The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Many of the scientific and societal challenges in understanding and preparing for global environmental change rest upon our ability to understand and predict the water cycle change at large river basin, continent, and global scales. However, current large-scale models, such as the land components of Earth System Models (ESMs), do not yet represent the terrestrial water cycle in a fully integrated manner or resolve the finer-scale processes that can dominate large-scale water budgets. This paper reviews the current representation of hydrologic processes in ESMs and identifies the key opportunities for improvement. This review suggests that (1) the development of ESMs has not kept pace with modeling advances in hydrology, both through neglecting key processes (e.g., groundwater) and neglecting key aspects of spatial variability and hydrologic connectivity; and (2) many modeling advances in hydrology can readily be incorporated into ESMs and substantially improve predictions of the water cycle. Accelerating modeling advances in ESMs requires comprehensive hydrologic benchmarking activities, in order to systematically evaluate competing modeling alternatives, understand model weaknesses, and prioritize model development needs. This demands stronger collaboration, both through greater engagement of hydrologists in ESM development and through more detailed evaluation of ESM processes in research watersheds. Advances in themore » representation of hydrologic process in ESMs can substantially improve energy, carbon and nutrient cycle prediction capabilities through the fundamental role the water cycle plays in regulating these cycles.« less

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Improving the representation of hydrologic processes in Earth System Models

Boundary conditions for displacement experiments through short laboratory soil columns [Dispersion coefficients]

[1] This paper investigates the actual extrapolation capacity of three hydrological models in differing climate conditions. We propose a general testing framework, in which we perform series of split-sample tests, testing all possible combinations of calibration-validation periods using a 10 year sliding window. This methodology, which we have called the generalized split-sample test (GSST), provides insights into the model's transposability over time under various climatic conditions. The three conceptual rainfall-runoff models yielded similar results over a set of 216 catchments in southeast Australia. First, we assessed the model's efficiency in validation using a criterion combining the root-mean-square error and bias. A relation was found between this efficiency and the changes in mean rainfall (P) but not with changes in mean potential evapotranspiration (PE) or air temperature (T). Second, we focused on average runoff volumes and found that simulation biases are greatly affected by changes in P. Calibration over a wetter (drier) climate than the validation climate leads to an overestimation (underestimation) of the mean simulated runoff. We observed different magnitudes of these models deficiencies depending on the catchment considered. Results indicate that the transfer of model parameters in time may introduce a significant level of errors in simulations, meaning increased uncertainty in the various practical applications of these models (flow simulation, forecasting, design, reservoir management, climate change impact assessments, etc.). Testing model robustness with respect to this issue should help better quantify these uncertainties.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011WR011721

Crash testing hydrological models in contrasted climate conditions: An experiment on 216 Australian catchments

Soil water content (SWC) plays a key role in parƟ Ɵ oning water and energy fl uxes at the land surface and in controlling hydrologic fl uxes such as groundwater recharge. Despite the importance of SWC, it is not yet measured in an operaƟ onal way at larger scales. The aim of this study was to invesƟ gate the potenƟ al of wireless sensor network technology for the nearreal-Ɵ me monitoring of SWC at the fi eld and headwater catchment scales using the recently developed wireless sensor network SoilNet. The forest catchment Wustebach (?27 ha) was instrumented with 150 end devices and 600 EC-5 SWC sensors from the ECH 2 O series by Decagon Devices. In the period between August and November 2009, more than six million SWC measurements were obtained. The observed spaƟ al variability corresponded well with results from previous studies. The very low scaƩ ering in the plots of mean SWC against SWC variance indicates that the sensor network data provide a more accurate esƟ mate of SWC variance than disconƟ nuous data from measurement campaigns, due, e.g., to fi xed sampling locaƟ ons and permanently installed sensors. The spaƟ al variability in SWC at the 50-cm depth was signifi cantly lower than at 5 cm, indicaƟ ng that the longer travel Ɵ me to this depth reduced the spaƟ al variability of SWC. Topographic features showed the strongest correlaƟ on with SWC during dry periods, indicaƟ ng that the control of topography on the SWC paƩ ern depended on the soil water status. InterpolaƟ on results indicated that the high sampling density allowed capture of the key paƩ erns of SWC variaƟ on. AbbreviaƟ ons: AIC, Akaike informaƟ on criterion; SWC, soil water content; WI wetness index.

Potential of Wireless Sensor Networks for Measuring Soil Water Content Variability

[1] In the shallow subsurface immediately below the land-atmosphere interface, it is widely recognized that the movement of water vapor is closely coupled to thermal processes. However, their mutual interactions are rarely considered in most soil water modeling efforts or in practical applications where it becomes necessary to understand the spatial and temporal distribution of soil moisture. The validation of numerical models that are designed to capture these processes is difficult due to the scarcity of field or laboratory data with accurately known hydraulic and thermal parameters of soils, limiting the testing and refinement of heat and water transfer theories. The goal of this paper is to perform controlled experiments under transient conditions of soil moisture and temperature and use this data to test existing theories and develop appropriate numerical models. Water vapor flow under varying temperature gradients was implemented on the basis of a concept that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion. To validate this new approach, we developed a long column apparatus equipped with a network of sensors and generated data under well-controlled thermal boundary conditions at the soil surface. The nonequilibrium approach yielded good agreement with the experimental results, validating the hypothesis that transport in the gas phase is better suited to be modeled with nonequilibrium liquid/gas phase change for highly transient field conditions where the thermal conditions at the land-atmosphere interface are constantly changing.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2010WR009533

Evaporation from soils under thermal boundary conditions: Experimental and modeling investigation to compare equilibrium- and nonequilibrium-based approaches

[1] Recently improved ECH2O soil moisture sensors have received significant attention in many field and laboratory applications. Focusing on the EC-5 sensor, a simple and robust calibration method is proposed. The sensor-to-sensor variability in the readings (analog-to-digital converter (ADC) counts) among 30 EC-5 sensors was relatively small but not negligible. A large number of ADC counts were taken under various volumetric water contents (θ) using four test sands. The proposed two-point α-mixing model, as well as linear and quadratic models, was fitted to the ADC – θ data. Unlike for conventional TDR measurements, the effect of sensor characteristics is lumped into the empirical parameter α in the two-point α-mixing model. The value of α was fitted to be 2.5, yielding a nearly identical calibration curve to the quadratic model. Errors in θ associated with the sensor-to-sensor variability for the two-point α-mixing model were ±0.005 cm3 cm−3 for dry sand and ±0.028 cm3 cm−3 for saturated sand. In the validation experiments, the highest accuracy in water content estimation was achieved when sensor-specific ADCdry and ADCsat were used in the two-point α-mixing model. Assuming that α = 2.5 is valid for most mineral soils, the two-point α-mixing model only requires the measurement of two extreme ADC counts in dry and saturated soils. Sensor-specific ADCdry and ADCsat counts are readily measured in most cases. Therefore, the two-point α-mixing model (with α = 2.5) can be considered as a quick, easy, and robust method for calibrating the ECH2O EC-5 sensor. Although further investigation is needed, the two-point α-mixing model may also be applied to calibrating other sensors.

Empirical two‐point α‐mixing model for calibrating the ECH2O EC‐5 soil moisture sensor in sands

[1] The macroscopic flow equations used to predict two-phase flow typically utilizes a capillary pressure-saturation relationship determined under equilibrium conditions. Theoretical reasoning, experimental evidence, and numerical modeling results have indicated that when one fluid phase replaces another fluid, this relationship may not be unique but may depend on the rate at which the phase saturations change in response to changes in phase pressures. This nonuniqueness likely depends on a variety of factors including soil-fluid properties and possibly physical scale. To quantify this dependency experimentally, direct measurements of equilibrium and dynamic capillary pressure-saturation relationships were developed for two Ottawa sands with different grain sizes using a 20 cm long column. A number of replicate air-water experiments were conducted to facilitate statistical comparison of capillary pressure-saturation relationships. Water and air pressures and phase saturations were measured at three different vertical locations in the sand column under different desaturation rates (1) to measure local capillary pressure-saturation relationships (static and dynamic); (2) to quantify the dynamic coefficient T , a measure of the magnitude of observed dynamic effects, as a function of water saturation for different grain sizes and desaturation rates; (3) to investigate the importance of grain size on measured dynamic effects; and (4) to assess the importance of sample scale on the magnitude of dynamic effects in capillary pressure. A comparison of the static and dynamic P c -S w relationships showed that at a given water saturation, capillary pressure measured under transient water drainage conditions is statistically larger than capillary pressure measured under equilibrium or static conditions, consistent with thermodynamic theory. The dynamic coefficient T , used in the expression relating the static and dynamic capillary pressures to the desaturation rate was dependant on porous media mean grain size but not on the desaturation rate. Results also suggest that the magnitude of the dynamic coefficient did not increase with the increased averaging volume considered in this study, as has been reported in the literature. This work suggests that dynamic effects in capillary pressure should be included in numerical models used to predict multiphase flow in systems when saturations change rapidly, particularly in fine-grained soil systems (e.g., CO 2 sequestration, enhanced oil recovery, air sparging for remediation).

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Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling

[1] Tempe cells and similar devices are often used for measurements of capillary pressure versus saturation relationships (retention curves) of soils. Average water saturation within the sample is often used as the representative saturation. For cases where the saturation distribution along the cell height is nonuniform, use of the height-averaged water saturation artificially smoothes the retention curve when the capillary pressure head reaches the displacement pressure head. This leads to an inaccurate representation of the retention curve in flow modeling. For nine test sands with a wide range of displacement pressure head values (6–78 cm of water), height-averaged and point-measured retention curves were simultaneously obtained to investigate the effect of the height-averaging procedure. A Tempe cell was used, which was modified by installing a small time domain reflectometry probe and a tensiometer at the midpoint of the sample height to measure water saturation and pressure, respectively. When the sample height is large relative to the displacement pressure head, the bulk drainage (initial drainage at the top of the sample) leads to inaccuracies in the determination of retention curves. For such cases, point-measured saturation should be used, otherwise height correction is necessary.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006WR005814

Comparison of height-averaged and point-measured capillary pressure–saturation relations for sands using a modified Tempe cell

The constitutive relationship between capillary pressure ( P c) and wetting fluid saturation ( S w), or retention curve, is needed to model multiphase flow in porous media. This relationship is usually measured under static conditions; however, transient flow is governed by a dynamic relationship between the P c and S w. Differences in P c measured under static and dynamic conditions are due to dynamic effects typically defined as a product of a dynamic coefficient (τ) and the rate of change in S w. To date, relatively few experimental studies have been conducted to directly quantify the magnitude of this effect. In this study, the magnitude of τ was quantified by measuring both static and dynamic retention curves in repeated drainage and wetting experiments using a field sand. The 95% confidence intervals for the static retention curves showed that the dynamic retention curves were statistically different. The measured τ for primary drainage generally increased with decreasing S w. The measured τ values were also compared with those estimated using a different approach based on redistribution time. The measured and estimated τ were in close agreement when the redistribution times were 146 s for the wetting cycle and 509 s for primary and main drainage cycles. The shape of the τ– S w relationship was largely controlled by the slope of the static retention curve. Numerical modeling demonstrated that a log-linear model relating τ and S w yielded the best match to experimental outflow results.

Toshihiro Sakaki

Papers

Evaporation from soils under thermal boundary conditions: Experimental and modeling investigation to compare equilibrium- and nonequilibrium-based approaches

Empirical two‐point α‐mixing model for calibrating the ECH2O EC‐5 soil moisture sensor in sands

Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling

Comparison of height-averaged and point-measured capillary pressure–saturation relations for sands using a modified Tempe cell

Direct Quantification of Dynamic Effects in Capillary Pressure for Drainage–Wetting Cycles