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air temperature is 0.7°C, with the highest monthly mean of 19.0°C in July and the lowest -21.2°C in January. Soil begins freezing at first November and melting around the following April. The investigated soils are classified as Mollisols according to USDA (1999). Four plots with different grazing intensities were investigated. Two plots were protected from grazing since 1979 (denoted as UG 79, 24 ha) and 1999 (UG 99, 35 ha). The other two plots were grazed: one was grazed only during winter time with 0.5 sheep units (ewe and lamb) ha -1 yr -1 (WG, 40 ha) and the other was heavily grazed with 2 sheep units ha -1 yr -1 (HG, 100 ha) during the whole year. In each plot, three profiles along transect were installed to measure soil moisture and temperature from June 2004 to June 2007. Data are recorded automatically by a data-logger at 30-min intervals in summer and at 1-h intervals in winter, respectively. Soil water content was measured at 5, 20, and 40 cm depth by theta-probes (Type ML2x). It refers to volumetric unfrozen water content in case the soil is frozen. To describe the detailed course of soil freezing and thawing profile, soil temperature was measured in five depths at 2, 8, 20, 40, and 100 cm using Platinum ground temperature probes (Pt-100). In 2004, undisturbed soil samples were taken at four layers of 4-8, 18-22, 30-34, and 40-44 cm to determine soil texture, bulk density, total C-content, water retention characteristics, and saturated hydraulic conductivity (Zhao et al., 2008). From the beginning of the experiment in 2004, an in situ automatic micrometeorological station was installed to record the precipitation and other variables necessary to estimate the reference FAO evapotranspiration (Allen et al., 1998). Snow is treated as snow-water equivalent when air temperature is lower than 0°C in the measurement or model. Plant parameters, such as vegetation coverage, leaf area index, and plant height were taken from vegetation measurements (Gao, 2007). The residue coverage and weight were also additionally recorded. Root samples were taken with a soil root auger in five depths of 0-10, 10-20, 20-50, 50-70, and 70-100 cm. Liquid and Ice Water Flow Variably saturated water flow for above- and sub-zero temperatures is 118
Chapter 6 Modeling of Coupled Water and Heat Transfer in Freezing and Thawing Soil described using the modified Richards equation (e.g., Hansson et al., 2004): ∂h ∂T ∂h ∂T [ ( h) + K ( h) + K ( h) + K ( θ ) + K ( θ ) ] S ∂θ ( h) pi ∂θi ( T ) ∂ ∂t + p t = z K w ∂ ∂ Lh ∂z Lh LT ∂z vh ∂z vT ∂z u − where θu [L 3 L -3 ] is the volumetric unfrozen water content (=θ+θv), θ is the volumetric liquid water content, θv is the volumetric vapor content, θi is the volumetric ice content, t is time, z is soil depth, pw and pi is the density of liquid and ice water, respectively, h is the pressure head, T is the temperature, and S is a sink/source term usually accounting for root water uptake. In Eq. 1, the first five terms on the right-hand side represent liquid flows due to gradient in pressure head (KLh, [L T -1 ]), gravity, and temperature (KLT, [L 2 T -1 K -1 ]), and vapor flows due to gradient in pressure head (Kvh) and temperature gradients (KvT), respectively. Eq. 1 is nonlinear, namely dependencies of the water content and the hydraulic conductivity on the gradient of pressure head and temperature, i.e. θ(h), θi(T), KLh(h), and KLT(h). The KLh is described by the following expressions (van Genuchten, 1980): θ ( h) −θ r 1 Se ( h) = = n θ −θ [ 1+ αh ] s K ( h) − Lh r m l 1/ m m 2 = Ks × Se ( 1− ( 1 Se ) ) [3] where Se is the effective saturation, θs and θr are the saturated and residual water contents, respectively; the symbols α [L -1 ], n, and m=1-1/n are empirical shape parameters, and the inverse of α is often referred to as the air entry value or bubbling pressure; Ks is the saturated hydraulic conductivity [L T -1 ], and L is a pore connectivity parameter, which normally a value of 0.5 is given. The hydraulic conductivity of frozen soil is significantly reduced by ice lenses, blocking parts of the pore space. To account for this blocking effect, the hydraulic conductivity in our study is reduced by an impedance factor, Ω (Lundin, 1990), which is multiplied by Q. Namely, the Ω reduces the hydraulic conductivity of the partially frozen soil, KfLh, as follows: KfLh =10 -ΩQ KLh [4] the parameter Q is the ratio of the ice content to the total water content, which accounts for the more significant blocking effects with the increase in ice [1] [2] 119
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SCHRIFTENREIHE Institut für Pflanz
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Aus dem Institut für Pflanzenernä
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I Table of contents I Table of cont
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controlling soil moisture are of pa
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Zusammenfassung Überweidung wird a
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Die Beweidung beieinflusst besonder
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II List of figures Fig. 2.1. Locati
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measured soil moisture in time stab
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III List of tables Table 2.1. Descr
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1.1 Background Chapter 1 Introducti
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Chapter 1 Introduction is also unce
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Chapter 1 Introduction water in spr
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Chapter 1 Introduction requires the
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Chapter 1 Introduction Krümmelbein
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Chapter 2 Spatial variability of so
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Chapter 3 Spatio-temporal variabili
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Chapter 3 Factors controlling spati
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Chapter 4 Temporal stability of soi
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Page 93 and 94: MRD(%) MRD(%) 100 80 60 40 20 0 -20
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Page 105 and 106: Chapter 5 Modeling Grazing Effects
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Page 167 and 168: References Chapter 7 General discus
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Page 173 and 174: Curriculum Vitae M.Sc. Ying Zhao Of
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