### Abstract

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 (θ), 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 β_{1}^{-1} ≈ ηR _{L}/ET_{max}, where ET_{max} is the maximum measured hourly ET and η is the soil porosity. The spectral model suggests that E_{s}(f) decays at f^{-2-α} at high f but almost white (i.e., f^{0}) 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 β_{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 ≪ β_{1}) and its memory, estimated from the data at 42 days. This underestimation is due to seasonality in ET_{max} and to a partial decoupling between ET and soil moisture at low frequencies.

Original language | English (US) |
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Article number | W05428 |

Journal | Water Resources Research |

Volume | 43 |

Issue number | 5 |

DOIs | |

State | Published - May 2007 |

### All Science Journal Classification (ASJC) codes

- Water Science and Technology

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## Cite this

*Water Resources Research*,

*43*(5), [W05428]. https://doi.org/10.1029/2006WR005356