Global spatial sensitivity of runoff to subsurface permeability using the active subspace method

- Active subspace methods identify runoff sensitivity to permeability field variations.
- Runoff is an approximate univariate function of the 3D field active variable.
- Dunnian runoff is most sensitive to large scale permeability perturbations.
- Hortonian runoff is most sensitive to local permeability change near the outlet.

Hillslope scale runoff is generated as a result of interacting factors that include water influx rate, surface and subsurface properties, and antecedent saturation. Heterogeneity of these factors affects the existence and characteristics of runoff. This heterogeneity becomes an increasingly relevant consideration as hydrologic models are extended and employed to capture greater detail in runoff generating processes. We investigate the impact of one type of heterogeneity - subsurface permeability - on runoff using the integrated hydrologic model ParFlow. Specifically, we examine the sensitivity of runoff to variation in three-dimensional subsurface permeability fields for scenarios dominated by either Hortonian or Dunnian runoff mechanisms. Ten thousand statistically consistent subsurface permeability fields are parameterized using a truncated Karhunen-Loéve (KL) series and used as inputs to 48-h simulations of integrated surface-subsurface flow in an idealized 'tilted-v' domain. Coefficients of the spatial modes of the KL permeability fields provide the parameter space for analysis using the active subspace method. The analysis shows that for Dunnian-dominated runoff conditions the cumulative runoff volume is sensitive primarily to the first spatial mode, corresponding to permeability values in the center of the three-dimensional model domain. In the Hortonian case, runoff volume is sensitive to multiple smaller-scale spatial modes and the locus of that sensitivity is in the near-surface zone upslope from the domain outlet. Variation in runoff volume resulting from random heterogeneity configurations can be expressed as an approximately univariate function of the active variable, a weighted combination of spatial parameterization coefficients computed through the active subspace method. However, this relationship between the active variable and runoff volume is more well-defined for Dunnian runoff than for the Hortonian scenario.