This experiment was conducted over three years (2019-2021) at the Zhejiang Agriculture and Forestry University Research Farm in Lin’an District, Hangzhou City, Zhejiang Province, China (30° 15’ 43’, 119° 43’ 25’) on a sandy loam soil. This region has a subtropical monsoon climate, with an altitude of 20–30 m above sea level and an average annual precipitation of 1435 mm. The monsoon season spans June to September. Climate change in 2019 was close to the average of the past decade. In 2020, precipitation was lower than previous year in July and August due to the influence of monsoon weather. In 2021, precipitation was higher than previous year in July and August due to the impact of typhoons. This experiment was conducted at different locations in Lin’an to avoid any potential residual effects of potassium fertilization ( Table 1 ). The previous crop was planted with winter wheat.

The experiment 2 and 3 were conducted from 2020-2021 at the Zhejiang Agriculture and Forestry University Research Farm in Lin’an, Zhejiang Province in China, using two nitrogen levels (N0: 0 kg ha⁻¹ and N1: 120 kg ha⁻¹) and five K fertilization rates (K0: 0, K1: 75, K2: 150, K3: 225, K4: 300 kg ha⁻¹) for two cultivars of ‘Shang 19’ and ‘Yan 25’. The experiment 1 was conducted at same site in 2019 using one nitrogen levels (N0: 0 kg ha⁻¹) and five K fertilization rates (K0: 0, K1: 75, K2: 150, K3: 225, K4: 300 kg ha⁻¹) for one cultivar of ‘Xinxing’ ( Table 1 ). Table 1 lists the soil total N, available potassium (K), and available phosphorus (P) for the three experiments. Urea and potassium sulfate are all applied as basal fertilizers to all plots. P₂O₅ (60 kg ha^-1) fertilizers were also basally incorporated in all plots before planting as monocalcium phosphate (Ca(H₂PO₄)₂) fertilizer. Three field experiments each processing were conducted using plot sizes of 6×4 m; plots were arranged in a randomized block design with three replicates. The planting density was 5.0 plants m⁻², row spacing was 25 cm. All the treatment are covered with mulch film, and the water source is natural irrigation. During the trial, all field management, including herbicide application and pest control, was carried out using local cultivation and management methods. The sampling dates are shown in Table 1 .

In 2019, transplant was carried out on June 9 and harvest was performed on September 8. In 2020, transplant was carried out on June 16 and harvest was performed on October 8. In 2021, transplant was carried out on May 14 and harvest was performed on September 22. Plant samples were collected from each treatment on 6 sampling dates during the whole growth period of sweetpotato ( Table 1 ). At each sampling date in each plot, five complete plants were harvested from each treatment. Each plant sample was complete divided into three sections: stems, leaves, and underground parts (including tubers roots and fibrous roots). Three bags of each clean fresh sample were randomly selected, each bag of 200g. (the underground part was washed and air dried). Samples were inactivated at 105 °C of dry oven for 30 min, and then dried for 3 days at 80°C of dry oven, measurement of each sample dry matter and calculated the dry rate. The dried tissues matter were ground in a hammer whirlwind grinding mill to pass a 100-mesh sieve, then powder (0.20 ± 0.01 g) was weighed, digested with concentrated H₂SO₄ and 30% H₂O₂ (Jones and Case, 1990), and analyzed for K nutrient content by using a flame spectrophotometer (FP6431) (Cate and Nelson, 1971).

A critical K dilution curve for the whole-plant of sweetpotato was constructed in accordance with the method of the critical N dilution curve (Justes, 1994) was as follows ( Figure 1 ):

In the formula: K_c (%) was plant critical K concentration, W is the plant dry matter (t ha^-1), where coefficient a represents the critical K concentration when W is 1 t ha^-1, and parameter b represents a “dilution coefficient”, which describes reduction in nutrient concentration associated with increment in whole-plant dry matter. The combined CKDC model was re-fitted one curve based on the critical K concentration point values constructed in the same organ sites for different cultivated species.

The accuracy of the model was evaluated by root mean square error (RMSE) and normalized root mean square error (n-RMSE), a common method used to identify the fitness of observed and estimated values. we used the RMSE model and independent validation data for validation. A smaller RMSE value indicated better consistency between the simulated value and the measured value, which implied better prediction accuracy. (Jamieson et al., 1991). If n-RMSE< 10%, model stability was considered excellent; if 10%< n-RMSE< 20%, model stability was considered good; if 20%< n-RMSE< 30%, model stability was considered poor.

Where n is the number of samples, Pi is an estimated value from the model, Qi is an observed value, and S is the averaged observed value.

The KNI is an indicator used to determine crop K status (Lemaire et al., 2007; Lv and Lu, 2021). The KNI at each sampling date was determined according to the actual K concentration (K_a) and the critical K concentration (K_c), as follows:

Thus, for KNI=1, K nutrition is optimal to obtain maximum biomass; for KNI< 1, K nutrition is limited obtain maximum biomass; and for KNI > 1, K nutrition is excessive obtain maximum biomass.

Excel, SPSS, and Curve Expert software were used for statistical and curve fitting analyses to build a quantitative model. Analysis of variance (ANOVA) was used to compare experimental groups using SPSS ver. 19. The differences dry matter values were in aboveground, under-ground and whole-plant between different K treatments were assessed using the least significant difference test (LSD, P< 0.05). The data from Experiments 1-3 were divided into K-limiting and non-K-limiting treatments using the LSD test (P< 0.1). The data of Experiments 2 and 3 conducted at each sampling date during the 2020 and 2021growing seasons were combined to construct the critical K dilution curve. The data of Experiment 1 conducted during the 2019 growing season were used to validate the CKDC. The differences in the critical K curves for the whole plant, aboveground and under-ground parts between the two N levels was compared using ANOVA at the 5% probability level.

The aboveground dry matter of sweetpotato plants includes leaves and stems. As shown in the Figure 2 , the aboveground dry matter of sweetpotato plants gradually increased after transplanting. Dry matter increased rapidly at the early stage, whereas it increased slowly at root expansion stage. There were significant differences for aboveground dry matter for the two cultivars under different K treatments. the aboveground dry matter in 2020 was significantly higher than that in 2021. In 2020, the dry matter was the highest at K1 treatment under the N0 mode, while the dry matter was the highest at the K2 treatment under N1 mode. In 2021, the dry matter was relatively higher at K2 treatment under the N0 mode, while the dry matter was relatively higher at the K2 and K3 treatment under N1 mode.

The plant K concentration increased with increasing K application during each growth period, and there were significant differences among the five K treatments ( Table 2 ). These findings indicate that increased application of K fertilizer within a specific range can improve the K concentration in shoots. However, the K concentration in the aboveground parts followed a downward trend throughout the growth period, decreasing rapidly from 30 to 60 days after planting. From 68 to 88 day after planting in 2021, dry matter accumulation significantly increased, whereas the K concentration in the aboveground parts follow a slowly decreasing tread.

Under different K rates, the underground dry matter of sweetpotato increased under the whole growth period. As shown in the Figure 3 , the underground dry matter increased slowly from 30 to 76 days after planting, dry matter increased rapidly from 76 to 112 days after planting. In 2020, ‘Shang 19’ and ‘Yan 25’ had the highest underground dry matter at K1 treatment under the N0 mode, while ‘Shang 19’ and ‘Yan 25’ had the highest underground dry matter at K2 treatment under the N1 mode. In 2021, ‘Shang 19’ and ‘Yan 25’ had relatively higher underground dry matter at K2 and K3 treatment under the N0 mode, while ‘Shang 19’ and ‘Yan 25’ had the highest underground dry matter at K4 treatment under the N1 mode. Moderate application of K promoted underground growth, but excessive application of K inhibited underground growth.

The K concentration in underground parts increased with increase of K application, and there were significant differences among the five K treatments ( Table 3 ). The K concentration in the underground parts followed a downward trend throughout the growth period. The K concentration in the underground parts decreased rapidly from 30 and 68 days after planting. From 68 days after planting, the K concentration in the underground parts decreased slowly.

The whole-plant dry matter of sweetpotato gradually increased after planting ( Figure 4 ). Dry matter rapidly increased during 70-100 days after planting. There were significant differences for plant dry matter of the two cultivars under different K treatments. The plant dry matter in 2020 were slightly higher than that in 2021. The dry matter under the N1 mode for both cultivars was significantly higher than that under the N0 mode. In 2020, the dry matter was the highest at K1 treatment under the N0 mode, while the dry matter was the highest at the K2 treatment under N1 mode. In 2021, the dry matter was relatively higher at K2 and K3 treatment under the N0 mode, while the dry matter was the highest at the K4 treatment under N1 mode.

As shown in Table 4 , there were significant differences for K concentration under different K treatments. K concentration consistently decreased during the growth period of sweetpotato. K concentration decreased significantly for K3 and K4 treatment at the early stages. The overall K concentration of ‘Shang19’ is higher than that of ‘Yan 25’. The variation range of K concentration for two cultivars is from 0.76% to 4.38%. K content tended to decrease after planting, whereas plant dry matter tended to increase with decreasing K concentration.

As shown in Table 5 , the CKDC for aboveground parts, underground parts and the whole plant under N1 mode were lower than that under N0 mode, and parameters a under N1 mode were also lower than that under N0 mode. The CKDC for aboveground parts under N1 mode was significantly lower than that under N0 mode at early stage of sweetpotato, and parameters a and b for the aboveground parts were significantly different between N0 and N1 levels (P<0.05). The CKDC for underground parts and the whole-plant under N1 mode were slightly lower than that under N0 mode, there is no significant differences for parameters a and b for underground parts and the whole plant between N0 and N1 levels (P>0.05). This is duo to the impact of N on aboveground dry matter is significantly greater than that on underground dry matter. The parameters a and b for ‘Shang 19’ were higher than that for ‘Yan 25’.

A common model was established by combining the CKDC for both sweetpotato cultivars in both years. Independent data of ‘Xin Xiang’ cultivated in 2019 were used for validation. The CKDC could distinguish K-limiting and non-K-limiting groups ( Figure 6 ). Almost all the data points limited by K were located below the CKDC, whereas the data points were not limited by K were located above the CKDC ( Figure 6 ). Results indicated the curve discriminated well between K-limiting and non-K-limiting treatments. The accuracy of the model was evaluated with RMSE and n-RMSE, by using eqs ( Table 6 ). Results showed that the n-RMSE all SD values were less than 10%, indicating ‘good’ agreement between observed and estimated values. As shown in Table 6 , the CKDC models had high accuracy for both N levels, indicating that they can be used for determination of K nutritional status for sweetpotato. Thus, the W-K_c model we established can be used for diagnosis plant nitrogen nutrition.

The KNI is used to determine a plant’s real-time K status. The whole-plabt KNI increased with the increase of K application. For the same K treatment, the KNI increased with the increase of N application. When KNI is closer to 1, the plant is in an optimal state of K nutrition to obtain maximum biomass. K1 and K2 were closer to 1 under the N0 level, whereas K2 and K3 were closer to 1 under the N1 level. KNI followed an overall trend of decreasing first and then increasing during plant growth ( Figure 7 ).

The critical K dilution curves (CKDC) were constructed based on K concentration and dry matter followed a negative exponential model ( Figure 5 ). According to the critical dilution curve, the K concentration decreases with the increase of dry matter, which is complying with the “law of dilution” proposed by Justes (1994). Previous reports have shown that the critical K concentration dilution curve of root tuber crops, such as potato (Cogo et al., 2006; Gómez et al., 2018) and cassava (Geraldine et al., 2020). The existing CKDC of cassava in the aboveground part was Kc=4.2W^-0.690 , while CKDC of cassava in the whole-plant was K_c=4.3W^-0.540 (Geraldine et al., 2020). The CKDC of three potato cultivars in whole-plant were ‘Asterix’ K_c=5.54W^-0.317 , ‘Suprema’ K_c=6.58W^-0.135 , ‘Capiro’ K_c=9.02W^-0.269 , respectively (Cogo et al., 2006; Gómez et al., 2018).

The coefficient a represents the value of Kc at the value of dry matter W of 1 t ha^-1. The coefficient a (4.20) of cassava in whole-plant was lower than that (4.31) of sweetpotato, and the coefficient a of sweetpotato in whole-plant was lower than that (9.02, 6.58, 5.54) of potato ( Figure 8 ). For the whole-plant of sweetpotato, potato and cassava species, the dry matter accumulation of cassava was higher than that of sweetpotato, and the dry matter accumulation of sweetpotato was higher than that of potato. The coefficient b (0.69) of cassava in whole-plant was higher than that (0.421) of sweetpotato, and the coefficient b of sweetpotato was higher than that (0.135, 0.269, 0.317) of potato, indicating that the potassium dilution degree of cassava was greater than that of sweetpotato and potato. This difference between species should be related to the intrinsic ratio of carbohydrates and potassium accumulated in the plant based on starch during root expansion growth. The growth cycle of “cassava > sweetpotato > potato”, resulting in higher dry matter accumulation of cassava and sweetpotato. This different growth cycle and dry matter accumulation led to obvious K dilution in cassava. With the progress of crop growth, % Kc gradually decreased at the aboveground and underground levels, and the trend was similar to that of % Kc at the whole plant level ( Figure 8 ).

The coefficient a (1.38 and 1.32) of CKDC in underground part was lower than that in the aboveground part (5.3 and 4.23), which was due to the K concentration in aboveground part was higher than that in underground part. The coefficient b (0.125 and 0.132) of CKDC in underground part was lower than that in the aboveground part (0.463 and 0.298), which showed that the decrease of the K concentration in the aboveground was greater than that in the underground. When the plant dry matter is lower than 4 t ha^-1, there is a significant decrease in shoot potassium concentration ( Figure 8 ). This is attributed to the allometric relationship between K concentration and plant W accumulation during the pre-tuberization period of sweetpotato. On the contrary, when the plant dry matter exceeded 4 t ha^-1, sweetpotato entered the root expansion stage, and the decrease of Kc is more slowly in underground part. This is due to the higher transfer rate of metabolic (leaf) and structural (stem) components of sweetpotato to plant (root) storage components to ensure yield and starch formation (Allen et al., 1976; Sharma and Arora, 1987).

The critical curves for K_c and KNI define a crop’s nutritional status, as reported by Gómez et al. (2017). The KNI can be used to determine the real-time nutritional status of a sweetpotato plant and quantify the fertilizer ratio (He et al., 2017; Soratto et al., 2022), thereby aiding the balanced application of K and N fertilizers. The KNI accurately reflects the K nutrition statuses of potato, cassava, and sweetpotato; it increases as the rate of K application increases. This study constructed CKDC for aboveground, underground and whole-plant, respectively. There was significant difference in CKDC for aboveground parts among different N treatments. Therefore, it is not stable enough for K nutrition diagnosis by using aboveground CKDC to construct KNI. Due to the small biomass in the underground during the early stages of sweetpotato, it may result in significant errors by using underground CKDC for potassium nutrition diagnosis in the early stages. In addition, there is a large amount of dry matter transport between the aboveground and underground parts during the growth period of sweetpotato, which also affects the accuracy of the CKDC of aboveground and underground parts. The CKDC constructed based on the whole-plant of sweetpotato is the most stable, with the highest R², and can be used to diagnose the potassium nutrition status of sweetpotato. Therefore, the KNI constructed based on the whole-plant CKDC can be used to determine K excess or insufficient during plant growth periods.

With the increase of K fertilizer application, the KNI value first increases and then decreases. Under the condition of potassium limitation, the yield of sweetpotato depends on the K state of the whole plant, and higher potassium can produce more yield. When KNI was higher than 0.84 for S19 under N0 level, relative yield of sweetpotato had a negative correlation with KNI ( Figure 7 ). When KNI was higher than 0.94 for S19 under N1 level, relative yield of sweetpotato had a negative correlation with KNI ( Figure 7 ). There is the same trend for Y25. Therefore, with the increase of N fertilizer application, the KNI corresponding to the maximum relative yield also increased, and the threshold for reducing sweetpotato yield caused by K fertilizer application gradually increases. There are some differences in the sensitivity of different cultivars to potassium nutrition ( Figure 9 ). Gómez et al. (2017) indicates that extravagant potassium consumption may limit tuber formation and tuber growth, consistent with this study ( Figure 9 ). Thus the KNI could be used to assess crop K status and CKDC and to determine the requirement for additional K fertilization using established relationships between the relative yield and KNI.

For aboveground parts of sweetpotato, coefficients a and b of the CKDC significantly differed under two N levels; there was no significant differences for underground parts. In the initial stage of growth (the first 60-80 days), the K concentration for aboveground parts under N1 treatment was 10.75% lower than that under N0 treatment, while the K concentration in underground parts under N1 treatment was 5.01% lower than that under N0 treatment. These differences were mainly because N fertilizer promotes the growth of leaves and stems at the early stage, and decreased aboveground K concentration. However, the dilution effect of N on the underground parts was weaker than its impact on aboveground parts. In the present study, N showed an increasing dilution effect on the critical K curve and improved KNI. The phenomenon of “law of dilution” through expansive growth was also explained by Lemaire et al. (2007) and Chakwizira et al. (2016).

Sweetpotato has a typical source–sink relationship, and there is a reciprocal relationship between N and K fertilizer. The dry matter of aboveground and whole-plant was more related to fertilization supply as evidenced by the significance of N × K fertilization interaction ( Table 7 ). Thus, balanced application of N and K fertilizer is essential to optimize sweetpotato quality and yield. Under the N1 level, the whole-plant CKDC showed greater accumulation of dry matter. High N led to increased whole-plant dry matter and a dilution of the K concentration (Li et al., 2012). Although some studies have shown that high N increases absorption of K, we found that the dilution effect of N on K was greater than the effect of N on K absorption, consistent with the results reported by Wang S et al. (2017).

We found that an appropriate amount of N application will reduce K_c ( Figure 6 ) and increased the KNI ( Figure 7 ). Compared to low nitrogen treatment, high nitrogen treatment requires higher K to achieve maximum yield ( Figure 3 ). Figure 9 also showed that the KNI corresponding to the maximum relative yield increased with the increase of N fertilizer application. Therefore, the amount of K fertilizer application should be based on the amount of soil N content. Under low N condition, low K was required to achieve high yield; under medium N condition, medium K was required to achieve high yield. There was an optimal N/K ratio that maximizes the yield of sweetpotato. This interaction between N and K is important for the growth of sweetpotato (Ding et al., 2008). In the present study, N and K had a positive relationship for crop growth and accumulation, which is consistent with previous findings (Wang et al., 2016; Wang J et al., 2017). In 2020, K1 and K2 treatments had higher yield under the N0 mode, while K2 and K3 treatments have higher yield under the N0 mode. In 2021, K2 and K3 treatments had higher yield under the N0 mode, while K3 and K4 treatments have higher yield under the N1 mode. This is due to the concentrated rainfall from June to July in 2021, which increased the available N in the soil. So, the corresponding K demand to achieve high yield for two N mode in 2021 also further increased. Therefore, efficient production requires an understanding of the effects of N and K on sweetpotato, as well as accurate determination of K nutritional status based on K concentrations in distinct parts of the sweetpotato. This information can help to timely use N and K fertilizers, and reduce the pressure on the growth of sweetpotato.