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Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement--soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.
Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, where which there are not enough research activities yet. Taking the constitutive relationships of soil water movement - soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Moreover, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the comb in results of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, eg, the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of the shape of the SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.