Fractal techniques and the surface roughness of talus slopes

Linear plots of log N against log G, where N is the number of steps of length G to span a transit, are conventionally used as evidence that geomorphic surfaces are self-similar fractals (i.e. the surfaces have a constant fractal dimension). In this study 42 transits on talus slope surfaces in Niagara and Letchworth Gorges, western New York, are investigated to ascertain whether they are self-similar. Log N-log G plots, which r² values in excess of 0·99 suggest are linear, are found upon more rigorous testing to be curvilinear. It is concluded that the talus slope surfaces are not self-similar, and that log N-log G plots are relatively insensitive to departures from self-similarity. The curvilinearity of the log N-log G plots is explained with the aid of a randomized square-wave model of the talus slope surfaces. This model is used to extend the range of measurement beyond that which was possible in the empirical analysis. The negative of the gradient of the log N -log G relation at a point is the fractal dimension D. Measurements made upon the randomized square-wave model indicate that the relation between D and scale of measurement has an asymmetrical wave shape with a peak (i.e. maximum D) where the scale of measurement is equal to the characteristic scale of roughness. In other words the value of D for a surface is not absolute but depends on the scale of measurement relative to the scale of roughness. Linear regression analysis reveals that at the scale of measurement employed in this study, D is positively correlated with particle size. This is because the values of D fall on the right-hand tail of the wave-shaped relation between D and scale of measurement. Transects (normal to the direction of slope) are found to have higher values of D than profiles (parallel to the direction of slope), and this is explained in terms of particle orientation, shape, and juxtaposition. Because D varies continuously with scale of measurement, there are considerable difficulties in using it to characterize and compare the surface roughness of talus slopes. Generalizing from talus slopes to other ground surfaces, it is evident that to the extent that any natural ground surface has a characteristic scale of roughness, it will depart from self-similarity, and D should be used with caution in quantifying the roughness of the surface. Geomorphologists are therefore urged to be more rigorous in their testing of self-similarity before employing D to characterize surface roughness.     

ROCK SURFACE ROUGHNESS AS AN INDICATOR OF DEGREE OF ROCK SURFACE WEATHERING

Rock surface weathering often leads to increased rock surface roughness, but roughness has proved difficult to quantify. Several instruments are available for micro-mapping and recording rock surface profiles, but the most appropriate for most purposes is the simple profile gauge. Short profiles can be recorded quickly and accurately. A range of roughness indices has been proposed in other areas of geomorphology and their efficacy as measures of roughness at scales of interest in studies of weathering is assessed. Some are too complex or labour-intensive and others are too sensitive to the scale of roughness to provide reliable measures of magnitude. The most appropriate indicator of both the scale and magnitude of roughness is the standard deviation of the differences between height values at a range of set horizontal intervals along a profile (the ‘deviogram’). Varying the measurement interval records roughness at different scales. A regression approach (root-mean-square roughness) provides a reliable measure of the magnitude of roughness at the maximum scale present. Three case studies confirm the efficacy of these approaches to studies of weathering of different rocks in different environments. Software is supplied which automates the calculation of roughness indices from gauge profiles.     

Hydraulics of interrill overland flow on rough,bare soil surfaces

A set of laboratory experiments on bare, rough soil surfaces was carried out to study the relationship between soil surface roughness and its hydraulic resistance. Existing models relating roughness coefficients to a measure of surface roughness did not predict the hydraulic resistance well for these surfaces. Therefore, a new model is developed to predict the hydraulic resistance of the surface, based on detailed surface roughness data. Roughness profiles perpendicular to the flow are used to calculate the wet cross‐sectional area and hydraulic radius given a certain water level. The algorithm of Savat is then applied to calculate the hydraulic resistance. The value for the equivalent roughness, which is used in the algorithm of Savat, could be predicted from the roughness profiles. Here, the tortuosity of the submerged part of the surface was used, which means that the calculated roughness depends on flow depth. The roughness increased with discharge, due to the fact that rougher parts of the surface became submerged at higher discharges. Therefore, a single measure of surface roughness (e.g. random roughness) is not sufficient to predict the hydraulic resistance. The proposed model allows the extension of the flow over the surface with increasing discharge to be taken into account, as well as the roughness within the submerged part of the surface. Therefore, the model is able to predict flow velocities reasonably well from discharge and roughness data only. Copyright © 2000 John Wiley & Sons, Ltd.     

Fault Roughness at Seismogenic Depths from LIDAR and Photogrammetric Analysis

Fault surface roughness is a principal factor influencing earthquake mechanics, and particularly rupture initiation, propagation, and arrest. However, little data currently exist on fault surfaces at seismogenic depths. Here, we investigate the roughness of slip surfaces from the seismogenic strike-slip Gole Larghe Fault Zone, exhumed from ca. 10 km depth. The fault zone exploited pre-existing joints and is hosted in granitoid rocks of the Adamello batholith (Italian Alps). Individual seismogenic slip surfaces generally show a first phase of cataclasite production, and a second phase with beautifully preserved pseudotachylytes of variable thickness. We determined the geometry of fault traces over almost five orders of magnitude using terrestrial laser-scanning (LIDAR, ca. 500 to <1 m scale), and 3D mosaics of high-resolution rectified digital photographs (10 m to ca. 1 mm scale). LIDAR scans and photomosaics were georeferenced in 3D using a Differential Global Positioning System, allowing detailed multiscale reconstruction of fault traces in Gocad^®. The combination of LIDAR and high-resolution photos has the advantage, compared with classical LIDAR-only surveys, that the spatial resolution of rectified photographs can be very high (up to 0.2 mm/pixel in this study), allowing for detailed outcrop characterization. Fourier power spectrum analysis of the fault traces revealed a self-affine behaviour over 3–5 orders of magnitude, with Hurst exponents ranging between 0.6 and 0.8. Parameters from Fourier analysis have been used to reconstruct synthetic 3D fault surfaces with an equivalent roughness by means of 2D Fourier synthesis. Roughness of pre-existing joints is in a typical range for this kind of structure. Roughness of faults at small scale (1 m to 1 mm) shows a clear genetic relationship with the roughness of precursor joints, and some anisotropy in the self-affine Hurst exponent. Roughness of faults at scales larger than net slip (>1–10 m) is not anisotropic and less evolved than at smaller scales. These observations are consistent with an evolution of roughness, due to fault surface processes, that takes place only at scales smaller or comparable to the observed net slip. Differences in roughness evolution between shallow and deeper faults, the latter showing evidences of seismic activity, are interpreted as the result of different weakening versus induration processes, which also result in localization versus delocalization of deformation in the fault zone. From a methodological point of view, the technique used here is advantageous over direct measurements of exposed fault surfaces in that it preserves, in cross-section, all of the structures which contribute to fault roughness, and removes any subjectivity introduced by the need to distinguish roughness of original slip surfaces from roughness induced by secondary weathering processes. Moreover, offsets can be measured by means of suitable markers and fault rocks are preserved, hence their thickness, composition and structural features can be characterised, providing an integrated dataset which sheds new light on mechanisms of roughness evolution with slip and concomitant fault rock production.     

3D float tracking: in situ floodplain roughness estimation

This paper presents a novel technique to quantify in situ hydrodynamic roughness of submerged floodplain vegetation: 3D float tracking. This method uses a custom‐built floating tripod that is released on the inundated floodplain and tracked from shore by a robotic total station. Simultaneously, an acoustic Doppler current profiler (ADCP) collects flow velocity profiles and water depth data. Roughness values are derived from two methods based on (1) run‐averaged values of water depth, slope and flow velocity to compute the roughness based on the Chézy equation, assuming uniform flow, (2) the equation for one‐dimensional free surface flow in a moving window. A sensitivity analysis using synthetic data proved that the median value of the roughness, derived using method 2, is independent of (1) the noise in water levels, up to 9 mm, (2) bottom surface slope, and (3) topographic undulations. The window size should be at least 40 m for a typical lowland river setup. Field measurements were carried out on two floodplain sections with an average vegetation height of 0·030 (Arnhem) and 0·043 m (Dreumel). Method 1 resulted in a Nikuradse roughness length of 0·08 m for both locations. Method 2 gave 0·12 m for Arnhem and 0·19 m for Dreumel. In Arnhem, a spatial pattern of roughness values was present, which might be related to fractional vegetation cover or vegetation density during the flood peak. 3D float tracking proved a flexible and detailed method for roughness determination in the absence of waves, and provided an unrestricted view from shore. Copyright © 2008 John Wiley & Sons, Ltd.     

Clast transport history influences Schmidt hammer rebound values

The Schmidt hammer (SH) is widely used in geomorphology for relative- and calibrated-exposure age dating surfaces and deposits within landforms. This study employs a laboratory-based methodology to assess the effects of surface roughness, clast roundness, and clast volume on SH rebound values (R-values) by analyzing samples from three modern depositional environments (i.e. river, alluvial fan, talus). Each environment contains clasts of Torlesse supergroup greywacke sandstones with distinct roundness and micro-scale roughness characteristics. Roundness, surface roughness, and clast volume were all found to influence R-values significantly. The R-values from different deposit types are statistically significant and could potentially create an apparent age divergence of several thousand years for samples with the same exposure-age. © 2020 John Wiley & Sons, Ltd.     

SURFACE ROUGHNESS EVOLUTION OF SOILS CONTAINING ROCK FRAGMENTS

Soil surface roughness is a dynamic property which determines, to a large extent, erosion and infiltration rates. Although soils containing rock fragments are widespread in the Mediterranean region, the effect of the latter on surface roughness evolution is yet poorly understood. Therefore, laboratory experiments were conducted in order to investigate the effect of rock fragment content, rock fragment size and initial moisture content of the fine earth on the evolution of interrill surface roughness during simulated rainfall. Surface elevations of simulated plough layers along transects of 50 cm length were measured before and after simulated rainfall (totalling 192.5 mm, I = 70 mm h⁻¹) with a laser microreliefmeter. The results were used to investigate whether systematic variations in interrill surface roughness along stony hillslopes in southeastern Spain could be attributed to rock fragment cover and rock fragment size. Soil surface elevations were measured along the contour lines (50 cm long transects) with a contact microreliefmeter. Roughness was expressed by two parameters related to the height and frequency of roughness elements, respectively: standard deviation of de-trended surface elevations (random roughness: RR), and correlation length (L) derived from exponential fits of the autocorrelation functions. The frequently used assumption that surface roughness (RR) of cultivated topsoils decreases exponentially with cumulative rain is not valid for soil surfaces covered by rock fragments. The RR of soils containing small rock fragments (1.7–2.7 cm) increased with cumulative rainfall after an initial decrease during the first 17.5 mm of rainfall. For soils containing large rock fragments (7.7 cm), RR increased with rainfall above a threshold rock fragment content by mass of 52 per cent. For a given rainfall application, RR increased non-linearly with rock fragment content. The correlation length for soils containing small rock fragments decreases with rock fragment content and is significantly lower than for soils with large rock fragments. Soils covered with small rock fragments (large RR and small L) are thus well protected against raindrop impact by a water film in the depressions between the rock fragments. On abandoned agricultural fields along hillslopes in southeastern Spain, rock fragments cover increases non-linearly with slope owing to selective erosion of finer particles on steep slopes. The increase of surface cover by large rock fragments (>25 mm) is even more pronounced. The simultaneous increase of rock fragment cover and rock fragment size with slope explains the non-linear increase of RR with slope. These relationships differ for soils covered by platy misaschists and those covered with cubic andesites. The variations in correlation length along the hillslopes are not clear, probably owing to a simultaneous increase in rock fragment cover and rock fragment size. These findings may provide a better prediction of soil surface roughness of interrill areas covered by rock fragments using slope angle and lithology.     

Assessing the age‐weathering correspondence of cosmogenic 21Ne dated Pleistocene surfaces by the Schmidt Hammer

The Schmidt Hammer (SH) method is used to quantify the rock weathering degree and has been proposed as a relative dating tool. Terrestrial Cosmogenic Nuclide (TCN) methods provide absolute exposure ages for erosive surfaces. Few works combine both methods for surfaces older than the Holocene. We compare data obtained by both methods for c. 150 ka bp glacial and fluvial erosive granite surfaces from northwest Spain. Rebound values (R) have been firstly compared with the rock density to assess the correlation with the rock strength, independently from influence of factors such as wetness and roughness in the R‐values. For erosive glacial surfaces older than 100 ka R‐values are confined in a narrow range, with no differences within errors. Stepped fluvial surfaces of 700 m to 70 m above present sea level show an inverse correspondence between TCN ages and R‐values, although no age predictions can be done on the basis of the R‐values. Thus, age inferences exclusively based on R‐values may not be realistic, but SH studies could be a useful tool for selecting surfaces for TCN dating. Copyright © 2009 John Wiley & Sons, Ltd.     

Study on effect of surface roughness on overland flow from different geometric surfaces through numerical simulation

Effect of variability in surface roughness on overland flow from different geometric surfaces is investigated using numerical solution of diffusion wave equation. Three geometric surfaces rectangular plane, converging and diverging plane at slopes 1 to 3% are used. Overland flow is generated by applying rainfall at constant intensity of 10 mm/h for period 30 min and 100 min. Three scenarios of spatial roughness conditions viz. roughness increasing in downstream direction, roughness decreasing in downstream direction and roughness distributed at random are considered. Effect of variability of roughness on overland flow in terms of depth, velocity of flow and discharge along the distance from upstream to downstream for different geometric surfaces are discussed in detail. Results from the study indicate that roughness distribution has significant effect on peak, time to peak and overall shape of the overland flow hydrograph. The peak occurs earlier for the scenario when roughness increases in downstream direction as compared to scenario when roughness is decreasing in downstream for all three geometric surfaces due to very low friction factor and more velocity at the top of the domain. The converging plane attains equilibrium state early as compared to rectangular and diverging plane. Different set of random values result in different time to peak and shape of hydrograph for rectangular and diverging plane. However, in case of converging plane, the shape of computed hydrographs remains almost similar for different sets of random roughness values indicating stronger influence of converging geometry than effect due to variation of roughness sequence on computed runoff hydrograph. Hierarchically, the influence of geometry on overland flow is stronger than the influence of slope and the influence of slope is stronger than the influence of roughness. Copyright © 2013 John Wiley & Sons, Ltd.     

Flow structure over square bars at intermediate submergence: Large Eddy Simulation study of bar spacing effect

Turbulent open-channel flow over 2D roughness elements is investigated numerically by Large Eddy Simulation (LES). The flow over square bars for two roughness regimes (k-type roughness and transitional roughness between d-type and k-type) at a relative submergence of H/k = 6.5 is considered, where H is the maximum water depth and k is the roughness height. The selected roughness configurations are based on laboratory experiments, which are used for validating numerical simulations. Results from the LES, in turn, complement the experiments in order to investigate the time-averaged flow properties at much higher spatial resolution. The concept of the double-averaging (DA) of the governing equations is utilized to quantify roughness effects at a range of flow properties. Double-averaged velocity profiles are analysed and the applicability of the logarithmic law for rough-wall flows of intermediate submergence is evaluated. Momentum flux components are quantified and roughness effect on their vertical distribution is assessed using an integral form of the DA-equations. The relative contributions of pressure drag and viscous friction to the overall bed shear stress are also reported.     

Large values of hydraulic roughness in subglacial conduits during conduit enlargement: implications for modeling conduit evolution

Hydraulic roughness accounts for energy dissipated as heat and should exert an important control on rates of subglacial conduit enlargement by melting. Few studies, however, have quantified how subglacial conduit roughness evolves over time or how that evolution affects models of conduit enlargement. To address this knowledge gap, we calculated values for two roughness parameters, the Darcy–Weisbach friction factor (f) and the Manning roughness coefficient (n), using dye tracing data from a mapped subglacial conduit at Rieperbreen, Svalbard. Values of f and n calculated from dye traces were compared with values of f and n calculated from commonly used relationships between surface roughness heights and conduit hydraulic diameters. Roughness values calculated from dye tracing ranged from 75–0.97 for f and from 0.68–0.09 s m^‐1/3 for n. Equations that calculate roughness parameters from surface roughness heights underpredicted values of f by as much as a factor of 326 and values of n by a factor of 17 relative to values obtained from the dye tracing study. We argue these large underpredictions occur because relative roughness in subglacial conduits during the early stages of conduit enlargement exceeds the 5% range of relative roughness that can be used to directly relate values of f and n to flow depth and surface roughness heights. Simple conduit hydrological models presented here show how parameterization of roughness impacts models of conduit discharge and enlargement rate. We used relationships between conduit relative roughness and values of f and n calculated from our dye tracing study to parameterize a model of conduit enlargement. Assuming a fixed hydraulic gradient of 0.01 and ignoring creep closure, it took conduits 9.25 days to enlarge from a diameter of 0.44 m to 3 m, which was 6–7‐fold longer than using common roughness parameterizations. Copyright © 2013 John Wiley & Sons, Ltd.     

Dimensionless critical shear stress evaluation from flume experiments using different gravel beds

Flume experiments were conducted using four different gravel beds (D₅₀ + 12–39 mm) and a range of marked particles (10–65 mm). The shear stresses were evaluated from friction velocities, when initial movement of marked particles occurred. Two kinds of equations were produced: first for the threshold of initial movement, and second for generalized movement. Equations of the type 0_c + a(D_i/D₅₀)^b, as proposed by Andrews (1983) are applicable even if the material is relatively well sorted. However, the values of a and b are lower (respectively 0·050 and -0·70) for initial movement. Generalized movement requires a higher shear stress (a + 0·068 and b + -0·80). D₉₀ of the bed material and y₀ (the bed roughness parameter) were also used as reference values in place of D₅₀. They produced lower values than in natural streams, mainly owing to the fact that the material used in the flume is better sorted: clusters are less well developed and the bed roughness is lower.     

Analysis of surface roughness in relation to soil loss and runoff at high rainfall intensities

The decay of roughness is an important factor governing surface processes such as infiltration and soil erosion. Thus the decay of surface roughness under different surface conditions was investigated and related to quantitative amounts of soil loss, runoff and sediment concentration in a laboratory experiment. Rainfall with an intensity of 128 mm/h was applied to a bare or mulched surfaces of a sandy loam soil with known surface roughness at specified time intervals. The decay of roughness as expressed by roughness ratio, in this experiment, was better predicted when related to an exponential function of the square root of cumulative kinetic energy of rainfall rather than with the cumulative rainfall. The roughness decay equations in literature did not predict breakdown under mulched surfaces accurately. Thus the exponent parameters of the roughness decay equations were adjusted to reflect the reduced decay occurring under mulched surfaces. In a bare soil, regression equations expressing the dependent variables as a function of initial roughness index were significant, but with low coefficients of determination, being 0·39 for soil loss, 0·12 for runoff and 0·36 for sediment concentration. In addition to initial roughness index, cumulative kinetic energy of rainfall was further included in the regressions. This led to an increase in coefficients of determination, which was 0·81 for soil loss, 0·74 for runoff and 0·49 for sediment concentration. The coefficients of determination (0·87 for soil loss, 0·85 for runoff and 0·51 for sediment concentration) were further increased when the final roughness index was included in addition to initial roughness index and cumulative kinetic energy in the regressions. This work shows that soil loss and runoff could be predicted from bare soil surface provided the initial roughness and the energy of rainfall is known. However, field verifications of these relationships are needed under different tillage tools and under natural rainfall. Copyright © 2002 John Wiley & Sons, Ltd.     

Fracture Toughness and Fracture Roughness Interrelationship in Thermally treated Westerly Granite

This paper presents an experimental work aimed at assessing the correlation between fracture toughness (K _IC ) and fracture roughness for a series of Westerly granite specimens thermally treated up to 850°C. Mode I fracture toughness as a function of thermal treatment is determined using Cracked Chevron Notched Brazilian Disc specimens. The degree of roughness of the resultant fracture surfaces is analyzed with the aid of a high accuracy, high precision stereo-topometric measurement system. Roughness and toughness values display a negative correlation as a function of temperature. Fracture toughness decreases with increasing temperature due to the gradual opening of grain-grain boundaries in response to thermal stresses. Mode I fractures preferentially follow these weakened grain-grain boundaries, which in addition to the thermal expansion of individual grains, result in rougher failure profiles with increasing temperature. At low temperature, a distinct anisotropy in roughness was observed in all fracture surfaces with higher roughness values perpendicular to the direction of fracture propagation. However, higher treatment temperatures resulted in the homogenization of fracture roughness in all directions. These results confirm the important link among petrofabric analysis, fracture toughness, and fracture roughness in response to thermal treatment.     

Evaluation of Terrestrial Laser Scanner and Structure from Motion photogrammetry techniques for quantifying soil surface roughness parameters over agricultural soils

The surface roughness of agricultural soils is mainly related to the type of tillage performed, typically consisting of oriented and random components. Traditionally, soil surface roughness (SSR) characterization has been difficult due to its high spatial variability and the sensitivity of roughness parameters to the characteristics of the instruments, including its measurement scale. Recent advances in surveying have greatly improved the spatial resolution, extent, and availability of surface elevation datasets. However, it is still unknown how new roughness measurements relates with the conventional roughness measurements such as 2D profiles acquired by laser profilometers. The objective of this study was to evaluate the suitability of Terrestrial Laser Scanner (TLS) and Structure from Motion (SfM) photogrammetry techniques for quantifying SSR over different agricultural soils. With this aim, an experiment was carried out in three plots (5 × 5 m) representing different roughness conditions, where TLS and SfM photogrammetry measurements were co-registered with 2D profiles obtained using a laser profilometer. Differences between new and conventional roughness measurement techniques were evaluated visually and quantitatively using regression analysis and comparing the values of six different roughness parameters. TLS and SfM photogrammetry measurements were further compared by evaluating multi-directional roughness parameters and analyzing corresponding Digital Elevation Models. The results obtained demonstrate the ability of both TLS and SfM photogrammetry techniques to measure 3D SSR over agricultural soils. However, profiles obtained with both techniques (especially SfM photogrammetry) showed a loss of high-frequency elevation information that affected the values of some parameters (e.g. initial slope of the autocorrelation function, peak frequency and tortuosity). Nevertheless, both TLS and SfM photogrammetry provide a massive amount of 3D information that enables a detailed analysis of surface roughness, which is relevant for multiple applications, such as those focused in hydrological and soil erosion processes and microwave scattering. © 2019 John Wiley & Sons, Ltd.     

Derivation ofK-indices using magnetograms constructed from digital data

The purpose of this study is to investigate the feasibility of deriving the traditionalK index from magnetograms plotted from recorded digital data. Digital magnetic data from Ottawa Observatory are available for theX, Y, andZ components in the form of 1 min averaged values and spot values at selected sampling intervals of 1 sec or greater. It is found that the lowerK values tend to be biased downward by one level when a digitizing interval greater than 30 sec is used for construction of the artificial magnetograms. However, for digitizing intervals of 30 sec or less the reconstructed analogue plots are just as reliable as standard-run Ruska magnetograms for the derivation ofK.Contribution from the Earth Physics Branch No. 1132.     

Evaluating morphological estimates of the aerodynamic roughness of debris covered glacier ice

Aerodynamic roughness length (z₀), the height above the ground surface at which the extrapolated horizontal wind velocity profile drops to zero, is one of the most poorly parameterised elements of the glacier surface energy balance equation. Microtopographic methods for estimating z₀ have become prominent in the literature in recent years, but are rarely validated against independent measures and are yet to be comprehensively analysed for scale or data resolution dependency. Here, we present the results of a field investigation conducted on the debris covered Khumbu Glacier during the post‐monsoon season of 2015. We focus on two sites. The first is characterised by gravels and cobbles supported by a fine sandy matrix. The second comprises cobbles and boulders separated by voids. Vertical profiles of wind speed recorded by a tower comprising five cup anemometers and deployed over both sites enable us to derive measurements of aerodynamic roughness that reflect their observed surface characteristics (0.0184 m and 0.0243 m, respectively). At the second site, z₀ also varied through time following snowfall (0.0055 m) and during its subsequent melt (0.0129 m), showing the importance of fine resolution topography for near‐surface airflow. To compare the wind profile data with microtopographic methods, we conducted structure from motion multi‐view stereo (SfM‐MVS) surveys across each patch and calculated z₀ using three previously published approaches. The fully three‐dimensional cloud‐based approach is shown to be most stable across different scales and these z₀ values are most correct in relative order when compared with the wind tower data. Popular profile‐based methods perform less well providing highly variable values across different scales and when using data of differing resolution. These findings hold relevance for all studies using microtopographic methods to estimate aerodynamic roughness lengths, including those in non‐glacial settings. Copyright © 2017 John Wiley & Sons, Ltd.     

Capturing the essential spatial variability in distributed hydrological modelling: Hydraulic roughness

The spatial variability of each parameter affecting storm runoff must be accounted for in distributed modelling. The objective of the work reported here is to assess the effects of using distributed versus lumped hydraulic roughness coefficients in the modelling of direct surface runoff. A spatially variable data set composed of Manning roughness coefficients is used to model direct surface runoff. To assess the information content (as measured by entropy) of spatially variable data and its significance in distributed modelling, various degrees of smoothing are applied. The error resulting from smoothing the hydraulic roughness coefficients is determined by modelling overland flow using a finite element solution. The Manning roughness coefficients were taken from field measurements of the Manning roughness coefficient at 0.6 m on a 14 m hillslope. These values were then used in a numerical simulation of outflow hydrographs to investigate the dependence of error on spatial variability. Our study focuses on the characteristics of spatial data used in distributed hydrological modelling. The field sites have fractal dimensions of ≈? 1.4, which is close to a Brownian variation. The sampling interval that captures the essential spatial variability of the Manning roughness coefficient does not seem to matter due to its Brownian variation in the field sites. Hence due to the nearly uniform random distribution, measurements at 0.6 m intervals are not necessary and larger intervals would yield results that are just as acceptable provided the mean value together with a uniformly random distribution is maintained for any size of finite element or sampling resolution. Because detailed measurements of hydraulic roughness are not practically available for deterministic catchment modelling, it is important to know that larger sampling resolutions may be used than 0.6 m.