Tamir Kamai

Comment on ''Field observations of soil moisture variability across scales'' by James S. Famiglietti et al.

[1] In a recent paper, Famiglietti et al. [2008] analyzed more than 36,000 ground-based soil moisture measurements to characterize soil moisture variability across spatial scales ranging from 2.5 m to 50 km. They concluded that the relationship between soil moisture standard deviation versus mean moisture content, sq (hqi), has a convex upward behavior with maximum values occurring at mean moisture contents of 0.17 cm cm 3 and 0.19 cm cm 3 for the 800-m and 50-km scale, respectively. On the basis of these data, they derived empirical relationships between the coefficient of variation and the mean soil moisture content in order to estimate the uncertainty in field observations of mean moisture content. The authors are to be commended for providing this valuable database to the scientific community. We agree with the authors that such data are important in improving our understanding about the importance of subgrid moisture variability in the parameterization and simulation of land surface processes. However, the authors limited themselves to an empirical description of the observed data by fitting exponential relationships to the mean moisture content versus coefficient of variation (CV) data. We feel that this is a missed opportunity and would like to argue that an interpretation based on established theories and concepts in soil hydrology and upscaling theories could provide alternative methods and new insights for interpreting such data sets. Specifically, it can be shown from soil physical concepts that for a homogeneous soil, the shape of the moisture retention curve can largely explain observed variations in surface soil moisture, at any specific observation scale. For heterogeneous soils, stochastic upscaling theories may be used to relate sq (hqi) to spatial variability in soil hydraulic properties. These theories can be used to predict sq (hqi) and to examine the sensitivity of this function with respect to soil hydraulic properties.

A kinetic model of gene transfer via natural transformation of Azotobacter vinelandii

Horizontal gene transfer allows antibiotic resistance and other genetic traits to spread among bacteria in the aquatic environment. Despite this important role, quantitative models are lacking for one mechanism of horizontal gene transfer, which is natural transformation. The rates of horizontal gene transfer of a tetracycline resistance gene through natural transformation were experimentally determined for motile and non-motile strains of Azotobacter vinelandii. We developed a mathematical model adapted from the mass action law that successfully described the experimentally determined rates of natural transformation of a tetracycline resistance gene for motile and non-motile strains of Azotobacter vinelandii. Transformation rates showed a rapid initial increase, followed by a decrease in the first 30 minutes of the experiment, and then a constant rate was maintained at a given cell and DNA concentration. The proposed model also described the relationship between transformation frequency and varied DNA or cell concentrations. The modeling results revealed that under the given experimental conditions, the gene transformation rate was limited both by the abundance of the tetracycline resistance gene and by cellular activities associated with cell–DNA interactions. This work establishes a quantitative model of natural transformation, suggests a need to further investigate the cell properties affecting transformation rates, and provides a basis for development of comprehensive models of horizontal gene transfer and quantitative risk assessment of antibiotic resistance gene dissemination in the aquatic environment.

Swimming Motility Reduces Deposition to Silica Surfaces.

The transport and fate of bacteria in porous media is influenced by physicochemical and biological properties. This study investigated the effect of swimming motility on the attachment of cells to silica surfaces through comprehensive analysis of cell deposition in model porous media. Distinct motilities were quantified for different strains using global and cluster-based statistical analyses of microscopic images taken under no-flow condition. The wild-type, flagellated strain DJ showed strong swimming as a result of the actively swimming subpopulation whose average speed was 25.6 μm/s; the impaired swimming of strain DJ77 was attributed to the lower average speed of 17.4 μm/s in its actively swimming subpopulation; and both the nonflagellated JZ52 and chemically treated DJ cells were nonmotile. The approach and deposition of these bacterial cells were analyzed in porous media setups, including single-collector radial stagnation point flow cells (RSPF) and two-dimensional multiple-collector micromodels under well-defined hydrodynamic conditions. In RSPF experiments, both swimming and nonmotile cells moved with the flow when at a distance ≥20 μm above the collector surface. Closer to the surface, DJ cells showed both horizontal and vertical movement, limiting their contact with the surface, while chemically treated DJ cells moved with the flow to reach the surface. These results explain how wild-type swimming reduces attachment. In agreement, the deposition in micromodels was also lowest for DJ compared with those for DJ77 and JZ52. Wild-type swimming specifically reduced deposition on the upstream surfaces of the micromodel collectors. Conducted under environmentally relevant hydrodynamic conditions, the results suggest that swimming motility is an important characteristic for bacterial deposition and transport in the environment.

Comment on "extending applicability of correlation equations to predict colloidal retention in porous media at low fluid velocity".

Predict Colloidal Retention in Porous Media at Low Fluid Velocity” R Ma et al. sought “to extend the correction offered by Nelson and Ginn” for the nonphysical collector efficiency (η) values given by correlation equations (including theirs, the MPFJ equation) of the colloid filtration theory (CFT) at low fluid velocities. Ma et al. demonstrate that the NG equation still yields η > 1 when small values of fluid velocity (∼10−7 m/s), porosity (∼0.25), and colloid diameter (dp ≤ 100 nm) exist concurrently, and address this by adopting the NG equation with a modified diffusion term (referred to herein as the MHJ equation) but stating it is “based on regression to mechanistic simulation results”. In this comment, we discuss important issues regarding equation comparisons, address the claim that low fluid velocity applications of CFT are “largely hypothetical”, and present a mathematical constraint that preserves the physics lost by the MHJ equation. The MHJ equation is presented as “an improvement for predicting η under a wider variety of fluid velocities” than prior correlation equations including the NG equation. However, Ma et al. recognize that their approach results in an incorrect dependence on velocity as η approaches unity and suggest correcting this via “asymptotes at the diffusion limit”; the transition point is never defined, though, leaving the suggested approach prone to ambiguous interpretation. Moreover, since the asymptote is η = 1 and the error of the MHJ equation is that it misrepresents the inverse relationship of η with velocity for η < 1, use of the asymptote will yield even larger errors. Not acknowledged by the authors is that the MHJ equation can also fail to capture the inverse relationship with colloid size (Figure 1a). Thus, the strategy employed to constrain the MHJ equation sacrifices key aspects of the physics of colloid deposition at low fluid velocities. The benefit of never exceeding unity must be weighed against these deficiencies to evaluate the claim that this is an “improvement”. Regarding inapplicability of the NG equation to “certain parametric conditions”, we note that η equations are commonly used to elucidate trends with respect to input parameters. Before we addressed the application of CFT at low fluid velocities, prior equations employed a power law dependence on the Peclet number (NPE) without any limiting factors. This results in high sensitivity with respect to NPE that gives extremely large errors for nanoparticles at low fluid velocities, that is, prior equations yield η values dramatically above unity with errors increasing as NPE decreases. In contrast, when the NG equation exceeds unity, the errors are relatively minor as the limiting factor moderates the error. Even when unity is exceeded slightly, the physical trends are maintained and, thus, the equation is qualitatively correct (whereas the MHJ equation is qualitatively incorrect in its reversing the trends with respect to velocity and colloid size). The benefits of constraining the MHJ equation to stay below unity are not worth the cost of losing salient aspects of the physics. Moreover, this trade-off is unnecessary as mathematical means exist to achieve the desired constraint without compromising the physics (as shown below). Regarding Ma et al.’s statements implying that all available η equations agree well with each other and with available data, this is demonstrated to be false in our prior comparison of available equations with 112 experiments, and disparities are much greater with respect to the new MHJ equation (Figure 1c). The MPFJ equation exceeded the factor-of-two level agreement 39 out of 112 times (versus 10 for the LH equation, 17 for both NG and TE, and 34 for RT). The MHJ equation exceeds this threshold 43 times. The MHJ equation performs particularly poorly for nanoparticles (dp ≤ 100 nm). The factorof-two threshold is exceeded for all nanoparticles in the data set with an average difference of a factor of 4.3 (compared to 1.6 for NG) greater than the experimental value and a maximum of 6.7 (compared to 2.3 for NG). For other submicrometer particles (100 nm < dp ≤ 1 μm), the MHJ equation also fares worse than all prior equations (average Figure 1. (a) NG equation, NG constrained equation, MHJ equation, and MHJ asymptote (dashed red line) applied to data of Nagasaki et al.(MPFJ equation values range from 1.9 to 9.4 and are not viewable). Note that the MHJ equation reverses the dependence on colloid size and use of the MHJ asymptote increases error magnitudes of subunity η values (b) Comparison of NG equation, NG constrained equation, MPFJ equation, and MHJ equation for low Darcy velocity (U = 0.04 m/d) and low porosity (0.25) (c) NG equation, NG constrained equation, MPFJ equation, and MHJ equation compared to data set of 112 experiments. The first-order deposition rate coefficient (kf) is computed based on each equation’s η value. Experiments 1−15 are nanoparticles (dp ≤ 100 nm); experiments 16−48 are larger submicrometer particles (100 nm < dp < 1 μm); experiments 49− 112 are large colloids (1 μm < dp ≤ 10.1 μm). The factor-of-two level agreement is bracketed by the dashed black lines at kf model/kf experiment = 0.5 and kf model/kf experiment = 2; perfect agreement (ratio = 1) is denoted by the solid black line. Correspondence/Rebuttal

Correction to “Soil water flux density measurements near 1 cm d−1 using an improved heat pulse probe design”

[1] The heat pulse probe (HPP) technique has been successfully applied for estimating water flux density (WFD). Estimates of WFD have been limited to values greater than 10 cm d , except for two recent studies with lower detection limits of 2.4 and 5.6 cm d . Although satisfactory for saturated soils, it is recognized that current HPP capabilities are limited for applications in the vadose zone, where WFD values are generally below 1 cm d . Since numerical sensitivity analysis has shown that large heater needle diameters may increase HPP capabilities in the lower flux density range, a HPP with a 4-mm-diameter heater needle was developed and tested. WFD values were obtained by fitting temperature data to the analytical solution for a pulsed cylindrical heat source of infinite length. Effective heater-thermistor distance and soil thermal diffusivity values were determined for specific heat input scenarios with zero WFD, prior to imposing water flow across the HPP needles. We showed excellent results in the range of 1–10 cm d 1 and satisfactory results in the range of 10– 1000 cm d . Citation: Kamai, T., A. Tuli, G. J. Kluitenberg, and J. W. Hopmans (2008), Soil water flux density measurements near 1 cm d 1 using an improved heat pulse probe design, Water Resour. Res., 44, W00D14, doi:10.1029/2008WR007036.

Colloid filtration prediction by mapping the correlation-equation parameters from transport experiments in porous media

Colloid filtration theory (CFT) is a conceptual construct for predicting the characteristic rate of colloid-surface collisions during transport in granular porous media. A central product of this theory is the correlation equation for predicting collection-efficiency (η), based exclusively on theoretical model development. Specifically, the η-equation has terms combining dimensionless groups (of physicochemical properties) with unknown parameters that are usually fitted so that the predicted η matches that determined by colloid-surface collisions simulated in idealized pore-scale models. In this study, we replace the simulated colloid-surface collisions in idealized models with experimental column-scale data on apparent colloid-surface collisions. A new correlation equation is obtained by minimizing the difference between η determined by the correlation equation and that determined experimentally, using data from a collection of experiments for favorable conditions for colloid filtration. In this way we parameterize a mechanistically-based η-equation with empirical evidence. The impact of different properties of colloids and porous media are studied by comparing experimental properties with different terms of the correlation equation. This comparison enables insight about the different processes that occur during colloid transport and retention in porous media, such as diffusion and interception, and provides directions for future CFT developments that will need to account for these processes differently than the current theory does. Additionally, we find that while most of the parameters of the presented η equation are only slightly different than those proposed in previous theoretical studies, the match between theory and observation is significantly improved. For the available experimental data, which provides a reasonable representation of property ranges for many applications of CFT, the proposed equation provides a closer match to the experimentally measured collection efficiencies compared to available theories to date. This article is protected by copyright. All rights reserved.