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Using wavelet analyses to identify temporal coherence in soil physical properties in a volcanic ash-derived soil
Agricultural and Forest Meteorology 285–286 (2020) 107909
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Agricultural and Forest Meteorology journal homepage: www.elsevier.com/locate/agrformet
Using wavelet analyses to identify temporal coherence in soil physical properties in a volcanic ash-derived soil
T
Sebastián Bravoa, Mauricio González-Changb,c, Dorota Deca,c, Susana Vallea,c, Ole Wendrothd, ⁎ Felipe Zúñigab,c,e, José Dörnera,c, ,1 a
Instituto de Ingeniería Agraria y Suelos, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile Departamento de Ciencias Naturales y Tecnología, Universidad de Aysén, Eusebio Lillo 667, Coyhaique, Chile c Centro de Investigación en Suelos Volcánicos, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile d Department of Plant and Soil Sciences, University of Kentucky, Lexington, KY, United States e Doctorado en Ciencias Agrarias, Escuela de Graduados, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile b
A R T I C LE I N FO
A B S T R A C T
Keywords: Andisol Physical properties Field lysimeter Continuous wavelet transform Cross-wavelet analysis
Lysimeters have been used for centuries to understand hydrological cycles. Nowadays, high-resolution weighing lysimeters allow precise determination of the water balance components. While major efforts have been focused on the definition of appropriate methodologies for data processing in order to obtain results with high accuracy, it is still unknown to what extent measurements registered by a lysimeter can reflect soil water dynamics and the transport phenomena in a defined agroecosystem. The aim of this work is to analyze temporally-coherent discrepancies in the estimation of soil parameters based on time series recorded inside and outside a lysimeter installed in a volcanic ash-derived soil. Continuous wavelet transforms and cross-wavelet analyses were used to understand temporal differences and similarities between time series, respectively. Inside and at a 2 m distance from the lysimeter, soil temperature, volumetric water content and matric potential were measured at different depths (10, 20 and 60 cm depth). Despite that the Pearson's correlation between the studied time series indicated good correlations (r2 > 0.95), the wavelet analyses showed that coherence obtained inside the lysimeter can temporarily differ from those monitored in the field at specific times during the year. The latter was quantified using a Dissimilarity Index (DI), which showed high values at particular moments throughout the year. The wavelet analyses used here are a valuable tool to assess time series temporal variations which are unnoticed by commonly-used statistics, such as the Pearson's correlation. A better understanding of soil water and temperature temporal dynamics can enhance our ability to model and predict these processes in soils.
1. Introduction Lysimeters have been used for more than 300 years to understand plant physiological processes related to soil constraints and for studying the hydrological cycles under field conditions (Goss and Ehlers, 2009). Nowadays, lysimeters are used in a broad range of applications in agriculture, forestry and environmental studies (Meissner et al., 2008), such as in nitrate leaching (Bakar et al., 1994), groundwater seepage (Fox et al., 2007), water use efficiency (Grip et al., 1989), evapotranspiration (Drexler et al., 2008), and for modelling the water balance (Wegehenkel et al., 2008). The above-mentioned broad range of applications have contributed to the development of different types of lysimeters, such as the high-resolution weighing lysimeter (von Unold
and Fank, 2008; Meissner et al., 2008; UMS, 2010). High-resolution weighing lysimeters allow precise determination of the water balance components. In modern lysimeters it is possible to use undisturbed soil monoliths, which are inserted into the soil profile in order to characterize water fluxes of natural soils under atmospheric boundary conditions (Fank and von Unold, 2007; Schrader et al., 2013; Peters et al., 2014; Hannes et al., 2015). Any disturbance during the lysimeter installment that affects soil structure due to mechanical stress and crack formations will affect the process dynamics and soil hydraulic properties to some extent, and then the lysimeter might not reflect the in situ soil conditions realistically. Soils in agricultural sciences have been studied principally with statistical models based on field observations considered independent
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Corresponding author at: Instituto de Ingeniería Agraria y Suelos, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile. E-mail address: [email protected] (J. Dörner). 1 Centro de Investigación en Suelos Volcánicos, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile. https://doi.org/10.1016/j.agrformet.2020.107909 Received 21 June 2019; Received in revised form 16 January 2020; Accepted 17 January 2020 0168-1923/ © 2020 Elsevier B.V. All rights reserved.
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registered between May and July, whereas the driest months were January and February (2 mm). The mean air temperature reached 11.8 °C with the maximum and minimum temperatures being 17.5 °C (January) and 7.7 °C (July), respectively. The studied soil is a Duric Hapludand (Valdivia Series according to CIREN, 2003) or a Petroduri-Silandic Andosol (WRB, 2006), which corresponds to a soil derived from volcanic ashes with a depth that can reach up to 3 m. Topography in the soil series is normally complex, with dominant slopes from 3 to 8%. Table 1 presents the soil horizon distribution after a morphological description conducted during the lysimeter installation and a physicochemical characterization from samples collected from each soil horizon. Disturbed soil samples were used to define the particle size distribution, particle density, bulk density (Sandoval et al., 2012), allophane content (Parfitt and Wilson, 1985) and organic carbon (Sadzawka et al., 2006). Undisturbed soil samples were used for assessing the water retention curve (WRC, n = 7 for each soil horizon) and the saturated hydraulic conductivity (n = 10 for each soil horizon) as previously conducted in Dörner et al. (2015). The amount of wide coarse pores (wCP), plant available water (PAW) and fine pores (FP) were calculated from the water retention curve. The saturated hydraulic conductivity (Ks) was measured using a constant head permeameter (Eijkelkamp Agrisearch Equipment, 2003). The amount of macropores (pores with a diameter > 50 μm) in the first two soil horizons reached levels between 5% and 8%, it increased in deeper soil horizons reaching values higher than 10% (until 168 cm depth), and then decreased again until 4%. The plant available water range had values between 15% and 42%, whereas the amount of fine pores ranged from 18% to 46%. The saturated hydraulic conductivity increased with soil depth ranging between 68 cm d−1 and 832 cm d−1 (Table 1). Finally, from an agricultural point of view, the soil was managed as a non-grazed pasture with the following dominant species: Lolium perenne L. and Trifolium repens L.
and randomly distributed (Nielsen and Alemi, 1989). However, soil state variables’ dynamics are a more or less continuous process through time and space, and state observations are related to the previous status in time or to the local neighborhood in space. Based on the continuity of processes, statistical models have been developed in order to analyze and understand the spatial and temporal heterogeneity of soils and their processes (Nielsen and Alemi, 1989; Wendroth et al., 1997; Nielsen and Wendroth, 2003). As one method of Fourier-based transforms, wavelet analyses have been developed and adapted to soil sciences for studying the occurrence of cyclic variations, their scale and their amplitude (Biswas and Si, 2011; He et al., 2007; Si and Zekele, 2005; Lark and Webster, 1999). In this sense, wavelet analysis can depict the behavior of one or several series of observations through time, while if common fluctuations between two time series are investigated, a cross-wavelet analysis can be used instead (Torrence and Compo, 1998; Grinsted et al., 2004; Li et al., 2019). Thus, studies assessing the coherence between two time series to understand soil water processes have been performed (Awe et al., 2015; Reyes et al., 2019), and the feasibility of using cross-wavelet analysis in hydrologically-based time series has also been studied (Sang, 2013). Despite the recent advances in analyzing soil-water-content time series using a cross wavelet approach, emphasis has been placed on studying soil spatial variability, while studies in which soil temporal variability is assessed are still rare (Reyes et al., 2019). In this sense, the cross-wavelet spectral analysis might be a promising statistical tool for disentangling currently unknown common temporal relationships between the soil time series of different soil parameters. In southern Chile, studying water balance is of a great interest due to the extreme physical properties of volcanic ash-derived soils within a region in which rainfall may reach up to 2500 mm year−1 (GonzálezReyes and Muñoz, 2013). Volcanic ash-derived soils are characterized by a very low bulk density (< 0.9 Mg m−3), and a well-defined interand intra-aggregate porosity (Dörner et al., 2010), which allows high saturated and unsaturated hydraulic conductivity and, consequently, rapid changes in the soil volumetric water content through time (Dörner et al., 2015; Dec et al., 2017). Also, volcanic ash-derived soils present swelling and shrinkage during wetting and drying cycles, respectively, that lead to changes in soil structure affecting soil water content dynamics (Dörner et al., 2010). This specific behavior may induce spatial and temporal changes in soil physical properties, especially, when the soil is disturbed e.g. by tillage (Dörner et al., 2012), animal trampling during grazing (Negrón et al., 2019) or after the lysimeter installment. Therefore, the objective of this work is to analyze the temporal variability in the soil water content, soil matric potential and soil temperature time series recorded within a lysimeter installed in a volcanic ash-derived soil related to field conditions without a lysimeter. In these terms, comparing these time series measured inside and outside a lysimeter could be a useful approach to assess the temporal representativeness of this high-resolution equipment in soils.
2.2. Lysimeter installation and measurements A Science Lysimeter (UMS-Germany; UMS, 2010), was installed in a site with a slope less than 2% and it has an area of 2 m2 and 2 m depth (a similar lysimeter was used in von Unold and Fank, 2008). Although soil disturbances might occur during the lysimeter installation, the soil monolith was not damaged during the cutting process and the site used to collect the monolith was minimally affected. The lysimeter was then equipped with different electronic sensors that collected data with a 10-min frequency and that were installed at 10, 20 and 60 cm depth (2 sensors of each kind per each depth). These were installed to measure the volumetric water content by a time domain reflectometer (0 to 100%; TRIME PICO 32 model, UMS-Germany); the matric potential by dielectric water potential sensors (−90 to −1000000 hPa; MPS-2 model, Decagon Device) and the soil temperature (−40 to 60 °C; MPS-2 model, Decagon Device). Additionally, one tensiometer was installed at 180 cm depth (1000 to −850 hPa; T8 sensor, UMS-Germany). The same number of sensors mentioned above were also installed in an undisturbed soil profile 2 m apart from the lysimeter in order to investigate the effect of lysimeter installation compared to natural field conditions (von Unold and Fank, 2008). As part of a drain water feedback control system, T8 sensors measured the water potential adjusting it continuously by 10 suction cups with a ceramic surface installed at the bottom of the monolith, which are connected to a bi-directional pump for controlling and ensuring that water flows and potentials into the lysimeter are identical to the real field situation.
2. Material and methods 2.1. Experimental field description The experimental field was located at the Universidad Austral de Chile's experimental field station (Estación Experimental Agropecuaria Austral (EEAA) (39°46′ S, 73°13′ W, 12 m a.s.l.)) in Valdivia, southern Chile (Fig. 1). The average annual temperature is 12 °C with a yearly mean rainfall of 2440 mm between 1901 and 2005 (González-Reyes and Muñoz, 2013), concentrated mainly in winter (Huber, 1970). During the experiment, rainfall was collected from a meteorological station (Campbell) located 10 m from the lysimeter. Since no temperature data was available, the average daily air temperature was obtained at the INIA station, located 40 km north from the study site (Fig. 2). During 2015, rainfall reached 1783 mm. A high amount of rainfall (941 mm) was
2.3. Data analyses Soil matric potential, soil temperature and soil water content data collected during 2015 were analyzed by a continuous wavelet 2
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Fig. 1. Site location and lysimeter installation.
When a continuous wavelet transform was obtained for each of the studied time series, it is possible to observe patterns that can differ between the time series recorded inside the lysimeter and at field conditions, while with a cross-wavelet approach the similarities between both time series can be investigated, as cross wavelet has been previously used for studying spectral coherence between two time series, highlighting concurrent cycles that might occur between them (Maraun and Kurths, 2004). The cross wavelet was normalized to correct potential biases in the power spectrum estimation (Veleda et al., 2012) and it used the Morlet mother wavelet function (Grinsted et al., 2004), with a significance level of 95%. For each depth (10, 20, 60 cm), the soil matric potential data recorded from the field and from the lysimeter were used to calculate the continuous wavelet and the crosswavelet transform. A similar approach was used when analyzing soil temperature and soil water content at different depths. The interpretation of the continuous wavelet transform followed Torrence and Compo (1998), while that for the cross-wavelet analysis was based on Maraun and Kurths (2004) and Grinsted et al. (2004). In the crosswavelet analysis, the phase between both time series is graphically presented as arrows within significant areas of coherence (Grinsted et al., 2004; Li et al., 2019). Arrows pointing to the right mean that both time series are in phase (positive correlation), while arrows pointing to the left, mean an anti-phase (negative) correlation
Fig. 2. Rainfall and air temperature during the studied period.
transform and by a cross-wavelet transform (Torrence and Compo, 1998). Soil matric potential data was Log transformed before performing wavelet analyses. A continuous wavelet transform was used to assess the dominant modes of variability within a time series, and how those modes vary through time (Torrence and Compo, 1998).
Table 1 General description of the volcanic ash soil (Duric Hapludand) at the lysimeter station. Depth [cm] 0–20 30–38 38–57 57–93 93–143 143–168 168–203 +203
Hor. [-] Ap B1 B2 B3 2Bw1 2Bw2 2Bw3 2BC
Sand [%] 11.3 11.7 25.6 16.7 26.2 42.8 35.6 36.3
Silt [%] 58.9 60.1 62.3 53.6 50.3 41.0 47.8 53.6
Clay [%] 29.8 28.3 12.2 29.7 23.6 16.2 16.7 10.2
Alloph. [%] 13.2 14.2 12.3 7.6 9.7 16.5 22.7 29.7
OM [%] 12.7 ± 0.3 11.5 ± 0.1 2.4 ± 0.1 0.9 ± 0.1 2.1 ± 0.1 2.0 ± 0.1 1.7 ± 0.1 2.9 ± 0.1
Bd
Pd −3
[Mg m ] 0.79 ± 0.01 0.72 ± 0.01 0.63 ± 0.01 0.74 ± 0.01 0.76 ± 0.01 0.75 ± 0.01 0.67 ± 0.01 0.56 ± 0.01
−3
[Mg m ] 2.24 ± 0.01 2.24 ± 0.01 2.46 ± 0.01 2.50 ± 0.01 2.49 ± 0.01 2.60 ± 0.01 2.43 ± 0.01 2.48 ± 0.01
AC
PAW
FP
Ks
[Vol.%] 4.99 ± 0.67 8.84 ± 0.44 13.76 ± 0.91 13.00 ± 0.71 12.37 ± 0.68 9.01 ± 0.53 6.82 ± 0.63 4.18 ± 0.79
[Vol.%] 41.88 ± 2.24 35.44 ± 2.17 31.25 ± 2.22 26.98 ± 2.50 18.27 ± 0.39 15.85 ± 0.52 20.67 ± 3.25 39.23 ± 0.77
[Vol.%] 17.97 ± 1.93 23.63 ± 2.10 29.34 ± 2.25 30.60 ± 2.17 38.97 ± 0.35 46.11 ± 0.45 45.13 ± 3.12 34.04 ± 0.79
[log(cm d−1)] 1.83 ± 0.4 1.95 ± 0.3 2.65 ± 0.2 2.63 ± 0.2 2.92 ± 0.2 2.72 ± 0.3 2.26 ± 0.3 2.65 ± 0.3
Hor. = Horizon; Alloph. = Allophane; OM = Organic matter; Bd = Bulk density; Pd = Particle density; AC = Air capacity; PAW = Plant available water; FP = Fine pores; Ks = Saturated hydraulic conductivity. Mean values ± 1 standard error is presented. 3
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row (at 10 cm depth), 4A (at 20 cm depth), and 5A (at 60 cm depth). The continuous wavelet transform for TLys (Fig. 3C, top row) shows significant cycles (denoted by contour lines) between 2 and 6 days early in the year, a 4-day cycle in July and another of around 14 days in November. These significant cycles occurred in TField as well, but a cycle of around 16 days also appeared from May to July (Fig. 3D, top row). In the cross-wavelet analysis, the soil temperature at 10 cm depth showed significant peaks that occurred at periods between 2 and 6 days around January, February and July, while from March to late June periods of 16 days appeared. In November, another peak occurred at a period of about 14 days (Fig. 3E, top row). When analyzing the continuous wavelet transform for TLys at 20 cm depth (Fig. 4C, top row), significant peaks of around 2 to 4 days occurred in January, and from 4 to 8 days in February. In March, a cycle of around 16 days appeared until June. Also, a small peak of 4 days appeared in July. During late October to mid November a significant cycle of around 12 days also appeared. Data from TField presented longer cycles (Fig. 4D, top row) compared to TLys, occurring mainly from March to November at scales between 14 and 30 days, approximately. In the cross-wavelet analysis, the soil temperature at 20 cm depth (Fig. 4E, top row), presented a long significant peak that occurred at a scale of around 14 and 18 days from January to late October, increasing its range from 4 to 18 days between late June and August, and between November and December. Soil temperature recorded at 60 cm depth in TLys had a 16-day cycle from April to June (Fig. 5C, top row), while in TField this cycle was only noticeable from May to June (Fig. 5D, top row). Interestingly, a cycle between 2 and 12 days appeared early in the year and this was significant only in TField. When analyzing the cross wavelet at 60 cm depth, one peak appeared in mid-January to February at a scale between 2 and 12 days, and another at periods around 16 and 40 days between May and October (Fig. 5E, top row). Arrows pointing to the right indicate a
between both (Grinstead et al., 2004). In addition, a Pearson's correlation between the different time series measured in the field and inside the lysimeter was calculated. In an attempt to quantify and temporally-identify the differences between time series recorded from inside the lysimeter and from field conditions, a Dissimilarity Index (DI) was calculated for each depth, time and the soil parameters analyzed here. Let's define ni as the depth in which measurements were taken, where n1, n2 and n3 correspond to 10, 20 and 60 cm depth, respectively. For each of the ni, the time series xi(t) and yi(t) were calculated for each time (t), where xi(t) and yi(t) correspond to the data recorded inside the lysimeter and at field conditions, respectively. Thus, for each ni at each time (t), DI was calculated as follows:
DIi (t ) =
x i (t ) − yi (t ) yi (t )
(1)
The Dissimilarity Index (DI) presented in Eq. (1) allows the temporal quantification of differences between the data collected inside the lysimeter and the data collected at field conditions, for each time (t) in the studied time series. Therefore, a high DI value (represented graphically as peaks in Figs. 3B, 4B and 5B), shows the difference between both time series at a specific time during the studied season. The wavelet analyses were performed using the R package “biwavelet” using R v.3.6.1 (R Core Team 2019). 3. Results 3.1. Wavelet analyses 3.1.1. Soil temperature wavelet analyses Soil temperature data recorded inside the lysimeter (TLys, black line) and under field conditions (TField, red line) are shown in Fig. 3A, top
Fig. 3. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 10 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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Fig. 4. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 20 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
although the small ones occurring from May to August in θLys reduced their scale in θField, and therefore, the number of significant peaks during that period decreased (Fig. 4D, middle row). In the cross-wavelet analysis, the soil water content had two peaks between April and May, one of around 16 days, and another about 60 days. In July, the peak was characterized by a period between 2 and 16 days. In addition, a peak in a scale between 2 and 12 days appeared in July, and another one of 16 days occurred in September, while in December the peak ranged from 2 to 16 days (Fig. 4E, middle row). At 60 cm depth, θLys had peaks between 2 and 8 days occurring in April, May and December. In July, the scale of the peak was between 2 and 16 days, and from August to September its scale ranged from 2 to 6 days (Fig. 5C, middle row). The θField data showed similar peaks between 2 and 6 days in April and May, but different ones in the MayJune period and in the August-October period that ranged between 14 and 20 days, approximately (Fig. 5D, middle row). Here, θField data showed longer cycles in Winter and Spring compared with θLys data. The cross-wavelet analysis presented fewer peaks compared to more superficial soil depths, with two peaks in the May-June period, one between 2 and 8 days, and another of around 16 days. In July, a significant peak at a period between 2 and 16 days occurred, while in September it occurred at a scale between 14 and 18 days (Fig. 5E, middle row). In the soil water content time series, right pointing arrows dominated at all depths, highlighting the positive correlation between θLys and θField.
positive correlation between both time series at significant cycles depicted by contour lines. For the soil temperature time series, right pointing arrows dominated at all depths, highlighting the positive correlation between TLys and TField. 3.1.2. Soil water content wavelet analyses The continuous wavelet transform for the soil water content measured at 10 cm depth (Fig. 3C, middle row) inside the lysimeter (θLys) showed a significant peak during early April at a scale between 2 and 16 days. Also, small peaks around 2 and 6 days occurred in May, July, August and November. In December, another one between 2 and 6 days appeared. In field conditions (Fig. 3D, middle row, θField), the peak shown in April for θLys was also present but occurred longer until late April. Smaller peaks appeared in θField compared to the ones obtained in θLys, but in December a cycle between 2 and 16 days appeared, which was longer than the one in θLys (Fig. 3C,D, middle row). At 10 cm depth the θLys wavelet transform showed greater and significant peaks in small cycles from May to November, while θField showed higher significant variations occurring in long cycles during April and December (Fig. 3C,D, middle row). In the cross-wavelet analysis, the soil water content measured in θLys and in θField revealed a significant peak at a scale between 2 and 16 days in April, two peaks around 16 days in July and September, and another in December at periods between 2 and 16 days (Fig. 3E, middle row). Also, small peaks between 2 and 6 days appeared in May, July, August and September (Fig. 3E, middle row). At 20 cm depth, the continuous wavelet transform for θLys (Fig. 4C, middle row) showed a 16-day significant peak in April, and another of around 14 days during the July-August period. Small cycles between 2 and 6 days occurred in May, July and August, while a long one appeared in December at a scale between 2 and 16 days (Fig. 4C, middle row). In θField data recorded at 20 cm depth (Fig. 4D, middle row), similar peaks appeared in April and December compared to θLys
3.1.3. Soil matric potential wavelet analyses The continuous wavelet transform for the soil matric potential obtained at 10 cm depth (Fig. 3C, bottom row) inside the lysimeter (ΨmLys), presented peaks between 2 and 18 days from March to April, and another from November to January that ranged between 2 and 16 days (Fig. 3C, bottom row). At field conditions (Fig. 3D, bottom row, 5
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Fig. 5. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 60 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
ΨmField) similar peaks are shown. At 20 cm depth, ΨmLys presented a peak of 16 days in April and another between November and January ranged between 2 and 16 days. In ΨmField a cycle between 2 and 60 days appeared in April (Fig. 4D,C, bottom row). Finally, at 60 cm depth (Fig. 5C,D, bottom row), similar patters as described for 20 cm depth were found. The cross-wavelet analysis at 10 cm depth, showed a significant peak at a period between 2 and 60 days that occurred between March and May, and another cycle between 2 and 16 days appearing between November and January (Fig. 3E, bottom row). A similar peak was exhibited at 20 cm depth (Fig. 4E, bottom row), and at 60 cm depth (Fig. 5E, bottom row). In the soil matric potential time series, right pointing arrows dominated at all depths, highlighting the positive correlation between ΨmLys and ΨmField.
increased to 0.28 during mid to late April, and then decreased to around 0.04 from May to September. In November and December peaks of 0.08 and 0.12 were calculated, respectively. At 60 cm depth (Fig. 5B, middle row), from February to April, DI varied from 0.22 to 0.32 and then suddenly decreased to 0 in late April. From May to December, DI varied from around 0.15 to 0.28. The soil matric potential DI at 10 cm depth (Fig. 3B, bottom row) showed two peaks between late April and early May of 0.12 and 0.17, respectively. In November, a peak of 0.27 also appeared. A similar trend in the temporal variation of DI occurred at 20 cm depth (Fig. 4B, bottom row), with peaks between mid April to early May of 0.37 and 0.18, respectively. In November, a peak of 0.25 was calculated. At 60 cm depth (Fig. 5B, bottom row), during early January DI presented a peak of 0.38, and another in early May of 0.61. The results given after calculating the DI are in agreement with the wavelet analyses presented above. By using Eq. (1) the temporal differences in the soil variables measured inside and outside the lysimeter at specific times during the season were identified.
3.2. Dissimilarity index between time series When comparing TLys against TField at 10 cm (Fig. 3B, top row), DI increased to 0.18 in February, oscillating between 0.04 and 0.17 between February and April. In July, a peak of 0.20 appeared, while in November this was 0.17. A similar trend is observed when measuring soil temperature at 20 cm depth, with a highest peak of 0.18 appearing in July (Fig. 4B, top row). At 60 cm depth (Fig. 5B, top row), a peak of 0.20 occurred in February, decreasing between 0.05 and 0.10 from February to April. From April to December, DI oscillated between 0 and 0.07. Soil water content also showed a temporal variation in DI. At 10 cm depth (Fig. 3B, middle row), a peak of 0.13 occurred in February, decreasing in late February close to 0 and then raising up to 0.33 in late April and May. During mid May, DI decreased to around 0.20, oscillating between this value until September. In December, a decrease from 0.27 to 0 was recorded. At 20 cm depth (Fig. 4B, middle row), DI
3.3. Pearson's correlation between soil time series Amongst all the studied soil time series, a high correlation was found between data recorded under field conditions and inside the lysimeter (Fig. 6). Correlation in soil temperature increased with depth, but decreased at both soil matric potential and soil water content. Despite these spatial changes, correlation between time series was above 0.95.
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Fig. 6. Pearson's correlations between data (T: Soil Temperature, Ψm: Soil Matric Potential; θ: Soil Water Content) recorded at field level and inside the lysimeter for the different studied depths and soil parameters.
4. Discussion
same soil series but under different land uses (Dörner et al., 2015), were related to the hydraulic properties of volcanic ash-derived soils. These soils present multimodal soil water retention curves, which reflect a well-defined hierarchy of inter- and intra-aggregate pores (Dörner et al., 2010, 2015; Rudiyanto et al., 2013) responsible for very high values of saturated hydraulic conductivity (Table 1). Some authors have mentioned that volcanic ash-derived soils present a sandy behavior when saturated as well as a large water holding capacity at higher matric potentials (Armas-Espinel et al., 2003; Dörner et al., 2010) causing rapid changes in soil water content (Dörner et al., 2015). This complex behavior in volcanic ash-derived soils could be responsible for developing complex patterns of coherence and variation through time between data collected inside and outside the lysimeter as presented with the wavelet analysis performed here, which can be also a valuable tool to assess time series temporal dynamics in other soil types.
4.1. Soil water and temperature dynamics during the studied period With increasing soil depth, the temperature decreased reducing its amplitude as well as shifting its phase. The latter, has been assessed in a Duric Histic Placaquand (e.g. Dec et al., 2017) and in other mineral soils (e.g. Tong et al., 2017), and reflects different soil temperature conditions in the profile, which depends on the soil thermal diffusivity (Horton et al., 1983) and, in turn, on the soil water content. Since soil temperature profiles inside and outside the lysimeter are apparently variable through time, if we consider the same level of energy input, we can assume that soil thermal properties could be temporarily affected due to physical changes influenced by water dynamics within the soil profile. The soil water content, measured in field conditions (θField) and inside the lysimeter (θLys), reflects the soil water storage capacity (see Table 1) of the Ap, B1 and B3 horizons (according to the installation depths of the sensors used). During dry months (January until March) the soil matric potential increased, reaching values exceeding the permanent wilting point (15.430 hPa) until 20 cm depth. This was also assessed by the θField which is in accordance with the water retention curves determined in the laboratory (the water content at pF 4.19 ranged between 18% and 31%). In addition, as rainfall increased during winter (June – September), the soil matric potential reflects near saturated conditions which are also confirmed by the measured volumetric water content. Changes in soil water content during wetting and drying cycles occurred very quickly (e.g. changed from 35% to 50% in 24 h approximately) and responded to rainfall and evapotranspiration dynamics. These dynamic changes, which have also been assessed in the
4.2. Wavelet analyses for temporal variability in soil time series In all the time series data obtained from all of the sensors used in this study, our results showed a strong correlation between the data collected inside and outside the lysimeter (Fig. 6, Pearson r2 between 0.95 and 0.99). However, Pearson's correlation can only identify linear correlations (Li et al., 2019). Aditionally, it is important to consider that the use of a big data set improves the capacity of getting good correlations (more than 500.000 data/year in this study). Therefore, an overall high correlation does not necessarily mean that this correlation is occurring at all times within the time series recorded inside and outside the lysimeter. The latter has been demonstrated by the results from the cross-wavelet analysis as variations in the temporal coherence between the recorded time series occurred. When water is added to a lysimeter (e.g., through rain), temporal and spatial changes in the 7
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periods of water saturation. Likewise, the distribution of these coherence patterns in the cross-wavelet analysis could indicate differences between long drought periods where the temperature is mainly transmitted by the solid and gaseous soil phases, while in periods of long water saturation water is the main soil phase for transmitting and accumulating heat (Dec et al., 2017). In relation to the volumetric soil water content, coherence patterns from the cross-wavelet analysis are oriented according to the seasonal distribution of rainy events, mainly from the autumnal season. Since there is a greater amount of water interconnecting the pores within the soil profile, the heterogeneity in the soil response could be temporarily diminished, producing a significant coherence between the measurements inside and outside the lysimeter. Soil matric potential results obtained by the MPS-2 sensors show that time series have a high coherence during the dry season (February), where the soil continues to decrease its moisture levels. These patterns disappear in depth as an increase in matric potential occurs until the first important rainy event in April ocurred (Fig. 2). When soil matric potential drastically decreases due to an increased water infiltration into the system, coherence appears at all depths, which could indicate the high humectation that occurred throughout the soil profile. After matric potential decreases, the cross-wavelet analysis does not produce any pattern, possibly due to the small variations in soil matric potential when high soil water content occurs caused by lateral flow and leveling out horizontal heterogeneity. As a descriptive view, cross wavelet plots show the coherence intensity between time series by a scale of colors. Considering the dark orange and light red zones through time we can also identify moderate coherency areas that are taking place outside the black contours of significance patterns, which are extended during all year with periods around 32 to 64 days for all analyzed parameters. As the Pearson's correlation has shown, this situation can represent an important correlation when is considering longer scales in the study of time series behavior between lysimeter and field conditions over the year. In this sense, with appropriate correlation and determined scales, lysimeters are a useful tool for accurate soil water and temperature studies, allowing us to solve the effects of spatial variability. It has to be mentioned that although a high correlation occurred between the studied time series recorded inside and outside the lysimeter (Fig. 6), the continuous wavelet transform showed differences in the scale of the cycles that appeared on each time series, suggesting differences in the magnitude of the data collected inside and outside the lysimeter probably related with the spatial variability exhibited through the porous matrix. The latter is in agreement with the results provided by the Dissimilarity Index (DI) calculated here. Also, the crosswavelet analysis showed significant coherence between these time series only at certain points (normally at extreme periods when the soil was near to field capacity or when near to the permanent wilting point) throughout the studied period (Figs. 3–5). Considering that using field lysimeters of this scale is a widely-used methodological approach to study soil water dynamics (Hannes et al., 2015; Peters et al., 2014; Schrader et al., 2013), attention should focus at interpreting data from lysimeters, paying attention to the soil physical-hydraulic conditions (and the particularties of each soil type, i.e. the behavior of an Arenosol may differ from a Vertisol or an Andisol) that can temporarily modify data representativeness. These considerations are relevant since the water balance obtained from a lysimeter should reflect the hydrological cycle of a defined ecosystem; however, if the soil is disturbed during the lysimeter installment and/or the field and the lysimeter measurements differs because intrinsic soil characteristics, then the accuracy of the data obtained by using a lysimeter will differ from a field condition, leading to biased results that decrease the effectiveness of soil modeling tools. The temporal patterns found here are repetitive, so a phenomenon that could be identified to have its own soil response to environmental effects can be suggested. Therefore, a high Pearson's correlation (>0.95)
distribution of the volumetric content of water occurs, which indicates a considerable horizontal water flow adjacent to the source of the water added to the system, mainly caused by lateral hydraulic gradients in the soil (Schmalholz et al., 2004). Considering that water is heterogeneously distributed when it occupies different spaces in the soil porous matrix, and the high frequency of data collection registered by the sensors used here, it is pertinent to consider that the spatial variability within the soil profile could cause an alteration on the temporal variability recorded. Thus, soil water dynamics through the porous matrix are mainly conditioned by the soil spatial variability. Furthermore, soil spatial variability has also shown to be temporally variable, describing a complex relationship between spatial and temporal variability when soil properties are recorded with high-frequency, highlighting the importance of the scale in the interpretation of soil processes. The continuous wavelet transform for individual times series from inside and outside the lysimeter allowed to visualize significant cycles that are different between both mentioned conditions. Soil temperature at 10 and 20 cm depth described interesting differences between TLys (Figs. 3C and 4C, top row) and TField (Figs. 3D and 4D; top row) which are related to the duration of the significant cycles found, as long cyclic patterns were mainly recorded outside the lysimeter. The continuous wavelet transform for the soil water content also showed differences between θLys and θField at 60 cm depth (Fig. 5C and D; middle row). Conversely, the matric potential data showed fewer significant cycles in which differences are related with the long duration of the cyclic patterns appearing only in ΨmLys at 20 and 60 cm depth (Figs. 4C and 5C; bottom row). In the cross-wavelet analysis, highly-temporal coherent patterns are identified between the data recorded inside and outside the lysimeter at different depths at specific times durig the season (for soil temperature, soil water content and soil matric potential). In Figs. 3E, 4E and 5E, cross-wavelet analysis shows that arrows are mainly pointing to the right, which means that the correlation between both time series is in phase (or positive) (Grindsted et al., 2004). In this sense, all patterns found in this study represent a high-coherency behavior in temporal variability between lysimeter and field conditions, which means that even with an intrinsic soil spatial variability, the time series behaved in a similar way at specifics periods. Despite this high coherency, low coherency periods are also reveiled through time having different cyclic variations. Short temporal patterns seem to reflect more extreme conditions, while long temporal patterns could be related to less-intensive soil processes in a larger time scale. For this reason, soil temperature coherence peaks occurred when high temperature was recorded in summer or when high soil moisture conditions in winter were registered (Figs. 3E and 4E, top row). A similar trend occurred for the soil water content, where short peaks appeared in times of heavy winter rain (Figs. 3E, 4E and 5E; middle row). The latter developed a high contrast between dry summer periods and those with high soil water saturation during winter. These findings suggest that the intrinsic error of the sensors used in recording these changes in the soil temperature and soil water content need to be considered, as both temperature and soil matric potential were obtained through direct contact between the soil and the MPS-2 sensors (Degré et al., 2017). This is important, considering the high shrinkage capacity of volcanic ash-derived soils (Dörner et al., 2009; Dorel et al., 2000), as the intensity of wetting and drying cycles might displace the soil adjacent to these sensors. Nevertheless, the significant coherence found in the cross-wavelet analyses suggests temporal high correlations between both time series despite the caveats of the sensors used, as well as the inherent soil spatial variability. Changes in the cross-wavelet coherence patterns for the soil temperature registered at different depths could be related to the large pore volume present in these soils and their great capacity to store water (Dörner et al., 2015). The latter suggests that water is acting as a regulating factor of the thermal behavior of an Andisol, especially in long 8
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isn't stable through time and with the crosswavelet analyses performed here, in addition to the DI calculated, it was possible to identify when this correlation is low, and when it is highly significant. The latter, is a usefull tool not only to study the yearly water balance, but also to better understand specific soil processes at specific moments during the year such as Nitrogen leaching, drying and wetting cycles, amongst others. Finally, considering that one of the current challenges in agricultural systems is to improve the water use efficiency (ODEPA, 2018; Levidow et al., 2014), then understanding soil water dynamics (e.g., during dry periods) remains as a key management tool for farmers. In this regard, more research is needed in order to properly define if the measurements conducted by high-resolution lysimeters really reflect the hydrological cycle in a defined soil system at specific time periods.
southern Chile. J. Soil Sci. Plant Nutr. 17, 141–154. https://doi.org/10.4067/S071895162017005000011. Degré, A., van der Ploeg, M., Caldwell, T., Gooren, H., 2017. Comparison of soil water potential sensors: a drying experiment. Vadose Zone J. 16, 1–8. https://doi.org/10. 2136/vzj2016.08.0067. Dorel, M., Roger-Estrade, J., Manichon, H., Delvaux, B., 2000. Porosity and soil water properties of Caribbean volcanic ash soils. Soil Use Manage. 16, 133–140. https:// doi.org/10.1111/j.1475-2743.2000.tb00188.x. Dörner, J., Dec, D., Peng, X., Horn, R., 2009. Efecto del cambio de uso en la estabilidad de la estructura y la función de los poros de un andisol (Typic Hapludand) del sur de Chile. R.C. Suelo Nutr. Veg. 9 (3), 190–209. https://doi.org/10.4067/S071827912009000300003. Dörner, J., Dec, D., Peng, X., Horn, R., 2010. Effect of land use change on the dynamic behaviour of structural properties of an Andisol in southern Chile under saturated and unsaturated hydraulic conditions. 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Geophys. 11, 561–566. https://doi.org/10.5194/npg-11-561-2004. Grip, H., Halldin, S., Lindroth, A., 1989. Water use by cultivated willow using estimated stomatal parameter values. Hydrol. Process. 3, 51–63. https://doi.org/10.1002/hyp. 3360030106. Lark, R.M., Webster, R., 1999. Analysis and elucidation of soil variation using wavelets. Eur. J. Soil Sci. 50, 185–206. https://doi.org/10.1046/j.1365-2389.1999.t01-100234.x. Levidow, L., Zaccaria, D., Maia, R., Vivas, E., Todorovic, M., Scardigno, A., 2014. Improving water-efficient irrigation: prospects and difficulties of innovative practices. Agric. Water Manag. 146, 84–94. https://doi.org/10.1016/j.agwat.2014.07. 012. Li, X., Xu, X., Liu, W., He, L., Xu, C., Zhang, R., Chen, L., Wang, K., 2019. Revealing the scale-specific influence of meteorological controls on soil water content in a karst depression using wavelet coherency. Agric. Ecosyst. Environ. 279, 89–99. Maraun, D., Kurths, J., 2004. Cross wavelet analysis: significance testing and pitfalls. Nonlinear Process. Geophys. 11, 505–514. https://doi.org/10.5194/npg-11-5052004. Meissner, R., Rupp, H., Seyfarth, M., 2008. Advances in out door lysimeter techniques. Water Air Soil Pollut: Focus 8, 217–225. https://doi.org/10.1007/s11267-0079166-2. Negrón, M., López, I., Dörner, J., 2019. Consequences of intensive grazing by dairy cows of contrasting live weights on volcanic ash top soil structure and pasture dynamics. Soil Tillage Research 189, 88–97. https://doi.org/10.1016/j.still.2018.12.025. Nielsen, D.R., Wendroth, O., 2003. Spatial and Temporal Statistics: Sampling Field Soils and Their Vegetation. Catena Verlag, Reiskirchen, Geoscience Publisher, Germany. 398 p. Nielsen, D.R., Alemi, M.H., 1989. Statistical opportunities for analyzing spatial and temporal heterogeneity of field soils. Plant Soil 115, 285–296. https://doi.org/10. 1007/BF02202595. ODEPA, 2018. Cambio Climático y Los Recursos Hídricos De Chile. 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5. Conclusion While the Pearson's correlation analysis between the studied time series recorded inside and outside the lysimeter indicated high correlations, the continuous wavelet analysis showed differences in the magnitude of temporal cycles that appeared throughout the studied period between time series. Accordingly, the cross-wavelet analysis showed significant coherence between the time series only at specific periods with lower coherence during the rest of the year at different scales. The latter, which can be related to swelling and shrinkage processes that induce changes in soil water dynamics, is also shown after calculating the DI when comparing time series recorded inside and outside the lysimeter. Thus, spectral analyses are a useful approach for improving the analyses of temporal water and thermal processes in soils, as presented in volcanic ash-derived soils that have extreme physical properties. Therefore, wavelet analyses, and especially the cross-wavelet analysis, are interesting tools to understand the coherence between time series helping to identify potential temporal differences in data recorded inside and outside a field lysimeter in soils. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests Acknowledgements The authors thanks Stephan Engelhardt for lysimeter installation in the field as well as for the training and helpful advices for its use. We gratefully acknowledge the contribution of Dr. Álvaro González and Dr. Gino Montecinos for insightful statistical advice. The lead author thanks Mónica Díaz and Ruth Espinoza for key support during laboratory analyses. The lysimeter was funded by the FONDEQUIPProject 130202. References Armas-Espinel, S., Hernández-Moreno, J., Muñoz-Carpena, R., Regalado, C., 2003. Physical properties of “sorriba” — cultivated volcanic soils from Tenerife in relation to andic diagnostic parameters. Geoderma 117, 297–311. https://doi.org/10.1016/ S0016-7061(03)00130-7. Awe, G., Reichert, J., Timm, L., Wendroth, O., 2015. Temporal processes of soil water status in a sugarcane field under residue management. Plan and Soil 387, 395–411. https://doi.org/10.1007/s11104-014-2304-5. Bakar, R.A., Goulding, K.W.T., Webster, C.P., Poulton, P.R., Powlson, D.S., 1994. Estimating nitrate leaching and denitrification by simultaneous use of Br and 15 N tracers. J. Sci. Food Agric. 66, 509–519. https://doi.org/10.1002/jsfa.2740660414. Biswas, A., Si, B., 2011. Application of continuous wavelet transform in examining soil spatial variation: a review. Math. Geosci. 43, 379–396. https://doi.org/10.1007/ s11004-011-9318-9. CIREN, 2003. Estudio Agrológico X Región. Publicación CIREN N° 123. Santiago. Dec, D., Zúñiga, F., Thiers, O., Paulino, L., Valle, S., Villagra, V., Tadich, I., Horn, R., Dörner, J., 2017. Water and temperature dynamics of Aquands under different uses in
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sequences of volcanic soils, New Zealand. In: Fernández Caldas, E. (Ed.), Volcanic soils. : In: Yaalon, d.H. (Ed.), Catena, Supplement N°7. Catena Verlag, Cremlingen, pp. 1–8. Peters, A., Nehls, T., Schonsky, H., Wessolek, G., 2014. Separating precipitation and evapotranspiration from noise - a new filter routine for high-resolution lysimeter data. Hydrol. Earth Syst. Sci. 18, 1189–1198. https://doi.org/10.5194/hess-18-11892014. R Core Team (2019) R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. Reyes, J., Wendroth, O., Matocha, C., Zhu, J., 2019. Delineating site-specific management zones and evaluating soil water temporal dynamics in a farmer’s field in Kentucky. Vadose Zone J. 18, 180143. https://doi.org/10.2136/vzj2018.07.0143. Rudiyanto, N., Toride, M., Sakai, M., van Genuchten, M., 2013. Estimating the unsaturated hydraulic conductivity of Andisols using the evaporation method. J. Jpn. Soc. Soil Phys. 125, 3–15. Sandoval, M., Dörner, J., Seguel, O., Cuevas, J., Rivera, D., 2012. Métodos de Análisis Físicos de Suelos. Universidad de Concepciön. Publicaciones Departamento de Suelos y Recursos Naturales, Chillán, Chile, número 5, 80 p. Sadzawka, A., Carrasco, M., Grez, R., Mora,M., Flores, H., Neaman, A. 2006. Métodos de análisis recomendados para los suelos de Chile. Revisiön 2006. Instituto de Investigaciones Agropecuarias, Serie Actas INIA N° 34. Santiago, Chile. 164 p. Sang, Y.F., 2013. A review on the applications of wavelet transform in hydrology time series analysis. Atmos. Res. 122, 8–15. https://doi.org/10.1016/j.atmosres.2012.11. 003. Schrader, F., Durner, W., Fank, J., Gebler, S., Pütz, T., Hannes, M., Wollschläger, U., 2013. Estimating precipitation and actual evapotranspiration from precision lysimeter measurements. Procedia Environ. Sci. 19, 543–552. https://doi.org/10.1016/j. proenv.2013.06.061.
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Using wavelet analyses to identify temporal coherence in soil physical properties in a volcanic ash-derived soil
T
Sebastián Bravoa, Mauricio González-Changb,c, Dorota Deca,c, Susana Vallea,c, Ole Wendrothd, ⁎ Felipe Zúñigab,c,e, José Dörnera,c, ,1 a
Instituto de Ingeniería Agraria y Suelos, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile Departamento de Ciencias Naturales y Tecnología, Universidad de Aysén, Eusebio Lillo 667, Coyhaique, Chile c Centro de Investigación en Suelos Volcánicos, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile d Department of Plant and Soil Sciences, University of Kentucky, Lexington, KY, United States e Doctorado en Ciencias Agrarias, Escuela de Graduados, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile b
A R T I C LE I N FO
A B S T R A C T
Keywords: Andisol Physical properties Field lysimeter Continuous wavelet transform Cross-wavelet analysis
Lysimeters have been used for centuries to understand hydrological cycles. Nowadays, high-resolution weighing lysimeters allow precise determination of the water balance components. While major efforts have been focused on the definition of appropriate methodologies for data processing in order to obtain results with high accuracy, it is still unknown to what extent measurements registered by a lysimeter can reflect soil water dynamics and the transport phenomena in a defined agroecosystem. The aim of this work is to analyze temporally-coherent discrepancies in the estimation of soil parameters based on time series recorded inside and outside a lysimeter installed in a volcanic ash-derived soil. Continuous wavelet transforms and cross-wavelet analyses were used to understand temporal differences and similarities between time series, respectively. Inside and at a 2 m distance from the lysimeter, soil temperature, volumetric water content and matric potential were measured at different depths (10, 20 and 60 cm depth). Despite that the Pearson's correlation between the studied time series indicated good correlations (r2 > 0.95), the wavelet analyses showed that coherence obtained inside the lysimeter can temporarily differ from those monitored in the field at specific times during the year. The latter was quantified using a Dissimilarity Index (DI), which showed high values at particular moments throughout the year. The wavelet analyses used here are a valuable tool to assess time series temporal variations which are unnoticed by commonly-used statistics, such as the Pearson's correlation. A better understanding of soil water and temperature temporal dynamics can enhance our ability to model and predict these processes in soils.
1. Introduction Lysimeters have been used for more than 300 years to understand plant physiological processes related to soil constraints and for studying the hydrological cycles under field conditions (Goss and Ehlers, 2009). Nowadays, lysimeters are used in a broad range of applications in agriculture, forestry and environmental studies (Meissner et al., 2008), such as in nitrate leaching (Bakar et al., 1994), groundwater seepage (Fox et al., 2007), water use efficiency (Grip et al., 1989), evapotranspiration (Drexler et al., 2008), and for modelling the water balance (Wegehenkel et al., 2008). The above-mentioned broad range of applications have contributed to the development of different types of lysimeters, such as the high-resolution weighing lysimeter (von Unold
and Fank, 2008; Meissner et al., 2008; UMS, 2010). High-resolution weighing lysimeters allow precise determination of the water balance components. In modern lysimeters it is possible to use undisturbed soil monoliths, which are inserted into the soil profile in order to characterize water fluxes of natural soils under atmospheric boundary conditions (Fank and von Unold, 2007; Schrader et al., 2013; Peters et al., 2014; Hannes et al., 2015). Any disturbance during the lysimeter installment that affects soil structure due to mechanical stress and crack formations will affect the process dynamics and soil hydraulic properties to some extent, and then the lysimeter might not reflect the in situ soil conditions realistically. Soils in agricultural sciences have been studied principally with statistical models based on field observations considered independent
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Corresponding author at: Instituto de Ingeniería Agraria y Suelos, Facultad de Ciencias Agrarias, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile. E-mail address: [email protected] (J. Dörner). 1 Centro de Investigación en Suelos Volcánicos, Universidad Austral de Chile, Campus Isla Teja, Valdivia, Chile. https://doi.org/10.1016/j.agrformet.2020.107909 Received 21 June 2019; Received in revised form 16 January 2020; Accepted 17 January 2020 0168-1923/ © 2020 Elsevier B.V. All rights reserved.
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registered between May and July, whereas the driest months were January and February (2 mm). The mean air temperature reached 11.8 °C with the maximum and minimum temperatures being 17.5 °C (January) and 7.7 °C (July), respectively. The studied soil is a Duric Hapludand (Valdivia Series according to CIREN, 2003) or a Petroduri-Silandic Andosol (WRB, 2006), which corresponds to a soil derived from volcanic ashes with a depth that can reach up to 3 m. Topography in the soil series is normally complex, with dominant slopes from 3 to 8%. Table 1 presents the soil horizon distribution after a morphological description conducted during the lysimeter installation and a physicochemical characterization from samples collected from each soil horizon. Disturbed soil samples were used to define the particle size distribution, particle density, bulk density (Sandoval et al., 2012), allophane content (Parfitt and Wilson, 1985) and organic carbon (Sadzawka et al., 2006). Undisturbed soil samples were used for assessing the water retention curve (WRC, n = 7 for each soil horizon) and the saturated hydraulic conductivity (n = 10 for each soil horizon) as previously conducted in Dörner et al. (2015). The amount of wide coarse pores (wCP), plant available water (PAW) and fine pores (FP) were calculated from the water retention curve. The saturated hydraulic conductivity (Ks) was measured using a constant head permeameter (Eijkelkamp Agrisearch Equipment, 2003). The amount of macropores (pores with a diameter > 50 μm) in the first two soil horizons reached levels between 5% and 8%, it increased in deeper soil horizons reaching values higher than 10% (until 168 cm depth), and then decreased again until 4%. The plant available water range had values between 15% and 42%, whereas the amount of fine pores ranged from 18% to 46%. The saturated hydraulic conductivity increased with soil depth ranging between 68 cm d−1 and 832 cm d−1 (Table 1). Finally, from an agricultural point of view, the soil was managed as a non-grazed pasture with the following dominant species: Lolium perenne L. and Trifolium repens L.
and randomly distributed (Nielsen and Alemi, 1989). However, soil state variables’ dynamics are a more or less continuous process through time and space, and state observations are related to the previous status in time or to the local neighborhood in space. Based on the continuity of processes, statistical models have been developed in order to analyze and understand the spatial and temporal heterogeneity of soils and their processes (Nielsen and Alemi, 1989; Wendroth et al., 1997; Nielsen and Wendroth, 2003). As one method of Fourier-based transforms, wavelet analyses have been developed and adapted to soil sciences for studying the occurrence of cyclic variations, their scale and their amplitude (Biswas and Si, 2011; He et al., 2007; Si and Zekele, 2005; Lark and Webster, 1999). In this sense, wavelet analysis can depict the behavior of one or several series of observations through time, while if common fluctuations between two time series are investigated, a cross-wavelet analysis can be used instead (Torrence and Compo, 1998; Grinsted et al., 2004; Li et al., 2019). Thus, studies assessing the coherence between two time series to understand soil water processes have been performed (Awe et al., 2015; Reyes et al., 2019), and the feasibility of using cross-wavelet analysis in hydrologically-based time series has also been studied (Sang, 2013). Despite the recent advances in analyzing soil-water-content time series using a cross wavelet approach, emphasis has been placed on studying soil spatial variability, while studies in which soil temporal variability is assessed are still rare (Reyes et al., 2019). In this sense, the cross-wavelet spectral analysis might be a promising statistical tool for disentangling currently unknown common temporal relationships between the soil time series of different soil parameters. In southern Chile, studying water balance is of a great interest due to the extreme physical properties of volcanic ash-derived soils within a region in which rainfall may reach up to 2500 mm year−1 (GonzálezReyes and Muñoz, 2013). Volcanic ash-derived soils are characterized by a very low bulk density (< 0.9 Mg m−3), and a well-defined interand intra-aggregate porosity (Dörner et al., 2010), which allows high saturated and unsaturated hydraulic conductivity and, consequently, rapid changes in the soil volumetric water content through time (Dörner et al., 2015; Dec et al., 2017). Also, volcanic ash-derived soils present swelling and shrinkage during wetting and drying cycles, respectively, that lead to changes in soil structure affecting soil water content dynamics (Dörner et al., 2010). This specific behavior may induce spatial and temporal changes in soil physical properties, especially, when the soil is disturbed e.g. by tillage (Dörner et al., 2012), animal trampling during grazing (Negrón et al., 2019) or after the lysimeter installment. Therefore, the objective of this work is to analyze the temporal variability in the soil water content, soil matric potential and soil temperature time series recorded within a lysimeter installed in a volcanic ash-derived soil related to field conditions without a lysimeter. In these terms, comparing these time series measured inside and outside a lysimeter could be a useful approach to assess the temporal representativeness of this high-resolution equipment in soils.
2.2. Lysimeter installation and measurements A Science Lysimeter (UMS-Germany; UMS, 2010), was installed in a site with a slope less than 2% and it has an area of 2 m2 and 2 m depth (a similar lysimeter was used in von Unold and Fank, 2008). Although soil disturbances might occur during the lysimeter installation, the soil monolith was not damaged during the cutting process and the site used to collect the monolith was minimally affected. The lysimeter was then equipped with different electronic sensors that collected data with a 10-min frequency and that were installed at 10, 20 and 60 cm depth (2 sensors of each kind per each depth). These were installed to measure the volumetric water content by a time domain reflectometer (0 to 100%; TRIME PICO 32 model, UMS-Germany); the matric potential by dielectric water potential sensors (−90 to −1000000 hPa; MPS-2 model, Decagon Device) and the soil temperature (−40 to 60 °C; MPS-2 model, Decagon Device). Additionally, one tensiometer was installed at 180 cm depth (1000 to −850 hPa; T8 sensor, UMS-Germany). The same number of sensors mentioned above were also installed in an undisturbed soil profile 2 m apart from the lysimeter in order to investigate the effect of lysimeter installation compared to natural field conditions (von Unold and Fank, 2008). As part of a drain water feedback control system, T8 sensors measured the water potential adjusting it continuously by 10 suction cups with a ceramic surface installed at the bottom of the monolith, which are connected to a bi-directional pump for controlling and ensuring that water flows and potentials into the lysimeter are identical to the real field situation.
2. Material and methods 2.1. Experimental field description The experimental field was located at the Universidad Austral de Chile's experimental field station (Estación Experimental Agropecuaria Austral (EEAA) (39°46′ S, 73°13′ W, 12 m a.s.l.)) in Valdivia, southern Chile (Fig. 1). The average annual temperature is 12 °C with a yearly mean rainfall of 2440 mm between 1901 and 2005 (González-Reyes and Muñoz, 2013), concentrated mainly in winter (Huber, 1970). During the experiment, rainfall was collected from a meteorological station (Campbell) located 10 m from the lysimeter. Since no temperature data was available, the average daily air temperature was obtained at the INIA station, located 40 km north from the study site (Fig. 2). During 2015, rainfall reached 1783 mm. A high amount of rainfall (941 mm) was
2.3. Data analyses Soil matric potential, soil temperature and soil water content data collected during 2015 were analyzed by a continuous wavelet 2
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Fig. 1. Site location and lysimeter installation.
When a continuous wavelet transform was obtained for each of the studied time series, it is possible to observe patterns that can differ between the time series recorded inside the lysimeter and at field conditions, while with a cross-wavelet approach the similarities between both time series can be investigated, as cross wavelet has been previously used for studying spectral coherence between two time series, highlighting concurrent cycles that might occur between them (Maraun and Kurths, 2004). The cross wavelet was normalized to correct potential biases in the power spectrum estimation (Veleda et al., 2012) and it used the Morlet mother wavelet function (Grinsted et al., 2004), with a significance level of 95%. For each depth (10, 20, 60 cm), the soil matric potential data recorded from the field and from the lysimeter were used to calculate the continuous wavelet and the crosswavelet transform. A similar approach was used when analyzing soil temperature and soil water content at different depths. The interpretation of the continuous wavelet transform followed Torrence and Compo (1998), while that for the cross-wavelet analysis was based on Maraun and Kurths (2004) and Grinsted et al. (2004). In the crosswavelet analysis, the phase between both time series is graphically presented as arrows within significant areas of coherence (Grinsted et al., 2004; Li et al., 2019). Arrows pointing to the right mean that both time series are in phase (positive correlation), while arrows pointing to the left, mean an anti-phase (negative) correlation
Fig. 2. Rainfall and air temperature during the studied period.
transform and by a cross-wavelet transform (Torrence and Compo, 1998). Soil matric potential data was Log transformed before performing wavelet analyses. A continuous wavelet transform was used to assess the dominant modes of variability within a time series, and how those modes vary through time (Torrence and Compo, 1998).
Table 1 General description of the volcanic ash soil (Duric Hapludand) at the lysimeter station. Depth [cm] 0–20 30–38 38–57 57–93 93–143 143–168 168–203 +203
Hor. [-] Ap B1 B2 B3 2Bw1 2Bw2 2Bw3 2BC
Sand [%] 11.3 11.7 25.6 16.7 26.2 42.8 35.6 36.3
Silt [%] 58.9 60.1 62.3 53.6 50.3 41.0 47.8 53.6
Clay [%] 29.8 28.3 12.2 29.7 23.6 16.2 16.7 10.2
Alloph. [%] 13.2 14.2 12.3 7.6 9.7 16.5 22.7 29.7
OM [%] 12.7 ± 0.3 11.5 ± 0.1 2.4 ± 0.1 0.9 ± 0.1 2.1 ± 0.1 2.0 ± 0.1 1.7 ± 0.1 2.9 ± 0.1
Bd
Pd −3
[Mg m ] 0.79 ± 0.01 0.72 ± 0.01 0.63 ± 0.01 0.74 ± 0.01 0.76 ± 0.01 0.75 ± 0.01 0.67 ± 0.01 0.56 ± 0.01
−3
[Mg m ] 2.24 ± 0.01 2.24 ± 0.01 2.46 ± 0.01 2.50 ± 0.01 2.49 ± 0.01 2.60 ± 0.01 2.43 ± 0.01 2.48 ± 0.01
AC
PAW
FP
Ks
[Vol.%] 4.99 ± 0.67 8.84 ± 0.44 13.76 ± 0.91 13.00 ± 0.71 12.37 ± 0.68 9.01 ± 0.53 6.82 ± 0.63 4.18 ± 0.79
[Vol.%] 41.88 ± 2.24 35.44 ± 2.17 31.25 ± 2.22 26.98 ± 2.50 18.27 ± 0.39 15.85 ± 0.52 20.67 ± 3.25 39.23 ± 0.77
[Vol.%] 17.97 ± 1.93 23.63 ± 2.10 29.34 ± 2.25 30.60 ± 2.17 38.97 ± 0.35 46.11 ± 0.45 45.13 ± 3.12 34.04 ± 0.79
[log(cm d−1)] 1.83 ± 0.4 1.95 ± 0.3 2.65 ± 0.2 2.63 ± 0.2 2.92 ± 0.2 2.72 ± 0.3 2.26 ± 0.3 2.65 ± 0.3
Hor. = Horizon; Alloph. = Allophane; OM = Organic matter; Bd = Bulk density; Pd = Particle density; AC = Air capacity; PAW = Plant available water; FP = Fine pores; Ks = Saturated hydraulic conductivity. Mean values ± 1 standard error is presented. 3
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row (at 10 cm depth), 4A (at 20 cm depth), and 5A (at 60 cm depth). The continuous wavelet transform for TLys (Fig. 3C, top row) shows significant cycles (denoted by contour lines) between 2 and 6 days early in the year, a 4-day cycle in July and another of around 14 days in November. These significant cycles occurred in TField as well, but a cycle of around 16 days also appeared from May to July (Fig. 3D, top row). In the cross-wavelet analysis, the soil temperature at 10 cm depth showed significant peaks that occurred at periods between 2 and 6 days around January, February and July, while from March to late June periods of 16 days appeared. In November, another peak occurred at a period of about 14 days (Fig. 3E, top row). When analyzing the continuous wavelet transform for TLys at 20 cm depth (Fig. 4C, top row), significant peaks of around 2 to 4 days occurred in January, and from 4 to 8 days in February. In March, a cycle of around 16 days appeared until June. Also, a small peak of 4 days appeared in July. During late October to mid November a significant cycle of around 12 days also appeared. Data from TField presented longer cycles (Fig. 4D, top row) compared to TLys, occurring mainly from March to November at scales between 14 and 30 days, approximately. In the cross-wavelet analysis, the soil temperature at 20 cm depth (Fig. 4E, top row), presented a long significant peak that occurred at a scale of around 14 and 18 days from January to late October, increasing its range from 4 to 18 days between late June and August, and between November and December. Soil temperature recorded at 60 cm depth in TLys had a 16-day cycle from April to June (Fig. 5C, top row), while in TField this cycle was only noticeable from May to June (Fig. 5D, top row). Interestingly, a cycle between 2 and 12 days appeared early in the year and this was significant only in TField. When analyzing the cross wavelet at 60 cm depth, one peak appeared in mid-January to February at a scale between 2 and 12 days, and another at periods around 16 and 40 days between May and October (Fig. 5E, top row). Arrows pointing to the right indicate a
between both (Grinstead et al., 2004). In addition, a Pearson's correlation between the different time series measured in the field and inside the lysimeter was calculated. In an attempt to quantify and temporally-identify the differences between time series recorded from inside the lysimeter and from field conditions, a Dissimilarity Index (DI) was calculated for each depth, time and the soil parameters analyzed here. Let's define ni as the depth in which measurements were taken, where n1, n2 and n3 correspond to 10, 20 and 60 cm depth, respectively. For each of the ni, the time series xi(t) and yi(t) were calculated for each time (t), where xi(t) and yi(t) correspond to the data recorded inside the lysimeter and at field conditions, respectively. Thus, for each ni at each time (t), DI was calculated as follows:
DIi (t ) =
x i (t ) − yi (t ) yi (t )
(1)
The Dissimilarity Index (DI) presented in Eq. (1) allows the temporal quantification of differences between the data collected inside the lysimeter and the data collected at field conditions, for each time (t) in the studied time series. Therefore, a high DI value (represented graphically as peaks in Figs. 3B, 4B and 5B), shows the difference between both time series at a specific time during the studied season. The wavelet analyses were performed using the R package “biwavelet” using R v.3.6.1 (R Core Team 2019). 3. Results 3.1. Wavelet analyses 3.1.1. Soil temperature wavelet analyses Soil temperature data recorded inside the lysimeter (TLys, black line) and under field conditions (TField, red line) are shown in Fig. 3A, top
Fig. 3. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 10 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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Fig. 4. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 20 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
although the small ones occurring from May to August in θLys reduced their scale in θField, and therefore, the number of significant peaks during that period decreased (Fig. 4D, middle row). In the cross-wavelet analysis, the soil water content had two peaks between April and May, one of around 16 days, and another about 60 days. In July, the peak was characterized by a period between 2 and 16 days. In addition, a peak in a scale between 2 and 12 days appeared in July, and another one of 16 days occurred in September, while in December the peak ranged from 2 to 16 days (Fig. 4E, middle row). At 60 cm depth, θLys had peaks between 2 and 8 days occurring in April, May and December. In July, the scale of the peak was between 2 and 16 days, and from August to September its scale ranged from 2 to 6 days (Fig. 5C, middle row). The θField data showed similar peaks between 2 and 6 days in April and May, but different ones in the MayJune period and in the August-October period that ranged between 14 and 20 days, approximately (Fig. 5D, middle row). Here, θField data showed longer cycles in Winter and Spring compared with θLys data. The cross-wavelet analysis presented fewer peaks compared to more superficial soil depths, with two peaks in the May-June period, one between 2 and 8 days, and another of around 16 days. In July, a significant peak at a period between 2 and 16 days occurred, while in September it occurred at a scale between 14 and 18 days (Fig. 5E, middle row). In the soil water content time series, right pointing arrows dominated at all depths, highlighting the positive correlation between θLys and θField.
positive correlation between both time series at significant cycles depicted by contour lines. For the soil temperature time series, right pointing arrows dominated at all depths, highlighting the positive correlation between TLys and TField. 3.1.2. Soil water content wavelet analyses The continuous wavelet transform for the soil water content measured at 10 cm depth (Fig. 3C, middle row) inside the lysimeter (θLys) showed a significant peak during early April at a scale between 2 and 16 days. Also, small peaks around 2 and 6 days occurred in May, July, August and November. In December, another one between 2 and 6 days appeared. In field conditions (Fig. 3D, middle row, θField), the peak shown in April for θLys was also present but occurred longer until late April. Smaller peaks appeared in θField compared to the ones obtained in θLys, but in December a cycle between 2 and 16 days appeared, which was longer than the one in θLys (Fig. 3C,D, middle row). At 10 cm depth the θLys wavelet transform showed greater and significant peaks in small cycles from May to November, while θField showed higher significant variations occurring in long cycles during April and December (Fig. 3C,D, middle row). In the cross-wavelet analysis, the soil water content measured in θLys and in θField revealed a significant peak at a scale between 2 and 16 days in April, two peaks around 16 days in July and September, and another in December at periods between 2 and 16 days (Fig. 3E, middle row). Also, small peaks between 2 and 6 days appeared in May, July, August and September (Fig. 3E, middle row). At 20 cm depth, the continuous wavelet transform for θLys (Fig. 4C, middle row) showed a 16-day significant peak in April, and another of around 14 days during the July-August period. Small cycles between 2 and 6 days occurred in May, July and August, while a long one appeared in December at a scale between 2 and 16 days (Fig. 4C, middle row). In θField data recorded at 20 cm depth (Fig. 4D, middle row), similar peaks appeared in April and December compared to θLys
3.1.3. Soil matric potential wavelet analyses The continuous wavelet transform for the soil matric potential obtained at 10 cm depth (Fig. 3C, bottom row) inside the lysimeter (ΨmLys), presented peaks between 2 and 18 days from March to April, and another from November to January that ranged between 2 and 16 days (Fig. 3C, bottom row). At field conditions (Fig. 3D, bottom row, 5
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Fig. 5. Time series data collected inside the lysimeter (black line) and at field conditions (red line) (A). The relative errors of the lysimeter measurements against the ones collected at field conditions are also presented (B). Continuous wavelet transform from data collected inside the lysimeter (C) and at field conditions (D), is shown altogether with the cross wavelet analysis (E) for the soil temperature (top row), volumetric water content (middle row) and matric potential (bottom row) measured at 60 cm depth in the soil profile. In C, D and E, contour lines denote statistical significance at 95%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
ΨmField) similar peaks are shown. At 20 cm depth, ΨmLys presented a peak of 16 days in April and another between November and January ranged between 2 and 16 days. In ΨmField a cycle between 2 and 60 days appeared in April (Fig. 4D,C, bottom row). Finally, at 60 cm depth (Fig. 5C,D, bottom row), similar patters as described for 20 cm depth were found. The cross-wavelet analysis at 10 cm depth, showed a significant peak at a period between 2 and 60 days that occurred between March and May, and another cycle between 2 and 16 days appearing between November and January (Fig. 3E, bottom row). A similar peak was exhibited at 20 cm depth (Fig. 4E, bottom row), and at 60 cm depth (Fig. 5E, bottom row). In the soil matric potential time series, right pointing arrows dominated at all depths, highlighting the positive correlation between ΨmLys and ΨmField.
increased to 0.28 during mid to late April, and then decreased to around 0.04 from May to September. In November and December peaks of 0.08 and 0.12 were calculated, respectively. At 60 cm depth (Fig. 5B, middle row), from February to April, DI varied from 0.22 to 0.32 and then suddenly decreased to 0 in late April. From May to December, DI varied from around 0.15 to 0.28. The soil matric potential DI at 10 cm depth (Fig. 3B, bottom row) showed two peaks between late April and early May of 0.12 and 0.17, respectively. In November, a peak of 0.27 also appeared. A similar trend in the temporal variation of DI occurred at 20 cm depth (Fig. 4B, bottom row), with peaks between mid April to early May of 0.37 and 0.18, respectively. In November, a peak of 0.25 was calculated. At 60 cm depth (Fig. 5B, bottom row), during early January DI presented a peak of 0.38, and another in early May of 0.61. The results given after calculating the DI are in agreement with the wavelet analyses presented above. By using Eq. (1) the temporal differences in the soil variables measured inside and outside the lysimeter at specific times during the season were identified.
3.2. Dissimilarity index between time series When comparing TLys against TField at 10 cm (Fig. 3B, top row), DI increased to 0.18 in February, oscillating between 0.04 and 0.17 between February and April. In July, a peak of 0.20 appeared, while in November this was 0.17. A similar trend is observed when measuring soil temperature at 20 cm depth, with a highest peak of 0.18 appearing in July (Fig. 4B, top row). At 60 cm depth (Fig. 5B, top row), a peak of 0.20 occurred in February, decreasing between 0.05 and 0.10 from February to April. From April to December, DI oscillated between 0 and 0.07. Soil water content also showed a temporal variation in DI. At 10 cm depth (Fig. 3B, middle row), a peak of 0.13 occurred in February, decreasing in late February close to 0 and then raising up to 0.33 in late April and May. During mid May, DI decreased to around 0.20, oscillating between this value until September. In December, a decrease from 0.27 to 0 was recorded. At 20 cm depth (Fig. 4B, middle row), DI
3.3. Pearson's correlation between soil time series Amongst all the studied soil time series, a high correlation was found between data recorded under field conditions and inside the lysimeter (Fig. 6). Correlation in soil temperature increased with depth, but decreased at both soil matric potential and soil water content. Despite these spatial changes, correlation between time series was above 0.95.
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Fig. 6. Pearson's correlations between data (T: Soil Temperature, Ψm: Soil Matric Potential; θ: Soil Water Content) recorded at field level and inside the lysimeter for the different studied depths and soil parameters.
4. Discussion
same soil series but under different land uses (Dörner et al., 2015), were related to the hydraulic properties of volcanic ash-derived soils. These soils present multimodal soil water retention curves, which reflect a well-defined hierarchy of inter- and intra-aggregate pores (Dörner et al., 2010, 2015; Rudiyanto et al., 2013) responsible for very high values of saturated hydraulic conductivity (Table 1). Some authors have mentioned that volcanic ash-derived soils present a sandy behavior when saturated as well as a large water holding capacity at higher matric potentials (Armas-Espinel et al., 2003; Dörner et al., 2010) causing rapid changes in soil water content (Dörner et al., 2015). This complex behavior in volcanic ash-derived soils could be responsible for developing complex patterns of coherence and variation through time between data collected inside and outside the lysimeter as presented with the wavelet analysis performed here, which can be also a valuable tool to assess time series temporal dynamics in other soil types.
4.1. Soil water and temperature dynamics during the studied period With increasing soil depth, the temperature decreased reducing its amplitude as well as shifting its phase. The latter, has been assessed in a Duric Histic Placaquand (e.g. Dec et al., 2017) and in other mineral soils (e.g. Tong et al., 2017), and reflects different soil temperature conditions in the profile, which depends on the soil thermal diffusivity (Horton et al., 1983) and, in turn, on the soil water content. Since soil temperature profiles inside and outside the lysimeter are apparently variable through time, if we consider the same level of energy input, we can assume that soil thermal properties could be temporarily affected due to physical changes influenced by water dynamics within the soil profile. The soil water content, measured in field conditions (θField) and inside the lysimeter (θLys), reflects the soil water storage capacity (see Table 1) of the Ap, B1 and B3 horizons (according to the installation depths of the sensors used). During dry months (January until March) the soil matric potential increased, reaching values exceeding the permanent wilting point (15.430 hPa) until 20 cm depth. This was also assessed by the θField which is in accordance with the water retention curves determined in the laboratory (the water content at pF 4.19 ranged between 18% and 31%). In addition, as rainfall increased during winter (June – September), the soil matric potential reflects near saturated conditions which are also confirmed by the measured volumetric water content. Changes in soil water content during wetting and drying cycles occurred very quickly (e.g. changed from 35% to 50% in 24 h approximately) and responded to rainfall and evapotranspiration dynamics. These dynamic changes, which have also been assessed in the
4.2. Wavelet analyses for temporal variability in soil time series In all the time series data obtained from all of the sensors used in this study, our results showed a strong correlation between the data collected inside and outside the lysimeter (Fig. 6, Pearson r2 between 0.95 and 0.99). However, Pearson's correlation can only identify linear correlations (Li et al., 2019). Aditionally, it is important to consider that the use of a big data set improves the capacity of getting good correlations (more than 500.000 data/year in this study). Therefore, an overall high correlation does not necessarily mean that this correlation is occurring at all times within the time series recorded inside and outside the lysimeter. The latter has been demonstrated by the results from the cross-wavelet analysis as variations in the temporal coherence between the recorded time series occurred. When water is added to a lysimeter (e.g., through rain), temporal and spatial changes in the 7
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periods of water saturation. Likewise, the distribution of these coherence patterns in the cross-wavelet analysis could indicate differences between long drought periods where the temperature is mainly transmitted by the solid and gaseous soil phases, while in periods of long water saturation water is the main soil phase for transmitting and accumulating heat (Dec et al., 2017). In relation to the volumetric soil water content, coherence patterns from the cross-wavelet analysis are oriented according to the seasonal distribution of rainy events, mainly from the autumnal season. Since there is a greater amount of water interconnecting the pores within the soil profile, the heterogeneity in the soil response could be temporarily diminished, producing a significant coherence between the measurements inside and outside the lysimeter. Soil matric potential results obtained by the MPS-2 sensors show that time series have a high coherence during the dry season (February), where the soil continues to decrease its moisture levels. These patterns disappear in depth as an increase in matric potential occurs until the first important rainy event in April ocurred (Fig. 2). When soil matric potential drastically decreases due to an increased water infiltration into the system, coherence appears at all depths, which could indicate the high humectation that occurred throughout the soil profile. After matric potential decreases, the cross-wavelet analysis does not produce any pattern, possibly due to the small variations in soil matric potential when high soil water content occurs caused by lateral flow and leveling out horizontal heterogeneity. As a descriptive view, cross wavelet plots show the coherence intensity between time series by a scale of colors. Considering the dark orange and light red zones through time we can also identify moderate coherency areas that are taking place outside the black contours of significance patterns, which are extended during all year with periods around 32 to 64 days for all analyzed parameters. As the Pearson's correlation has shown, this situation can represent an important correlation when is considering longer scales in the study of time series behavior between lysimeter and field conditions over the year. In this sense, with appropriate correlation and determined scales, lysimeters are a useful tool for accurate soil water and temperature studies, allowing us to solve the effects of spatial variability. It has to be mentioned that although a high correlation occurred between the studied time series recorded inside and outside the lysimeter (Fig. 6), the continuous wavelet transform showed differences in the scale of the cycles that appeared on each time series, suggesting differences in the magnitude of the data collected inside and outside the lysimeter probably related with the spatial variability exhibited through the porous matrix. The latter is in agreement with the results provided by the Dissimilarity Index (DI) calculated here. Also, the crosswavelet analysis showed significant coherence between these time series only at certain points (normally at extreme periods when the soil was near to field capacity or when near to the permanent wilting point) throughout the studied period (Figs. 3–5). Considering that using field lysimeters of this scale is a widely-used methodological approach to study soil water dynamics (Hannes et al., 2015; Peters et al., 2014; Schrader et al., 2013), attention should focus at interpreting data from lysimeters, paying attention to the soil physical-hydraulic conditions (and the particularties of each soil type, i.e. the behavior of an Arenosol may differ from a Vertisol or an Andisol) that can temporarily modify data representativeness. These considerations are relevant since the water balance obtained from a lysimeter should reflect the hydrological cycle of a defined ecosystem; however, if the soil is disturbed during the lysimeter installment and/or the field and the lysimeter measurements differs because intrinsic soil characteristics, then the accuracy of the data obtained by using a lysimeter will differ from a field condition, leading to biased results that decrease the effectiveness of soil modeling tools. The temporal patterns found here are repetitive, so a phenomenon that could be identified to have its own soil response to environmental effects can be suggested. Therefore, a high Pearson's correlation (>0.95)
distribution of the volumetric content of water occurs, which indicates a considerable horizontal water flow adjacent to the source of the water added to the system, mainly caused by lateral hydraulic gradients in the soil (Schmalholz et al., 2004). Considering that water is heterogeneously distributed when it occupies different spaces in the soil porous matrix, and the high frequency of data collection registered by the sensors used here, it is pertinent to consider that the spatial variability within the soil profile could cause an alteration on the temporal variability recorded. Thus, soil water dynamics through the porous matrix are mainly conditioned by the soil spatial variability. Furthermore, soil spatial variability has also shown to be temporally variable, describing a complex relationship between spatial and temporal variability when soil properties are recorded with high-frequency, highlighting the importance of the scale in the interpretation of soil processes. The continuous wavelet transform for individual times series from inside and outside the lysimeter allowed to visualize significant cycles that are different between both mentioned conditions. Soil temperature at 10 and 20 cm depth described interesting differences between TLys (Figs. 3C and 4C, top row) and TField (Figs. 3D and 4D; top row) which are related to the duration of the significant cycles found, as long cyclic patterns were mainly recorded outside the lysimeter. The continuous wavelet transform for the soil water content also showed differences between θLys and θField at 60 cm depth (Fig. 5C and D; middle row). Conversely, the matric potential data showed fewer significant cycles in which differences are related with the long duration of the cyclic patterns appearing only in ΨmLys at 20 and 60 cm depth (Figs. 4C and 5C; bottom row). In the cross-wavelet analysis, highly-temporal coherent patterns are identified between the data recorded inside and outside the lysimeter at different depths at specific times durig the season (for soil temperature, soil water content and soil matric potential). In Figs. 3E, 4E and 5E, cross-wavelet analysis shows that arrows are mainly pointing to the right, which means that the correlation between both time series is in phase (or positive) (Grindsted et al., 2004). In this sense, all patterns found in this study represent a high-coherency behavior in temporal variability between lysimeter and field conditions, which means that even with an intrinsic soil spatial variability, the time series behaved in a similar way at specifics periods. Despite this high coherency, low coherency periods are also reveiled through time having different cyclic variations. Short temporal patterns seem to reflect more extreme conditions, while long temporal patterns could be related to less-intensive soil processes in a larger time scale. For this reason, soil temperature coherence peaks occurred when high temperature was recorded in summer or when high soil moisture conditions in winter were registered (Figs. 3E and 4E, top row). A similar trend occurred for the soil water content, where short peaks appeared in times of heavy winter rain (Figs. 3E, 4E and 5E; middle row). The latter developed a high contrast between dry summer periods and those with high soil water saturation during winter. These findings suggest that the intrinsic error of the sensors used in recording these changes in the soil temperature and soil water content need to be considered, as both temperature and soil matric potential were obtained through direct contact between the soil and the MPS-2 sensors (Degré et al., 2017). This is important, considering the high shrinkage capacity of volcanic ash-derived soils (Dörner et al., 2009; Dorel et al., 2000), as the intensity of wetting and drying cycles might displace the soil adjacent to these sensors. Nevertheless, the significant coherence found in the cross-wavelet analyses suggests temporal high correlations between both time series despite the caveats of the sensors used, as well as the inherent soil spatial variability. Changes in the cross-wavelet coherence patterns for the soil temperature registered at different depths could be related to the large pore volume present in these soils and their great capacity to store water (Dörner et al., 2015). The latter suggests that water is acting as a regulating factor of the thermal behavior of an Andisol, especially in long 8
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isn't stable through time and with the crosswavelet analyses performed here, in addition to the DI calculated, it was possible to identify when this correlation is low, and when it is highly significant. The latter, is a usefull tool not only to study the yearly water balance, but also to better understand specific soil processes at specific moments during the year such as Nitrogen leaching, drying and wetting cycles, amongst others. Finally, considering that one of the current challenges in agricultural systems is to improve the water use efficiency (ODEPA, 2018; Levidow et al., 2014), then understanding soil water dynamics (e.g., during dry periods) remains as a key management tool for farmers. In this regard, more research is needed in order to properly define if the measurements conducted by high-resolution lysimeters really reflect the hydrological cycle in a defined soil system at specific time periods.
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5. Conclusion While the Pearson's correlation analysis between the studied time series recorded inside and outside the lysimeter indicated high correlations, the continuous wavelet analysis showed differences in the magnitude of temporal cycles that appeared throughout the studied period between time series. Accordingly, the cross-wavelet analysis showed significant coherence between the time series only at specific periods with lower coherence during the rest of the year at different scales. The latter, which can be related to swelling and shrinkage processes that induce changes in soil water dynamics, is also shown after calculating the DI when comparing time series recorded inside and outside the lysimeter. Thus, spectral analyses are a useful approach for improving the analyses of temporal water and thermal processes in soils, as presented in volcanic ash-derived soils that have extreme physical properties. Therefore, wavelet analyses, and especially the cross-wavelet analysis, are interesting tools to understand the coherence between time series helping to identify potential temporal differences in data recorded inside and outside a field lysimeter in soils. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests Acknowledgements The authors thanks Stephan Engelhardt for lysimeter installation in the field as well as for the training and helpful advices for its use. We gratefully acknowledge the contribution of Dr. Álvaro González and Dr. Gino Montecinos for insightful statistical advice. The lead author thanks Mónica Díaz and Ruth Espinoza for key support during laboratory analyses. The lysimeter was funded by the FONDEQUIPProject 130202. References Armas-Espinel, S., Hernández-Moreno, J., Muñoz-Carpena, R., Regalado, C., 2003. Physical properties of “sorriba” — cultivated volcanic soils from Tenerife in relation to andic diagnostic parameters. Geoderma 117, 297–311. https://doi.org/10.1016/ S0016-7061(03)00130-7. Awe, G., Reichert, J., Timm, L., Wendroth, O., 2015. Temporal processes of soil water status in a sugarcane field under residue management. Plan and Soil 387, 395–411. https://doi.org/10.1007/s11104-014-2304-5. Bakar, R.A., Goulding, K.W.T., Webster, C.P., Poulton, P.R., Powlson, D.S., 1994. Estimating nitrate leaching and denitrification by simultaneous use of Br and 15 N tracers. J. Sci. Food Agric. 66, 509–519. https://doi.org/10.1002/jsfa.2740660414. Biswas, A., Si, B., 2011. Application of continuous wavelet transform in examining soil spatial variation: a review. Math. Geosci. 43, 379–396. https://doi.org/10.1007/ s11004-011-9318-9. CIREN, 2003. Estudio Agrológico X Región. Publicación CIREN N° 123. Santiago. Dec, D., Zúñiga, F., Thiers, O., Paulino, L., Valle, S., Villagra, V., Tadich, I., Horn, R., Dörner, J., 2017. Water and temperature dynamics of Aquands under different uses in
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