# Field Calibration of TDR to Assess the Soil Moisture of Drained Peatland Surface Layers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}cm

^{−3}.

## 1. Introduction

^{2}and 46% of this area is classified as peatland where the peat forming process was stopped [8]. Stopping the forming process was associated with artificial land drainage in response to agricultural, forestry and horticultural demands [9]. The great majority of drained peatland is used as meadow and pasture, and only a limited percent as arable land [10]. Drainage of peat soils leads to the formation of a new organic soil material in the surface layers known as muck (moorsh), which has a granular structure where the original plant remains are not recognizable and contains more mineral matter than peat [11].

_{2}emissions [15]. A literature review shows that there are three major factors used to quantify the amount of CO

_{2}emission from drained peat soils, i.e., soil temperature [16,17,18], soil moisture content status [17,19,20] and water table depth [21]. The increase of soil temperature and optimal soil moisture status create favorable conditions for the increase of CO

_{2}efflux. Soil moisture content is one of the main hydrological factors to be assessed in the calibration and validation of activities in global soil moisture products (spaceborne), as well as in order to increase the understanding of water, energy and carbon flux exchanges at the active surface on a local scale [22].

_{a}) of the medium [25]. The attractiveness of the TDR method results from the simple non-destructive and quick measurement of the dielectric constant which can be transformed using the calibration curve to the volumetric soil moisture content. However, many TDR probes on the market are often not properly tested for the high dielectric permittivity values of peat soils and that the algorithms for the TDR waveform analysis might fail in that range [26]. The relationship between the measured K

_{a}and moisture content can be derived either by using the dielectric mixing model [27,28] or by empirical equations [25]. In peat soils, in most cases, the calibration curves are empirical equations obtained by fitting a mathematical model of the measured dielectric constant to the gravimetrically measured soil moisture content data. The majority of calibration equations for peat soils are third-order polynomials with respect to the raw measured dielectric constant [22,23,29,30,31,32] or its transformed form as a square root [33]. The polynomial calibration equations are very flexible and more efficient than the manufacturer default relationships (determined by developers of the TDR measurement systems) but they are appropriate as a site- or soil-specific equations which enables improved accuracy of soil moisture content estimation [34]. A more general calibration equation for the organic materials can also be expressed in the form of a nonlinear relationship between the soil moisture content and the dielectric constant [22,35,36]. Another popular group of empirical equations constitutes the linear relationship between the soil moisture content and the square root of the dielectric constant. Malicki et al. [37] developed an empirical model which incorporates soil bulk density as second covariate, in addition to the Ka

^{0.5}, thereby improving the moisture content predictions for a broad range of soils, also including organic soils. Oleszczuk et al. [38], using a similar data analysis technique, obtained a general empirical model describing soil moisture content as a function of the dielectric constant, bulk density and ash content for different top organic soil layers from the Biebrza River Valley. However, this type of calibration procedure, apart from the dielectric constant measurements, requires extra knowledge regarding other soil properties in order to predict its moisture content status. Despite the large number of calibration equations for determination of the soil moisture content using TDR, they were developed mostly under laboratory conditions and their use is limited to specific sites or dedicated soils.

_{a}values can be improved at the site scale by introducing the bioindicators describing the biodiversity of plant species and the state of habitats into the calibration equation.

## 2. Materials and Methods

#### 2.1. Study Area and Site Characteristics

#### 2.2. Field Measurements and Basic Soil Properties

^{3}volume), coaxially inserted in the place of K

_{a}measurements. The collected soil cores were sealed with a rubber cover at both ends and packed into thermal plastic bags to avoid water loss through evaporation and stored in a cooler at 4 °C until laboratory tests were conducted. In laboratory conditions, each soil sample was weighed and was oven dried at 105 °C for 24 h after air drying. Soil bulk density was calculated by dividing the oven-dry sample weight by the core volume. Gravimetric moisture content was calculated for each sample and then converted to volumetric moisture content by multiplying the gravimetric moisture content by soil bulk density. In total, 278 measurements regarding the soil moisture content, soil bulk density and dielectric constants were obtained (the measurement data for each site are shown in Table 1).

_{p}) of the analyzed upper layers of six soil profiles was calculated assuming that an increase of ash content of about 1% causes an increase of the ρ

_{p}parameter of about 0.011 g cm

^{−3}with respect to the nominal value equal to 1.451 g cm

^{−3}[60,61].

#### 2.3. Soil Water Retention Characteristics

^{3}) were collected in three replications from the top layers (at depth 7.5 cm) of the six studied peat-muck soil profiles in order to determine soil water retention characteristics (pF curves). The moisture content values in the range of predefined matric potential from 0.4 to 2 pF were determined on a sand table, whereas the amount of water retained at pF: 2.2, 2.5, 2.7, 3.4 and 4.2 was measured in pressure chambers [62]. The pF curves for each soil profile are represented in this study by average values of moisture content at nine predefined soil matric potentials.

#### 2.4. Botanical Composition of Plant Cover

^{2}, each located next to the place of the soil property measurements. The biomass samples were stored in paper bags and then the dry weight of each species was determined in laboratory conditions. Based on the gravimetric measurements, the mass percentage of the particular species as a total dry mass was calculated. The list of 70 vascular species in total was made for all selected sites can be seen in Table S1. The floristic type of the meadow community was determined based on the dominant species, which accounted for at least 30% of the biomass. “Pure” types (domination of one species), “mixed” types (predomination of two species together constituting at least 30% of the biomass) were specified. To characterize the habitat conditions for all meadow communities, the weighted means of Ellenberg’s indices [50,52] were calculated. The proportion (%) of vascular plants in biomass samples was multiplied by the Ellenberg index of this species, i.e., light—L (1–9); soil moisture—F (1–12); soil acidity—R (1–9); soil nitrogen—N (1–9) according to [45], and then the results of multiplication for all species of plant community were summed. The value obtained was divided by 100 and, in this way, the values of individual features for the whole community were obtained. Additionally, the species composition of each site was characterized using the biodiversity Shannon–Weiner’s index [63,64]. The calculation results of the Ellenberg indices (L, F, R, N) and Shannon–Weiner’s indices (H’) are presented in the Supplementary Materials shown in Table S2.

#### 2.5. Data Analysis

_{v}) and the dielectric constant (K

_{a}) for all sites and the whole range of the analyzed dataset. This type of regression is a piecewise linear model, which describes the relationship between response and explanatory variables and is represented by at least two straight lines crossed in a breakpoint [65]. In this study, it was assumed that the established model is continuous, including the breakpoints (Ψ). When there is only one breakpoint, the simplest piecewise regression model can be written as follows [66]:

_{0}is intercept, β

_{1}and β

_{1}+ β

_{2}are the slopes of the segmented lines (β

_{2}can be interpreted as a difference in slopes), and e values are assumed to be independent errors with a zero mean and constant variance. The normality of e values has been tested using the Shapiro–Wilk test and the p-value statistic. The iterative techniques included in the R segmented package [67], was applied to identify the breakpoint (Ψ) and to fit the regression model into the collected data. The broken-line model (segmented regression) was used to establish the general broken-line model (GBLM) and site-specific broken-line model (SSBLM).

_{r}value (SSM-R). The calculations were made using the RWeka package [69]. For this purpose, we used the M5Rules algorithm [70,71] belonging to the regression tree method. The basic assumption of this type of algorithm is dividing the entire set of samples by selecting one independent input variable among all and then performing the binary split into at least two child sets, which should increase the purity of the data compared with its single parent node [72]. The nodes which cannot be further partitioned are called leaves. After growing the tree and the pruning process (removing the leaf with insignificant influence on purity) the linear regression can be fitted for the growing leaf in order to improve the fit of the model [70,73]. The tree construction process, as described above, provides an approximation of function specific for each final node which can lead to sharp discontinuities occurring between adjacent leaves and requires smoothing of the tree after the full set of rules has been produced [74]. During the learning process, we applied a cross-validation scheme [75] to establish the SSM-D model. We used all six possible different combinations of the data from five sites for the training of the M5Rules algorithm, the remaining dataset was used for testing. Each analyzed dataset included continuous variables, i.e., soil moisture content (θ

_{v}) and dielectric constant (K

_{a}) measured for all investigated sites, as well as categorical covariates represented by bioindices (F, L, N, R, H’). The M5Rules algorithm was run six times to fit the data and the best SSM-D model was selected using the RMSE value for testing of the data. After that the SSM-D was iteratively smoothed and the threshold value ψ

_{r}and θ

_{vr}was determined, finally resulting in SSM-R model determination.

## 3. Results and Discussion

#### 3.1. Soil Properties and Botanical Composition of Plant Cover

_{b}) in the upper layers were comparable with peat soils agriculturally cultivated in England [76], Sweden [77], Norway [78] and Germany [79]. The ash content in the analyzed mucky soil was low and this results from the lack of temporary river flood conditions on the selected sites during moorsh soil development. The average porosity of the studied moorsh horizons was lower, approximately 0.05 to 0.10 cm

^{3}cm

^{−3}compared to the underlying original peat deposits [40,42,61].

^{3}cm

^{−3}, whereas in the study of [42], in the peat soils, the amount of gravitational water was higher and equal to approximately 0.34 cm

^{3}cm

^{−3}. However, the soil moisture content at the permanent wilting point (pF = 4.2) of the studied mucky layers was relatively high and remains in the same range as in the peat soils [42]. The obtained results of hydro-physical properties of the mucky layers show an increment of mineral compounds in the soil matrix compared to the peat soils, which indicates that the structure of this organic material dramatically changed due to drainage [80] and cultivation practice, and evolved from fibrous into a grainy or humic structure [61].

#### 3.2. Analysis of Existing Relationships between Dielectric Constant and Soil Moisture Content in Organic Soils

^{3}cm

^{−3}. Despite the reasonably good results of the RMSE statistic, the mentioned equations gave a satisfactory prediction of soil moisture content at different ranges of dielectric constant changes. The most appropriate literature model P4 enabled a reasonably good approximation of the soil moisture content in the range of dielectric constant between 10 and 20. The highest overestimation of soil moisture content (of about 0.15 cm

^{3}cm

^{−3}) occurred when the dielectric constant was equal to 30. Figure 2 also shows the measured data of the soil moisture content and the dielectric constant and their fitting using the logarithmic model (NL_own) The following form of equation was obtained:

^{3}cm

^{−3}) in comparison to the P4 and PS2 models. However, Equation (4) overestimated the moisture content by as much as 0.15 cm

^{3}cm

^{−3}in the middle range of the dielectric constant changes.

#### 3.3. General and Site-Specific Relationships between Dielectric Constant and Soil Moisture Content

_{v}and K

_{a}). For this purpose, the segmented linear regression was applied and the model parameters (Equations (1) and (3)) were estimated iteratively [67]. The results of the statistical computation indicated that the established continuous general broken-line model (GBLM) included one threshold parameter (Ψ), and can be written as:

_{a}equal to 31.49 (Figure 3). The 95% confidence interval for this parameter was wide and ranged from 27.22 to 35.76 (Figure 3). Residuals from the model (Equations (5) and (6), or (5) and (7)) were normally distributed around the average which was confirmed by the Shapiro–Wilk testing statistic (W = 0.9919) and the p-value (0.1302). The RMSE value for the GBLM equations equals to 0.0405 cm

^{3}cm

^{−3}and is essentially lower than the estimates determined for the equations indicated in Table 4. This type of broken-line relationship is often used to assess the threshold value where the effect of the covariate changes. In the fields of hydrology and soil hydrology, the piecewise linear regressions (PLR) and the determined threshold values are used to explain the influence of the vegetation cover fraction on the reduction of runoff [84] and the erodibility coefficient [85]. In the water study, the two-segmented broken-line equation is applied for predicting water electrical conductivity using a portable X-ray fluorescence meter [86]. The meaning of a break-point in this study of the TDR calibration curve can be explained as the point depending on the soil water retention characteristic (horizontal lines on Figure 4). The threshold value (Ψ) with the confidence interval in general was included between horizontal lines which indicated the moisture contents at matric potential between pF values from 2.0 to 2.7. The average moisture content at break point (θ

_{ψ}= 0.6044 cm

^{3}cm

^{−3}) was approximately equal to soil moisture content at pF = 2.2 (θ

_{v}= 0.6020 cm

^{3}cm

^{−3}). The validity of the threshold value can be explained by bulk density changes (Figure 4).

^{−3}, whereas at the “dry” range (segment dry) its estimates are equal to 0.33 g cm

^{−3}. It can be concluded that below the breakpoint of the θ

_{v}(K

_{a}) characteristic, the significant increase of bulk density indicates the essential soil volume changes. The field study conducted for similar soils confirmed that, apart from the soil moisture contents changes [87], the soil bulk density also changes in space and time [40].

_{v}(K

_{a}). The segmented model gave a weak prediction of the soil moisture content for site II (bias equal to approximately 0.044 cm

^{3}cm

^{−3}) as well as in the dry range of the soil moisture content in sites VI, V and IV.

_{1}, β

_{1}+ β

_{2}) and intercepts (β

_{0}) enabled the calculation of the breakpoint value separately for the soil from the specific sites. The parameters of the SSBLM models are summarized in Table 5.

_{1}+ β

_{2}) were generally flatter than in the “dry” range (β

_{1}) and relatively more variable (CV = 24%) mainly because of the lowest slope of the θ

_{v}(K

_{a}) relationship for site II. Except for this site, the slope parameters in the “wet” range were also not essentially different. The Ψ parameter represents a wide range of changes in the dielectric constant (Table 5) which directly influences the really wide scatter of the soil moisture content (θ

_{Ψ}) estimated at break point (Ψ). Despite the low CV value, the moisture content at the break points (θ

_{Ψ}) ranged from 0.50 to 0.70 cm

^{3}cm

^{−3}which represents a relatively wide scatter for this type of soil. The comparison of θ

_{Ψ}values with the range of moisture content of pF curves indicated that the threshold values were included in the range of the soil matric potential approximately between pF = 2.0 (site II) to pF = 2.5 (site IV).

_{v}(K

_{a}) relationship changes. The RMSE values were varied depending on the site data. For the calibration curves from sites III, V and VI, the values did not exceed 0.03 cm

^{3}cm

^{−3}. The RMSE values for the rest of the developed SSBLM equations were slightly higher and varied from 0.036 cm

^{3}cm

^{−3}(site I) to 0.041 cm

^{3}cm

^{−3}(site IV). It should be stressed that logarithmic type models developed for specific site were less accurate and the RMSE value was generally higher (of about 0.005 to 0.012 cm

^{3}cm

^{−3}) in comparison to the SSBLM models. The logarithmic models underestimated the soil moisture content by as much as 0.07 cm

^{3}cm

^{−3}in the wet range of calibration curve. From this reason for further analysis, we applied broken-line model parameters as an approximation of the non-linear relationship between K

_{a}and θ

_{v}.

#### 3.4. Applicability Analysis of the Bio-Indices in Soil Moisture Prediction and Hydro-Physical Properties of Mucky Soils

_{0}) and indicator L of the Ellenberg scale. However, the β

_{0}also correlates with “productivity” of the ecosystem (N) as well as with the Shannon–Weiner index (H’). The slope in the “dry” range of the calibration curves (β

_{1}) was strongly but negatively correlated with “productivity” of the ecosystem (N) determined on the basis of the plant cover as well as positively correlated with the ash content (AC) of the analyzed soils. Nevertheless, both of the explained covariates (AC and N) were moderately and negatively correlated, which can suggest that the increase of the AC amount in the soil causes reduction of the “productivity” of the analyzed ecosystems. The slope in the “wet” range of the calibration curves (β

_{1}+ β

_{2}) can be approximated using the soil moisture substrate indicator (F), which in the case of our studied sites describes fresh soil with moderate wetness [51]. Due to the low range of the F indicator changes and moderate variation of the β

_{1}+ β

_{2}parameter, the prediction of the slope in the “wet” range of the calibration curve can be more complex than simple application of the linear relationship. The estimation of this parameter is especially important for the organic soils where soil moisture changes in the wet range strongly influence the soil degradation processes and physical soil properties. On the other hand, the β

_{1}+ β

_{2}parameters were highly correlated with soil pF curve characteristics. From the data presented in Figure 6, it can be observed that these parameters were also negatively correlated with soil moisture contents measured at the predefined soil matric potentials ranging from pF = 1.5 to pF = 4.2. Moreover, it should be stressed that the moisture of the soil substrate (indicator F) was also highly correlated with the moisture content of the pF curves (Figure 6) which, in general, is in agreement with the statements made in [50]. Based on the correlation analysis, it can be noted that the slope in the “wet” range of the field calibration curves can be fairly well determined using the moisture indicator of the Ellenberg scale, or more precisely using the soil moisture content at pF = 2 as a soil type (site) specific predictor.

#### 3.5. Calibration Model Development of Soil Moisture Content as a Function of Dielectric Constant and Botanical Indices of Soil Cover Using the Regression Tree Method

_{1}, β

_{1}+ β

_{2}) can be averaged (Equations (5) and (7)), however, this requires finding out the threshold Ψ values. The quality of both attempts depends mainly on the prediction of the SSBLM parameters based on the bioindicators of the soil cover as the simplest explanatory variables. However, error in the estimation of the parameters affects the accuracy of the soil moisture prediction. Therefore, taking into account the temporal stability of the investigated ecosystems (supported by water supply and farmer practice), we developed a calibration equation which in one approach includes the relationship between soil moisture content and dielectric constant and the bioindicators’ influence. For this reason, we used the M5Rules algorithm belonging to regression tree methods (see description in Section 2.5).

_{train}. The main independent variable in each training model, which binary split our dataset into two child sets, was dielectric constant (K

_{a}). In the second stage of the cross-validation scheme we reduced the number of variables to the commonly appearing covariates in the training model stage. For this reason, different sets of explanatory variables were tested. Finally, we found the appropriate combination of the variables i.e., K

_{a}, F, L and H’ (SM—set of model) in the model for which at each split of the data the RMSEcv values were close to the RMSE

_{train}(Table 6). Additionally, in Table 6 the RMSEcv values determined in cross-validation procedure performed for the GBLM model are also included. A last SSM-D model fitting was conducted using the mentioned combination of variables (SM) as single fit to all data. Fortunately, the resulted SSM-D model includes two nodes for which the linear regression models have been established (Figure 8).

_{a}= 30.845) similarly to the segmented regression model (Equations (5) and (7)). It should be stressed that the value of 30.845 is included in the confidence interval of the GBLM model. The slope of the line below the splitting point (dry range) was equal to 0.0127 (regression parameter at K

_{a}variable) and was also comparable with its value determined using segmented regression (GBLM). The position of this line along the soil moisture content axis (the value of intercept) was improved by the H’ and L values (specific measures) of the site. Above the K

_{a}= 30.845, the slope was equal to 0.0075 (nearly the same as in GBLM), however, the position of the line can be determined using covariates represented by F, L, bioindicators. However, it should be stressed that the influence of the L value was marginal for soil moisture prediction (wet range) which results from the regression coefficient at this variable.

_{r}which enables establishing a continuous soil moisture content prediction model in the whole range of the dielectric constant changes (site-specific model with re-fitting of ψ

_{r}value, SSM-R). This is especially important for monitoring of this feature. The uncertainty of this kind of the procedure was tested using the RMSE value as a criterion of losing quality in the model compared to the SSM-D model. The ψ

_{r}values are in fact the re-established criterion of the splitting of the dataset which enables, again, application of the linear equations developed for both leaves (Figure 8).

_{a}= 30.845 is similar to the ψ value of the GBLM model) and this results in discontinuities occurring between adjacent leaves. However, we propose to use the SSM-D model in the case when the TDR user does not want to perform a refitting (SSM-R). In the SSM-R model approach, additionally in the post-processing procedure, the threshold value in the form of ψ

_{r}parameter is obtained. In this sense, the SSM-R model is the smoothed form of the SSM-D model and can be treated as a site-specific model similar to SSBLM. The inconveniences of the modelling approach as well as the importance of threshold value in mucky soils should be further investigated.

## 4. Conclusions

^{3}cm

^{−3}. The main expectation from TDR users is to be able to obtain relatively accurate moisture content determination in field conditions. The results of our investigations showed that the proposed calibration curve (GBLM) composed of two segments meets those requirements with the acceptable error of soil moisture determination in field conditions (RMSE = 0.04 cm

^{3}cm

^{−3}). Despite the relatively good approximation of moisture content by the broken-line models (GBLM, SSBLM) developed during this study, these are only empirical equations, which should be subject to an interpretation derived from further investigation of the segmented line parameters. It is important to stress that in the case of the GBLM model, the existence of the two independent slopes separated by the threshold value ψ has been proved empirically by the statistically significant difference in soil bulk densities in both ranges of dielectric constant changes. We propose that further investigation should be focused on the assessment of the influence of soil air content on the slope of calibration equation in the dry range and assessment of the physical meaning of the threshold value ψ.

_{1}+ β

_{2}) in the “wet” range of calibration equation was also correlated with a decrease of moisture content at pressure head corresponding to pF = 2. This tendency was also observed in the correlation between the F (substrate moisture) indicator and β

_{1}+ β

_{2}slope. Moreover, it can be concluded that the F classifier of the habitats determined only on the basis of plant species’ composition is also highly correlated with the soil water retention characteristic at the investigated sites. Therefore, the performed research confirmed that the plant cover of the habitat depends on the water-related properties of the soil peatlands.

_{a}), covariates represented by the following parameters: Substrate moisture (F), and light intensity (L).

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of study sites (based on http://mapy.geoportal.gov.pl).

**Figure 2.**Measured data of dielectric constant and soil moisture content for different sites together with own empirical relationship (NL_own) and relationships listed in Table 4.

**Figure 3.**Field measurements and fitted GBLM for the relationship between soil moisture content and dielectric constant. The horizontal dotted black lines indicate the soil moisture content at predefined pressure head. The red vertical line indicates the average value of the breaking point (ψ = 31.49) whereas the red dotted vertical line is the 95% confidence interval.

**Figure 4.**Boxplot of soil bulk density for “dry” and “wet” segments of the measured dataset (dotted line indicates overall average soil bulk density). The scattered point indicates the soil bulk density value with respect to sites. The dotted horizontal line indicates the overall soil bulk density average. The diamond symbol indicates the average soil bulk density for each segment of the dataset. The red dots indicate the outliers.

**Figure 5.**Field measurements and fitted models of the relationship between the soil moisture content and dielectric constant for specific sites. (

**a**) Site I; (

**b**) site II; (

**c**) site III; (

**d**) site IV; (

**e**) site V; (

**f**) site VI.

**Figure 6.**Correlation graph of the analyzed variables. Arrows in green and red indicate statistically significant positive and negative correlations. Dark yellow arrows indicate not statistically significant correlations. The labelled cells indicate statistically significant correlation between different types of variables regarding the state of the habitats, SSBLM and soil hydro-physical properties.

**Figure 7.**Linear regression lines between parameters of the broken-line model and explanatory variables: (

**a**) the Ellenberg index L - light vs. the intercept β

_{0}of SSBLM; (

**b**) the Ellenberg index N – productivity vs. the slope β

_{1}of SSBLM; (

**c**) the Ellenberg index F – moisture vs. the slope β

_{1}+ β

_{2}of SSBLM; (

**d**) the biodiversity index – H’ vs. the breakpoint (Ψ) of SSBLM.

**Figure 8.**Diagram representing graphical explanation of the SSM-D and site-specific model with re-fitting of ψ

_{r}value (SSM-R) models.

Sites | N1 ^{1} | Actual Soil Bulk Density | N2 ^{1} | Ash Content | Particle Density | Porosity | ||||
---|---|---|---|---|---|---|---|---|---|---|

(g cm^{−3}) | (%) | (g cm^{−3}) | (cm^{3} cm^{−3}) | |||||||

Mean | Min | Max | SD ^{2} | Mean | SD ^{2} | Mean | Mean | |||

I | 81 | 0.3025 | 0.2256 | 0.3883 | 0.0349 | 26 | 14.91 | 1.72 | 1.6150 | 0.8127 |

II | 23 | 0.3123 | 0.2770 | 0.3540 | 0.0199 | 6 | 16.75 | 1.15 | 1.6353 | 0.8090 |

III | 45 | 0.3541 | 0.2830 | 0.4271 | 0.0338 | 26 | 18.79 | 0.82 | 1.6577 | 0.7864 |

IV | 27 | 0.3432 | 0.3102 | 0.3780 | 0.0174 | 9 | 18.42 | 0.86 | 1.6536 | 0.7925 |

V | 51 | 0.2968 | 0.2211 | 0.3680 | 0.0310 | 16 | 17.94 | 0.93 | 1.6483 | 0.8199 |

VI | 51 | 0.3082 | 0.2361 | 0.3712 | 0.0331 | 17 | 18.69 | 1.95 | 1.6566 | 0.8140 |

^{1}N1, N2—measurement numbers of actual soil bulk density and ash content respectively.

^{2}SD—standard deviation of selected basic properties.

Sites | Soil Moisture Content at Predefined Soil Matric Potentials pF (cm^{3} cm^{−3}) | ||||||||
---|---|---|---|---|---|---|---|---|---|

pF = 0.4 | pF = 1.0 | pF = 1.5 | pF = 2.0 | pF = 2.2 | pF = 2.5 | pF = 2.7 | pF = 3.4 | pF = 4.2 | |

I | 0.803 | 0.783 | 0.728 | 0.645 | 0.606 | 0.564 | 0.547 | 0.385 | 0.309 |

II | 0.808 | 0.799 | 0.786 | 0.694 | 0.660 | 0.608 | 0.571 | 0.441 | 0.360 |

III | 0.775 | 0.758 | 0.730 | 0.649 | 0.599 | 0.553 | 0.530 | 0.379 | 0.330 |

IV | 0.790 | 0.774 | 0.727 | 0.677 | 0.576 | 0.502 | 0.476 | 0.356 | 0.303 |

V | 0.819 | 0.812 | 0.724 | 0.616 | 0.559 | 0.521 | 0.504 | 0.335 | 0.248 |

VI | 0.802 | 0.750 | 0.723 | 0.658 | 0.612 | 0.583 | 0.562 | 0.393 | 0.343 |

Values of Basic Statistics | |||||||||

Mean ^{1} | 0.7995 | 0.7793 | 0.7363 | 0.6565 | 0.6020 | 0.5552 | 0.5317 | 0.3815 | 0.3155 |

SD ^{2} | 0.0152 | 0.0237 | 0.0245 | 0.0270 | 0.0347 | 0.0391 | 0.0362 | 0.0361 | 0.0392 |

CV ^{3} | 1.90 | 3.04 | 3.33 | 4.11 | 5.76 | 7.04 | 6.81 | 9.46 | 12.42 |

^{1}mean—arithmetic average (cm

^{3}cm

^{−3}).

^{2}SD—standard deviation (cm

^{3}cm

^{−3}).

^{3}CV—coefficient of variation (%).

**Table 3.**The habitat conditions and the Shannon–Weiner’s index of the meadow communities in the examined sites (mean values).

Sites | Ellenberg’s Indices | H ’^{5} | Floristic Type | |||
---|---|---|---|---|---|---|

L ^{1} | F ^{2} | R ^{3} | N ^{4} | |||

I | 4.96 | 5.62 | 2.39 | 4.34 | 2.26 | Poa pratensis + Festuca rubra |

II | 6.80 | 6.22 | 4.43 | 6.29 | 2.09 | Phalaris arundinacea |

III | 5.50 | 5.03 | 1.03 | 3.32 | 2.18 | Holcus lanatus + P. pratensis |

IV | 6.37 | 5.12 | 2.83 | 4.27 | 2.43 | Achillea millefolium + Odontites serotina |

V | 3.43 | 5.03 | 3.35 | 2.00 | 2.24 | F. rubra |

VI | 3.14 | 5.50 | 3.21 | 1.50 | 1.50 | F. rubra |

^{1}L—light.

^{2}F—soil moisture.

^{3}R—soil acidity.

^{4}N—soil nitrogen

^{5}H’—Shannon–Weiner’s index.

**Table 4.**Selected literature calibration models for time domain reflectometry (TDR) methods and root mean square error (RMSE) statistics with respect to all collected dataset, as well as for data of the “dry” and “wet” segment of the general broken-line model (GBLM).

NO | Calibration Models | Soil | θ_{v} Range | K_{a} Range | Independent Variable | Function | Root Mean Square Error RMSE (cm^{3} cm^{−3}) | ||
---|---|---|---|---|---|---|---|---|---|

Overall Range of Data | Segments of GBLM Model | ||||||||

“dry” | “wet” | ||||||||

1 | P1 [23] | O | 0.03–0.55 | ~3–35 | K_{a} | p | 0.4262 | 0.0924 | 0.5015 |

2 | P2 [29] | SM | 0.20–0.90 | ~5–60 | K_{a} | p | 0.0704 | 0.0764 | 0.0678 |

3 | P3 [30] | O | 0.00–0.75 | ~1–60 | K_{a} | p | 0.0748 | 0.1097 | 0.0546 |

4 | P4 [31] | SC | 0.30–0.80 | ~10–65 | K_{a} | p | 0.0571 | 0.0797 | 0.0448 |

5 | P5 [32] | B | 0.60–0.90 | ~29–75 | K_{a} | p | 0.1130 | 0.1672 | 0.0815 |

6 | PS1[33] | SM | 0.00–0.98 | ~3–75 | sqrt (K_{a}) | p | 0.1090 | 0.1364 | 0.0957 |

7 | PS2 [33] | SM | 0.00–0.98 | ~3–75 | sqrt (K_{a}) | p | 0.0586 | 0.0789 | 0.0480 |

8 | LS1 [81] | O | 0.10–0.80 | ~2–40 | sqrt (K_{a}) | l | 0.0958 | 0.0666 | 0.1053 |

9 | LS2 [82] | Fo | 0.00–0.70 | ~1–40 | sqrt (K_{a}) | l | 0.0908 | 0.0643 | 0.0996 |

10 | LS3 [83] | SM | 0.00–0.95 | ~2–73 | sqrt (K_{a}) | l | 0.0653 | 0.0801 | 0.0582 |

11 | NL_own * | Mu | 0.22–0.81 | 6–61 | ln(K_{a}) | nl | 0.0452 | 0.0586 | 0.0385 |

12 | GBLM * | Mu | 0.22–0.81 | 6–61 | K_{a} | ls | 0.0405 | 0.0508 | 0.0356 |

_{v}—volumetric soil moisture content (cm

^{3}cm

^{−3}); K

_{a}—dielectric constant (-); p—polynomial, l—linear; nl—nonlinear; ls—segmented linear; *—this study; O-organic soils, SC—Sphagnum, Carex peat SM-Sphagnum moss, B—blanket peat; Fo—forest soils, Mu—muck soils.

Sites | β_{0} | β_{1} | β_{1} + β_{2} | Ψ | θ_{Ψ} |
---|---|---|---|---|---|

(cm^{3} cm^{−3}) | (cm^{3} cm^{−3}) | (cm^{3} cm^{−3}) | (-) | (cm^{3} cm^{−3}) | |

I | 0.2157 | 0.0125 | 0.00800 | 27.42 | 0.5585 |

II | 0.2456 | 0.0129 | 0.00380 | 35.25 | 0.7003 |

III | 0.1941 | 0.0144 | 0.00660 | 27.26 | 0.5866 |

IV | 0.2587 | 0.0133 | 0.00640 | 18.29 | 0.5020 |

V | 0.1330 | 0.0139 | 0.00810 | 34.98 | 0.6192 |

VI | 0.0740 | 0.0147 | 0.00613 | 42.14 | 0.6935 |

Values of basic statistics | |||||

Mean ^{1} | 0.1869 | 0.01362 | 0.00651 | 30.89 | 0.6100 |

SD ^{2} | 0.0709 | 0.00086 | 0.00157 | 8.32 | 0.0776 |

CV ^{3} | 37.93 | 6.31 | 24.12 | 26.93 | 12.72 |

^{1}mean—arithmetic average.

^{2}SD—standard deviation.

^{3}CV—coefficient of variation (%).

**Table 6.**Summary of the cross-validation approach for establishing the site-specific model discontinuous (SSM-D) calibration model for the TDR method in mucky soils.

Model | Training Dataset | n_{train.} | n_{test.} | Model Variables | RMSE_{train} | RMSE_{cv} | |
---|---|---|---|---|---|---|---|

SM | GBLM | ||||||

SSM-D1 | I, II, III, IV, V | 227 | 51 | K_{a}, F, L, N, H’ | 0.0351 | 0.0351 | 0.0406 |

SSM-D2 | II, III, IV, V, VI | 196 | 82 | K_{a}, F, N, R, H’ | 0.0321 | 0.0326 | 0.0406 |

SSM-D3 | I, III, IV, V, VI | 256 | 22 | K_{a}, F, N, L, R, H’ | 0.0318 | 0.0426 | 0.0411 |

SSM-D4 | I, II, IV, V, VI | 233 | 45 | K_{a}, F, L, N | 0.0362 | 0.0363 | 0.0406 |

SSM-D5 | I, II, III, V, VI | 251 | 27 | K_{a}, F, L, N, H’ | 0.0301 | 0.0304 | 0.0409 |

SSM-D6 | I, II, III, IV, VI | 227 | 57 | K_{a}, F, L, N, R, H’ | 0.0363 | 0.0368 | 0.0408 |

_{train,cv}(cm

^{3}cm

^{−3}) for training model and for cross-validation scheme respectively; SM—set of model parameters including K

_{a}, F, H’ and L variables.

**Table 7.**Values of RMSE for the different types of TDR calibration models established in this study.

Sites | RMSE ^{1} for Different Calibration Models | |||
---|---|---|---|---|

GBLM | SSBLM | SSM-D | SSM-R | |

overall | 0.0405 | 0.0318 | 0.0351 | 0.0351 |

I | 0.0361 | 0.0359 | 0.0370 | 0.0370 |

II | 0.0623 | 0.0386 | 0.0489 | 0.0489 |

III | 0.0264 | 0.0231 | 0.0270 | 0.0263 |

IV | 0.0559 | 0.0410 | 0.0450 | 0.0450 |

V | 0.0405 | 0.0300 | 0.0322 | 0.0318 |

VI | 0.0349 | 0.0226 | 0.0273 | 0.0312 |

^{1}RMSE—root mean square error (cm

^{3}cm

^{−3}).

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Gnatowski, T.; Szatyłowicz, J.; Pawluśkiewicz, B.; Oleszczuk, R.; Janicka, M.; Papierowska, E.; Szejba, D.
Field Calibration of TDR to Assess the Soil Moisture of Drained Peatland Surface Layers. *Water* **2018**, *10*, 1842.
https://doi.org/10.3390/w10121842

**AMA Style**

Gnatowski T, Szatyłowicz J, Pawluśkiewicz B, Oleszczuk R, Janicka M, Papierowska E, Szejba D.
Field Calibration of TDR to Assess the Soil Moisture of Drained Peatland Surface Layers. *Water*. 2018; 10(12):1842.
https://doi.org/10.3390/w10121842

**Chicago/Turabian Style**

Gnatowski, Tomasz, Jan Szatyłowicz, Bogumiła Pawluśkiewicz, Ryszard Oleszczuk, Maria Janicka, Ewa Papierowska, and Daniel Szejba.
2018. "Field Calibration of TDR to Assess the Soil Moisture of Drained Peatland Surface Layers" *Water* 10, no. 12: 1842.
https://doi.org/10.3390/w10121842