We present the basic theory of stable isotopes (δ(¹⁸O) and δ(D)) of freezing water solutions in the environment set within a water isotope-augmented version of FREZCHEM(V15). We validate this model with a couple of examples. The isotope-capable FREZCHEM is simplified to run much faster using set-piece initial chemistries to calculate the freezing temperature of the remaining water. The fast version is embedded in a semi-empirical model for residual liquid water in sub-zero soils. A uniform specific soil column is driven with a defined seasonal temperature wave. The co-isotopes of the residual water and ice are calculated as a function of time and depth. The model is applied to clayey soils of the sort sampled in detail in a 10 (10 to 20 m) core suite from the Mackenzie Delta, Canada. The stable isotopes are compared to the model ones and the match is quite good except in the uppermost 2.5 m, where an upturn in the model δ(¹⁸O) curve is smaller. If the upper 2.5 m of icy soil is populated with “modern” water, and below by late glacial meltwater the size of the upturn in δ(¹⁸O) starting at 2.5 m is reproduced by the model.

中文翻译：

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使用任意水化学和土壤特定经验残余水函数的永久冻土中残余液态水和地面冰的稳定同位素模型

我们提出了稳定同位素（δ( ¹⁸O) 和 δ(D)) 在 FREZCHEM(V15) 的水同位素增强版本中设置的环境中的冷冻水溶液。我们用几个例子验证了这个模型。具有同位素能力的 FREZCHEM 被简化为使用固定件初始化学物质来计算剩余水的冻结温度，从而运行得更快。快速版本嵌入在零以下土壤中残余液态水的半经验模型中。统一的特定土柱由定义的季节性温度波驱动。残余水和冰的共同位素作为时间和深度的函数进行计算。该模型应用于在加拿大麦肯齐三角洲的 10（10 至 20 m）岩心套件中详细采样的粘土质土壤。将稳定同位素与模型进行比较，除了最上面的 2.5 m 外，匹配度非常好，¹⁸ O) 曲线较小。如果上层 2.5 m 的冰土充满“现代”水，而下层是晚期冰川融水，则模型再现了从 2.5 m 处开始的δ( ¹⁸ O)上升的大小。