Quantifying watershed surface depression storage: determination and application in a hydrologic model

Hydrologic models often require correct estimates of surface macro‐depressional storage to accurately simulate rainfall–runoff processes. Traditionally, depression storage is determined through model calibration or lumped with soil storage components or on an ad hoc basis. This paper investigates a holistic approach for estimating surface depressional storage capacity (DSC) in watersheds using digital elevation models (DEMs). The methodology includes implementing a lumped DSC model to extract geometric properties of storage elements from DEMs of varying grid resolutions and employing a consistency zone criterion to quantify the representative DSC of an isolated watershed. DSC obtained using the consistency zone approach is compared to DSC estimated by “brute force” (BF) optimization method. The BF procedure estimates optimal DSC by calibrating DRAINMOD, a quasi‐process based hydrologic model, with observed streamflow under different climatic conditions. Both methods are applied to determine the DSC for relatively low‐gradient coastal plain watersheds on forested landscape with slopes less than 3%. Results show robustness of the consistency zone approach for estimating depression storage. To test the adequacy of the calculated DSC values obtained, both methods are applied in DRAINMOD to predict the daily watershed flow rates. Comparison between observed and simulated streamflow reveals a marginal difference in performance between BF optimization and consistency zone estimated DSCs during wet periods, but the latter performed relatively better in dry periods. DSC is found to be dependent on seasonal antecedent moisture conditions on surface topography. The new methodology is beneficial in situations where data on depressional storage is unavailable for calibrating models requiring this input parameter. Copyright © 2012 John Wiley & Sons, Ltd.     

The use of small‐format and low‐altitude aerial photos for the realization of high‐resolution DEMs in mountainous areas: application to the Super‐Sauze earthflow (Alpes‐de‐Haute‐Provence,France)

Geomorphologists have to make choices and compromises, as acquisition techniques of geometrical information are numerous, depending on the specific complexity of the targeted three‐dimensional objects and the requirements of the end user. This article presents the methodology and the results over a well known and documented site. This ready‐to‐use, low‐altitude, aerial photo methodology reveals itself to be a satisfying compromise between cost, accuracy and difficulty of implementation. The selected equipment package is light enough to enable a quick reaction to unexpected events and the tools and methods are competitive with field acquisition techniques. An evaluation has demonstrated a sub‐metric accuracy for the final result. Copyright © 2002 John Wiley & Sons, Ltd.     

The Kinect: a low‐cost,high‐resolution,short‐range 3D camera

We present a novel application of the Kinect?, an input device designed for the Microsoft® Xbox 360® video game system. The device can be used by Earth scientists as a low‐cost, high‐resolution, short‐range 3D/4D camera imaging system producing data similar to a terrestrial light detection and ranging (LiDAR) sensor. The Kinect contains a structured light emitter, an infrared camera (the combination of these two produce a distance image), a visual wavelength camera, a three‐axis accelerometer, and four microphones. The cost is ~ US $100, frame rate is 30 Hz, spatial and depth resolutions are mm to cm depending on range, and the optimal operating range is 0.5 to ~5 m. The resolution of the distance measurements decreases with distance and is ≤1 mm at 0.5 m and ~75 mm at 5 m. We illustrate data collection and basic data analysis routines in three experiments designed to demonstrate the breadth and utility of this new sensor in domains of glaciology, stream bathymetry, and geomorphology, although the device is applicable to a number of other Earth science fields. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigating the geomorphological potential of freely available and accessible structure‐from‐motion photogrammetry using a smartphone

We test the acquisition of high‐resolution topographic and terrain data using hand‐held smartphone technology, where the acquired images can be processed using technology freely available to the research community. This is achieved by evaluating the quality of digital terrain models (DTM) of a river bank and an Alpine alluvial fan generated with a fully automated, free‐to‐use, structure‐from‐motion package and a smartphone integrated camera (5 megapixels) with terrestrial laser scanning (TLS) data used to provide a benchmark. To evaluate this approach a 16.2‐megapixel digital camera and an established, commercial, close‐range and semi‐automated software are also employed, and the product of the four combinations of the two types of cameras and software are compared. Results for the river bank survey demonstrate that centimetre‐precision DTMs can be achieved at close range (10 m or less), using a smartphone camera and a fully automated package. Results improve to sub‐centimetre precision with either higher‐resolution images or by applying specific post‐processing techniques to the smartphone DTMs. Application to an entire Alpine alluvial fan system shows the degradation of precision scales linearly with image scale, but that (i) the expected level of precision remains and (ii) difficulties in separating vegetation and sediment cover within the results are similar to those typically found when using other photo‐based techniques and laser scanning systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of depression storage capacity on overland‐flow generation for rough horizontal surfaces: water transfer distance and scaling

Overland‐flow triggering on rough surfaces was investigated using an understanding‐oriented model. The model was based on conditioned‐walker technique and developed to simulate and analyse the evolution of puddle connection on numerically generated rough surfaces. The percolation theory gave a theoretical framework to formalize model outputs and to study overland‐flow scaling. Overland‐flow triggering appeared consistent with a percolation process. A scale‐change exponent was suggested. New insights based on the concept of transfer distance of water were emphasized. Transfer distance enabled us to analyse the water redistribution inside a field and helped to define rainfall efficiency when infiltration occurred. Copyright © 2002 John Wiley & Sons, Ltd.     

Erodibility of low‐compaction steep‐sloped reclaimed surface mine lands in the southern Appalachian region,USA

The use of loose spoils on steep slopes for surface coal mining reclamation sites has been promoted by the US Department of Interior, Office of Surface Mining for the establishment of native forest, as prescribed by the Forest Reclamation Approach (FRA). Although low‐compaction spoils improve tree survival and growth, erodibility on steep slopes was suspected to increase. This study quantified a combined K_C factor (combining the effects of the soil erodibility K factor and cover management C) for low compaction, steep‐sloped (>20°) reclaimed mine lands in the Appalachian region, USA. The combined K_C factor was used because standard Unit Plot conditions required to separate these factors, per Revised Universal Soil Loss Equation (RUSLE) experimental protocols, were not followed explicitly. Three active coal mining sites in the Appalachian region of East Tennessee, each containing four replicate field plots, were monitored for rainfall and sediment yields during a 14‐month period beginning June 2009. Average cumulative erosivity for the study sites during the monitoring period was measured as 5248.9 MJ·mm·ha^?1·h^?1. The K_C ranged between 0.001 and 0.05 t·ha·h·ha^?1·MJ^?1·mm^?1, with the highest values occurring immediately following reclamation site construction as rills developed (June – August 2009). The K_C for two study sites with about an 18–20 mm spoil D₈₄ were above 0.01 t·ha·h·ha^?1·MJ^?1·mm^?1 during rill development, and below 0.003 t·ha·h·ha^?1·MJ^?1·mm^?1 after August 2009 for the post‐rill development period. The K_C values for one site with a 40 mm spoil D₈₄ were never above 0.008 t·ha·h·ha^?1·MJ^?1·mm^?1 and also on average were lower, being more similar to the other two sites after the rill development period. Based on an initial K_C factor (K_e) measured during the first few storm events, the average C factor (C_e) was estimated as 0.58 for the rill development period and 0.13 for the post‐rill development period. It appears that larger size fractions of spoils influence K_C and C_e factors on low‐compaction steep slopes reclamation sites. Copyright © 2013 John Wiley & Sons, Ltd.     

Micro‐geomorphology determines community structure of biological soil crusts at small scales

Biological soil crusts (BSCs) are ubiquitous communities of diminutive organisms such as cyanobacteria, green algae, lichens, mosses and others associated closely with particles of surface soil, forming a cohesive thin horizontal layer. The ecological roles of BSCs affecting soil nutrient cycling, stability and hydrological processes, influencing the germination and establishment of vascular plants, and serving as habitats for numerous arthropods and microorganism have been well documented. We tested the hypothesis that micro‐geomorphological features determine the spatial distribution of BSCs by reallocating related abiotic resources at small‐ and medium‐scales in the Tengger Desert. Our results showed that higher soil pH and higher total potassium content in topsoil positively correlated with the colonization of cyanobacteria and algae in the earliest successional stages of BSCs, while increasing dust deposition onto the topsoil enhanced the development of lichen and mosses in the later stages of BSCs. Increasing soil moisture raised the proportion of mosses and lichen in BSCs, this will possibly change the ecological functions of BSCs, such as nitrogen‐fixation by cyanobacteria, due to the conversion from a complex to relative simple type of BSC. Micro‐geomorphology has created various habitats at a small‐scale affecting colonization and development of cryptogams. This paper considers the contribution of micro‐geomorphology to biodiversity in the extreme arid desert systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of the performance of flow‐routing algorithms used in GIS‐based hydrologic analysis

Flow direction and specific catchment area were calculated for different flow‐routing algorithms using TAPES‐G and TauDEM. A fuzzy classification was used along with eight topo–climatic attributes to delineate six landscape classes from a 10‐m USGS DEM. A series of maps and tabular outputs were produced to compare flow‐routing predictions in different parts of the study area in the Santa Monica Mountains of southern California. The matched pair t‐test was used to compare the performance of pairs of specific catchment area grids across six user‐defined fuzzy landscape classes. The results show that (1) the ‘source’ cells predicted with the D∞, DEMON, and FD8 algorithms were confined to hilltops; (2) two single flow‐routing algorithms (Rho8, D8) produced poor results; and (3) the choice of flow‐routing algorithm has potentially important consequences for the calculation of upslope contributing areas, sediment transport capacity, topographic wetness, and several other topographic indices. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of terrain smoothing on topographic shielding correction factors for cosmogenic nuclide‐derived estimates of basin‐averaged denudation rates

Estimation of spatially averaged denudation rates from cosmogenic nuclide concentrations in sediments depends on the surface production rates, the scaling methods of cosmic ray intensities, and the correction algorithms for skyline, snow and vegetation shielding used to calculate terrestrial cosmogenic nuclide production. While the calculation of surface nuclide production and application of latitude, altitude and palaeointensity scaling algorithms are subjects of active research, the importance of additional correction for shielding by topographic obstructions, snow and vegetation is the subject of ongoing debate. The derivation of an additional correction factor for skyline shielding for large areas is still problematic. One important issue that has yet to be addressed is the effect of the accuracy and resolution of terrain representation by a digital elevation model (DEM) on topographic shielding correction factors. Topographic metrics scale with the resolution of the elevation data, and terrain smoothing has a potentially large effect on the correction of terrestrial cosmogenic nuclide production rates for skyline shielding. For rough, high‐relief landscapes, the effect of terrain smoothing can easily exceed analytical errors, and should be taken into account. Here we demonstrate the effect of terrain smoothing on topographic shielding correction factors for various topographic settings, and introduce an empirical model for the estimation of topographic shielding factors based on landscape metrics. Copyright © 2008 John Wiley and Sons, Ltd.     

SCALES: a large‐scale assessment model of soil erosion hazard in Basse‐Normandie (northern‐western France)

The cartography of erosion risk is mainly based on the development of models, which evaluate in a qualitative and quantitative manner the physical reproduction of the erosion processes (CORINE, EHU, INRA). These models are mainly semi‐quantitative but can be physically based and spatially distributed (the Pan‐European Soil Erosion Risk Assessment, PESERA). They are characterized by their simplicity and their applicability potential at large temporal and spatial scales. In developing our model SCALES (Spatialisation d'éChelle fine de l'ALéa Erosion des Sols/large‐scale assessment and mapping model of soil erosion hazard), we had in mind several objectives: (1) to map soil erosion at a regional scale with the guarantee of a large accuracy on the local level, (2) to envisage an applicability of the model in European oceanic areas, (3) to focus the erosion hazard estimation on the level of source areas (on‐site erosion), which are the agricultural parcels, (4) to take into account the weight of the temporality of agricultural practices (land‐use concept). Because of these objectives, the nature of variables, which characterize the erosion factors and because of its structure, SCALES differs from other models. Tested in Basse‐Normandie (Calvados 5500 km²) SCALES reveals a strong predisposition of the study area to the soil erosion which should require to be expressed in a wet year. Apart from an internal validation, we tried an intermediate one by comparing our results with those from INRA and PESERA. It appeared that these models under estimate medium erosion levels and differ in the spatial localization of areas with the highest erosion risks. SCALES underlines here the limitations in the use of pedo‐transfer functions and the interpolation of input data with a low resolution. One must not forget however that these models are mainly focused on an interregional comparative approach. Therefore the comparison of SCALES data with those of the INRA and PESERA models cannot result on a convincing validation of our model. For the moment the validation is based on the opinion of local experts, who agree with the qualitative indications delivered by our cartography. An external validation of SCALES is foreseen, which will be based on a thorough inventory of erosion signals in areas with different hazard levels. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatial patterns and temporal stability of soil moisture across a range of scales in a semi‐arid environment

The antecedent soil moisture status of a catchment is an important factor in hydrological modelling. Traditional Hortonian infiltration models assume that the initial moisture content is constant across the whole catchment, despite the fact that even in small catchments antecedent soil moisture exhibits tremendous spatial heterogeneity. Spatial patterns of soil water distribution across three transects (two in a burnt area and one in an unburnt area) in a semi‐arid area were studied. At the transect scale, when the factors affecting soil moisture were limited to topographical position or local topography, spatial patterns showed time stability, but when other factors, such as vegetation, were taken into account, the spatial patterns became time unstable. At the point scale, and in the same areas, topographical position was the main factor controlling time stability. Scale dependence of time stability was studied and local topography and vegetation presence were observed to play an important role for the correlation between consecutive measures depending on the scale. Copyright © 2000 John Wiley & Sons, Ltd.     

Multi‐scale assimilation of root zone soil water predictions

When hydrology model parameters are determined, a traditional data assimilation method (such as Kalman filter) and a hydrology model can estimate the root zone soil water with uncertain state variables (such as initial soil water content). The simulated result can be quite good. However, when a key soil hydraulic property, such as the saturated hydraulic conductivity, is overestimated or underestimated, the traditional soil water assimilation process will produce a persistent bias in its predictions. In this paper, we present and demonstrate a new multi‐scale assimilation method by combining the direct insertion assimilation method, particle swarm optimisation (PSO) algorithm and Richards equation. We study the possibility of estimating root zone soil water with a multi‐scale assimilation method by using observed in situ data from the Wudaogou experiment station, Huaihe River Basin, China. The results indicate there is a persistent bias between simulated and observed values when the direct insertion assimilation surface soil water content is used to estimate root zone soil water contents. Using a multi‐scale assimilation method (PSO algorithm and direct insertion assimilation) and an assumed bottom boundary condition, the results show some obvious improvement, but the root mean square error is still relatively large. When the bottom boundary condition is similar to the actual situation, the multi‐scale assimilation method can well represent the root zone soil water content. The results indicate that the method is useful in estimating root zone soil water when available soil water data are limited to the surface layer and the initial soil water content even when the soil hydraulic conductivities are uncertain. Copyright © 2011 John Wiley & Sons, Ltd.     

Complexity‐reduction modelling for assessing the macro‐scale patterns of historical soil moisture in the Euro‐Mediterranean region

Complexity‐reduction modelling can be useful for increasing the understanding of how the climate affects basin soil moisture response upon historical times not covered by detailed hydrological data. For this purpose, here is presented and assessed an empirical regression‐based model, the European Soil Moisture Empirical Downscaling (ESMED), in which different climatic variables, easily available on the web, are addressed for simplifying the inherent complexity in the long‐time studies. To accommodate this simplification, the Palmer Drought Severity Index, the precipitation, the elevation and the geographical location were used as input data in the ESMED model for predicting annual soil moisture budget. The test area was a large region including central Europe and Mediterranean countries, and the spatial resolution was initially set at 50 km. ESMED model calibration was made according to the soil moisture values retrieved from the Terrestrial Water Budget Data archive by selecting randomly 285 grid points (out of 2606). Once parameterized, ESMED model was performed at validation stage both spatially and temporally. The spatial validation was made for the grid points not selected in the calibration stage while the comparison with the soil moisture outputs of the Global Land Data Assimilation System–NOAH10 simulations upon the period 1950–2010 was carried out for the temporal validation. Moreover, ESMED results were found to be in good agreement with a root‐zone soil moisture product obtained from active and passive microwave sensors from various satellite missions. ESMED model was thus found to be reliable for both the temporal and spatial validations and, hence, it might represent a useful tool to characterize the long‐term dynamics of soil moisture–weather interaction. Copyright © 2013 John Wiley & Sons, Ltd.     

Near‐infrared spectroscopy of a hydroecological indicator: new tool for determining sustainable yield for Floridan aquifer system

Pond‐cypress (Taxodium ascendens Brong.) is a dominant canopy species in depressional wetlands of the south‐eastern Coastal Plain. Unsustainable withdrawals from the karst Floridan aquifer system have caused premature decline and death of pond‐cypress trees, presumably owing to altered hydroperiods (which alter the flow of water and nutrients in trees). There has been no scientifically based means to determine sustainable yield from this regional aquifer system or to detect early stages of physical/ecological damage associated with groundwater mining and aquifer storage and recovery (ASR, which also can alter natural hydroperiods). In this study, the relationship between visual symptoms (indicators) of stress or premature decline, and spectral reflectance was evaluated using dried, milled branch tips collected from natural stands of mature pond‐cypress. Depressional systems evaluated represented four of the six aquifer system subregions where subsurface perturbations from groundwater mining: (i) were presumed not to be occurring (reference wetlands); (ii) may be occurring but are not documented; and (iii) have been confirmed. Sampled trees were assigned to one of three stress classes (1, no/minimal; 2, moderate; 3, severe) based on the visual indicators. Partial least squares–linear discriminant analysis of second derivative spectral transformations in the visible/shortwave near‐infrared (NIR) region (400–1100 nm) and the NIR region (1100–2500 nm) was used to evaluate the samples in assigned classes. Class 1 samples were discriminated from combined class 2 and 3 samples in the NIR region with 100% and 97% accuracy for consecutive winter sample periods (before bud‐break). The percentage of correctly classified samples in this spectral region was lower (85%) for summer samples (full leaf‐out). Second‐derivative models for the NIR region developed from the winter data sets predicted assigned classes for alternate winter's samples with an accuracy of 97% and 100%. High correlation between spectral reflectance of dried, milled branch tips collected from mature pond‐cypress in winter and visual indicators of premature decline suggests in situ pond‐cypress are hydroecological indicators of anthropogenic subsurface hydroperiod perturbations. This approach provides objective means for early detection of unsustainable aquifer yield and adverse impacts from ASR activities in the south‐eastern Coastal Plain. Used in conjunction with hydrological monitoring and modelling, the hydroecological indicators should provide the means with which sustainable yield in the south‐eastern Coastal Plain can be achieved and maintained. Copyright © 2003 John Wiley & Sons, Ltd.     

Microtopography,water storage and flow patterns in a fine‐textured soil under agricultural use

Agricultural use of soils implies tillage and often compaction and therefore influences processes on soil surface and affects infiltration of water into the subsoil. Although many studies on soil surface processes or flow patterns in soils exist, works relating both are rare in literature. We did two tracer experiments with Brilliant Blue FCF on a tilled and compacted plot and a non‐tilled one to investigate water storage on the soil surface during simulated rainfall and changes of soil microtopography, to analyse the associated flow patterns in the soil and to relate both to tillage and compaction. Our results show that storage was larger on the tilled and compacted plot than on the non‐tilled one. After tillage, transport processes above the plough pan were partly disconnected from those underneath because macropores were disrupted and buried by the tillage operation. However, preferential flow along cracks occurred on both plots and the macropores buried below the tillage pan still functioned as preferential flow paths. Therefore, we conclude that the studied soil is susceptible to deep vertical solute propagation at dry conditions when cracks are open, irrespective of tillage and compaction. Copyright © 2012 John Wiley & Sons, Ltd.     

Spatio‐temporal distribution of near‐surface and root zone soil moisture at the catchment scale

Soil moisture is highly variable both spatially and temporally. It is widely recognized that improving the knowledge and understanding of soil moisture and the processes underpinning its spatial and temporal distribution is critical. This paper addresses the relationship between near‐surface and root zone soil moisture, the way in which they vary spatially and temporally, and the effect of sampling design for determining catchment scale soil moisture dynamics. In this study, catchment scale near‐surface (0–50 mm) and root zone (0–300 mm) soil moisture were monitored over a four‐week period. Measurements of near‐surface soil moisture were recorded at various resolutions, and near‐surface and root zone soil moisture data were also monitored continuously within a network of recording sensors. Catchment average near‐surface soil moisture derived from detailed spatial measurements and continuous observations at fixed points were found to be significantly correlated (r² = 0·96; P = 0·0063; n = 4). Root zone soil moisture was also found to be highly correlated with catchment average near‐surface, continuously monitored (r² = 0·81; P < 0·0001; n = 26) and with detailed spatial measurements of near‐surface soil moisture (r² = 0·84). The weaker relationship observed between near‐surface and root zone soil moisture is considered to be caused by the different responses to rainfall and the different factors controlling soil moisture for the soil depths of 0–50 mm and 0–300 mm. Aspect is considered to be the main factor influencing the spatial and temporal distribution of near‐surface soil moisture, while topography and soil type are considered important for root zone soil moisture. The ability of a limited number of monitoring stations to provide accurate estimates of catchment scale average soil moisture for both near‐surface and root zone is thus demonstrated, as opposed to high resolution spatial measurements. Similarly, the use of near‐surface soil moisture measurements to obtain a reliable estimate of deeper soil moisture levels at the small catchment scale was demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

A practical method for estimating dynamic soil stiffness on surface of multi‐layered soil

It is important to estimate the influence of layered soil in soil–structure interaction analyses. Although a great number of investigations have been carried out on this subject, there are very few practical methods that do not require complex calculations. In this paper, a simple and practical method for estimating the horizontal dynamic stiffness of a rigid foundation on the surface of multi‐layered soil is proposed. In this method, waves propagating in the soil are traced using the conception of the cone model, and the impulse response function can be calculated directly and easily in the time domain with a good degree of accuracy. The characteristics of the impedance, that is the transformed value to the frequency domain of the obtained impulse response, are studied using two‐ to four‐layered soil models. The cause of the fluctuation of impedance is expressed clearly from its relation to reflected waves from the lower layer boundary in the model. Copyright © 2005 John Wiley & Sons, Ltd.     

Role of biological soil crust cover in bioweathering and protection of sandstones in a semi‐arid landscape (Torrollones de Gabarda,Huesca, Spain)

Sandstone structural landscapes in the semi‐arid Torrollones de Gabarda area (Province of Huesca, NE Spain) are often covered by a well developed biological soil crust of lichens, mosses and cyanobacteria and black coatings on vertical surfaces. By using scanning electron microscopy with backscattered detector imaging, the biological soil crust studied evidenced high activity in the sandstone–crust interface. Processes such as physical disintegration, etching and dwelling as well as biomineralization by calcium oxalate and ?xation of mineral particles by extracellular polymeric substances were observed. On the horizontal sandstone surfaces these processes may cause the occurrence of gnammas and the development of a protective coating that favours intense ?aking when the crust is disturbed. On the sandstone cliffs, columnar and tafoni weathering development is clearly guided by the protective action of the biological soil crust. These qualitative observations are important to develop methodologies to address their quantitative importance in geomorphological processes in semi‐arid landscapes. Copyright © 2004 John Wiley & Sons, Ltd.     

Remote sensing of river stage using the cross‐sectional inundation area‐river stage relationship (IARSR) constructed from digital elevation model data

Remote sensing of discharge and river stage from space provides us with a promising alternative approach to monitor watersheds, no matter if they are ungauged, poorly gauged, or fully gauged. One approach is to estimate river stage from satellite measured inundation area based on the inundation area – river stage relationship (IARSR). However, this approach is not easy to implement because of a lack of data for constructing the IARSR. In this study, an innovative and robust approach to construct the IARSR from digital elevation model (DEM) data was developed and tested. It was shown that the constructed IARSR from DEM data could be used to retrieve water level or river stage from satellite‐measured inundation area. To reduce the uncertainty in the estimated inundation area, a dual‐thresholding method was proposed. The first threshold is the lower limit of pixel value for classifying water body pixels with a relatively high‐level certainty. The second threshold is the upper limit of pixel value for classifying potentially flooded pixels. All pixels with values between the first threshold and the second threshold and adjacent to the classified water body pixels may be partially flooded. A linear interpolation method was used to estimate the wetted area of each partially flooded pixel. In applying the constructed IARSR to the estimated inundation areas from 11 Landsat TM images, 11 water levels were obtained. The root mean square error (RMSE) of the estimated water levels compared with the observed water levels at the US Geological Survey (USGS) gauging station on the Trinity River at Liberty in Liberty County, Texas, is about 0.38 m. Copyright © 2012 John Wiley & Sons, Ltd.