Critical Pressure Head Research Articles

Comment on “Modified expression for unsaturated hydraulic conductivity according to Mualem–van Genuchten to allow proper computations at low pressure heads” by M. Heinen

AbstractThis comment concerns evaluation of the Mualem–van Genuchten (MvG) unsaturated soil hydraulic functions at very low (negative) pressure heads as described recently in an important study by Heinen. He showed that below some critical pressure head, the unsaturated hydraulic conductivity should be approximated by a power function, even when evaluated using double precision computations. We show that a more precise approximation is possible when the approximation is formulated in terms of effective fluid saturation (Se) rather than the pressure head, h. More general constraints are also provided when the approximated hydraulic conductivity equation should be used. The alternative formulation and constraints were implemented earlier in the SOHYP and RETC software packages.

Modified expression for hydraulic conductivity according to Mualem–van Genuchten to allow proper computations at low‐pressure heads

AbstractWater retention and hydraulic conductivity characteristics are key input data in studies on soil water dynamics in the vadose zone. The most well‐known analytical functions to describe these characteristics are those given by Mualem and van Genuchten, where van Genuchten showed that both can be described by a limited set of shared parameters. Analytically, there are no restrictions on the range of pressure heads for which these characteristics can be used. Experience, however, has shown that for certain sets of parameters, the hydraulic conductivity cannot be computed accurately at low‐pressure heads. This is due to the accuracy of (double precision) floating point operations in computer code. It is shown that for low‐pressure heads, the Mualem function approaches a power function. An adapted version of the Mualem–van Genuchten (MvG) expression for the hydraulic conductivity is proposed: between saturation and a soil‐dependent critical pressure head, the classical Mualem expression is valid and below this critical pressure head a power function is used. The power function is defined such that it matches the Mualem value at the critical pressure head. No accuracy problems will occur when using the power function until the result approaches the smallest possible (double precision) floating point value that significantly differs from zero.

Application of high-resolution meteorological data from NCAM-WRF to characterize agricultural drought in small-scale farmlands based on soil moisture deficit

We discussed the applicability of high-resolution meteorological data simulated by the NCAM-Weather Research and Forecasting (NCAM-WRF) model to investigate spatially distributed soil-moisture deficits in site-scale farmland areas. A gridded soil water budget model was developed to utilize the 90 m NCAM-WRF meteorological data to predict soil moisture content (SMC) at multiple depths. The applicability of the NCAM-WRF climatic variables to predict SMC was evaluated by comparing the SMC estimates with in-situ observations at the monitoring site. We used the Quantile Mapping (QM) method to correct the biases of NCAM-WRF precipitation outputs. The SMC estimates derived from the newly developed soil water budget model showed a good agreement with observations, and we proved that the bias-corrected NCAM-WRF precipitation data could improve the predictability of the temporal evolution of SMCs. For characterizing agricultural drought during the crop growing season, we presented a novel approach to estimate the magnitude, duration, and severity of agricultural drought events based on crop's critical pressure head. We mapped the distribution of SMC, soil matric potential (SMP), and drought severity at the 90-m resolution, and the results showed that applying the NCAM-WRF climatic variables to the modeling of SMC/SMP profiles can lead to drought characterization on site-scale while accounting for the spatial variability of rainfall and other climatic variables.

Measurement and modeling of the spatiotemporal dynamics of beach surface moisture content

Abstract The spatiotemporal dynamics of surface moisture exert a significant influence on the operation of aeolian transport systems at many beaches. However, we currently lack the detailed understanding of variability in surface moisture required to incorporate it into aeolian models. This problem is addressed here through direct measurements and simulation modeling of beach surface moisture over a twelve-day period, and through quantification of the relative contributions of evaporation, condensation and groundwater inputs to surface moisture. It was found that the beach surface can be characterized spatially in terms of three moisture zones: a consistently dry zone ( 40%). The relative influence of groundwater inputs was found to decrease moving landward, as the depth of the water table increased and the amplitude of tidally-induced water table fluctuations decreased. The critical pressure head (groundwater depth) at which evaporation begins to impose a demonstrable influence on surface moisture variability was found to be 90–100 cm. Temporally, beach surface moisture is a function of the lunar tidal cycle at longer-term time scales (weekly), and diurnal tidal and evaporation cycles. A numerical model was used to simulate capillary transfers of moisture from the water table to the surface, and moisture losses due to evaporation. The model was found to reliably replicate the measured spatiotemporal variability in surface moisture. In the dry zone, where most aeolian transport would be expected to occur, simulated moisture contents were typically within ±0.2% of measured volumetric contents.

The Shape of the Transpiration Reduction Function under Plant Water Stress

Assuming transpiration to be reduced after a critical pressure head (usually chosen as −1.5 MPa or −150 m) at the root surface has been reached, transpiration rates in this so‐called falling‐rate phase were analyzed numerically for soils described by the van Genuchten–Mualem equations (numerical soils). The analysis was based on the differential equation describing radial flow to a single root. Numerically, the system was simulated by an implicit scheme. It is shown that, at limiting hydraulic conditions, relative transpiration (ratio between actual and potential transpiration) is equal to relative matric flux potential (ratio between actual matric flux potential and matric flux potential at the onset of limiting hydraulic conditions). Given this equality, transpiration reduction functions as a function of soil water content and as a function of time are presented for five types of analytical soils: a constant diffusivity, Green and Ampt, Brooks and Corey, versatile nonlinear, and exponential soil. While in the case of constant diffusivity, relative transpiration decreases as a linear function of water content, for the remaining four cases the decrease is a concave function of soil water content. Numerical simulations also result in a concave shape, unless the difference between water content at the onset of limiting hydraulic conditions and at permanent wilting is very small, for example, at high root densities. These discrepancies may be explained by the relative importance of a transition period between the constant‐ and falling‐rate phases.

Optimization of operational factors of a membrance bioreactor with gravity drain

A new membrane bioreactor with gravity drain for municipal wastewater treatment was tested and its operational factors were investigated in this study. These factors include pressure head, MLSS, aeration intensity (an air flow rate per unit floor area) and temperature. Results of batch experiments showed that a critical pressure head of the MBR was 0.85-1.5 m-H2O. At a pressure head of 0.85 m-H2O, statistical analysis of batch experiments showed that aeration intensity significantly affected membrane flux, and the MLSS had no impact on membrane flux under a temperature of 22.0 +/- 1.0 degrees C. Results of the long-term continuous experiment showed that temperature significantly affected membrane flux. The impact of temperature on membrane flux in this case was about 4-10 times of that analyzed by using a classical cake layer model. During this experiment, the average removal efficiencies of COD, BOD5 and NH4+-N were over 85%, 97% and 94%, respectively.

Effect of capillary pressure on interdendritic liquid flow

The top free surface of a mushy zone composed of columnar dendrites is exposed to air and the interdendritic liquid is made to flow down out of the specimen by applying pressure difference across the specimen. The liquid flow rate is measured as functions of applied pressure head, fraction liquid and primary and secondary arm spacings of columnar dendrites lying parallel to the flow direction. At a pressure head smaller than a critical value, the flow rate is two orders of magnitude smaller than that in the case where the top of the mushy zone is covered with bulk liquid. Above the critical pressure head, the flow rate increases rapidly with increasing pressure head. The results can be explained in terms of the capillary pressure, acting at the free surface of the interdendritic liquid, as a resistance to liquid flow. It is suggested that the capillary pressure is one of the most important factors in the formation of porosity in castings when the free surface of the riser solidifies to form a mushy zone.

A method for computing and comparing upward flow of water in soils from a water table using the flux/unsaturated conductivity ratio

A new method, based on an analysis of the k-h curves in relation to their use in the flow equation, is proposed for the study of steady-state upward flow of water in soils from a water table and for the computation of the pressure head profiles. This method utilizes the flux/unsaturated conductivity ratio to provide a simplified but accurate means of computing pressure head profiles, using an algebraic equation for any given rate of upward flow, between specific values of pressure heads. The values of the parameters to be used in solving this equation can be read directly from the k-h curves. In many soils, upward flow can be characterized by two parameters, namely, the slope of the k-h curve and the upper limit h,, of the critical pressure head range, thus giving a basis for direct comparison. This method can be applied to k-h curves with any integer or non-integer value of slope. Equations are also derived from which the maximum depth to water table for any rate of upward flow can be read directly from the k-h curves of certain soils. The flux/unsaturated conductivity ratio is also used to define the critical range of unsaturated conductivity, and the corresponding critical pressure head range within which the absolute values of conductivity significantly affect the shape of the pressure head profile. The use of the flux/unsaturated conductivity method, and the critical ranges for analysing k-h curves in order to predict and compare upward flow in homogeneous and layered soils, are discussed.

Comparison of Empirical Relationships between Pressure Head and Hydraulic Conductivity and Some Observations on Radially Symmetric Flow

It is shown that the critical pressure head used by Bouwer is equal to the difference in matric flux potential at pressure heads zero and minus infinity divided by the hydraulic conductivity at pressure head zero. The critical pressure head and the saturated hydraulic conductivity are used to define a dimensionless pressure head, hydraulic conductivity, and matric flux potential. For six empirical relationships between pressure head and hydraulic conductivity, the associated matric flux potential and critical pressure head have been evaluated. The plots of the dimensionless hydraulic conductivity and mattic flux potential versus pressure head provide a clear basis for comparing the six models. A discussion of steady, p‐dimensional, radially symmetric flow (without gravity) illustrates the occurrence of the matrio flux potential and the critical pressure head in flow problems. Expressions are obtained for the steady flux, the maximum steady flux, and the change in steady flux as a function of changes in pressure head at two points. One‐dimensional, cylindrically symmetric, and radially symmetric flows are discussed as special cases. The results for the radially symmetric case suggest a new method for in situ determination of the hydraulic conductivity as a function of the pressure head.

Unsaturated Flow in Ground-Water Hydraulics

Water tables as zero-pressure surfaces do not separate saturated hydraulic conductivity from impermeability in systems of flow of water through soil. Hydraulic conductivity relationships on the negative pressure side of the water table are a property of the soil and must be experimentally determined. The various methods for obtaining these relations are examined, and curves relating hydraulic conductivity to negative soil-water pressure are shown for 28 soils. These curves, which are generally sigmoid, can be simplified to step functions for including flow at negative soil-water pressure in the analysis of steady flow systems. Such systems are then solved with a certain negative pressure (called the critical pressure head), rather than with zero pressure, at boundaries where the system is in contact with atmospheric air in the soil. Critical pressure heads calculated for the 28 soils show that this factor may vary from -15 cm of water or more for sands to -100 cm water or less for structureless loams and clays. The procedure is demonstrated for systems with mainly horizontal flow, downward flow, and for flow through restricting layers.