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skills/typst-physica/examples.typ
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skills/typst-physica/examples.typ
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#import "@local/modern-cug-report:0.1.3": *
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#show: doc => template(doc, footer: "CUG水文气象学2025", header: "")
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== 1 Richards方程
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Richards方程:
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$ pdv(theta, t) = nabla dot [K(theta) nabla H] + S $
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其中:
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- $theta$:体积含水量 [L^3/L^3]
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- $t$:时间 [T]
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- $S$:源汇项 [1/T]
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总水头 $H$ 由基质势 $h$ 和重力势 $z$ 组成:
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$ H = h + z $
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== 2 质量守恒定律
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对于土壤控制体积,质量守恒方程为:
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$ pdv(rho theta, t) + nabla dot (rho q) = rho S $
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假设水密度 $rho$ 为常数,简化为:
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$ pdv(theta, t) + nabla dot q = S $
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== 3 上边界层条件
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上边界通常受大气条件控制,主要包括:
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*降雨入渗条件:*
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$ -K(theta) pdv(H, z) |_(z=0) = q_("infiltration") $
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*蒸发条件:*
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$ -K(theta) pdv(H, z) |_(z=0) = q_("evaporation") $
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