The topography of a catchment has a major impact on the hydrological, geomorphological. and biological processes active in the landscape. The spatial distribution of topographic attributes can often be used as an indirect measure of the spatial variability of these processes and allows them to be mapped using relatively simple techniques. Many geographic information systems are being developed that store topographic information as the primary data for analysing water resource and biological problems. Furthermore, topography can be used to develop more physically realistic structures for hydrologic and water quality models that directly account for the impact of topography on the hydrology. Digital elevation models are the primary data used in the analysis of catchment topography. We describe elevation data sources, digital elevation model structures, and the analysis of digital elevation data for hydrological, geomorphological, and biological applications. Some hydrologic models that make use of digital representations of topography are also considered.

Digital terrain modelling: A review of hydrological, geomorphological, and biological applications

We analyze the degree of spatial organization of soil moisture and the ability of terrain attributes to predict that organization. By organization we mean systematic spatial variation or consistent spatial patterns. We use 13 observed spatial patterns of soil moisture, each based on over 500 point measurements, from the 10.5 ha Tarrawarra experimental catchment in Australia. The measured soil moisture patterns exhibit a high degree of organization during wet periods owing to surface and subsurface lateral redistribution of water. During dry periods there is little spatial organization. The shape of the distribution function of soil moisture changes seasonally and is influenced by the presence of spatial organization. Generally, it is quite different from the shape of the distribution functions of various topographic indices. A correlation analysis found that ln(a), where a is the specific upslope area, was the best univariate spatial predictor of soil moisture for wet conditions and that the potential radiation index was best during dry periods. Combinations of ln(a) or ln(a/tan(β)), where β is the surface slope, and the potential solar radiation index explain up to 61% of the spatial variation of soil moisture during wet periods and up to 22% during dry periods. These combinations explained the majority of the topographically organized component of the spatial variability of soil moisture a posteriori. A scale analysis indicated that indices that represent terrain convergence (such as ln(a) or ln(a/tan(β))) explain variability at all scales from 10 m up to the catchment scale and indices that represent the aspect of different hillslopes (such as the potential solar radiation index) explain variability at scales from 80 m to the catchment scale. The implications of these results are discussed in terms of the organizing processes and in terms of the use of terrain attributes in hydrologic modeling and scale studies. A major limitation on the predictive power of terrain indices is the degree of spatial organization present in the soil moisture pattern at the time for which the prediction is made.

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Observed spatial organization of soil moisture and its relation to terrain indices

In this paper we develop a conceptual and observational case in which soil water patterns in temperate regions of Australia switch between two preferred states The wet state is dominated by lateral water movement through both surface and subsurface paths, with catchment terrain leading to organization of wet areas along drainage lines We denote this as nonlocal control The dry state is dominated by vertical fluxes, with soil properties and only local terrain (areas of high convergence) influencing spatial patterns We denote this as local control The switch is described in terms of the dominance of lateral over vertical water fluxes and vice versa When evapotranspiration exceeds rainfall, the soil dries to the point where hydraulic conductivity is low and any rainfall that occurs essentially wets up the soil uniformly and is evapotranspired before any significant lateral redistribution takes place As evapotranspiration decreases and/or rainfall increases, areas of high local convergence become wet, and runoff that is generated moves downslope, rapidly wetting up the drainage lines In the wet to dry transitional period a rapid increase in potential evapotranspiration (and possibly a decrease in rainfall) causes drying of the soil and “shutting down” of lateral flow Vertical fluxes dominate and the “dry” pattern is established Three data sets from two catchments are presented to support the notion of preferred states in soil moisture, and the results of a modeling exercise on catchments from a range of climatic conditions illustrate that the conclusions from the field studies may apply to other areas The implications for hydrological modeling are discussed in relation to methods for establishing antecedent moisture conditions for event models, for distribution models, and for spatially distributing bulk estimates of catchment soil moisture using indices

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Preferred states in spatial soil moisture patterns: Local and nonlocal controls

Soil moisture is spatially and temporally highly variable, and it influences a range of environmental processes in a nonlinear manner. This leads to scale effects that need to be understood for improved prediction of moisture dependent processes. We provide some introductory material on soil moisture, and then review results from the literature relevant to a variety of scaling techniques applicable to soil moisture. This review concentrates on spatial scaling with brief reference to results on temporal scaling. Scaling techniques are divided into behavioral techniques and process-based techniques. We discuss the statistical distribution of soil moisture, spatial correlation of soil moisture at scales from tens of meters to thousands of kilometers and related interpolation and regularization techniques, and the use of auxiliary variables such as terrain indices. Issues related to spatially distributed deterministic modeling of soil moisture are also briefly reviewed.

Scaling of Soil Moisture: A Hydrologic Perspective

Water repellency in soils: a historical overview

Nonisotropic sloping soil leads to a horizontal flow component during rain and infiltration. Splashing of raindrops and flow in the transition zone between the soil bulk and the air also lead to lateral flow. The result is concentration of moisture in concave spots to the point of saturation and even seepage out of the soil. The same occurs at steep soil cuts. Such moisture concentration can explain the formation of runoff during rainfall at low rates that do not exceed infiltration capacity, partial area contribution to runoff, net recharge of groundwater by low-rate rainfall, the formation of rills and gullies in a relatively dry area, delay of runoff after a certain total amount of rain irrespective of rain intensity, variations in soil formation in different parts of the landscape, poor distribution of irrigation water in nonplane fields, and leaching of the soil surface by water that was assumed to run only above the surface.

Surface Hydrology: I—Explanation of Phenomena

In a nonuniform soil with rotational symmetry the properties change along a coordinate n that forms an angle \Ia\N with the vertical. During infiltration there will be a flow component in the parallel direction s downstream, which is proportional to the rain itself and the slope. The horizontal flow is proportional to the vertical flow, the slope, and the coefficient of anisotropy. The last has been calculated for a soil made up distinct layers. In the limiting case of very thin layers or near the saturation point, the vertical and horizontal conductivities are, respectively, the expected arithmetic and harmonic means familiar from saturated flow. The coefficient of anisotropy increases with the rate of vertical flow to a power greater than unity. The horizontal flow component can be many times the vertical one. It finds application in pollution problems and in the study of the underground water regime.

Surface Hydrology: IV°Flow in Sloping, Layered Soil

Streamlines bend after they enter a nonuniform, sloping soil. On penetrating to a more permeable soil layer they bend downstream. This can occur in unsaturated soil above a sloping water table or in a layer in which water accumulates because of the presence of less permeable underlying layer. We considered the general case of a nonuniform soil with rotational symmetry at an angle to the vertical, i.e., a sloping soil. General proof is provided that the soil generally behaves as a anisotropic medium so that infiltration also invloves a horizontal net flow component. This net flow component is proportional to the slope, the vertical flow, and the coefficient of anisotropy. The existence of such a mechanism can account for the concentration of water in concave spots, possible seepage, and runoff and erosion phenomena at low rates of rainfall. It can also explain how a previous rainfall leads to earlier onset of runoff during the next rain, etc.

Surface Hydrology: III°Causes of Lateral Flow

This paper describes the second in a series of three models for optimal operation of multi-quality water supply systems. This second model, which is termed the Q-H (flow-head) model, seeks to determine the optimal operation of pumps and valves, and does not consider water quality aspects. However, the model belongs to the group of three models Tor multi-quality systems because it is one of the two building blocks (the other is the flow-quality Q-C) of a full-llow-quality-head (Q-C-H) model. This Q-H model is based on continuous representations of the head-flow and power-flow functions of the pumping stations, which in turn results in a continuous non-convex optimization model. For a given flow distribution in the network, Q0, the Q0-H model is solved for the optimal operation of pumps and valves. The flow distribution is then modified by changing the circular flows, using a projected gradient method combined with the Complex Method which employs the results of the Q0-H solution, such that the locally opti...

Optimal operation of multi-quality water supply systems-ii: the q-h model

One of three complementary models for optimal operation of multi-quality water supply systems is presented. The other two models are the subject of companion papers. The model, which is known as the Q-C (flow-quality) model, includes mass continuity of water and constituents. However, the hydraulic constraints do not appear explicitly. To prevent infeasibilities or unreasonable hydraulic conditions arising from the lack of hydraulic constraints, limits and a cost are associated with the flow in each pipe. The constraints in the model include dilution conditions which depend on flow direction. These dilution conditions are introduced into the model by an exponential function, resulting in a smooth continuous nonlinear programming problem, which is transformed into an equivalent problem and solved by a modified projected gradient method. The method is insensitive to scaling of variables, and the computational complexity depends only slightly on the number of water quality parameters. The method is demonstra...

Gideon Sinai

Papers

Surface Hydrology: I—Explanation of Phenomena

Surface Hydrology: IV°Flow in Sloping, Layered Soil

Surface Hydrology: III°Causes of Lateral Flow

Optimal operation of multi-quality water supply systems-ii: the q-h model

Optimal operation of multi-quality water supply systems-i: introduction and the q-c model