Scale and location dependent time stability of soil water storage in a maize cropped field

Catena 188 (2020) 104420

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Scale and location dependent time stability of soil water storage in a maize cropped field

T

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Duminda N. Vidana Gamagea, Asim Biswasb, , Ian B. Strachana a b

Department of Natural Resources Sciences, McGill University, Ste-Anne-de-Bellevue, Quebec, Canada School of Environmental Sciences, University of Guelph, Guelph, Ontario, Canada

A R T I C LE I N FO

A B S T R A C T

Keywords: Temporal stability Scales Seasonal pattern Fiber optics Transects Dry and wet seasons

Time stability of soil water storage (SWS) is the similarity of spatial patterns of soil water storage over time and is scale and location dependent due to multivariate effects of controlling factors. However, our understanding of scale and location dependency of the time stability of SWS and its seasonally dependent controls in cropped fields is inadequate. This study examined the scale and location dependent time stability of SWS at multiple depths, over different seasons in a cropped field in western Quebec, Canada. Soil water content was measured at 0.05, 0.10 and 0.20 m depths along six transects (128 locations per transect) using the actively heated fiber optic (AHFO) technique. Wavelet coherency analysis was used to examine the scale and location dependent time stability of SWS over different seasons. Results showed strong intra-seasonal time stability across all scales, locations and depths during the dry period in the summer due to a dominant control of evapotranspiration (ET). The weak inter-seasonal time stability of SWS showed the change in the dominant processes controlling the spatial patterns of SWS in different seasons. While the intra-seasonal time stability was also strong during the wet period of autumn, correlations were not significant across all scales, locations and depths, likely due to the dominant effects of smaller to medium scale processes. The results of the study clearly showed that the dominant hydrological processes controlling the time stability of SWS at different depths during a dry period in summer were different than that of a wet period in autumn. The change in the dominant hydrological processes affected the spatial scales and the locations of the similarity of the spatial patterns of SWS in the field. Therefore, the analysis outcome can be used to identify the change in the sampling domain as controlled by the hydrological processes operating at different scales and locations delivering the maximum information with minimum sampling effort.

1. Introduction

multiple spatial and temporal scales. Because SWS exhibits strong spatial and temporal variability, many sampling points are required to obtain an accurate estimate of field averaged SWS (Bell et al., 1980; Dari et al., 2019; Entin et al., 2000; Western et al., 1999). However, SWS may show distinct and consistent patterns in the distribution within a catchment or a field (Western et al., 1999) as a result of systematic or consistent spatial patterns of the controlling processes and factors. For example, factors like topography, parent material, vegetation and climate may result in regular or consistent patterns within a field (Kachanoski and de Jong, 1988). If a field is repeatedly surveyed for SWS, some locations could be consistently wetter or drier than the field averaged SWS. Vachaud et al. (1985) were among the first to show that spatial patterns of SWS changed little with time despite large variation over time and space in the field. The concept of similarity in the spatial patterns of SWS overtime was termed

Soil water storage (SWS) is a key variable affecting a number of surface and subsurface hydrological processes such as run-off, infiltration, evapotranspiration (ET) and drainage across various spatial and temporal scales (Famiglietti et al., 1998; Grayson et al., 1997; Ji et al., 2015; Yan et al., 2017). Therefore, understanding the behaviour and spatiotemporal dynamics of SWS can provide valuable insights into hydrological processes (Robinson et al., 2008; Vereecken et al., 2008; Western et al., 2002) as well as essential information for various hydrologic, climatic, and general circulation models (Famiglietti et al., 1998). SWS is controlled by a suite of environmental factors operating across multiple scales (Blöschl and Sivapalan, 1995; She et al., 2014). The complexity of the environmental factors and their multivariate effects result in strong spatial and temporal variability of SWS across

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Corresponding author. E-mail address: [email protected] (A. Biswas).

https://doi.org/10.1016/j.catena.2019.104420 Received 2 December 2018; Received in revised form 4 December 2019; Accepted 13 December 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. (a) The study area consists of three main blocks A, B and C. Blue and green rectangles within the main block are subplots (15 × 75 m) of free drainage (FD) and controlled drainage (CD). Two water houses facilitate the measurement of drainage water; (b) The fiber optic cable configuration. Fiber optic cables are installed at 0.05, 0.10 and 0.20 m depths in two free drainage sub-plots. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

‘time stability’. One of the most important applications of the time stability is to identify locations which best represent the mean areal soil moisture of an area. This strategy is advantageous because it can significantly reduce the required number of samples while maintaining a high prediction accuracy (Gao and Shao, 2012). Many studies have investigated the concept of time stability to describe the temporal dynamics of SWS across various land uses, depths, time periods and sampling schemes (Biswas, 2014b; Brocca et al., 2009; Comegna and Basile, 1994; Cosh et al., 2008; Hu et al., 2010a; Hu et al., 2009; Vachaud et al., 1985). The spatial pattern of the controlling factors is reflected in the spatial pattern of SWS (Western et al., 1998). Moreover, the spatial patterns of various controlling factors are spatial dependent (Goovaerts, 1994) and the spatial dependency of the factors makes the pattern of SWS highly scale dependent (Entin et al., 2000). Therefore, SWS can be characterized as a combination of different spatial frequency components, which are representative of different scale processes. Processes that vary rapidly in space are represented as high frequency components (small-scale processes), while those that vary slowly are represented by low frequency components (large-scale processes) (Si and Zeleke, 2005). The scale and the location of the spatial pattern of SWS will be dependent on the local and non-local controlling factors. In addition, these factors may change over time, thus the scale and the location of time stability of the SWS can also change over time. However, there remains a general paucity in studies that have examined the scale and location dependency of the time stability of SWS and this is especially true for cropped fields where there is no information on the scale and location dependent time stability of SWS in surface soils (≤20 cm). In such settings, strong evaporative (Hupet and Vanclooster (2002). and root water uptake and throughfall patterns (Fernandez-Illescas et al., 2001) have been shown to control soil water variability. In wetter soils, variability in saturated hydraulic conductivity, air entry pressure, and particle size distribution have been shown to lead to an increase in spatial variability of soil water content (Famiglietti et al., 1998; Vereecken et al., 2007a). Studies are required to examine how the scale and location of time stability of SWS change over time due to the differences in the dominating hydrological processes. This requires to analyze the time series of SWS in the scale and

location domain. Although the time stability analysis introduced by Vachaud et al. (1985) was attractive, it does not account for the spatial auto-correlation of SWS. Given that SWS is usually scale dependent (i.e. spatially auto-correlated), Entin et al. (2000); Kachanoski and de Jong (1988) used spatial coherency analysis to explain the scale dependence of time stability. However, one of the disadvantages of spatial coherency analysis is the requirement of stationarity of the SWS spatial series, which is rarely satisfied in a realistic case. Spatial coherency analysis provides time stability of SWS at different spatial scales, but it loses information on the locations of time stability. Most often, SWS spatial series are nonstationary and the variations at different scales are localized within the field. Wavelet coherency is a method that can be used to identify the scale and location-dependent similarity of the spatial patterns of soil properties (Si and Zeleke, 2005) and Biswas and Si (2013) and Biswas (2014b) have used this to examine the time stability of SWS across different seasons and depths (from 20 to 40 cm) in a hummocky landscape. Wavelet coherency based on the wavelet transform can deal with non-stationarity in the SWS spatial series and examines the correlation between spatial patterns of two variables at different scales and locations (Biswas, 2014a). Understanding the changes in scales and locations of spatial patterns of SWS through time due to the changing hydrological processes would provide information to minimize the sampling efforts while obtaining an accurate field average of SWS. For example, if the spatial patterns of SWS are similar across larger spatial scales and at many locations of a field, a small number of measurement locations will be enough to quantify the spatio-temporal variability of soil water content. Therefore, the objective of this study was to examine the scale and location dependent time stability of SWS spatial patterns at different seasons and depths in a cropped field located in southwestern Quebec, Canada.

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2. Materials and methods

Table 1 Measured soil properties at different depths in the study area.

2.1. Site description The study site was a 4.2 ha experimental cornfield located near Coteau du Lac, Quebec, Canada (Fig. 1a) approximately 60 km west of Montréal. The soil is classified as a Soulanges very fine sandy loam (Lajoie and Stobbe, 1951), has a mean depth of 0.50–0.90 m and overlies clay deposits from the Champlain Sea. The field has a flat topography, with an average slope of < 0.5% (Kaluli et al., 1999). The study site consisted of three blocks (A, B and C) and each block comprised eight subplots (15 m × 75 m). In the center of each subplot, a tile drain had been installed at 1.0 m depth. These drains discharge into two buildings located on the northern side of the field. Each block had provision for free drainage (FD) (4 sub-plots) and control drainage (CD) with sub-irrigation (4 sub-plots) (Fig. 1a). Heating and ventilation help to keep a thermally stable environment inside each building which facilitates year-round measurement of drainage volume.

Soil Property

0.05 m

0.10 m

0.20 m

Clay (%) Silt (%) Sand (%) Textural class Bulk density (Mgm−3)

9.52 ± 1.51* 41.52 ± 24* 48.96 ± 1.57* Loam 1.44 ± 0.21*

10.70 ± 0.01* 40.13 ± 2.68* 49.18 ± 2.68* Loam 1.41 ± 0.15*

10.09 ± 0.02* 39.53 ± 1.38* 50.38 ± 1.36* Loam 1.37 ± 0.12*

* Standard deviation of four replicates.

analysis, Spearman rank correlation explains the nonlinear association between two spatial series. If Ri, t is the rank of the SWS observed at location i on time t and Ri, t ' is the rank of the SWS, at the same location, but on time t ' , then the Spearman’s rank correlation coefficient, rs is calculated as n

rs = 1 −

2.2. Data collection

6∙ ∑i = 1 (Ri, t − Ri, t ' )2 n (n2 − 1)

(1)

A value of rs = 1 corresponds to identical ranks for any locations; i.e., perfect time stability of the spatial pattern between times t and t ' . The closer that rs is to 1, the more stable the spatial pattern is (Vachaud et al., 1985). Spearman's rank correlations of Transect 2 and 5 (representing the two subplots) were selected to explain the time stability of the overall spatial patterns of SWS. High-rank correlation coefficients between any two SWS series indicated a strong time stability at respective depths at the measurement scale. Scale and location-specific similarity of the spatial patterns of SWS at different depths was examined using wavelet coherency. Wavelet coherency, an advanced mathematical technique, is a measure of correlation between two spatial or temporal series at different scales and locations. In this study, we used wavelet coherency analysis to examine the correlation (similarity) of two SWS spatial series of the same transect at different times. Wavelet coherency analysis was repeated for all the individual transects to understand the time stability of SWS patterns of individual transects and depths. Theory of the wavelet transform, and wavelet coherency is well documented in the literature and a detailed description of the theory of wavelet transform can be found in Farge (1992) and Kumar and Foufoula-Georgiou (1997) while information on wavelet coherency can be found in Grinsted et al. (2004), Si and Zeleke (2005) and Biswas and Si (2011). Here, we present a summary of wavelet coherence analysis as a detailed discussion is beyond the scope of this manuscript. Wavelet coherency required the calculation of wavelet coefficients for each of the two SWS spatial series and cross-wavelet coefficients between them. The wavelet transform calculated wavelet coefficients for each of the two SWS spatial series at different scales and locations. Therefore, wavelet transform can decompose the total variation of an SWS spatial series into multiple scales and locations. The wavelet spectra (square of wavelet coefficients) of each SWS spatial series were used to represent the variance of SWS spatial series at different scales and locations along the transect. The continuous wavelet transform (CWT) of a SWS spatial series of length N (Yj , i = 1, 2, ⋯N ) with equal incremental distance δx can be defined as the convolution of Yj with the scaled and normalized wavelet (Torrence and Compo, 1998).

A distributed soil water sensing technique was developed using the actively heated fiber optics (AHFO) technique. The AHFO technique consisted of a distributed temperature sensing (DTS) system and a heating unit. The DTS system consisted of a DTS instrument (Linear Pro series model N4386B, AP Sensing, Böblingen, Germany) with a fiber optic cable (BRUsteel, Brugg Cable AG, Brugg, Switzerland) connected to it. The DTS instrument had two channels with a maximum measurement range of 4 km. The fiber optic cable consisted of a stainlesssteel loose tube containing four multimode 50 μm cores and 125 μm cladding fibers; the steel tube was armored with stainless steel strands and was further enclosed in a protective nylon jacket. The external cable diameter was 3.8 mm. A custom designed plow was used to install the fiber optic cable into 18 transects at three depths 0.05, 0.10 and 0.20 m (6 × 3) in two sub plots of Block A (Fig. 1b). The length of a transect was 73.6 ± 0.3 m (including the turns) and the distance between two cable transects was 3.75 m. The heating unit applied 240 V to each cable transect to produce heat pulses of five minutes and power intensity of 7.28 W m−1 every six hours starting from 12.00 a.m. on the morning of 22 July 2016 to 6.00 p.m. on the evening of 17 October 2016. Soil water content (SWC) was predicted by relating the temperature increment of the cable during a heat pulse (thermal response) to independent SWC measurements through calibration relationships (Sayde et al., 2014; Sayde et al., 2010; Vidana Gamage et al., 2018a; Vidana Gamage et al., 2018b). Accordingly, SWC was measured at 0.5 m sampling interval along the fiber optic cable every six hours starting 12.00 am on 22 July 2016 through to 6.00 p.m. on 17 October 2016 (344 measurements) with an accuracy of 3–4% (Vidana Gamage et al., 2018a). More details of the development of the AHFO technique and soil water measurement can be found in Vidana Gamage et al. (2018a). SWC obtained from 128 locations per transect were used in this study. SWS at each depth was calculated by multiplying the SWC with the respective depth interval (i.e. 0.05 for 0–0.05 m, 0.10 for 0.05–0.10 m, and 0.20 for 0.10–0.20 m depth). In 2016, corn (cultivar Mycogen-2R426) was planted on 8th May with nitrogen (111 kg/ha), phosphate (38 kg P2O5/ha) and potash (25 kg K2O/ha) applied; harvest was 20th October. The seasonal rainfall was 542 mm (from May to October) and was very similar to the 30-year average (1981–2010) seasonal rainfall of 564 mm. Intact soil core samples from the respective depths were collected for soil bulk density and texture determination (Table 1).

WiY (s ) =

δx s

N

∑ Yjψ ⎡ (j − 1) i=1

⎣

δx ⎤ s ⎦

(2)

where ψ [ ] is, the mother wavelet function and s represents scale. Wavelet coefficients, WiY (s ) , are expressed as a + ib where a and b are the real and imaginary components of WiY (s ) , respectively. For the polar form of complex numbers, WiY (s )= |WiY (s )| (cosθ + isinθ), where a θ = arctan b ,which is called the phase or argument of WiY (s ) (Briggs

2.3. Data analysis Overall time stability of SWS spatial patterns was assessed using Spearman's rank correlation analysis. Unlike Pearson correlation

et al., 2005). The wavelet power spectrum is defined as |WiY (s )|2 and the

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local phase can be defined from WiY (s ) . In extracting local phase information, Morlet wavelet function is commonly used in CWT. Morlet wavelet can be represented as (Grinsted et al., 2004).

ψ (η) = π −1/4eiϖη − 0.5η

2

coherency at that scale and location is not significantly different from the background red noise, hence, we accept the null hypothesis. Otherwise, the wavelet coherency is significantly different from the background red noise. A wavelet coherency graph is a colour contour graph with locations in X-axis and scales in Y-axis and it shows scale-dependent correlation coefficients at different locations. The colour bar indicated the strength of correlation (red is the highest) while the direction of arrows showed the phase or type of the correlation with right being positive and left being negative. We present only the wavelet coherence graphs which represented scale-dependent correlations between two SWS spatial series measured on two dates of the transects at depths. Intra-seasonal and inter-seasonal scale and location dependent time stability of SWS are discussed using the wavelet coherency graphs. In this study, correlation coefficients were calculated for 54 scales (between 1 and 21 m) at 128 locations along the transect. Therefore, the total number of wavelet coherency was 6912. Based on the dominant coherencies, the scales were classified into four groups; fine scales (< 2 m), small scales (2–4 m), medium scales (4–10 m) and large scales (> 10 m). It should be noted that the separation into different scales was based on the size of the study plots. The coherency of the spatial patterns of SWS between two dates was also assessed by mean wavelet coherence (MWC) at respective scales (< 2 m, 2–4 m, 4–10 m, > 10 m) and all scales together. Further, the percent area of significant coherence (PASC) relative to the whole wavelet scale–location domain was also calculated at respective scales. The SWS spatial series measured on 22 July was compared with 11 August, 20 September and 15 October 2016 to examine the scale and location dependent time stability between seasons (inter-seasonal). Similarly, intra-seasonal time stability was assessed using the SWS spatial series measured on 22 and 11 August and 1 and 15 October, respectively. The wavelet coherency analysis was performed using the MATLAB code (The MathWorks Inc., Natrick, MA) written by Grinsted et al. (2004) and is freely available at http://noc.ac. uk/using-science/crosswavelet-wavelet-coherence. Surface plots of SWC were generated using the spatial series of SWC measured on 22 July, 11 August, 20 September, 01 October and 15 October to explain the spatial patterning of soil water over time at depths. In addition to soil water, rainfall (from a tipping bucket gauge) and evapotranspiration (ET; from eddy covariance) were measured in situ. The drainage volume from subplots was measured using a facility available in water house I (Fig. 1b).

(3)

where ω is dimensionless frequency and η is dimensionless space (η = s / x ). The Morlet wavelet (ω = 6) is good for feature extraction because it provides a good balance between space and frequency localization. The wavelet can be stretched in space ( x ) by varying its scale (s ) (Si and Zeleke, 2005). The cross-wavelet transform provided the covariance between two SWS spatial series at multiple scales and locations (cross wavelet spectra) (Biswas et al., 2008; Si and Zeleke, 2005). The cross-wavelet power spectrum between two SWS spatial series measured in two different dates Y and Z can be defined as

|WiYZ (s )| = |WiY (s ) WiZ¯ (s )| where WiY and Z . W¯iZ

(4)

WiZ

and are the wavelet coefficients of the spatial series Y is the complex conjugate of WiY , the wavelet coefficients for SWS of the measurement series Z . While the cross-wavelet spectra represent the covariance at a scale and location, the wavelet coherency is the correlation between two variables at each scale and location. Wavelet coherency between two SWS series can be defined as (Torrence and Webster, 1999)

Ri2 (s ) =

S (s−1

|S (s−1WiYZ (s ))|2 |WiY (s )|2 ) S (s−1 |WiZ (s )|2 )

(5)

where s is a smoothing operator and can be written as:

S (W ) = Sscale (Sspace (W (s, τ )))

(6)

where τ denotes the location and Sscale and Sspace denote the smoothing along the wavelet scale axis and the spatial domain, respectively (Si and Zeleke, 2005). The smoothing function is the normalized real Morlet wavelet and has a similar footprint as the Morlet wavelet:

1 τ2 exp ⎛− 2 ⎞ s 2π ⎝ 2s ⎠ ⎜

⎟

(7)

Therefore, the smoothing along locations can be written as: N

Sspace (W (s, τ )) =

∑ ⎛W (s, τ ) ∙ ⎜

k=1

⎝

1 (τ − xk )2 ⎞ ⎞ exp ⎛− ⎟ |s 2s 2 ⎠ ⎠ s 2π ⎝ ⎜

⎟

(8) 3. Results and discussion

The Fourier transform of Eq. (7) will be exp (−2s 2ω2) , where ω is the frequency. Therefore, according to the convolution theorem, the Eq. (8) can be implemented using Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) and is written as

Sspace (W (s, x )) = IFFT (FFT (W (s, τ ))(exp (−2∙s 2ω2)))

3.1. Temporal evolution of spatial patterns of soil water High ET and low rainfall between 22 July and 11 August resulted in a low total SWS (temporal mean SWS = 67 mm) within 0–0.20 m depth (Fig. 2). The difference between the maximum and minimum SWS was smaller (e.g. 4 mm) and attributed to low rainfall during the period. Although two alternate drying and wetting periods were observed between 11 August and 20 September, the total SWS started to increase at the high rainfall and reached a temporal average of 92 mm (Fig. 2). The difference between the maximum and minimum SWS during the period from 11 August to 20 September was higher (33 mm) than during the period from 22 July to 11 August (4 mm) and the larger difference indicated more variation in SWS. A lack of rainfall during the period from 21 September to 02 October led to a decrease in total SWS (temporal mean total SWS = 84 mm). However, the total SWS during the above period continued to be higher than the total SWS observed during the early dry period of summer (22 July–11 August). This indicated a smaller loss of water from the soil due to lower crop uptake compared to the early summer. All three soil layers showed a weaker spatial variation in SWC with relatively dry (VWC < 30%) conditions except some localized areas at 20 and 60 m locations along the transect on 22 July. These spatial

(9)

The smoothing along scales can be written as:

Sscale (W (sk , x )) =

1 2m + 1

k+m

∑ j=k−m

(Sspace (W (sj, x ))Π(0.6sj ))|x (10)

where Π is the rectangle function, |x implies at a fixed x value and j is the index for the scales. The factor of 0.6is the empirically determined scale decorrelation length for the Morlet wavelet (Si and Zeleke, 2005; Torrence and Compo, 1998). In significant testing, usually wavelet coherency measured SWS is compared with an assumed background. Accordingly, the null hypothesis is that there is no significant difference between wavelet coherency measured SWS and the assumed background. Gaussian white and red noises or permutation test can be used in significant testing of wavelet coherency (Pardo-Igúzquiza and Rodrı́guez-Tovar, 2000). Because the soil properties are generally autocorrelated, the red noise was used for the significant testing. When the wavelet coherency between two measured SWS series at a scale and location falls within the 95% confidence interval, the wavelet 4

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Fig. 2. Variation of daily rainfall (RF), evapotranspiration (ET), drainage and total soil water storage (0–0.20 m depth) during the experimental period from 22 July to 17 October. ET data is only available until early September. The two breaks in the SWS curve correspond to two days where soil water content data is unavailable due to power failure.

corresponding depths (Fig. 3). As expected, results indicated that the overall spatial patterns were more similar among the SWS series measured close in time or within a season (intra-season) (e.g. 22 July and 11 August) than among the SWS series measured further away in time or in different seasons (inter-season) (e.g. 22 July and 20 September) (Biswas and Si, 2013). 3.2. Time stability of overall spatial patterns Intra-seasonal time stability of transects 2 & 5 was stronger than that of the inter-seasonal time stability at all depths. For example, correlation coefficients between 22 July and 11 August (summer) and 01 October and 15 October (autumn) were 0.93, and 0.86 (transect 2) and 0.89, and 0.90 (transect 5) at 0.05 m depth (Fig. 4a and d). The strengths of correlation coefficients also increased across depths (Fig. 4a–c, d–f) which indicated a higher persistence of spatial patterns of SWS in deeper layers than the surface (0.05 m) within the same season. Inter-seasonal time stability was also stronger at 0.05 and 0.10 m depths but not at 0.20 m depth. For example, correlation coefficients between 22 July and 20 September and 22 July and 01 October ranged from 0.73 to 0.55 and from 0.78 to 0.57, respectively. However, the strength of the correlation was lower compared to that of intra-seasonal correlation. On the other hand, non-significant correlations were observed between the SWS spatial series measured in early summer (22 July) and early (20 September) and late (01 October) autumn for the 0.20 m depth (Fig. 4 c and f). Overall, the correlation coefficients gradually decreased with the increasing time difference between measurements in both transects. 3.3. Scale and location dependent time stability Fig. 3. Spatial patterns of volumetric soil water content at measurement times: 22 July, 11 August, 20 September, 01 October and 15 October at 0.05, 0.10 and 0.20 m depths. Y distance indicates the distance along a transect and X distance shows the distance increment (3.75 m) between transects.

Wavelet coherency plots between 22 July and11 August (dry period of summer) and 01 and 15 October (wet period of autumn) represented the intra-seasonal time stability while between 22 July (dry period of summer) and 20 September (early autumn) and 01 October (late autumn) explained the inter-seasonal time stability. The scale and location dependent intra-seasonal time stability differed from the inter-seasonal time stability. During the dry period of summer, significant correlations (Red shades) between 22 July and 11 August were observed at larger scales (> 10 m) and many locations across all the transects (Figs. 5–10). Moreover, the strength of the correlation was higher as the depth increased. For example, MWC increased with the depth at all scales along Transects 2 and 5. (Table 2). Moreover, the magnitude of correlations at finer scale (< 2 m) was lower at 0.05 m depth compared to that of 0.10 and 0.20 m depths. MWC at finer scale (< 2 m) was lower than that of the other scales (2–4, 4–0 and > 10 m) also for Transects 2 and 5

patterns of SWC continued to be similar on 11 August at corresponding depths (Fig. 3). Unlike 22 July and 11 August, substantial variations in the spatial patterns of SWC were observed at all depths on 20 September. Localized drier areas of SWS were observed in the start, mid and end locations (Y distance) along the transects at 0.10 and 0.20 m depths (Fig. 3). All layers progressively became drier due to the low rainfall between 21 September and 02 October. Localized drier areas observed on 20 September were persistent and became more pronounced during the above period. Interestingly, the spatial patterns of SWC observed on 15 October were similar to those on 20 September at 5

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Fig. 4. Correlation plots showing the Spearman rank correlation coefficients between the SWS measurements series of 22 July, 28 July, 11 August, 20 September, 01 October and 15 October. (a–c) and (d–f) represent the 0.05 m, 0.10 and 0.20 m depths of transect 2 and 5, respectively. The color scale indicates the strength of the correlation. Dark red color indicates a strong negative correlation (r = −1) and dark blue color indicates a strong positive correlation (r = 1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 1. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of the correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation. 6

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Fig. 6. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 2. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of the correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation.

Fig. 7. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 3. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation. 7

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Fig. 8. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 4. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation.

Fig. 9. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 5. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of the correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation. 8

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Fig. 10. Wavelet coherency between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at 0–0.05, 0.05–0.10 and 0.10–0.20 m depths of Transect 6. The X axis indicates location along the transect (m), the Y axis indicates scale (m), the color scale indicates the strength of the correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation.

(Table 2). PASC also showed a similar trend at finer scale for 0.05 m depth compared that of the 0.10 and 0.20 m depths. Strong and significant correlations of SWS spatial series were observed between 01 and 15 October. However, correlations were not significant across all the scales and locations compared to that of the SWS measured during the dry period of summer (22 July and 11 August). A loss of time stability at scales < 8 m was noticeable particularly at 0.10 and 0.20 m depths (Figs. 5–10). Though the MWC and PASC increased with depth and scale (Table 2), differences in the magnitudes of the correlations were observed as compared to that during the dry period of summer (Figs. 5–10). Moreover, no significant correlations at medium scales (8–16 m) at the beginning and end locations of Transects 5 and 6 were observed at 0.10 and 0.20 m depths (Figs. 9 and 10). Overall, inter-seasonal correlations (22 July–20 September and 22

July–01 October) were not strong as compared to that of intra-seasonal (22 July–11 August and 01 October–15 October). For example, the magnitudes of correlations between 22 July and 20 September were low at all scales and depths especially for Transects 1 to 3 (Figs. 5–7). The maximum MWC and PASC of transect 2 at all scales were 0.41 and 13.83%, respectively (Table 2). However, the magnitude and the area representing the significant correlations of Transects 4 to 6 were relatively higher, particularly at 0.05 m depth at 4–8 m scales (Figs. 8–10). For example, MWC and PASC of Transect 5 were 0.66 and 15.51%, respectively at 4–10 m scales (Table 3). However, the deepest layer (0.2 m) showed no significant correlations across all the locations. Correlations of SWS spatial series between 22 July and 01 October showed almost similar patterns to that of between 22 July and 20 September. For example, the surface layer (0.05 m) of Transect 5 had

Table 2 Mean wavelet coherence and percent area of significant coherence between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at depths of transect 2 (T2). T2

22 July–28 July

22 July–11 Aug

22 July–20 Sep

MWC

D1

D2

D3

D1

D2

D3

D1

D2

D3

D1

D2

D3

D1

D2

D3

<2 m 2–4 m 4–10 m > 10 m All

0.37 0.62 0.76 0.95 0.69

0.70 0.83 0.93 0.96 0.86

0.72 0.71 0.96 0.97 0.85

0.39 0.63 0.72 0.85 0.66

0.58 0.77 0.92 0.88 0.80

0.74 0.76 0.93 0.98 0.86

0.23 0.35 0.39 0.34 0.33

0.27 0.37 0.46 0.20 0.33

0.38 0.49 0.45 0.30 0.41

0.34 0.44 0.59 0.55 0.49

0.32 0.49 0.50 0.18 0.38

0.40 0.44 0.55 0.32 0.43

0.37 0.57 0.87 0.91 0.70

0.54 0.77 0.77 0.95 0.76

0.44 0.70 0.84 0.95 0.74

PASC (%) <2 m 2–4 m 4–10 m > 10 m All

1.70 12.24 21.24 24.07 59.42

12.66 18.79 27.82 24.07 83.35

24.07 29.63 14.86 13.53 82.09

2.50 9.70 19.59 24.07 55.93

9.64 17.43 27.56 19.78 74.41

13.17 15.51 29.43 24.07 82.18

0.36 2.04 0.90 0.00 3.30

0.42 3.31 2.43 0.65 6.81

0.69 6.57 6.57 0.00 13.83

1.04 3.96 8.87 0.68 14.55

1.26 6.25 4.20 0.22 11.92

1.85 2.60 7.49 0.00 11.95

1.79 7.94 28.73 23.51 61.98

5.92 18.97 22.03 24.07 70.99

3.56 14.12 27.45 24.07 69.20

D1, D2, and D3 are 0–0.05, 0.05–0.10 and 0.10–0.20 m depths. 9

22 July–01 Oct

01 Oct–15 Oct

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Table 3 Mean wavelet coherence and the percent area of significant coherence between 22 July and 11 August, 22 July and 20 September, 22 July and 01 October and 01 October and 15 October at depths of Transect 5. T5

22 July–28 July

22 July–11 Aug

22 July–20 Sep

22 July–01 Oct

01 Oct–15 Oct

MWC

D1

D2

D3

D1

D2

D3

D1

D2

D3

D1

D2

D3

D1

D2

D3

<2 m 2–4 m 4–10 m > 10 m All

0.41 0.69 0.78 0.74 0.67

0.66 0.81 0.93 0.98 0.85

0.90 0.97 0.95 0.96 0.95

0.51 0.67 0.78 0.87 0.71

0.64 0.74 0.88 0.65 0.74

0.81 0.84 0.89 0.96 0.88

0.27 0.39 0.66 0.47 0.46

0.27 0.24 0.48 0.52 0.38

0.32 0.37 0.30 0.30 0.32

0.37 0.56 0.58 0.48 0.50

0.30 0.33 0.45 0.50 0.40

0.33 0.37 0.40 0.43 0.38

0.52 0.73 0.74 0.72 0.68

0.46 0.52 0.80 0.92 0.69

0.52 0.73 0.74 0.72 0.68

PASC (%) <2 m 2–4 m 4–10 m > 10 m All

3.50 14.11 19.78 8.33 45.72

10.72 18.61 28.76 24.07 82.16

19.42 24.07 29.63 24.07 97.19

4.89 13.93 20.95 24.07 63.85

10.71 15.52 27.53 6.76 60.52

16.31 20.43 26.48 24.07 87.28

0.95 3.59 15.51 4.22 24.28

0.17 0.04 5.92 5.19 11.33

2.05 1.92 2.00 0.49 6.47

2.56 8.25 11.37 2.52 24.70

1.23 0.09 0.43 6.29 8.04

0.91 2.21 4.77 2.40 10.30

4.59 15.36 18.32 13.04 51.30

3.72 5.77 21.11 24.07 54.67

4.59 15.36 18.32 13.04 51.30

stability of the SWS spatial patterns at 0.10 and 0.20 m depths than the surface layer (0.05 m) may be due to the minimal effect of environmental forcing such as ET on the deeper layers. Generally the surface layers are susceptible to changes in any meteorological condition such as solar radiation, rainfall and wind (Hu et al., 2010b) and show stronger variability. Significant correlations between the SWS spatial series across all spatial scales, locations and depths during the dry period of summer indicated that the SWS values could be similar across larger spatial domains in the field as controlled by the strong ET demand. The loss of time stability of SWS spatial patterns between summer and autumn indicated the changes in the processes controlling them (Figs. 5–7). ET gradually decreased from August to September, while rainfall events caused to increase in the total SWS (maximum SWS = 103 mm). Under wet conditions, spatial patterns of soil water are mainly controlled by the variations in hydraulic conductivity and porosity (Famiglietti et al., 1998; Vereecken et al., 2007b). Wavelet coherency between 22 July and 20 September and 22 July and 01 October (transect 1 to 3) indicated a loss of time stability particularly at 0.20 m depth (Figs. 5–7). This indicated the occurrence of significant changes in the processes controlling the spatial patterns of SWS at deeper layers compared to that of in the surface layer (0.05 m) during the wet period of autumn. The loss of time stability at scales < 8 m and 8–16 m between the 01 October and 15 October indicated that the operating processes were different to that of the dry period of summer particularly in deeper layers (0.10 and 0.20 m depths). Also, poorer correlations across all the scales, locations and depths during the autumn compared to that of the summer indicated less similarity of SWS values across larger spatial domain in the field. Total SWS on 01 October was 83 mm, and it reached a maximum of 103 mm thereafter, attributed from high rainfall received during the period from 03 October to15 October. The changes in the controlling processes with an increase in soil wetness likely led to the loss of intra-seasonal time stability during the recharge period. Interestingly, peak drainage flow occurred during the time between 01 October and 15 October (Fig. 2). Therefore, loss of small to medium scale time stability could be attributed to the variations in the soil porosity and preferential drainage occurred during the recharge period (wet period of the autumn). Localized drying areas along the transects on 15 October, at 0.10 and 0.20 m depths were also visible (Fig. 3). These localized drying patterns could be due to the preferential flow patterns from the tile drains in the studied plots.

MWC and PASC of 0.58 and 11.37% at 4–10 m scales (Table 3). Strong correlations indicated strong time stability while weak correlations showed a loss of time stability or a change in spatial patterns in SWS resulted from a change in the controlling processes at different scales, locations and, depths (Biswas and Si, 2013). Both rank correlation and wavelet coherency analysis indicated strong intra-seasonal time stability of SWS which can be due to similar processes operating within a particular season (Martínez-Fernández and Ceballos, 2005). The time stability of SWS spatial patterns could also depend on the wet or dry states of the soil due to the different processes controlling the spatial patterns in wet and dry states. (Gomez-Plaza et al., 2000; Grayson et al., 1997). During summer, high water demand from ET generally exceeded the supply from rainfall (Fig. 2). High crop water uptake generally resulted in dry soil conditions in all three layers. When the soil water decreased to a threshold level (between field capacity and permanent wilting point), the dominant processes controlling the spatial patterns of SWS switches from drainage to evapotranspiration (Pan and Peters-Lidard, 2008). The wavelet coherency between the total SWS (0.20 m) and the ET showed significant correlations (red shades) during the initial 30 days, particularly at temporal scales of 16 days (Fig. 11). This indicated that ET was a dominant process influencing the spatial patterns of SWS during the dry period of summer. An increase in MWC and PASC with the increase in scale (i.e. > 10 m) indicated that ET operated at large spatial scales during the dry period of summer. Also, stronger time

Fig. 11. Wavelet coherency between the total soil water storage and evapotranspiration. The X axis indicates the number of days since the measurement started (i.e. 22 July) and the Y axis indicates temporal scale (days), the color scale indicates the strength of correlation, the black solid line indicates 95% significance level and the direction of the arrow indicates the type of correlation.

4. Conclusions This paper examined the scale and location dependent time stability of SWS at multiple depths in a cropped field during a growing season. The results of the study clearly showed that the dominant hydrological 10

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processes controlling the time stability of SWS at different depths during the dry period in summer were different from those controlling the time stability of SWS during the wet period in autumn. The change in the dominance of the operating processes likely affected the spatial scales and the locations of the similarity of the spatial patterns of SWS in the field. Therefore, the results can be used to identify the change in the sampling domain as controlled by the hydrological processes operating at different scales and locations delivering the maximum information with minimum sampling effort. For example, spatial patterns of SWS were more stable and similar across all scales and many locations along the transects during the dry period of summer than the wet period of autumn. Therefore, it may require a small number of measurement points during the dry period of summer while a relatively large number of measurement points during the wet period of autumn to obtain an accurate field average of SWS. Future studies should compare the sparse and dense sampling strategies to estimate an accurate field average of SWS during dry and wet periods of different seasons.

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Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This project was funded by grants to Asim Biswas from FRQNT (Fonds de recherche du Québec – Nature et technologies, 2015-NC180817) and NSERC (Natural Sciences and Engineering Research Council of Canada, RGPIN-2014-04100). The authors would also like to thank Guy Vincent, Maxime Leclerc and Yakun Zang, Kelly Nugent, Scott MacDonald, Tracy Rankin, Mi Lin and Rasika Burghate for assistance in data collection, sensor cable installation and retrieval in the field. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.catena.2019.104420. References Bell, K.R., Blanchard, B.J., Schmugge, T.J., Witczak, M.W., 1980. Analysis of surface moisture variations within large-field sites. Water Resour. Res. 16, 796–810. Biswas, A., 2014a. Landscape characteristics influence the spatial pattern of soil water storage: similarity over times and at depths. Catena 116, 68–77. Biswas, A., 2014b. Season- and depth-dependent time stability for characterising representative monitoring locations of soil water storage in a hummocky landscape. Catena 116, 38–50. Biswas, A., Si, B.C., 2011. Application of continuous wavelet transform in examining soil spatial variation: a review. Math. Geosci. 43, 379–396. Biswas, A., Si, B.C., 2013. Scale Dependence and Time Stability of Nonstationary Soil Water Storage in a Hummocky Landscape Using. Global Wavelet Coherency. Biswas, A., Si, B.C., Walley, F.L., 2008. Spatial relationship between o15N and elevation in agricultural landscapes. Nonlinear Processes Geophys. 15, 397-n/a. Blöschl, G., Sivapalan, M., 1995. Scale issues in hydrological modelling:a review. Hydrol. Process. 9, 251–290. Briggs, C.M., Breiner, J., Graham, R., 2005. Contributions of Pinus Ponderosa Charcoal to Soil Chemical and Physical Properties. The ASACSSA-SSSA International Annual Meetings Salt Lake City, USA. Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2009. Soil moisture temporal stability over experimental areas in Central Italy. Geoderma 148, 364–374. Comegna, V., Basile, A., 1994. Temporal stability of spatial patterns of soil water storage in a cultivated Vesuvian soil. Geoderma 62, 299–310. Cosh, M.H., Jackson, T.J., Moran, S., Bindlish, R., 2008. Temporal persistence and stability of surface soil moisture in a semi-arid watershed. Remote Sens. Environ. 112, 304–313. Dari, J., Morbidelli, R., Saltalippi, C., Massari, C., Brocca, L., 2019. Spatial-temporal variability of soil moisture: addressing the monitoring at the catchment scale. J. Hydrol. 570, 436–444. Entin, J.K., et al., 2000. Temporal and spatial scales of observed soil moisture variations in the extratropics. J. Geophys. Res.: Atmos. 105, 11865–11877. Famiglietti, J.S., Rudnicki, J.W., Rodell, M., 1998. Variability in surface moisture content along a hillslope transect: Rattlesnake Hill, Texas. J. Hydrol. 210, 259–281.

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