Garry R. Willgoose

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.

A coupled channel network growth and hillslope evolution model: 1. Theory

This paper presents a model of the long-term evolution of catchments, the growth of their drainage networks, and the changes in elevations within both the channels and the hillslopes. Elevation changes are determined from continuity equations for flow and sediment transport, with sediment transport being related to discharge and slope. The central feature of the model is that it explicitly differentiates between the sediment transport behavior of the channels and the hillslopes on the basis of observed physics, and the channel network extension results solely from physically based flow interactions on the hillslopes. The difference in behavior of channels and hillslopes is one of the most important properties of a catchment. The flow and sediment transport continuity equations in the channel and the hillslope are coupled and account for the long-term interactions of the elevations in the hillslope and in the channels. Sediment transport can be due to fluvial processes, creep, and rockslides. Tectonic uplift may increase overall catchment elevations. The dynamics of channel head advance, and thus network growth, are modeled using a physically based mechanism for channel initiation and growth where a channel head advances when a channel initiation function, nonlinearly dependent on discharge and slope, exceeds a threshold. This threshold controls the drainage density of the basin. A computer implementation of the model is introduced, some simple simulations presented, and the numerics of the solution technique described.

One-dimensional soil moisture profile retrieval by assimilation of near-surface observations: a comparison of retrieval algorithms

This paper investigates the ability to retrieve the true soil moisture and temperature profiles by assimilating near-surface soil moisture and surface temperature data into a soil moisture and heat transfer model. The direct insertion and Kalman filter assimilation schemes have been used most frequently in assimilation studies, but no comparisons of these schemes have been made. This study investigates which of these approaches is able to retrieve the soil moisture and temperature profiles the fastest, over what depth soil moisture observations are required, and the effect of update interval on profile retrieval. These questions are addressed by a desktop study using synthetic data. The study shows that the Kalman filter assimilation scheme is superior to the direct insertion assimilation scheme, with retrieval of the soil moisture profile being achieved in 12 h as compared to 8 days or more, depending on observation depth, for hourly observations. It was also found that profile retrieval could not be realised for direct insertion of the surface node alone, and that observation depth does not have a significant effect on profile retrieval time for the Kalman filter. The observation interval was found to be unimportant for profile retrieval with the Kalman filter when the forcing data is accurate, whilst for direct insertion the continuous Dirichlet boundary condition was required for an increasingly longer period of time. It was also found that the Kalman filter assimilation scheme was less susceptible to unstable updates if volumetric soil moisture was modelled as the dependent state rather than matric head, because the volumetric soil moisture state is more linear in the forecasting model.

On the effect of digital elevation model accuracy on hydrology and geomorphology

This study compares published cartometric and photogrammetric digital elevation models (DEMs) of various grid spacings with a ground truth data set, obtained by ground survey, and studies the implications of these differences on key hydrologic statistics. Inferred catchment sizes and stream networks from published DEMs were found to be significantly different than those from the ground truth in most instances. Furthermore, the width functions and cumulative area relationships determined from the published DEMs were found to fall consistently outside the 90% confidence limits determined from the ground truth for more than 60% of the relationship, suggesting that these hydrologic properties are poorly estimated from published DEMs. However, the slope-area relationships determined from published DEMs were found to be less sensitive to catchment shape, size, and stream network, with the relationship falling outside the 90% confidence limits for less than 40% of the relationship for all catchments identified from the published DEMs. A published relationship linking the horizontal resolution with the vertical accuracy of the DEM was tested, predicting a horizontal resolution of about 10 m for the published DEMs tested.

Revisiting the hypsometric curve as an indicator of form and process in transport‐limited catchment

Hypsometry has historically been used as an indicator of geomorphic form of catchments and landforms. Yet there has been little work aimed at relating hypsometry to landform process and scale. This paper uses the SIBERIA catchment evolution model to explore linkages between catchment process and hypsometry. SIBERIA generates results that are qualitatively and quantitatively similar to observed hypsometric curves for physically realistic parameters. However, we show that not only does the hypsometry reflect landscape runoff and erosion process, but it is strongly dependent on channel network and catchment geometry. We show that the width to length ratio of the catchment has a significant influence on the shape of the hypsometric curve, though little on the hypsometric integral. For landforms dominated by fluvial sediment transport, the classic Strahler ‘mature’ hypsometric curve is only generated for catchments with roughly equal width and length. Narrow catchments show a hypsometric curve more similar to Strahlers ‘monadnock’ form. For landscapes dominated by diffusive transport, the simulated hypsometric curve is concave-down everywhere, this being consistent with curves reported for some example catchments in France. Because the transition between diffusive dominance to fluvial is scale-dependent, with larger catchments exhibiting greater fluvial dominance, then the hypsometric curve is a scale-dependent descriptor of landforms. Experimental results for simulated landforms from a small-scale rainfall-erosion simulator are reported. It is shown that SIBERIA yields satisfactory fits to the data, confirming its ability to predict the form of the hypsometric curve from a simple model of geomorphic processes.

A coupled channel network growth and hillslope evolution model: 2. Nondimensionalization and applications

This paper explores the scaling and similitude properties of the system of governing equations for a catchment evolution model that was presented in an accompanying paper (Willgoose et al., this issue). Similitude is an important concept that allows the quantification of the similarities of, and differences between, two catchments. Through the use of a small number of nondimensional numbers the governing physics of the channel network and surrounding hillslopes in a catchment may be summarized. These nondimensional numbers lead to similarity conditions that allow for the quantitative comparison of data between field catchments and between the field scale and the controlled experimental scale. Derived relationships are presented for the drainage density of the channel network and the rate at which the network grows, parameterized using the nondimensional numbers. Drainage density is shown to be mostly a function of the hillslope channel initiation number that relates the slopes and lengths of hillslopes in a very simple fashion. Finally, it is shown that the form of a channel network is very sensitive to initial conditions. Though the exact form of the network and the hillslopes may vary greatly, along with their topological statistics, physical statistics such as drainage density are only slightly affected.

A PHYSICAL EXPLANATION OF AN OBSERVED LINK AREA-SLOPE RELATIONSHIP

An observed log-log linear relationship between channel slope and contributing area is explained by the erosional physics that lead to catchment form. It is postulated that tectonic uplift is in balance with the fluvial erosion down wasting that dominates catchment erosion, and it is shown that this relationship results in the observed log-log linear relationship at dynamic equilibrium. In addition, it has been observed that there are deviations from this log-log linear relationship near the catchment divide, with observed slopes being lower than those predicted from the relationship. This is explained by noting that for small areas, fluvial erosion effects are dominated by soil creep and rain splash, modeled by diffusive physics. The area at which this deviation from log-log linearity occurs is that point on the hillslope at which diffusive physics, like soil creep and rain splash, begin to dominate fluvial erosion. These predictions are confirmed by numerical simulations using a catchment evolution model.

A physical explanation for an observed area-slope-elevation relationship for catchments with declining relief

A general relationship between the contributing area, slope, and mean elevation of catchments with relief declining after a tectonic uplift event is presented. This relationship is based on the continuity equation for runoff and erosion processes in the catchment. The key hypothesis underlying this relationship is that as a catchment declines, the nondimensionalized catchment approaches a constant form. This hypothesis is verified for computer simulated catchments. The area-slope-elevation relationship covers several cases: catchments declining toward a peneplain; catchments declining from a high slope dynamic equilibrium (resulting from a high rate of tectonic uplift) to a low slope one (resulting from a lower rate of tectonic uplift); and catchments declining from an elevated initial condition, as, for example, in the decline of a mine spoil heap. A previously published relationship between slope and area for catchments in dynamic equilibrium and based on runoff and erosion physics is shown to be a special case of this general relationship. The new area-slope-elevation relationship is compared with data from simulated catchments and a field catchment. It is thus shown that for declining catchments the area-slope-elevation relationship is a good predictor of catchment form for catchments with declining relief. It is argued that the slope-area-elevation relationship is sufficient, with the planiform drainage pattern, to completely define the elevation properties of the catchment such as, for instance, the hypsometric curve.

One-Dimensional Soil Moisture Profile Retrieval by Assimilation of Near-Surface Measurements: A Simplified Soil Moisture Model and Field Application

The Kalman filter assimilation technique is applied to a simplified soil moisture model for retrieval of the soil moisture profile from near-surface soil moisture measurements. First, the simplified soil moisture model is developed, based on an approximation to the Buckingham‐Darcy equation. This model is then used in a 12month one-dimensional field application, with updating at 1-, 5-, 10-, and 20-day intervals. The data used are for the Nerrigundah field site, New South Wales, Australia. This study has identified (i) the importance of knowing the depth over which the near-surface soil moisture measurements are representative (i.e., observation depth), (ii) soil porosity and residual soil moisture content as the most important soil parameters for correct retrieval of the soil moisture profile, (iii) the importance of a soil moisture model that represents the dominant soil physical processes correctly, and (iv) an appropriate forecasting model as far more important than the temporal resolution of near-surface soil moisture measurements. Although the soil moisture model developed here is a good approximation to the Richards equation, it requires a root water uptake term or calibration to an extreme drying event to model extremely dry periods at the field site correctly.

Characterisation of the hydrology of an estuarine wetland

The intertidal zone of estuarine wetlands is characterised by a transition from a saline marine environment to a freshwater environment with increasing distance from tidal streams. An experimental site has been established in an area of mangrove and salt marsh wetland in the Hunter River estuary, Australia, to characterise and provide data for a model of intertidal zone hydrology. The experimental site is designed to monitor water fluxes at a small scale (36 m). A weather station and groundwater monitoring wells have been installed and hydraulic head and tidal levels are monitored over a 10-week period along a short one-dimensional transect covering the transition between the tidal and freshwater systems. Soil properties have been determined in the laboratory and the field. A two-dimensional finite element model of the site was developed using SEEP/W to analyse saturated and unsaturated pore water movement. Modification of the water retention function to model crab hole macropores was found necessary to reproduce the observed aquifer response. Groundwater response to tidal fluctuations was observed to be almost uniform beyond the intertidal zone, due to the presence of highly permeable subsurface sediments below the less permeable surface sediments. Over the 36 m transect, tidal forcing was found to generate incoming fluxes in the order of 0.22 m 3 /day per metre width of creek bank during dry periods, partially balanced by evaporative fluxes of about 0.13 m 3 /day per metre width. During heavy rainfall periods, rainfall fluxes were about 0.61 m 3 /day per metre width, dominating the water balance. Evapotranspiration rates were greater for the salt marsh dominated intertidal zone than the non-tidal zone. Hypersalinity and salt encrustation observed show that evapotranspiration fluxes are very important during non-rainfall periods and are believed to significantly influence salt concentration both in the surface soil matrix and the underlying aquifer. q 1998 Elsevier Science B.V. All rights reserved.