Unsaturated Hydraulic Conductivity Curves Research Articles

Averaging or adding domain conductivities to calculate the unsaturated soil hydraulic conductivity

AbstractRecent models of the unsaturated hydraulic conductivity curve (UHCC) are the sum of separate UHCCs for domains of capillary water, film water, and water vapor. This requires parallel, noninteracting domains. A theoretical framework for aggregating domain conductivities to a bulk soil UHCC is presented to identify and possibly relax implicit assumptions about domain configuration. The paper develops arithmetic, harmonic, and geometric averages of the liquid‐water conductivities that can be arithmetically averaged with the vapor conductivity. However, current models for capillary and film conductivities are intrinsic, that is, valid within their respective domain. The vapor conductivity is a bulk conductivity, that is, it gives the conductivity of the gaseous domain as it manifests itself in the soil. Conversion relationships use the domain volume fractions as approximations of the as‐yet unknown weighting factors to convert between intrinsic and bulk conductivities. This facilitates consistent averaging of domain conductivities. Even with consistent averaging, a truly physically accurate model of the UHCC based on domain conductivities is fundamentally elusive. Nevertheless, models based on the three averages and the unweighted sum of the domain conductivities produce good fits to data for two soils but diverge in the dry range. The fitted curves for the capillary and film water depend on the averaging (or adding) method. Hence, they are not strictly characteristic of their respective domains. The true intrinsic domain conductivity functions may be impossible to determine.

A Simple Model for Estimating the Hydraulic Conductivity of Unsaturated Soil

Describing the hydraulic conductivity of unsaturated soil is very important in predicting water transport. Most current models have complex forms and generally need to be calibrated by the measured unsaturated hydraulic conductivity curve. A simple model, by which it is possible to conveniently predict the unsaturated hydraulic conductivity, is proposed in this study. The soil–water characteristic curve and hydraulic conductivity curve are separated into three parts. The soil–water characteristic curve is represented by Fredlund and Xing’s equation. A simple model composed of three lines is proposed for estimating the hydraulic conductivity of unsaturated soil. The model parameters can be conveniently calibrated from the measured soil–water characteristic curve and saturated hydraulic conductivity. Finally, the proposed model is validated by the experimental data from different soils. The proposed model provides a simple approach to estimating the hydraulic conductivity of unsaturated soil, which is more convenient for practical application.

Predicting soil hydraulic properties for binary mixtures – concept and application for constructed Technosols

Abstract. Constructed Technosols are an important means of substituting natural soil material, such as peat and geogenic material, for use in urban green infrastructure. One characteristic of Technosols important to their role in urban green infrastructure, specifically with respect to urban water management, is their soil hydraulic properties (SHPs). The SHPs depend on the composition of the constructed Technosols (e.g. their components and their mixing ratio). The diversity of possible components and the infinite number of mixing ratios practically prohibit the experimental identification of the composition needed to achieve suitable soil hydrological functions. In this study, we propose a compositional model for predicting the water retention curves (WRCs) of any binary mixture based on the measured WRCs of its two pure components only (basic scheme) or with one additional mixture (extended scheme). The unsaturated hydraulic conductivity curves (HCCs) are predicted based on the modelled WRCs. The compositional model is developed from existing methods for estimating the porosity of binary mixtures. The model was tested on four data sets of measured WRCs of different binary mixtures. The distribution of water and air in 50 cm high soil columns filled with these mixtures was predicted under hydrostatic conditions in order to assess their suitability for typical urban applications. The difference between the maxima of the pore size distributions ΔPSDmax (m) of the components indicates the applicability of the compositional approach. For binary mixtures with small ΔPSDmax, the water content deviations between the predicted and the measured WRCs range from 0.004 to 0.039 cm3 cm−3. For mixtures with a large ΔPSDmax, the compositional model is not applicable. The prediction of the soil hydraulic properties of any mixing ratio facilitates the simulation of flow and transport processes in constructed Technosols before they are produced (e.g. for specific urban water management purposes).

Prediction of hydraulic and petrophysical parameters from indirect measurements of electrical resistivity to determine soil-water retention curve – studies in granular soils

The characterization of unsaturated soils using hydromechanical methods is an essential requirement in soil science. However, current laboratory techniques used to obtain soil water retention and unsaturated hydraulic conductivity curves are time-consuming. To address this issue, a method based on indirect measures (electrical resistivity/electrical conductivity) was developed to quantitatively characterize soils. A novel unsaturated semi-empirical hydrogeophysical model of soils was developed by incorporating the hydrodynamic, geophysical, and petrophysical characteristics of soils. The model assumes that the parameters influencing the variation in the volumetric water content with matric suction and electrical resistivity are the same. The electrical resistivity characteristic curve (ERCC) defines a function that correlates environmental variables, electrical resistivity, soil water status, matric suction, hydraulic and petrophysical parameters, and fluid electrical resistivity. Model validation confirmed that the proposed approach can estimate the soil water retention curve (SWRC) via the indirect measures, and the results agreed with the experimental data. This indicates that it is possible to determine the SWRC and unsaturated hydraulic conductivity function of soil using the described approach.

The assessment of the effectiveness of the unimodal and bimodal models to evaluate the water flow through nature-based solutions substrates.

Nature-based solutions are popular techniques for managing stormwater. Most of them allow porous media as their main layer. The description of the Soil Water Retention Curve (SWRC) as the Unsaturated Hydraulic Conductivity Curve (UHCC) is often required to run the hydrological simulations with the physically based models. Using the unimodal and bimodal models to assess the SWRC and UHCC of soils is a widespread technique but their evaluation is often present in literature only in terms of curve fitting. Based on these assumptions, this work presents the performance assessment of the van Genuchten unimodal and bimodal models by functional evaluation of them based on the runoff from several substrates. Four substrates were investigated to define the structure, the SWRC, and the UHCC. Results showed that all substrates had a bimodal behaviour with lowest values of RMSE (RMSE_Θ = 0.0023 to 0.0037, RMSE_K = 0.0636 to 0.1284). Finally, a numerical simulation using the HYDRUS-1D model was performed for a three-month data set to check the effectiveness of the unimodal model instead of the bimodal one. The findings have shown that the unimodal model must be preferred instead of the bimodal because it has fewer parameters and assured low discrepancies in runoff volume (ε=0.00% to 6.25%).

Soil Classification: A New Approach for Grouping Soils Using Unsaturated Hydraulic Conductivity Data

AbstractGrouping soils based on similarities in their textural, taxonomic, and/or structural properties has broad applications to pedology, hydrology, and soil science. In this study, we present a new approach for classifying soils using hydraulic conductivity data. We apply concepts from critical path analysis and calculate critical pore sizes at various water saturations from the unsaturated hydraulic conductivity curves. Soils with similar critical pore size at the same effective water saturation are then grouped into the same class. To demonstrate the practical application of the proposed soil classification method, we use 102 samples including nine soil textures from the UNSODA database. Applying a curve clustering method, we find eight different soil classes within the studied data set.

Pedotransfer functions for estimating soil hydraulic properties from saturation to dryness

Current pedotransfer functions (PTFs) for estimating soil hydraulic curves are mostly developed to predict parameters of the Mualem-van Genuchten hydraulic functions. The Mualem-van Genuchten functions are recognised to be inadequate in representing soil water retention hydraulic conductivity curves at low pressure head ranges. This study presents neuroFX, a suite of PTFs, for estimating soil water retention and unsaturated hydraulic conductivity curves from saturation to complete dryness based on the Fredlund-Xing-Wang (FXW) model. The PTFs were calibrated using the neuro-m neural networks approach with three different sets of inputs: (1) SSCBD uses the sand, silt, and clay fractions, and bulk density; (2) SSC uses the sand, silt and clay fractions, and (3) soil textural class input. NeuroFX PTFs were trained using fitted parameters of the FXW model from selected data in the UNSODA database and validated using 5-fold cross-validation that was repeated 10 times. NeuroFX provides an uncertainty estimate of hydraulic parameters. The prediction quality of neuroFX was compared with two existing PTFs: ROSETTA and Brunswick-Weber (BW) PTFs. Based on multiple criteria, we found that neuroFX performed better than ROSETTA and BW PTFs in the same test sample. NeuroFX PTF with the SSCBD input yielded the best prediction of soil water retention and unsaturated hydraulic conductivity curves with RMSE in water content of 0.052 cm3 cm−3 and RMSE in log10(K) = 0.732 (in the magnitude of cm day−1), indicating the importance of including bulk density in the input of PTFs. NeuroFX was then used to map parameters of the FXW model for the whole of the continental USA over 6 depth intervals. The code of neuroFX in R software is available in Supplementary Material 1.

A new transfer function model for the estimation of non-point-source solute travel times

The scope of this work is to present a new fast and reliable transfer function model, which simulates the spatio-temporal distribution of non-point-source solutes along the unsaturated zone, suitable to be used at large scales within a web-based Decision Support System. With the assumptions of a) a gravity induced water flow, b) a non-reactive solute and c) a purely convective flow, the model uses the transfer functions, i.e., the travel time (TT) probability density functions, derived from the unsaturated hydraulic conductivity curve k(θ). The output concentration of a solute is simply the convolution of the transfer functions with the input concentrations to the system. A model sensitivity analysis, based on Monte Carlo simulations, was carried out, showing that saturated water content and the tortuosity parameter τ were the parameters that affected the mean TT more. The model was validated against concentration experiments carried out on four large soil columns. Results were really good for all soils, with the best agreement with R2 = 0.97, RMSE = 0.11 and ME = −0.01. Moreover, the outputs obtained applying the model to 46 soil profiles sampled in the Valle Telesina, in Southern Italy, completely characterised from the hydrological point of view, were compared with those obtained from the Richard-based model Hydrus 1D. The result of the comparisons gave a very high correlation coefficient (above 0.8), a mean absolute error between the two models of around 40 days and a percent bias of −16%. Finally, the application of transfer function model to a large spatial extent is presented, to show its possible use for the groundwater vulnerability assessment.

HYPROP measurements of the unsaturated hydraulic properties of a carbonate rock sample

The unsaturated hydraulic properties provide important theoretical and practical information about fluid flow in soils and rocks for a range of soil, environmental and engineering applications. In this study we used the evaporation (HYPROP) and chilled-mirror dew point (WP4C) methods to estimate the water retention and unsaturated hydraulic conductivity curves of an Indiana Limestone carbonate rock sample. The obtained data were analyzed in terms of unimodal and bimodal VG (van Genuchten, 1980) and PDI (Peters et al., 2015) type functions. Bimodal functions were found to produce excellent descriptions for the unsaturated hydraulic data we measured, slightly better than the standard unimodal formulations. For our particular test using an Indiana Limestone rock sample, we did not find much improvement when accounting for film and corner flow using the PDI formulation, relative to the VG model. As far as we know, this is the first time the HYPROP methodology was applied to a rock sample.

Effective hydraulic conductivity of stony soils: General effective medium theory

Despite a longstanding interest in understanding the effects of rock fragments on soil hydraulic properties, physically-based models to describe the effective hydraulic conductivity of stony soils are still rare. The conductivity of stony soils is mostly described by simple scaling approaches, assuming impermeable rock fragments. We present a model based on the general effective medium (GEM) theory to calculate the effective hydraulic conductivity of stony soils. The model accounts for the volumetric content, shape, and orientation of rock fragments in the main direction of water flow. Rock fragments can either be permeable or impermeable in the model which allows to calculate the effective unsaturated hydraulic conductivity curve of stony soils over the full range of soil matric potentials. Existing models assume rock fragments to be isolated and their application is therefore limited to low to moderately stony soils. In GEM model interaction between rock fragments is allowed, which makes it applicable in stony soils with high contents of rock fragments. The mathematical simplicity of the model makes it suitable for practical applications and provides a strong theoretical basis for improving predictions of flow and transport in hydrological models applied in forested and agricultural watersheds and mountainous areas.

Estimation of tropical soils’ hydraulic properties with inverse method and tension infiltrometer field data

In the last few years, many studies have been published by authors from several countries offering approximations and use of the inverse method. However, the unique environmental conditions and distinct properties of the tropical soils in Brazil require extra considerations and the need to adjust these methods to tropical soil conditions. Considering the above, this determined the parameters of the van Genuchten (1980) model (θs, θr, α, n) of the water retention curve in the soils. It also determined the parameter (Ks) of the soil’s hydraulic conductivity curve by solving an inverse problem using the HYDRUS-2D model, considering cumulative infiltration data collected in the field by means of an infiltration test using the tension infiltrometer. It then compared the hydraulic properties determined by these methods in relation to the standard laboratory method. The inverse method was able to efficiently determine the water retention curves in the soils here studied; however, it was not possible to reliably determine the unsaturated hydraulic conductivity curve.

Comparison of soil hydraulic properties estimated from steady-state experiments and transient field observations through simulating soil moisture in regenerated Sphagnum moss

Growing Sphagnum moss for peatland restoration and fibre farming requires the proper moisture regime be maintained; thus, there is a desire to optimize growth by creating ideal hydrological conditions. However, it is uncertain which parameterization method is most suitable to describe field-scale processes and which soil water retention model and hydraulic conductivity curve (approach) is the most acceptable to use. Parameterizations of the van Genuchten – Mualem (VGM) equation were done using RETC, curve fitting to direct measurements of the water retention and unsaturated hydraulic conductivity curves; and Hydrus-1D, inverse modelling to field observations of soil moisture. The acceptability of each parameterization was tested by comparing soil moisture estimates based on forward simulations to observed soil moisture in two regenerated moss profiles, established in 1970 and 2006 cases, respectively. The transient field model simulated soil moisture well, and had an RMSE of 0.05 and 0.06 for 1970 and 2006, respectively. The most error occurred during the wettest and driest periods of the simulations. Simulated soil moisture was consistently drier than the observed soil moisture, in the steady-state laboratory simulation, and had markedly higher RMSE, 0.14 and 0.27 for the 1970 and 2006 profiles, respectively. The estimate of the VGM α parameter, an approximately the inverse of the air-entry pressure, fit to direct measurements of the retention and unsaturated hydraulic conductivity curves was an order of magnitude higher than that fit to field observation. The results of the simulation suggest that inverse modelling to field soil moisture should be used to estimate VGM parameters to more accurately represent field-scale soil moisture dynamics.

Simulation of Water Infiltration Process into a Porous Unsaturated Soil: Application on Tangier’s Bay Region-Morocco

The study is focused on numerical simulation of the infiltration process of polluted water originating from a wadi into the unsaturated soil of a bay. This study addresses the linkage between unsaturated zone and groundwater and it discusses the ability of the unsaturated soil to receive the water dried at once by the wadi and the bay. The simulation requires a number of trials, something that is experimentally expensive and sometimes impossible. The infiltration process is governed by the Richard’s equation. To solve this later, the knowledge of soil water properties such as pressure head, water content and hydraulic conductivity is needed. Hence, the water retention and unsaturated hydraulic conductivity curves near saturation have been established for a range of water content going from h = (− 25 m; 25 m) to h = (− 175 m; 175 m). These curves are obtained using the simulating computer program Hydrus 2D/3D. Numerical results have been calibrated with the Musy and Soutter (Physique du sol (soil physics), Universite de Technologie Compiegne, Lausanne, 1991) type relationships. It has been explained that the infiltration process from the saturated zones to the unsaturated zone is relatively slow depending on the soil structure.

Multi-step outflow and evaporation experiments – Gaining large undisturbed samples and comparison of the two methods

The aim of the study was the comparison of the soil hydraulic properties determined based on two different experimental methods of four large and macroporous soil samples. An undisturbed cylindrical soil column (h = 60 cm and d = 30 cm) was obtained at a natural slope and quartered horizontally in the laboratory. The four sub-samples were saturated and subsequently drained using the extended multi-step outflow method (XMSO). Retention curves and unsaturated hydraulic conductivity curves were derived via inverse modeling based on the measured drainage and corresponding pore water pressure. After resaturation the evaporation method (EVA) was used on the same four samples. The samples were exposed to evaporation and the effective water contents and the average pore water pressures were recorded over time to determine soil hydraulic functions.While both methods yielded similar results in the medium moisture range, the advantage of the XMSO-method is its higher information content with respect to the hydraulic conductivity close to water saturation whereas the advantage of the EVA-method is its fast execution. Moreover, the EVA-method is easier to handle and has significantly lower computational requirements than the XMSO-method.Furthermore, since the four soil samples represent a soil profile in the field, a depth dependent characterizing of the soil profile was possible and showed that the soil properties near saturation are greatly dominated by the ratio of macropores in the sample and that a decrease in the macropore ratio with soil depth was clearly reflected in the hydraulic functions.

Influence of Stone Content on Soil Hydraulic Properties: Experimental Investigation and Test of Existing Model Concepts

Core Ideas Unsaturated hydraulic conductivity of stony soils was determined in medium moisture range. Evaporation method works for stony soils, even if stone contents are high. Theoretical scaling models showed a good agreement with measurements for moderate stone contents. Model results and measurements differ markedly for soils with high stone contents. Studying the role of gravel, stones, or rock fragments on effective soil hydraulic properties (SHPs) is crucial for understanding and predicting soil water processes such as evaporation, redistribution, and water and solute transport through soils containing significant amounts of coarse inclusions. We conducted a laboratory study in which we investigated the effect of stones on the water retention and unsaturated hydraulic conductivity curves of soil–stone mixtures. Stony soils were created by packing predefined masses of soil particles (sand and sandy loam) with diameters <2 mm and crushed basalt (2–5 and 7–15 mm). The resulting mixtures ranged from 0 to 40% (v/v) stone content. The SHPs were determined with the simplified evaporation method. The measurements yielded plausible water retention and hydraulic conductivity curves across a wide moisture range. Results qualitatively showed the expected dependencies of SHPs on volumetric stone content, characterized by a reduction of soil water content and hydraulic conductivity across the whole pressure head range. Measured data suggested that coarse inclusions in soil tend to widen the effective pore‐size distribution. Prediction of SHPs of the stony soils, performed by fitting a flexible SHP model to the data of the background soil and scaling it with approaches from the literature, worked well for low stone contents. However, for volumetric stone contents of 25 and 40%, measured SHPs differed substantially from the properties predicted by simple scaling models.

Factorial kriging analysis leverages soil physical properties and exhaustive data to predict distinguished zones of hydraulic properties

Measurement of unsaturated hydraulic properties of soil is a time-consuming endeavor which limits the scale of studies. A stratified sampling scheme could enable more efficient use of samples but some information about the strata is needed a priori. The aim of this study is to define zones of soil hydraulic properties using remotely sensed and soil physical inputs. Samples were collected from 50 locations at 4 depth intervals in a 20.8 ha field located along the margin of the Venice Lagoon, Italy, and characterized by paleo-channel structures and highly heterogeneous soils. Water retention curves (WRC) and unsaturated hydraulic conductivity curves (UHC) were determined via inversion of measurements taken in the lab using the Wind method. Factorial kriging analysis (FKA) was applied separately to hydraulic parameters and soil physical properties and the 4 depths treated as independent samples. The mapped principal components (PCs) were used in a fuzzy-c means algorithm to define zones of like properties. To examine the physical significance of these zones, curve parameters and hydraulic curves were investigated. Zonation was able to distinguish between θs (saturated water content), n (shape parameter) and α (inverse of air entry), while θr (residual water content) and Ks (saturated conductivity) were not statistically different between the groups. For curve comparisons, WRCs were found to be significantly different between zones at all tensions while effective saturation curves (Se) differ for the majority of tensions (except at 28 cm), and UHCs did not differ. The spatial relevance of the zones was examined by overlaying hydraulic zones with zones defined using the FKA and fuzzy-c means approach from soil physical properties such as texture and bulk density. The hydraulic zones overlaid the physical property zones with an areal accuracy ranging from 46.66% to 92.41%. The similarity between these zone sets suggests that there is a potential to predict hydraulic zones from zones defined from soil physical properties. This work illustrates the potential to incorporate geospatial statistics in a stratified sampling scheme for hydraulic properties.

Hydraulic properties of peat soils along a bulk density gradient—A meta study

AbstractOur understanding of hydraulic properties of peat soils is limited compared with that of mineral substrates. In this study, we aimed to deduce possible alterations of hydraulic properties of peat soils following degradation resulting from peat drainage and aeration. A data set of peat hydraulic properties (188 soil water retention curves [SWRCs], 71 unsaturated hydraulic conductivity curves [UHCs], and 256 saturated hydraulic conductivity [Ks] values) was assembled from the literature; the obtained data originated from peat samples with an organic matter (OM) content ranging from 23 to 97 wt% (weight percent; and according variation in bulk density) representing various degrees of peat degradation. The Mualem‐van Genuchten model was employed to describe the SWRCs and UHCs. The results show that the hydraulic parameters of peat soils vary over a wide range confirming the pronounced diversity of peat. Peat decomposition significantly modifies all hydraulic parameters. A bulk density of approximately 0.2 g cm−3 was identified as a critical threshold point; above and below this value, macroporosity and hydraulic parameters follow different functions with bulk density. Pedotransfer functions based on physical peat properties (e.g., bulk density and soil depth) separately computed for bog and fen peat have significantly lower mean square errors than functions obtained from the complete data set, which indicates that not only the status of peat decomposition but also the peat‐forming plants have a large effect on hydraulic properties. The SWRCs of samples with a bulk density of less than 0.2 g cm−3 could be grouped into two to five classes for each peat type (botanical composition). The remaining SWRCs originating from samples with a bulk density of larger than 0.2 g cm−3 could be classified into one group. The Mualem‐van Genuchten parameter values of α can be used to estimate Ks if no Ks data are available. In conclusion, the derived pedotransfer functions provide a solid instrument to derive hydraulic parameter values from easily measurable quantities; however, additional research is required to reduce uncertainty.

3D soil hydraulic database of Europe at 250 m resolution

AbstractSoil hydraulic properties are required in various modelling schemes. We propose a consistent spatial soil hydraulic database at 7 soil depths up to 2 m calculated for Europe based on SoilGrids250m and 1 km datasets and pedotransfer functions trained on the European Hydropedological Data Inventory. Saturated water content, water content at field capacity and wilting point, saturated hydraulic conductivity and Mualem‐van Genuchten parameters for the description of the moisture retention, and unsaturated hydraulic conductivity curves have been predicted. The derived 3D soil hydraulic layers (EU‐SoilHydroGrids ver1.0) can be used for environmental modelling purposes at catchment or continental scale in Europe. Currently, only EU‐SoilHydroGrids provides information on the most frequently required soil hydraulic properties with full European coverage up to 2 m depth at 250 m resolution.

Analysis of the Hysteretic Hydraulic Properties of Unsaturated Soil

Core Ideas We devised a setup to measure hydraulic properties using the multistep flux method. Results showed good agreement with the data obtained with the hanging water column. However, they deviated slightly from independent data obtained with the HYPROP. Knowledge of the unsaturated soil hydraulic properties is essential for modeling water flow and solute transport processes in variably saturated subsurface systems. Various experimental setups have been developed over the years to measure the hydraulic properties. We devised a relatively simple setup for simultaneous measurement of the water retention and unsaturated hydraulic conductivity curves using multistep flux (MSF) and hanging water column (HWC) experiments. Our focus was especially on medium‐ and coarse‐textured sands having relatively narrow particle‐size distributions as reflected by the van Genuchten–Mualem (VGM) hydraulic parameter n. Values of the VGM parameter n for some of the sands we used were as high as 15. We also measured the hydraulic properties using the HYPROP evaporation method. The MSF and HWC results showed excellent agreement, but deviated slightly from independent data obtained with the HYPROP measurement system.

Biofilm effect on soil hydraulic properties: Experimental investigation using soil‐grown real biofilm

AbstractUnderstanding the influence of attached microbial biomass on water flow in variably saturated soils is crucial for many engineered flow systems. So far, the investigation of the effects of microbial biomass has been mainly limited to water‐saturated systems. We have assessed the influence of biofilms on the soil hydraulic properties under variably saturated conditions. A sandy soil was incubated with Pseudomonas Putida and the hydraulic properties of the incubated soil were determined by a combination of methods. Our results show a stronger soil water retention in the inoculated soil as compared to the control. The increase in volumetric water content reaches approximately 0.015 cm3 cm−3 but is only moderately correlated with the carbon deficit, a proxy for biofilm quantity, and less with the cell viable counts. The presence of biofilm reduced the saturated hydraulic conductivity of the soil by up to one order of magnitude. Under unsaturated conditions, the hydraulic conductivity was only reduced by a factor of four. This means that relative water conductance in biofilm‐affected soils is higher compared to the clean soil at low water contents, and that the unsaturated hydraulic conductivity curve of biofilm‐affected soil cannot be predicted by simply scaling the saturated hydraulic conductivity. A flexible parameterization of the soil hydraulic functions accounting for capillary and noncapillary flow was needed to adequately describe the observed properties over the entire wetness range. More research is needed to address the exact flow mechanisms in biofilm‐affected, unsaturated soil and how they are related to effective system properties.