Pedotransfer functions for estimating water retention of alluvial 3 SCIENCE ANNUAL DOI: 10.2478/ssa-2018-0001 Vol. 69 No. 1/2018: 3–10

PIOTR HEWELKE1, EDYTA HEWELKE2*, RYSZARD OLESZCZUK1, MARCIN KWAS1

1 Warsaw University of Life Sciences – SGGW, Faculty of Civil and Environmental Engineering, Department of Environmental Improvement, Nowoursynowska Str. 159, 02-776, Warsaw, Poland 2 Warsaw University of Life Sciences – SGGW, Faculty of Civil and Environmental Engineering, Laboratory Water Center, Ciszewskiego Str. 6, 02-776, Warsaw, Poland

The application of pedotransfer functions in the estimation of water retention in alluvial soils in ¯u³awy Wiœlane, northern Poland

Abstract: The aim of the studies was the assessment of the usefulness of selected pedotransfer function for calculating the water retention of alluvial soils in ¯u³awy Wiœlane. ¯u³awy Wiœlane are an important area, both as far as agricultural production and environmental values are concerned. The analysis accounted for three models, i.e.: van Genuchten-Wösten, Varellyay and Miero- nienko, Hewelke et al. Based on 122 dataset of alluvial soils from the ¯u³awy area, the statistical relationships between the measured values of total available water and values calculated for individual models were analysed. The studies carried out indicate that the analysed pedotransfer functions are characterized by different compatibilities with results obtained by means of direct measurement. The lowest average errors of fit were obtained for the Hewelke et al. and van Genuchten models. Keywords: Soil water retention, of soils, matrix potential, total available water, multiple regression equations

INTRODUCTION Lamorski et al. 2017, Oleszczuk et al. 2018). Among the developed models, we can distinguish continu- The water retention of soils is a functional rela- ous functions, enabling the moisture content of soil tionship between the matrix potential and volumetric (θ) to be calculated for any given matrix potential soil moisture content (pF curve). In agricultural eco- (h), as well as discontinuous functions, making it systems, it determines the choice of crops, crop yields possible to indicate the θ(h) relationships for characte- and necessary farming infrastructure and agro-tech- ristic θ values. Extensive compilations and an analysis nology (e.g. Hewelke et al. 2013, Czy¿ 2000). Know- of the models describing function for estimating ledge of soil water retention is essential to assessing water retention curves of soils can be found in particular the water balance, especially in short time frames as in Guber and Pachepsky (2010). Empirical material well as predicting soil droughts and the course of for the particular solutions covers a very diverse soil flooding in a catchment. Due to the complicated and sample set (collection) reaching as many as a few tho- time-consuming process of the direct measurement usand, e.g. Rawls and Brakensiek (1982) – 5320 samples, of the pF curve, indirect methods are proposed, using Wösten et al. (1999) – 4030 samples. relationships between the physical properties of soils ¯u³awy Wiœlane is an important area, both as far and their moisture content. These methods are referred as agricultural production and the natural environment to as pedotransfer functions and their suitability were are concerned. Due to the share of polders (approx. demonstrated by (e.g. Pachepsky and Rawls 2004, 45 thousand ha) and areas around polders (approx. Guber and Pachepsky 2010, Vereecken et al. 2010). 72 thousand ha), they pose a particular challenge to Studies on pedotransfer functions have been carried water management (Nowicki and Liziñski 2004). out by many authors (e.g. Trzecki 1974, 1976; Varallyay Alluvial soils make up over 90% of soils in Vistula and Mironienko 1979, Van Genuchten 1980, Rawls River Delta; they are characterised by high diversity, and Brakensiek 1982, Varallyay et al. 1982, Walczak from very light to very heavy textured soils. The 1984, Carsel and Parrish 1988, Wösten et al. 1999, peculiarity of ¯u³awy alluvial soils results from the Vereecken et al. 1989, 2010; Schaap et al. 2001, course of alluvial processes. The accumulation of Pachepsky and Rawls 2004, Walczak et al. 2004, Vistula river sediments under high humidity condi- Dexter et al. 2008, Gnatowski et al. 2006, 2010; tions causes specific soil compaction and further Guber and Pachepsky 2010, Skalova et al. 2011, Puhl- accumulation of organic matter. The ¯u³awy area is mann and von Wilpert 2012, Hewelke et al. 2013, considered one of the most valuable and most fertile 2015, 2017; Brogowski and Kwasowski 2015, in Poland (Orzechowski et al. 2004). The morphological

* Dr. Edyta Hewelke, [email protected] http://ssa.ptg.sggw.pl/issues2018/691 4 PIOTR HEWELKE, EDYTA HEWELKE, RYSZARD OLESZCZUK, MARCIN KWAS and retention characteristics of these soils have been The model described by Hewelke et al. (2013) presented by Brandyk (1988) among others. Nearly comprises multiple regression equations and allows 40% of ¯u³awy Wiœlane is in a polder system, with to define characteristic states of moisture content at each polder characterized by significant agro-hydro- 7 values of the matrix potential expressed by the pF logical integrity. Because of this fact, knowledge of indicator on the basis of a known content of selected soil water retention comprises important information particle fractions, and specific density for rational water management both in the area of of soil and organic matter content. For the value of a given polder as well as the entire ¯u³awy water system. the potential corresponding to pF=2.0 and pF=4.2 The aim of the studies presented in the article was indicators, regression equations allowing for the the assessment of the suitability of selected pedotransfer moisture content of soil to be calculated take the form functions for calculating the retention abilities of of: ¯u³awy Wiœlane (Vistula River Delta) alluvial soils. 2 θpF=2.0 = (-18.7247 + 47.3855·ρb – 21.073·rb – METHODOLOGY 0.0855538·SPLAW + 0.000200187·SPLAW 2 – 0.00000689571·PIA 2 ·SPLAW + Three models of pedotransfers were analized: van 0.0240447·ρ ·SPLAW)2 Genuchten-Wösten (van Genuchten 1980, Wösten et p al. 1999), Varallyay and Mironienko (Varallyay and 2 Mironienko 1979, Varallyay et al. 1982) and Hewelke θpF=4.2= (-3.87197 + 17.8961·ρb – 9.75799·ρb – et al. (2013). 0.000323457·SPLAW 2 + 0.00618455· 2 2 Van Genuchten (1980) describes the θ(h) depen- ρb PIA – 0.0000108911·PIA ·SPLAW + 2 dency in the form of a continuous function expressed 0.0433843·ρb·SPLAW) by a non-linear regression formula: where: θ − θ r – bulk density, (Mg m–3), θ h( ) = θ + s r b r n m –3 +1( | ⋅α h | ) rp – specific density (Mg m ); where: PIA – fraction contents for equivalent 3 –3 diamters 1–0.1 mm (%); θs – saturated moisture content [cm cm ], 3 –3 SPLAW – content of particles smaller than θr – residual moisture content [cm cm ], h – soil matrix potential [cm], 0.02 mm (%). α, n, m = 1 – 1/n – parameters of pF curve (cm–1), (−) respectively. Assessment of the presented methods in terms of the possibility of applying them to calculate the water retention of alluvial soils in ¯u³awy Wiœlane was carried The values of θs as well as α and n can be calculated on the basis of empirical relationships provided by out assuming the total amount of water available to Wösten et al. (1999). Varallyay and Mironienko plants as a criterion (total available water – TAW), (Varallyay and Mironienko 1979, Varallyay et al. comprising the difference between soil moisture content 1982) present the water retention characteristics of at vales of pF=2.0 and pF=4.2. Based on the dataset soil in the form of a discontinuous function expressed of alluvial soils in the area of ¯u³awy, the statistical by the general formula: relationships between measured and calculated values for individual models were analysed. The studied θ = b + b ⋅⋅⋅x + b ⋅⋅⋅x + b ⋅⋅⋅x ⋅⋅⋅ x + b ⋅⋅⋅x 2 + b ⋅⋅⋅x 2 dataset originates from 19 soil profiles of alluvial soils pF 0 1 1 2 2 3 1 2 4 1 5 2 and covers 122 soil samples taken from various horizons. where: The undisturbed, standard (100 cm3) soil samples

θpF – soil moisture content for a respective value of were collected in three replicates for determination the pF indicator, of soil water retention characteristic. Additionally the b0, b1, b2, b3, b4, b5 – constant number coefficients disturbed samples (bags) were collected for measure for respective pF indicator and given specific bulk density, particle size distributions and classes, x1, x2 – variable coefficients indicating loss-on-ignition, which represents . respective soil texture classes or bulk density. The analyses of soil particle size distribution were The Varallyay and Mironienko’s method allows conducted by Casagrande in Prószyñski modification for calculating soil moisture content for 9 characteristic areometric method and the soil textural classes were values of the matrix potential on the basis of soil classified according to the previous Polish Society of texture classes and bulk density of soil for distinguished (Polish Soil Classification, 1989) standard. soil types. Pedotransfer functions for estimating water retention of alluvial soils 5

The retention curves were measured in the laboratory The coefficient of random variation V indicates using reference methods (Klute 1986). The moisture what of the average level of the modelled phenome- content values in the range from 0 to 2 were determined non the root mean square error comprises and is on a sand table, whereas the amounts of water at the pF: expressed by the formula: 2.7, 3.4 and 4.2 were measured in pressure chambers. S Assessment of the possibilities of applying the V = analysed models to indicate total available water was y carried out using regression analysis. The model is In connection with the above, V specifies the average the better fitted to the empirical data the smaller the error made when calculating TAW in the analysed case differences between the observed and calculated using a model. values. Statistical measures comprising the coefficient 2 of determination R , root mean square error S, as well RESULTS as the coefficient of random variation V were applied to assess the compatibility between the measured and The summarised basic soil property statistic of the calculated values (Kot et al. 2011). dataset have been presented in Table 1. The analysed 2 Coefficient of determination R is a dimensionless series of Vistula alluvial soils is characterized by high quantity of the goodness of model fit and, in its basic diversity in terms of soil texture classes. It is repre- form, is defined by the formula: sented by soils ranging from to soils. The Σn (í − í)2 following texture classes were distinguished: sands R =2 1=i i Σn (í − )y 2 – 23.1%, – 12.1%, loams – 50.9% and clays – 1=i i 14.0%. The content of individual fractions in the where: entire population is between 4 to 95% for sand i – number of observation, (1.0–0.1 mm), (0.1–0.02 mm) from 2 to 84% and n – total number of observations, clay (≤0.02 mm) from 3 to 89%. Analysed soil bulk –3 yi – measured value, density ranged from 1.21 to 1.59 Mg m , specific –3 íi – calculated value, density from 2.34 to 2.72 Mg m and the content of y – average value from sample. organic matter from 0.2 to 11.1%. The coefficient of determination indicates what The values of basic statistics characterizing the part of the analysed phenomenon is explained by the analysed soil water retention properties have been estimated regression equation. presented in Table 2. At the state close to soil saturation Root mean square error S is defined by the formula: (pF=0.4), the average value of soil moisture content n 2 amounted to about 47.5% and gradually decreased Σ i 1= (yi − í) S = √ reaching value (pF=4.2) at n about 18.4%. In the group of sands, the majority of where: water occurs in macropores, which is correlated with i – number of observation, decreasing moisture content in the scope of total n – total number of observations, water available to plants. Along with an increase in yi – measured value, the contents of silt and clay fractions, the amount of íi – calculated value. gravitational water and, at the same time, the value Root mean square error informs how much the of field water capacity (pF=2) increases. The coefficients actual measured values of the variable differ on average of variability of the moisture content were observed from theoretical values obtained using the considered to have increased (from about 12.9% to 56%) along model. with an increase of the potential of the soil water.

TABLE. 1. Summary statistics of basic soil properties of the dataset (n=122)

erusaemlacitsitatS ]%[elcitrapfotnetnoC cificepS ytisnedkluB cinagrO ytisned rettam dnaS tliS yalC mgM[ 3– ] mgM[ 3– ] ]%[ eulavnaeM 89.93 24.22 35.73 85.2 03.1 44.4 noitaiveddradnatS 75.62 97.31 79.32 11.0 41.0 88.2 eulavmuminiM 00.4 00.2 00.3 31.2 21.1 02.0 eulavmumixaM 00.59 00.48 00.98 27.2 95.1 01.11 ]%[VC,ytilibairavfotneiciffeoC 64.66 15.16 58.36 62.4 67.01 68.46 6 PIOTR HEWELKE, EDYTA HEWELKE, RYSZARD OLESZCZUK, MARCIN KWAS

TABLE 2. Value of basic statistics of measured volumetric moisture content θ [vol. %] of the soils at predefined values of pF

erusaemlacitsitatS θ Fp 4.0= θ Fp 0.1= θ Fp 5.1= θ Fp 0.2= θ Fp 7.2= θ Fp 4.3= θ Fp 2.4= eulavnaeM 15.74 95.54 62.24 87.73 61.23 06.52 93.81 noitaiveddradnatS 41.6 18.6 79.6 49.11 76.21 88.11 92.01 eulavmuminiM 19.53 10.13 30.51 10.6 45.3 50.2 50.1 eulavmumixaM 15.75 20.55 35.25 10.05 20.54 18.83 00.33 ]%[VC,ytilibairavfotneiciffeoC 29.21 49.41 22.12 06.134.93 1 24.64 69.55

Water retention curves, identified directly and of θs, α and n parameters for the analysed soil popu- calculated according to the analysed models have been lation have been presented in Table 3. presented in Figure 1, also accounting for the course Total available water (TAW) identified empirically of the curve optimized according to the RETC for the entire population ranged from 6 to 33% by programme (van Genuchten et al. 1991). The value mean value 20.6% and coefficient of variability of parameters for the van Genuchten formula were 30.3%. The linear relationship between measured and calculated using the Wösten’s equation (Wösten et calculated value of TAW for each of the models have al. 1999) as well as the RETC programme (van been presented in Figure 2. Coefficient of regression Genuchten et al. 1991) optimizing the course of the β for analysed relationship amounted from 0.87 to 1.14. pF curve determined empirically. The characteristics

a

b

FIGURE 1. Water retention curves determined directly and calculated using the analysed models for: a – sandy soil and b – clay soil Pedotransfer functions for estimating water retention of alluvial soils 7

TABLE 3. Value of basic statistics of parameters θs, α and n for van Genuchten’s formula

serusaemlacitsitatS retemaraP θs retemaraP α retemaraP n ot.ccA ot.ccA ot.ccA ot.ccA ot.ccA ot.ccA netsöW CTER netsöW CTER netsöW CTER eulavnaeM 34.54 05.74 6650.0 0240.0 1723.1 5552.1 noitaiveddradnatS 98.4 96.4 1900.0 7790.0 8971.0 7422.0 eulavmuminiM 45.43 88.63 5620.0 5100.0 5151.1 9180.1 eulavmumixaM 68.35 55.65 7570.0 5749.0 5609.1 1834.2 ]%[VC,ytilibairavfotneiciffeoC 67.01 78.9 51.61 97.732 55.31 98.71

FIGURE 2. Relationship between measured and calculated (by analysed models) values of total available water (TAW)

DISCUSSION from 6% for sands to 33% for clays. The obtained results of the soil retention capacities are generally in The analysis of the soil texture classes, soil bulk accordance with those provided in literature regarding and specific density and content of organic matter alluvial soils of the Vistula River Delta and indicate confirm that the studied population of soil samples is their significant morphological and spatial diversity characterized by significant variation of physical (e.g. Brandyk 1988). properties. These properties decide about the abilities The courses of θ(h) functions approximate the me- of the soil to retain water and are usually applied as asured course in various degrees calculated on the explanatory variables in pedotransfer functions (e.g. basis of the analysed models. Approximation of the Trzecki 1974, 1976; Walczak 1984, Vereecken et al. measureved curve is rather in agreement for sandy 1989, Wösten et al. 1999). Significant variation in soils for all of the analyzed models. For heavier retention capacity is confirmed by the laboratory soils, these differences may be significant (Fig. 1). results of soil water desorption curves. In the analysed Comparing the α parameters (Table 3) indicates soils, the amount of water available to plants ranged significant differences between the values calculated 8 PIOTR HEWELKE, EDYTA HEWELKE, RYSZARD OLESZCZUK, MARCIN KWAS

TABLE 4. Statistical measures of assessing the compatibility of calculated and measured TAW values for analysed models

tnemssessafoerusaemlacitsitatS nethcuneGnaV –yayllaraV .lateekleweH –nethcuneGnaV netsöW– okneinoriM CTER noissergerfotneiciffeoC (β) 4510.1 5968.0 7241.1 499.0 noitanimretedfotneiciffeoC R( 2) 524.0 922.0 546.0 488.0 rorreerauqsnaemtooR )S( 03.5 16.7 92.4 58.2 noitairavmodnarfotneiciffeoC )V( 72.0 93.0 22.0 51.0 according to Wösten’s formula and were obtained the explanatory variables accounted for in the according to the RETC programme on the basis of models. Many authors (Dom¿a³ 1979, Walczak 1984, the measured pF curve. Based on the whole population, Watts and Dexter 1997, Czy¿ et al. 2003) highlight it can be concluded that variability of the α the significant influence of the soil management on parameter calculated according to Wösten’s formula their retention abilities. Witkowska-Walczak (2000) is low and characterized by a coefficient of variability and Dexter et al. (2008) indicate the aggregate structure CV=16.2%, while α obtained on the basis of the as a factor affecting retention. The amount of water measured pF curve is characterized by a coefficient available to plants may also be shaped by the contents of variation of as much as 237.8% (Table 3). This of specified minerals and chemical properties of soils means that the values of the θ(h) function calculated connected with them (Kaba³a and Musztyfaga 2015). using Wösten’s formula may differ significantly from values obtained on the basis of measurement. The CONCLUSIONS observed situation is characteristic for empirical models, where fit to actual values is determined by 1. The analysed soils from the Delta Vistula River the parameters of the model. area (¯u³awy Wiœlane) comprise alluvial soils of The statistical measures of assessing the compati- highly diversified physical and water retention bility between measured and calculate TAW value properties. The total available water content (Fig. 2) have been given in Table 4. The presented measured according to the standard laboratory measures show that the highest value of R2 for methodology ranged from 6% for sands to 33% relationships between the measured and calculated for clays. TAW values were obtained for the Hewelke et al. 2. The smallest error of fit for the assessment of total model (2013) i.e., R2 = 0.645 at β = 1.143. Van Ge- available water (TAW) was obtained for the nuchten’s model with Wösten’s coefficients is cha- Hewelke et al. model. This amounts to V = 0.22 racterized by slightly worse fit, R2 = 0.425 at α = with a coefficient of determination of R2 = 0.645 1.015. If parameters identified on the basis of the and regression coefficient of β = 1.143. measured retention curve (RTEC programme) are 3. An especially good fit (R2 = 0.994, β = 1.015) was used for the van Genuchten formula, the obtained observed for the van Genuchten model under the compatibility between measured and calculated TAW condition of applying parameters identified on the values is very high, R2 = 0.884 at β = 0.994. This basis of the measured θ(h) function (RETC model). observation is significant from the point of view of 4. Applying pedotransfer functions may significantly the need to discretize the retention curve in numerical limit the time and financial outlays for the assess- solutions of flow equations in an unsaturated soil me- ment of total available water. On the other hand, it dium. Significantly poorer fit was obtained for the should be born in mind that they have a local nature, Varallyay model, resulting in R2 = 0.229 at β = 0.248. as a result of which differences in precision of A similar hierarchy of models is indicated by the root retention assessment may be significant. There is mean square error and coefficient of random variation. a good basis for applying these functions in practice, The obtained root mean square error for the Hewelke especially at the level of research work and et al. as well as Genucthen-Wösten models were S = large-scale projects. 4.25 and S = 5.30 respectively. This means that the average error of fit for these models is V = 0.22 and ACKNOWLEDGMENTS V = 0.27 of the average TAW value respectively. For the Varallyay model, this is significantly higher and We thank the reviewer, the editor and the editorial amounts to 0.39. The studies carried out confirm the office for their insightful suggestions and comments local nature of pedotransfer function, which stems that have helped to improve the quality of the manu- also from the influence of various factors other than script. Pedotransfer functions for estimating water retention of alluvial soils 9

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Zastosowanie wybranych funkcji pedotransfer do wyznaczania retencji wodnej mad

Streszczenie: Celem badañ by³a ocena przydatnoœci wybranych funkcji pedotransfer do obliczania retencji wodnej mad na ¯u³a- wach Wiœlanych. ¯u³awy Wiœlane stanowi¹ wa¿ny obszar zarówno dla produkcji rolniczej, jak i z uwagi na bogactwo œrodowiska przyrodniczego. W analizie uwzglêdniono trzy modele: van Genuchtena-Wöstena, Varellyaya i Mieronienki oraz Hewelke i in. Na podstawie 122 próbek glebowych pochodz¹cych z 19 profili mad z obszaru ¯u³aw analizowano zwi¹zki statystyczne pomiêdzy pomierzonymi wartoœciami potencjalnej retencji u¿ytecznej a wartoœciami obliczonymi dla poszczególnych modeli. Przeprowadzo- ne badania wykaza³y, ¿e analizowane funkcje pedotransfer charakteryzuj¹ siê ró¿nym dopasowaniem do wyników uzyskiwanych na drodze pomiaru bezpoœredniego. Najmniejsze œrednie b³êdy dopasowania uzyskano dla modeli Hewelke i in. i van Genuchtena. S³owa kluczowe: retencja wodna gleby, wilgotnoœæ gleby, potencja³ macierzysty, ca³kowita woda dostêpna, równanie regresji wielokrotnej