On the spectrum of soil moisture from hourly to interannual scales
The spectrum of soil moisture content at scales ranging from 1 hour to 8 years is analyzed for a site whose hydrologic balance is primarily governed by precipitation (p), and evapotranspiration (ET). The site is a uniformly planted loblolly pine stand situated in the southeastern United States and is characterized by a shallow rooting depth (RL) and a near-impervious clay pan just below RL. In this setup, when ET linearly increases with increasing root zone soil moisture content (θ), an analytical model can be derived for the soil moisture content energy spectrum (Es(f), where f is frequency) that predicts the soil moisture "memory" (taken as the integral timescale) as β1-1 ≈ ηR L/ETmax, where ETmax is the maximum measured hourly ET and η is the soil porosity. The spectral model suggests that Es(f) decays at f-2-α at high f but almost white (i.e., f0) at low f, where α is the power law exponent of the rainfall spectrum at high f (α ≈ 0.75 for this site). The rapid E s(f) decay at high f makes the soil moisture variance highly imbalanced in the Fourier domain, thereby permitting much of the soil moisture variability to be described by a limited number of Fourier modes. For the 8-year data collected here, 99.6% of the soil moisture variance could be described by less than 0.4% of its Fourier modes. A practical outcome of this energy imbalance in the frequency domain is that the diurnal cycle in ET can be ignored if β1-1 (estimated at 7.6 days from the model) is much larger than 12 hours. The model, however, underestimates the measured Es(f) at very low frequencies (f ≪ β1) and its memory, estimated from the data at 42 days. This underestimation is due to seasonality in ETmax and to a partial decoupling between ET and soil moisture at low frequencies. Copyright 2007 by the American Geophysical Union.
Katul, GG; Porporato, A; Daly, E; Oishi, AC; Kim, HS; Stoy, PC; Juang, JY; Siqueira, MB
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