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On the spectrum of soil moisture from hourly to interannual scales

机译：从每小时到每年一次的土壤水分谱

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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.
机译：在一个水文平衡主要受降水（p）和蒸散量（ET）控制的地点，分析了1小时到8年范围内的土壤水分含量谱。该地点是位于美国东南部的均匀种植的火炬松林，其特征是生根深度浅（R_L），并且在R_L下方有近乎不透水的粘土盘。在此设置中，当ET随着根区土壤水分含量（θ）的增加而线性增加时，可以得出土壤水分含量能谱（E_s（f），其中f为频率）的分析模型，从而预测“土壤水分”的记忆“（作为积分时间标度）为β_1〜（-1）≈ηR_L/ ET_（max），其中ET_（max）是每小时测得的最大ET，η是土壤孔隙度。频谱模型表明，E_s（f）在高f处在f〜（-2-α）处衰减，但在低f处几乎呈白色（即f〜0），其中α是高f处降雨谱的幂律指数（此站点的α≈0.75）。 E_s（f）在高f处快速衰减，使土壤水分变化在傅立叶域中高度失衡，从而允许用有限数量的傅立叶模式描述大部分土壤水分的变异性。对于这里收集的8年数据，土壤水分变化的99.6％可以用不到0.4％的傅里叶模式描述。频域中这种能量失衡的实际结果是，如果β_1〜（-1）（根据模型的7.6天估计）远大于12小时，则可以忽略ET中的昼夜周期。但是，该模型低估了在非常低的频率（f β_1）处测得的E_s（f）及其记忆，这是根据42天的数据估算得出的。这种低估是由于ET_（max）的季节性以及低频下ET与土壤水分之间的部分解耦所致。

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