# Heat Capacity of Drained Peat Soils
## 3 Results
### Heat Capacity Data
#### 3.1.3 Statistical Analysis of Heat Capacity Data  
The correlation matrix graph (Figure 5) shows that \(C_{0}\) and \(C_{1}\) parameters were highly correlated with the soil nitrogen contents and C:N ratio.  
Figure 4: Results of the thermal probe (KD2 Pro) measurements (**a**,**b**) and basic soil-related properties (**c**,**d**). Soil depth in cm.  
It was also evident that \(C_{0}\) was weakly correlated to soil physical properties (\(P_{o},\rho_{b}\)) and organic carbon content (C). Figure 6 illustrates the empirical relationships between selected soil properties and heat capacity parameters. In general, the data presented in Figure 6 indicate that an increase in N content caused an increase in both linear parameters of the \(c_{p}(T)\) relation. It can be concluded that N, one of the main soil chemical components responsible for its degradation [6,50,51], importantly affects the heat capacity of peat-muck soils. Approximately 60% (detailed statistical measures are included in Table 3) of \(C_{0}\) changes were explained by the linear relation with soil N content only. Similar results were obtained for \(C_{0}\) using the C:N ratio. The \(C_{1}\) parameter could also be approximated using N, which explains 75% of the variation of the \(c_{p}(T)\) slope. The \(C_{1}\) parameter could also be interpolated nonlinearly using ash content data (AC) in the range from 1.5% to 30% (Figure 6d). The quality of the prediction of the heat capacity parameters varied and a relatively weak estimation of \(C_{0}\) can be expected (Table 3). Further data analysis using the ordinary least square technique shows that the prediction of the \(C_{0}\) and \(C_{1}\) parameters improves with the development of two- or three-variable models. The predictability for the \(C_{0}\) parameter increases when considering the following three soil features: percentages of nitrogen, organic carbon, and ash content (Equation (5)). For the \(C_{1}\) parameters, the prediction was improved when using C:N and AC (Equation (6)).  
\[C_{0}=1.582+0.12491\cdot\text{N}-0.013050\cdot\text{C}-0.009981\cdot\text{AC} \tag{5}\]  
\[C_{1}=5.787\times 10^{-3}-5.115\times 10^{-5}\cdot\text{C:N}-3.955\times 10^{-5} \cdot\text{AC} \tag{6}\]  
\[C_{1}=5.530\times 10^{-2}-3.553\times 10^{-5}\cdot\text{C:N}-3.011\times 10^{-2} \cdot\rho_{b}-5.053\times 10^{-2}\cdot P_{o} \tag{7}\]  
The advantage of Equations (5) and (6) stems from the fact that both parameters were explained using the same type of variables representing soil chemical properties. These equations confirm that these properties had a major influence on the heat capacity data (parameters \(C_{0}\) and \(C_{1}\)). Nevertheless, pairs of RMSE value (Table 3) indicate that the best prognostic model for the \(C_{1}\) prediction was established when combining the chemical and physical properties (Equation (7)).  
Figure 5: The Pearson correlation matrix describing the statistical relationship between soil thermal, physical, and chemical properties. The dark brown panels indicate a strong negative correlation, while a strong positive correlation between soil parameters is denoted by dark blue panels. The correlations with \(p\)-value > 0.05, which are considered insignificant, are represented by white blank panel.  
Figure 6: Empirical relationships between \(c_{p}(T)\) equation parameters \(C_{0}\) (**a**,**b**) and \(C_{1}\) (**c**,**d**) and chemical properties of peat-moorsh soils. The shape of the point markers indicates the soil type. Basic descriptive statistics for the equations are given in Table 3.