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Different modeling techniques can be used to estimate the saturated conductivity of a porous medium based on computed tomography (CT) images. In this research, two methods are intercompared: direct modeling using the Navier–Stokes (NS) approach and simplified geometry pore network (PN) modeling. Both modeling approaches rely on pore media geometry which was determined using an X-ray CT scans with voxel size 2 μm. An estimate of the saturated conductivity using both methods was calculated for 20 samples prepared from sand with diverse particle size distributions. PN-estimated saturated conductivity was found to be statistically equivalent to the NS-determined saturated conductivity values. The average value of the ratio of the PN-determined conductivity to the NS-determined conductivity (KsatPN/NS) was equal to 0.927. In addition to the NS and PN modeling approaches, a simple Kozeny-Carman (KC) equation-based estimate was made. The comparison showed that the KC estimate overestimated saturated conductivity by more than double (2.624) the NS estimate. A relationship was observed between the porous media specific surface and the KsatPN/NS ratio. The tortuosity of analyzed samples was estimated, the correlation between the porous media tortuosity and the specific surface of the samples was observed. In case of NS modelling approach the difference between pore media total porosity and total porosity of meshes, which were lower, generated for simulations were observed. The average value of the differences between them was 0.01. The method of NS saturated conductivity error estimation related to pore media porosity underestimation by numerical meshes was proposed. The error was on the average 10% for analyzed samples. The minimum value of the error was 4.6% and maximum 19%.

This research proposes an innovative Kriging-approximation simulated annealing (KASA) optimization algorithm to increase optimization efficiency and reduce the computation time for the parameter calibration of simulation model. The newly developed KASA optimization algorithm utilizes the simulated annealing algorithm to search the global optimum; meanwhile, Kriging approximation, a statistical estimation method, is incorporated with simulated annealing to interpolate unknown objective values in solution spaces. Furthermore, this research establishes a network-based porous media flow simulation (NET-PFS) model and then KASA is applied in the calibration of the NET-PFS representative pore network. NET-PFS is a pore network based model constructing a representative pore network to approximate soil characteristics and pore geometry with limited access to pore-scale imaging processes. NET-PFS is applied to estimate the permeability of a sand-packing porous media. NET-PFS establishes a framework for simplifying the pore network but remaining the same hydraulic conductivity and the flow status of pore networks with limited information about the pore structure. In the case study, a quartz sand-packing porous media is scanned by X-ray micro computed tomography. The NET-PFS model is applied to estimate the hydraulic conductivity and flow velocity distribution from the original pore network. The results demonstrate the proposed KASA algorithm effectively calibrated the NET-PFS model; in addition, a representative pore network and the determined flow status in the pore network is presented by NET-PFS.

The results of the multifractal analysis performed for meteorological time series coming from four stations in Poland and Bulgaria located in varying climatic zones are presented. To assess climatic shift response (in 2001/2002), the analysis was conducted separately for two subsets. To analyze long-distance power-law correlations within the studied time series and evaluate the differences in dynamics of the climate between the analyzed sites and periods of time, the multifractal detrended fluctuation analysis methodology (MF-DFA) was proposed. It was revealed that the multifractal properties of precipitation differ considerably from other analyzed quantities. The singularity spectra were susceptible to climatic shift, what was indicated by the changes of spectra parameters. It was especially apparent for asymmetry, which changed from being right- to left-skewed, implying the occurrence of more extreme events. Similarities in the dynamics of meteorological processes for each of the climatic zones were proven by the close relation of respective multifractal spectra parameters coming from closely spatially related localizations.

In the years 2008-2011, an environmental study was conducted for Polish soils, focusing on the south-eastern Poland soils, as they exhibit significant acidification. This study aimed at assessing the current pHKCl and the supply of basic macro- (P, K, Mg and S-SO4) and microelements (B, Cu, Fe, Mn and Zn) in the collected soil samples, and also at determining their relationship with the soil agronomic category, humus content and pH class. Soil reaction and humus and macronutrient content were positively correlated with the amount of colloidal clay and particles < 0.02 mm. In the majority of cases, the macro-element content in the soil was positively correlated with soil pH and humus content. As for microelements, a usually significant and positive correlation was found between the soil agronomic category and the content of manganese, iron and zinc, whereas for the content of boron and copper, no such relationship was observed. A significant and positive correlation between soil reaction and the content of manganese, iron and boron was also found. Such correlations were not observed in relation to copper and zinc content. Statistical analysis indicated that the content of boron and manganese depended to the greatest extent on the investigated physicochemical properties.

Large-scale crop simulations with process-based models rely on meteorological input data of coarse spatial resolution. We assess how spatial aggregation of meteorological data to coarser resolutions affects the data’s temporal properties. This is largely unknown as is the impact which this aggregation effect (AE) has on simulations which use such aggregated data as input. In simulations of crop yield AE may exceed 10% in single years. We hypothesize that AE should be analysed with regard to both temporal and spatial input data properties. For this purpose, we analysed changes in temporal multifractal properties of meteorological variables due to spatial averaging from 1 to 100 km resolution. Results show that temporal properties of the time series were affected depending on the meteorological variable. We argue that the magnitude of this effect depends on local orography and climate. Similar impact of spatial aggregation on temporal properties can therefore be expected in regions of comparable orography and climate. These changes in multifractal properties potentially affect results of continuous dynamic simulations.

Soil chronosequences in Alpine areas have often been applied to trace physical, mineralogical and chemical soil properties over time. How the soil pore system of undisturbed soils evolves, however, has not yet been clarified. We therefore investigated two soil chronosequences in the Swiss Alps spanning a time period from a few decades up to the Early Holocene/Late Pleistocene. One soil sequence developed on siliceous parent material in the Sustenpass (proglacial area of the Stein glacier), with soils aged from 30a to 10 ka while the second developed on calcaric parent material in the Klausenpass, with soils aged from 110a to 14 ka (proglacial area of the Griess glacier). We hypothesised that the overall pore size of the topsoil and consequently the relative proportion of macropores decrease with increasing soil age. The pore size characteristics were determined by using X-ray computed tomography. Independent of the parent material (calcareous vs siliceous), macroporosity decreased with time. The greatest changes seemed to occur between the Little Ice Age (LIA) and about 3–4 kyr of soil evolution. Vegetation composition and the functional richness of the plant community exert an influence on soils that developed on siliceous parent material by giving rise to more small pores. Besides pore sizes, pore characteristics also changed with time. In general, the tortuous structure of the soils became more complex with time. The evolution of the pore characteristics such as tortuosity, number and length of pore networks seem also to be related to biologic factors such as root properties, plant species and soil organic matter composition. It remains, however unanswered how these time-dependent biologic factors interact with and influence in detail the pore network. This aspect certainly merits investigation in greater detail in the future.

Crop growth simulation models can differ greatly in their treatment of key processes and hence in their response to environmental conditions. Here, we used an ensemble of 26 process-based wheat models applied at sites across a European transect to compare their sensitivity to changes in temperature (−2 to +9°C) and precipitation (−50 to +50%). Model results were analysed by plotting them as impact response surfaces (IRSs), classifying the IRS patterns of individual model simulations, describing these classes and analysing factors that may explain the major differences in model responses. The model ensemble was used to simulate yields of winter and spring wheat at four sites in Finland, Germany and Spain. Results were plotted as IRSs that show changes in yields relative to the baseline with respect to temperature and precipitation. IRSs of 30-year means and selected extreme years were classified using two approaches describing their pattern. The expert diagnostic approach (EDA) combines two aspects of IRS patterns: location of the maximum yield (nine classes) and strength of the yield response with respect to climate (four classes), resulting in a total of 36 combined classes defined using criteria pre-specified by experts. The statistical diagnostic approach (SDA) groups IRSs by comparing their pattern and magnitude, without attempting to interpret these features. It applies a hierarchical clustering method, grouping response patterns using a distance metric that combines the spatial correlation and Euclidian distance between IRS pairs. The two approaches were used to investigate whether different patterns of yield response could be related to different properties of the crop models, specifically their genealogy, calibration and process description. Although no single model property across a large model ensemble was found to explain the integrated yield response to temperature and precipitation perturbations, the application of the EDA and SDA approaches revealed their capability to distinguish: (i) stronger yield responses to precipitation for winter wheat than spring wheat; (ii) differing strengths of response to climate changes for years with anomalous weather conditions compared to period-average conditions; (iii) the influence of site conditions on yield patterns; (iv) similarities in IRS patterns among models with related genealogy; (v) similarities in IRS patterns for models with simpler process descriptions of root growth and water uptake compared to those with more complex descriptions; and (vi) a closer correspondence of IRS patterns in models using partitioning schemes to represent yield formation than in those using a harvest index. Such results can inform future crop modelling studies that seek to exploit the diversity of multi-model ensembles, by distinguishing ensemble members that span a wide range of responses as well as those that display implausible behaviour or strong mutual similarities.

PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2016WR019533 Key Points: The main wetting branch of the soil water retention curve is estimated based on its main drying branch The machine learning method is used for analysis Results are compared with classical methods of estimating the main wetting branch Supporting Information: Supporting Information S1 Data Set S1 Correspondence to: K. Lamorski, k.lamorski@ipan.lublin.pl Citation: Lamorski, K., J. r Sim˚unek, C. Slawi nski, and J. Lamorska (2017), An estimation of the main wetting branch of the soil water retention curve based on its main drying branch using the machine learning method, Water Resour. Res., 53, doi:10.1002/2016WR019533. Received 19 JUL 2016 Accepted 28 JAN 2017 Accepted article online 3 FEB 2017 An estimation of the main wetting branch of the soil water retention curve based on its main drying branch using the machine learning method unek 2 , Cezary Slawi n ski 1 , and Joanna Lamorska 3 Krzysztof Lamorski 1 , Ji r i Sim˚ Institute of Agrophysics, Polish Academy of Sciences, Lublin, Poland, 2 Department of Environmental Sciences, University of California Riverside, Riverside, California, USA, 3 Institute of Agricultural Sciences, State School of Higher Education in Chelm, Chelm, Poland Abstract In this paper, we estimated using the machine learning methodology the main wetting branch of the soil water retention curve based on the knowledge of the main drying branch and other, optional, basic soil characteristics (particle size distribution, bulk density, organic matter content, or soil specific surface). The support vector machine algorithm was used for the models’ development. The data needed by this algorithm for model training and validation consisted of 104 different undisturbed soil core samples collected from the topsoil layer (A horizon) of different soil profiles in Poland. The main wetting and drying branches of SWRC, as well as other basic soil physical characteristics, were determined for all soil samples. Models relying on different sets of input parameters were developed and validated. The analysis showed that taking into account other input parameters (i.e., particle size distribution, bulk density, organic matter content, or soil specific surface) than information about the drying branch of the SWRC has essentially no impact on the models’ estimations. Developed models are validated and compared with well-known models that can be used for the same purpose, such as the Mualem (1977) (M77) and Kool and Parker (1987) (KP87) models. The developed models estimate the main wetting SWRC branch with estimation errors (RMSE 5 0.018 m 3 /m 3 ) that are significantly lower than those for the M77 (RMSE 5 0.025 m 3 /m 3 ) or KP87 (RMSE 5 0. 047 m 3 /m 3 ) models. 1. Introduction Soil water retention curves (SWRCs) are one of the most important soil hydrological characteristics required for both agricultural and environmental research related to the vadose zone. SWRCs link the soil water con- tent with the soil water potential and represent indispensable information for the modeling of soil water flow processes. Although laboratory measurements are the ultimate source of information about retention curves, for many reasons SWRCs are commonly estimated using various statistical models, such as the so- called pedotransfer functions (PTF) [e.g., Vereecken et al., 1989, 2016; Schaap et al., 2001]. The main reason for using PTF estimations of SWRCs instead of direct measurements is their long duration and high cost. Typical steady state equilibrium measurements of the retention curve for a full range of soil water potentials can last several months. PTFs estimate SWRCs based on various physical and chemical soil characteristics. For example, particle size dis- tribution and dry bulk density are commonly used predictor variables in PTFs. Additional soil variables such as organic carbon content, soil-specific surface area, and/or cation exchange capacity can also be used. There were numerous PTF models developed utilizing different statistical and/or soft computing methods for SWRC estimation. Early PTFs were often developed using statistical regression [Rawls et al., 1982; Vereecken et al., € sten et al., 1999; Walczak et al., 2006], leading to some still often used models. Various soft computing 1989; W o methods of statistical inference such as artificial neural networks (ANN) [Schaap et al., 2001; Jana et al., 2008], th et al., the k-nearest neighbors algorithm (k-NN) [Nemes et al., 2006; Botula et al., 2013], regression trees [T o 2012, 2015], or support vector machines (SVM) [Lamorski et al., 2008] were used later on. C 2017. American Geophysical Union. V All Rights Reserved. LAMORSKI ET AL. Soil water retention curves of many soil materials exhibit hysteretic behavior, which means that the depen- dence between the soil water potential (h) and the soil water content (h) is not unique and depends on the ESTIMATION OF WETTING FROM DRYING BRANCH OF RC

Climate dynamics were assessed using multifractal detrended fluctuation analysis (MF-DFA) for sites in Finland, Germany and Spain across a latitudinal transect. Meteorological time series were divided into the two subsets (1980–2001 and 2002–2010) and respective spectra of these subsets were compared to check whether changes in climate dynamics can be observed using MF-DFA. Additionally, corresponding shuffled and surrogate time series were investigated to evaluate the type of multifractality. All time series indicated underlying multifractal structures with considerable differences in dynamics and development between the studied locations. The source of multifractality of precipitation time series was two-fold, coming from the width of the probability function to a greater extent than for other time series. The multifractality of other analyzed meteorological series was mainly due to long-range correlations for small and large fluctuations. These results may be especially valuable for assessing the change of climate dynamics, as we found that larger changes in asymmetry and width parameters of multifractal spectra for divided datasets were observed for precipitation than for other time series. This suggests that precipitation is the most vulnerable meteorological quantity to change of climate dynamics.