## 3 Results
### The Application of Formula Fertilization Models  
#### 3.3.1 The Establishment of Formula Fertilization Models  
The models of recommended formula fertilization for broccoli were established. The total nutrient amount from soil and fertilizer meeting the demand of the same production goal was equal in all farmland blocks, including different recommended fields and fertilizer response functions in trial fields. However, the recommended field was the same as production area, with the same soil characteristics as the fertilizer effect function in the trial fields. The plots indicate the same crop variety with the uniform culture model, which can be expressed as follows:  
\[\rm{F_{R}}+S_{R}=F_{T}+S_{T} \tag{9}\]  
\(\rm{F_{R}}\) is the nutrient amount of recommended fertilizer in the recommended plot;  
\(\rm{S_{R}}\) is the nutrient amount of soil supply in the recommended plot;  
\(\rm{F_{T}}\) is the nutrient amount of recommended fertilizer in the fertilizer effect function trial plot;  
\(\rm{S_{T}}\) is the nutrient amount of soil supply in the fertilizer effect function trial plot  
From the Equation (9),  
\[\rm{F_{R}}=F_{O}+S_{T}-S_{R}.\]  
where \(\rm{F_{O}}\) represents the optimal nutrient amount from a recommended N, P, or K fertilizer as different production targets in trial plot, and it was obtained from the response function of a N, P, or K fertilizer as part of the target of maximum yield; for instance, the amount of optimally recommended N, P, and K fertilizers are N (ZSHL) 365.95 kg/ha, N (HL-5) 405.83 kg/ha; \(\rm{P_{2}O_{5}}\) (ZSHL) 101.97 kg/ha, \(\rm{P_{2}O_{5}}\) (HL-5) 96.74 kg/ha; and \(\rm{K_{2}O}\) (ZSHL) 194.52 kg/ha, \(\rm{K_{2}O}\) (HL-5) 202.44 kg/ha, respectively, the maximum yields were 13,608.59 kg/ha (ZSHL) and 18,288.05 kg/ha (HL-5) in the establishing trial for the effect functions of N, P, and K fertilizers.  
\(\rm{S_{T}}\) and \(\rm{S_{R}}\) can be calculated from:  
\[\rm{S_{T}}(S_{R})=D_{T}(D_{R})\times C_{E} \tag{10}\]  
Figure 3: Potassium fertilizer contribution to broccoli yield.  
\(\rm D_{T}\) and \(\rm D_{R}\) were determined as values of soil nutrients from the recommended and the trial plot, respectively.  
\(\rm C_{E}\) is a revised coefficient, which can be calculated as follows:  
\[\rm C_{E}=A_{L}/(D_{R}\times 2.25) \tag{11}\]  
\(\rm A_{L}\) is the absorbed nutrient amount of the crop in the non-fertilized plot, which can be calculated as follows:  
\[\rm A_{L}=AUP\times P_{L} \tag{12}\]  
AUP is the absorbed nutrient amount of crop unit production, and the N, P, and K values of unit production in cabbage vegetables were 0.41, 0.05, and 0.38, respectively [8]. \(\rm P_{L}\) is crop production in the lack of fertilizer plot.  
Equation (13) can be formulated using the Equations (9)-(12).  
\[\rm F_{R}=F_{O}+(D_{T}-D_{R})\times AUP\times P_{L}/2.25D_{R} \tag{13}\]  
\(\rm F_{O}\) and \(\rm P_{L}\) can be obtained from the response function of the N, P, and K fertilizer [11; 18]. \(\rm D_{T}\) and \(\rm D_{R}\) can be determined using soil nutrient testing on the different recommended plots and the function establishment trial plot. The Equation (13) can be used to recommend N, P, and K fertilization under different production targets in different plots.