Predicting Geomorphic and Hydrologic Risks after Wildfire Using Harmonic and Stochastic Analyses

Wildfire is a landscape-scale disturbance that often alters hydrological processes and sediment flux during subsequent storms. Vegetation loss from wildfires induce changes to sediment supply such as channel erosion and sedimentation and streamflow magnitude or flooding. These changes enhance downstream hazards, threatening human populations and physical aquatic habitat over various time scales. Using Williams Canyon, a basin burned by the Waldo Canyon Fire (2012) as a case study, we utilize deterministic and statistical modeling methods (Fourier series and first order Markov chain) to assess pre- and post-fire geomorphic and hydrologic characteristics, including of precipitation, enhanced vegetation index (EVI, a satellite-based proxy of vegetation biomass), streamflow, and sediment flux. Local precipitation, terrestrial Light Detection and Ranging (LiDAR) scanning, and satellite-based products are used for these time series analyses. We present a framework to assess variability of periodic and nonperiodic climatic and multivariate trends to inform development of a post-wildfire risk assessment methodology. To establish the extent to which a wildfire affects hydrologic and geomorphic patterns, a Fourier series was used to fit pre- and post-fire geomorphic and hydrologic characteristics to yearly temporal cycles and subcycles of 6, 4, 3, and 2.4 months. These cycles were analyzed using least-squares estimates of the harmonic coefficients or amplitudes of each sub-cycle's contribution to fit the overall behavior of a Fourier series. The stochastic variances of these characteristics were analyzed by composing first-order Markov models and probabilistic analysis through direct likelihood estimates. Preliminary results highlight an increased dependence of monthly post-fire hydrologic characteristics on 12 and 6-month temporal cycles. This statistical and probabilistic analysis provides a basis to determine the impact of wildfires on the temporal dependence of geomorphic and hydrologic characteristics, which can be incorporated into post-fire mitigation, management, and recovery-based measures to protect and rehabilitate areas subject to influence from wildfires.