Rodger B. Grayson

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

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.

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

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.

Physically based hydrologic modeling: 2. Is the concept realistic?

Future directions for physically based, distributed-parameter models intended for use as hydrologic components of sediment and nutrient transport models are discussed. The attraction of these models is their potential to provide information about the flow characteristics at points within catchments, but current representations in process-based models are often too crude to enable accurate, a priori application to predictive problems. The difficulties relate to both the perception of model capabilities and the fundamental assumptions and algorithms used in the models. In addition, the scale of measurement for many parameters is often not compatible with their use in hydrologic models. The most appropriate uses of process-based, distributed-parameter models are to assist in the analysis of data, to test hypotheses in conjunction with field studies, to improve our understanding of processes and their interactions and to identify areas of poor understanding in our process descriptions. The misperception that model complexity is positively correlated with confidence in the results is exacerbated by the lack of full and frank discussion of a models capability /limitations and reticence to publish poor results. This may ultimately diminish the opportunity to advance understanding of natural processes because the managers of research resources are given the impression that the answers are already known and are being provided by models. Model development is often not carried out in conjunction with field programs designed to test complex models, so the link with reality is lost.

Towards areal estimation of soil water content from point measurements: time and space stability of mean response

Areal estimates of soil moisture over large areas are required for the ground truthing of remotely sensed measurements and for establishing catchment-wide antecedent conditions for runoff simulations. There is a mismatch in scale between field (point) measurements and the areal estimates from both remote sensing and simulation modelling, so attention must be focused on developing sampling strategies that are able to determine accurate areal estimates of soil moisture using present (essentially point) techniques. In this paper, we use the concepts of time stability, applied to catchments with significant relief, to investigate the existence of certain parts of the landscape which consistently exhibit mean behaviour irrespective of the overall wetness. We denote these as catchment average soil moisture monitoring (CASMM) sites. Four data sets from three catchments (Tarrawarra, R5-Chickasha and Lockyersleigh) are examined. The catchments range in size from 10.5 ha to 27 km2. Soil moisture measurements are made using time domain reflectometry (TDR) or neutron moisture meters (NMMs), over depths from 30 to 120 cm. Time-stable locations representing mean areal moisture content are found in each catchment, i.e. CASMM sites exist. Although this analysis is preliminary, it points towards the possibility of a methodology for determining a sampling regime that could provide reliable estimates of areal mean soil moisture in complex terrain from a limited number of sample locations.

Toward capturing hydrologically significant connectivity in spatial patterns

Many spatial fields exhibit connectivity features that have an important influence on hydrologic behavior. Examples include high-conductivity preferred flow paths in aquifers and saturated source areas in drainage lines. Connected features can be considered as arbitrarily shaped bands or pathways of connected pixels having similar (e.g., high) values. Connectivity is a property that is not captured by standard geostatistical approaches, which assume that spatial variation occurs in the most random possible way that is consistent with the spatial correlation, nor is it captured by indicator geostatistics. An alternative approach is to use connectivity functions. In this paper we apply connectivity functions to 13 observed soil moisture patterns from the Tarrawarra catchment and two synthetic aquifer conductivity patterns. It is shown that the connectivity functions are able to distinguish between connected and disconnected patterns. The importance of the connectivity in determining hydrologic behavior is explored using rainfall-runoff simulations and groundwater transport simulations. We propose the integral connectivity scale as a measure of the presence of hydrologic connectivity. Links between the connectivity functions and integral connectivity scale and simulated hydrologic behavior are demonstrated and explained from a hydrologic process perspective. Connectivity functions and the integral connectivity scale provide promising means for characterizing features that exist in observed spatial fields and that have an important influence on hydrologic behavior. Previously, this has not been possible within a statistical framework.

Physically based hydrologic modeling: 1. A terrain‐based model for investigative purposes

THALES, a simple distributed parameter hydrologic model is presented and applied to two catchments in Australia and the United States, each with different dominant hydrologic responses. The model simulates Hortonian overland flow and runoff from saturated source areas and is used to identify some of the barriers to modeling the hydrology of small catchments. At Wagga Wagga in New South Wales, Australia, runoff is produced from saturated source areas, whereas on the Lucky Hills catchments at Walnut Gulch in Arizona, Hortonian overland flow processes dominate. Simulations at Wagga Wagga are based on published parameters and field data measured as part of an intensive field program and result in a relatively poor fit of the outflow hydrographs for a series of storms. The simulated position and growth of saturated areas coincides with the limited available information, indicating that at least the gross effects of subsurface water movement are being represented. For the Lucky Hills catchments, the hydrographs at the catchment outlet and points within the catchment are simulated for a storm series. The results are highly dependent on the parameter values, which are poorly defined, highlighting the lack of measured field data and lack of methodology for the collection of data at a scale appropriate for such models. The model structure is also shown to have a major influence on the output. The influence of simulating surface flow as sheet flow or rill flow or through a series of ephemeral gullies, as well as the choice of the surface roughness parameter and antecedent soil water conditions, is shown to have a profound effect on the distributed flow depth and velocity predictions. By fitting model parameters, a simulation assuming Hortonian overland flow produced similar results at the catchment outlet to those based on partial area runoff. These results are of concern since it is common to calibrate and verify hydrologic models based on the accuracy with which the catchment outflow is predicted. The internal estimates of flow characteristics following such a calibration often provide the input to sediment and nutrient transport models. Models such as THALES produce an enormous amount of information and have the theoretical potential to provide a “universal” tool for the representation of hydrologic response. However, problems of verification and validation of such models are acute. These problems relate to the difficulty in measuring/deriving parameters a priori, measurement of the catchment response in sufficient detail for testing, and the validity of the fundamental assumptions and algorithms used in model development.

A quasi-dynamic wetness index for characterizing the spatial distribution of zones of surface saturation and soil water content

A quasi-dynamic wetness index that accounts for variable drainage times since a prior rainfall event is derived from simple subsurface flow theory. The method is tested through a series of field observations and numerical experiments using a spatially distributed, dynamic hydrologic model. The quasi-dynamic wetness index is shown to be a useful extension of previously developed static indices for predicting the location of zones of soil saturation and the distribution of soil water (i.e., the soil water content overlying a shallow impermeable or semiimpermeable layer). The new index is not constrained by the steady state assumption that forms the basis of existing indices.

Geostatistical characterisation of soil moisture patterns in the Tarrawarra catchment

Abstract Spatial soil moisture patterns have been measured in the 10.5 ha Tarrawarra catchment in temperate south-eastern Australia on 13 occasions using time domain reflectometry (TDR). Measurements are made on regular grids of between 500 and 2000 points for each occasion. The spatial correlation structure of these soil moisture patterns is analysed. Sample variograms are found to have a clear sill and a nugget. Exponential variogram models, including a nugget, fit the sample variograms closely. The geostatistical structure is found to evolve seasonally. High sills (15–25 (%v/v) 2 ) and low correlation lengths (35–50 m) are observed during the wet winter period. During the dry summer period sills are smaller (5–15 (%v/v) 2 ) and correlation lengths are longer (50–60 m). This seasonal evolution is explained on the basis of the importance of lateral redistribution of moisture during different seasons. Both a nugget effect due to measurement error and variability at small scales contribute to the variability at the 10 m scale, which is the smallest scale in most of the data sets. For one occasion four soil moisture patterns containing 514 samples were collected on 10 × 20 m grids. These patterns are offset by 2 m in an easterly and/or a northerly direction. Variograms for these four patterns are similar which indicates that variograms used for the structural analysis are highly reliable. An analysis based on transects subsampled from typical summer and winter soil moisture patterns indicates that a substantial number of data points (more than about 300) are needed to obtain meaningful sample variograms.

TERRAIN-BASED CATCHMENT PARTITIONING AND RUNOFF PREDICTION USING VECTOR ELEVATION DATA

An automated method of partitioning catchments into interconnected elements using a “stream tube” approach and vector or contour-based digital elevation models is briefly described. With this form of partitioning, hydrologic models can be structured based on the hydraulics of flow within a catchment and the effects of topography on runoff producing mechanisms and spatially distributed flow characteristics (such as flow depth and velocity) can be directly, and realistically, accounted for in the models. The method allows complex three-dimensional flow problems to be reduced to a series of coupled one-dimensional problems in areas with complex terrain. Two simple process-oriented hydrologic models that demonstrate the utility of this form of partitioning are presented. The first models subsurface flow-saturation overland flow and the second models Hortonian overland flow. Observed and predicted runoff hydrographs and the dynamic expansion and contraction of runoff source areas on a small laboratory microcatchment are presented. Also shown are predicted runoff hydrographs and surface flow velocities on a small rangeland catchment in the United States.

The Tarrawarra Data Set: Soil moisture patterns, soil characteristics, and hydrological flux measurements

Experiments investigating the spatial variability of soil moisture conducted in the 10.5 ha Tarrawarra catchment, southeastern Australia, are described. The resulting data include high-resolution soil moisture maps (over 10,000 point measurements at up to 2060 sites), information from 125 soil cores, over 1000 soil moisture profiles from 20 sites, 2500 water level measurements from 74 piezometers, surface roughness and vegetation measurements, meteorological and hydrological flux measurements, and topographic survey data. These experiments required a major commitment of resources including 250 person days in the field, with a further 100 person days in the laboratory preparing for field trips and checking and collating data. These data are available on the World Wide Web (http://www.civag.unimelb.edu.au/data/).