# 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
Considering the critical nature of soil physicochemical property indicators in maize crop production in Keshan Farm, this study was revised based on the PI model. In order to assess the surface condition of the soil more accurately, we evaluated only the top soil layer of the ploughed soil. On the basis of retaining the original soil pH suitability index \(D\), water content \(A\) and soil bulk weight \(C\), we added the total nitrogen index \(B\), quick-acting phosphorus index \(E\), and quick-acting potassium index \(F\), and constructed a modified PI model (MPI) applicable to the evaluation of topsoil:  
\[\text{MPI}=A\times B\times C\times D\times E\times F \tag{6}\]  
Multiple parameters of the soil have a differential effect on the overall fertility level, and the measured values of each parameter have significant differences in magnitude, making a simple summation calculation impossible. To overcome this problem, a standardized approach is used in this paper. When the measured value of a parameter belongs to the \"poor\" grade, i.e., P \(\leq\) Xa:  
\[E=\frac{P}{X_{a}}(E\leq 1) \tag{7}\]  
When the measured value of a parameter falls within the \"qualified\" grade, i.e., Xa < P \(\leq\) Xb:  
\[E=1+\frac{P-X_{a}}{X_{b}-X_{a}}(1{<}E\leq 2) \tag{8}\]  
When the measured value of a parameter belongs to the \"medium\" grade, i.e., Xb < P \(\leq\) Xc:  
\[E=2+\frac{P-X_{b}}{X_{c}-X_{b}}(2{<}E\leq 3) \tag{9}\]  
When the measured value of a parameter belongs to the \"good\" grade, i.e., Xc < P \(\leq\) Xd:  
\[E=3+\frac{P-X_{c}}{X_{d}-X_{c}}(3{<}E\leq 4) \tag{10}\]  
When the measured value of a parameter belongs to the \"excellent\" grade, i.e., Xd < P:  
\[E=4 \tag{11}\]  
In the above formulae, \(E\) represents the quality index of available phosphorus (\(P\)) in the soil, P denotes the measured value of soil available phosphorus, and Xa, Xb, Xc, and Xd are the grading standard values. By employing this standardization method, the single quality indexes of the same level attribute become more comparable, enhancing comparability. When the measured value (\(P\)) exceeds the optimal standard (Xd), the single quality index (\(E\)) no longer increases, reflecting that the crop (corn) does not necessarily benefit from higher soil attribute values. In other words, after reaching a certain optimal level of nutrient content, further fertilization to increase content does not contribute to increased crop yield. Based on this, the optimized evaluation formula for the soil available phosphorus quality index \(E\) in this experiment is as follows:  
\[ \begin{split} E&=3+\frac{P-10}{10},P>10\\ E&=2+\frac{P-5}{5},5<P\leq 10\\ E&=1+\frac{P-3}{2},3\leq P\leq 5\\ E&=\frac{\text{P}}{3},P<3\end{split}  \tag{12}\]  
Based on the soil evaluation score formulated by [PERSON] [15], we further subdivided the total nitrogen quality index and available potassium quality index in the soil to ensure that the actual scores fall within the range of 0 to 1, in accordance with the requirements of the PI model. In the end, we obtained the calculation formulas for the total nitrogen index (\(B\)) and available potassium index (\(F\)):  
\[ \begin{split} B&=1,N>0.20\\ B&=\frac{N-0.10}{0.1},0.10<N\leq 0.20\\ B&=0,N\leq 0.10\end{split}  \tag{13}\]  
\[ \begin{split} F&=1,K>200\\ F&=\frac{K-100}{100},100<K\leq 200\\ F&=0,K<100\end{split}  \tag{14}\]The subdivision and standardization methods contribute to a more accurate quantification of the impact of total nitrogen and available potassium on soil nutrient conditions. This optimization of surface soil assessment aligns with the design principles of the PI model.