Reprint of: Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model

Integrated hydrologic models coupled to land surface models require several input parameters to characterize the land surface and to estimate energy fluxes. Uncertainty of input parameter values is inherent in any model and the sensitivity of output to these uncertain parameters becomes an important consideration. To better understand these connections in the context of hydrologic models, we use the ParFlow-Common Land Model (PF-CLM) to estimate energy fluxes given variations in 19 vegetation and land surface parameters over a 144-hour period of time. Latent, sensible and ground heat fluxes from bare soil and grass vegetation were estimated using single column and tilted-v domains. Energy flux outputs, along with the corresponding input parameters, from each of the four scenario simulations were evaluated using active subspaces. The active subspace method considers parameter sensitivity by quantifying a weight for each parameter. The method also evaluates the potential for dimension reduction by identifying the input-output relationship through the active variable - a linear combination of input parameters. The aerodynamic roughness length was the most important parameter for bare soil energy fluxes. Multiple parameters were important for energy fluxes from vegetated surfaces and depended on the type of energy flux. Relationships between land surface inputs and output fluxes varied between latent, sensible and ground heat, but were consistent between domain setup (i.e., with or without lateral flow) and vegetation type. A quadratic polynomial was used to describe the input-output relationship for these energy fluxes. The reduced-dimension model of land surface dynamics can be compared to observations or used to solve the inverse problem. Considering this work as a proof-of-concept, the active subspace method can be applied and extended to a range of domain setups, land cover types and time periods to obtain a reduced-form representation of any output of interest, provided that an active subspace exists.