On the spectrum of soil moisture from hourly to interannual scales

[1] 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 (R-L) and a near-impervious clay pan just below R-L. In this setup, when ET linearly increases with increasing root zone soil moisture content (theta), an analytical model can be derived for the soil moisture content energy spectrum (E-s( f), where f is frequency) that predicts the soil moisture "memory'' ( taken as the integral timescale) as beta(-1)(1) approximate to eta R-L/ETmax, where ETmax is the maximum measured hourly ET and h is the soil porosity. The spectral model suggests that E-s(f) decays at f(-2-alpha) at high f but almost white (i.e., f(0)) at low f, where alpha is the power law exponent of the rainfall spectrum at high f (alpha approximate to 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 beta(-1)(1) ( estimated at 7.6 days from the model) is much larger than 12 hours. The model, however, underestimates the measured E-s(f) at very low frequencies (f << beta(1)) 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.