# Research on Evaluation Methods of Black Soil Farmland Productivity Based on Field Block Scale
## 2 Materials and Methods
### Topsoil Productivity Evaluation Model
#### 2.2.2 PI Model and Its Revisions  
The PI model was first proposed by [PERSON] [6] in 1979 to assess the effect of soil properties on crop yield. It has been modified by some researchers in the past [25; 26; 27]. On the basis of [PERSON]'s improved PI model, the special case of organic matter and soil bulk density in the black soil area of Northeast China was considered, and the growth of maize was taken as an example [28]. The optimized PI model was established by dividing the soil \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Soil Impact Factor** & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline soil texture & gravel & & & & Fine & Top & & & & \\ soil & & & Coarse & sandy & sandy & sandy & & sand & sandy & \\ soil & & & sandy & soil/ & soil/ & soil/ & sand & sand & sandy & loam \\  & & & soil/ clay & loamy & powdery & & and silt & sand & clay & \\ organic & & & & clay & clay & clay & & & & \\ material & & \textless{}1 & & 1–1.5 & & 1.5-2.5 & & 2.5–3.5 & & \textgreater{}3.5 \\ /\% & & & & & & & & & \\ available nitrogen & & & & & & & & & \\ /mg/kg & & & & & & & & & \\ available & & & & & & & & & \\ phosphorus/(mg/kg) & & & & & & & & & \\ available potassium & & & & & & & & & \\ /(mg/kg) & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\ pH & & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\ erosion & & & & & & & & \\ degree & & & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Soil impact factor score sheet. depth of 200 cm into 20 layers and selecting the soil physicochemical indicators [6] The soil physico-chemical indexes were selected to establish PI model:  
\[\text{PI}=\sum_{i=1}^{n}\left(A_{i}\times B_{i}\times C_{i}\times D_{i}\times E _{i}\times WF_{i}\right) \tag{3}\]  
In the formula, PI represents the Soil Productivity Index, where i denotes different soil layers. As this study focuses on the surface soil productivity assessment method, deeper soil layers are not considered. Nevertheless, it is essential to understand that, in the formula, A represents the Suitability Index of soil available water content for root growth, B represents the Suitability Index of soil aeration for root growth, C represents the Suitability Index of soil bulk density for root growth, D represents the Suitability Index of soil pH for root growth, E represents the Suitability Index of soil electrical conductivity for root growth, and WF represents the root weight factor of the soil. Each suitability index is standardized to a numerical value between 0.000 and 1.000, with values closer to 0 indicating inhibition of crop growth and values closer to 1 indicating suitability for crop growth. Referring to the research by [PERSON] [26], three key indicators were selected, namely the Suitability Index of soil available water content (A), Suitability Index of soil bulk density (C), and Suitability Index of soil pH (D). The calculation formula for the Suitability Index of soil available water content refers to the research findings of scholars such as [PERSON] [29], providing an improvement to the surface soil evaluation:  
\[ \begin{array}{l}A=0,AWC\leq 3\%\\ A=5\times AWC,3\%<AWC\leq 20\%\\ A=1,AWC>20\%\end{array}  \tag{4}\]  
In the equation, A represents the Suitability Index of soil available water content, where AWC represents the soil's available water content expressed in volume percentage. The calculation is based on field capacity and wilting point humidity. The Suitability Index of soil pH (D) refers to the calculation formula proposed by [PERSON] [26], with improvements made for surface soil assessment:  
\[ \begin{array}{l}D=0,pH\leq 2.9\\ D=-1.31+0.446\times pH,2.9<pH\leq 5.0\\ D=0.12+0.16\times pH,5.0<pH\leq 5.5\\ D=1,5.5<pH\leq 6.5\\ D=2.086-0.167\times pH,6.5<pH\leq 8.0\\ D=0.75,pH>8.0\end{array}  \tag{5}\]  
The soil bulk density calculation method is consistent with the approach used in [PERSON]'s modified PI model [27].