment, Switzerland, utilizing precipitation, evaporation, and discharge data for calibration. The model consists of a two-flow-component non-linear recharge model and system response functions. We explore the parameter space with Markov chain Monte Carlo (MCMC) sampling to generate posterior parameter samples. We additionally sample randomly from uniform priors, obtaining unconditioned samples, with a Latin hypercube sampling scheme. The Nash-Sutcliffe efficiency (NSE) is used as scalar model output. Lower dimensional structure could be identified independently of the sampling method used. From uniform prior samples, directions were identified in which the model changes drastically, while the MCMC directions give a more local representation around the optimal solution. We found that the MCMC based method provided results from which observed system properties were extractable. These scructures may subsequently be used to effectively calibrate the model in a lower dimensional setting.