Close interconnection between climate, soil and topography

In the previous discussion, all possible combinations of climate, soil and topographic regimes, or virtual basins, have been treated equally. However, not all these combinations are equally feasible in nature. In other words, the possibilities for these combinations of conditions to exist in natural catchments are not equal. Some of the virtual basins must be more possible than the others. These more feasible virtual basins themselves are then more likely to follow the existing universal principles emergent at certain spatial and temporal scales. The Budyko Hypothesis is one of the universal principles valid for annual water balance at the catchment scale (Budyko, 1948). It is therefore assumed here that only those combinations which as the model inputs lead to the hydrological responses respecting the Budyko Hypothesis are most likely existing in nature. The climate-soil-topography combinations, or virtual basins, are hereby constrained by the Budyko Hypothesis and narrowed down to a small range. Inspired by the assertion of Freeze (1980) (please refer to the introduction section), we then start to investigate the possible close interconnections between climate, soil and topography within these constrained virtual basins.

The solid line in Figure 4.10(a) is plotted according to Budyko’s formula (Budyko, 1948). Notice here EP /P is used instead of γ simply to respect the original Budyko

curve. The total evaporation E here equals to the sum of the evaporation from soil and water surface, as stated by Equ. (16)~(18). Considering the uncertainty in the Budyko Hypothesis itself, only those virtual basins have been picked out giving total evaporation values within ( (E/P)theoretical −ε1 , (E/P)theoretical +ε2 ). Here (E/P)theoretical is the theoretical value of E /P given by Budyko’s formula. ε and ₁ ε are the error items. ₂ ε ₁ is estimated as the 10% of the difference between (E/P)theoretical and the lowest possible value of E /P which is zero.

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2

ε is estimated as the 10% of the difference between (E/P)theoretical and the highest possible value of E /P

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The value of 10% is somehow arbitrary here, and it could be some other values such as 5% or 15%. The virtual basins chosen by this way are denoted as behavioral virtual basins hereafter as shown in Figure 4.10(a).

Budyko hypothesis as a universal principle of annual water balance, although still empirical, emerges at the catchment scale. The arising of this catchment-scale pattern might be due to the possible tight interconnection between climate, soil and topographic controls themselves. One promising way to investigate this interconnection is to construct the dimensionless descriptors defined in Section 4.3.2 from these behavioral virtual basins, and look at the interactions between them. Figure 4.10(b) shows the interconnection between dryness index γ and drainage index β when the total runoff only consists of Dunne overland runoff and subsurface runoff, i.e., Horton overland runoff is little. Comparing with Figure 4.7 and 8, the ranges of β value are significantly narrower in Figure 4.10(b). This is pleasingly consistent with Freeze’s assertion “If one fixes the mean hydraulic conductivity of hillslope, then there is only a very narrow range of topographic slopes that can lead to runoff generated by the Dunne mechanism. If one fixes the topographic slope of a hillslope, then there is only a very narrow range of hydraulic conductivities that will lead to a water table that is high enough to allow the Dunne mechanism to be operative in a given climatic regime” (Freeze, 1980). Another common feature for all three types of soils in Figure 4.8(b) is that the value of β increases with γ . The Budyko Hypothesis is not only about annual evaporation, but in fact also about annual runoff. For annual water balance, we have

P E P Q ₌₁₋ (4.27)

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To meet the annual water balance implied by the Budyko Hypothesis, certain amount of runoff has to be generated and reach the catchment outlet. Under more arid climate, i.e., larger γ , evaporative power is stronger. The subsurface water has to run faster downstream to form up enough saturated area so that certain amount of Dunne overland runoff and subsurface runoff is generated, otherwise it will be evaporated finally. It is essentially the competition between the vertical movement and lateral movement of subsurface water that necessitates the increasing of β with γ .

In Figure 4.10(b), the values of β for silt and clay loam are apparently larger than those values of β for sand. One of the major differences between sand and the other types of soil is that, comparing with silt and clay soil, sand soil tends to hold much less water in unsaturated zone instead of recharging to saturated zone, as shown in Eqn. (4.2) and (4.3). So in sand soil, most of soil water is mobile under gravity and in favor of lateral flow which leads to Dunne overland runoff and subsurface flow. In silt or clay soil, a major part of soil water is immobile and subject to evaporation, and only a small part of soil water is available for lateral movement. Therefore in silt or clay soil, larger drainage capacity is necessary to compete with evaporation and generate enough Dunne overland runoff and subsurface flow to meet the water balance suggested by the Budyko Hypothesis. The last but not the least difference between sand soil and silt/clay soil in the plots of Figure 4.10(b) is that under arid climates (for instance, γ >1.0), silt or clay soil does not favor the dominance of Dunne overland runoff and subsurface flow. Larger amount of soil water in unsaturated zone and strong evaporative power under arid climate imply that evaporation totally dominates over lateral flow regarding soil water. This suggests that the combinations of silt/clay soil and arid climate are not likely leading to such water balance with Dunne overland runoff and subsurface flow as the major runoff components while still respecting the Budyko Hypothesis. That is, this situation rarely happens in natural catchments.

It is feasible, however, under arid climate and silt/clay soil, Horton overland runoff dominates in runoff generation while the Budyko Hypothesis is still respected, as shown in Figure 4.11(a). Figure 4.11(b) shows the interconnection between

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dryness index γ and infiltration index α when the total runoff is dominated by Horton overland runoff. According to the Budyko Hypothesis, the more arid the climate is, the less runoff will be generated. This is consist with the fact shown in Figure 4.11(b) that infiltration index α increases with dryness index γ , since the increasing of α implies the less fraction of precipitation being transformed into Horton overland runoff, as also shown in Figure 4.6.