Potassium balance in paddy fields under conventional rice straw recycling versus cow dung compost application in mixed crop–livestock systems in Japan

ABSTRACT Potassium (K) fertilizer consumption in rice production has increased in developing countries where negative K balance was observed, but it has recently decreased in Japan. This situation raises a question of how K fertilization is managed in Japanese paddy fields and how it affects soil K balance and soil K status. Rice straw (RS) is a good source of K, and RS recycling after harvesting is a common practice in Japan. However, in mixed crop–livestock systems, RS is taken at harvesting time to use as the feed for cows and substituted with the application of cow dung compost (CDC) to the fields. We investigated soil K balance and soil K status in 8 (2017) and 10 (2018) pairs of adjacent RS- and CDC-treated fields in Mamurogawa, Yamagata, Japan. The K balance was calculated from K inputs (RS or CDC, fertilizer, and irrigation water) and K outputs (plant uptake and leaching). K fertilizer application varied widely in both treatments, with no significant difference between RS and CDC fields. K fertilizer was applied in amounts lower than those recommended for paddy rice in the study area in 56% of the fields in both treatments. The K balance was positive in most fields with RS recycling even if K fertilizer application was lower than recommended, but it was negative in half of the fields where RS was substituted with CDC. Most fields in the RS treatment had higher soil exchangeable K than the standard value for fertile soil. Therefore, K input through RS is sufficient for maintaining positive K balance, whereas K input in the CDC treatment from CDC or fertilizer may need to be increased to ensure positive K balance.


Introduction
Potassium (K) is an essential macronutrient for growth and development of all plants, including rice (Brouder 2011). It plays a role in enzyme activity, water retention, and stomatal movement (Marschner 1995). K deficiency inhibits plant growth and decreases crop yield.
In intensive agricultural systems, the overall uptake of K by crops has increased markedly, which has shifted K balances toward negative values. Negative K balances under intensive rice cropping have been reported in Asian countries because of the inadequate application of K fertilizers, which has resulted in the depletion of native K reserves (Dobermann, Sta Cruz, and Cassman 1996). The consumption of K fertilizers in agriculture in many developing countries has increased, while in Japan it has recently decreased (FAO, 2021). The fact that inadequate K application leads to negative K balance in paddy fields in some countries raises a question of how K fertilizers are applied in Japanese paddy fields and what the soil K balance and soil K status in farmers' paddy fields are.
One of the main causes of K deficiency in rice paddy fields is biomass removal from soil in the form of rice straw (RS) (Smil 1999), because most of the K taken up by the rice plant remains in the RS at harvesting (Dobermann and Fairhurst 2000;Fageria et al. 2010). Saha et al. (2009) reported negative K balance in rice-based cropping systems after RS removal, even with the application of the recommended amounts of K fertilizers. Therefore, RS recycling after harvesting is important for maintaining K balance. RS incorporation increases the K pool in paddy soil as microbial biomass K and exchangeable K (Yamashita et al. 2014) andK uptake (Ponnamperuma 1984).
In Yamagata Prefecture, Japan, RS is commonly cut and spread in the fields by combine harvesters at harvest and is incorporated into the soil in the next cropping season. This practice has been conducted since combine harvesters were introduced in the 1970s. However, in mixed crop-livestock systems, RS is removed from the field, used as the feed for cows, and then cow dung compost (CDC) is applied to the field. CDC is a good source of nitrogen (N), phosphorus (P), and K (Khem et al. 2018;Nguyen et al. 2020a). We have observed that CDC supplies more N and P than does RS in farmers' paddy fields (Nguyen et al. 2020a). The higher N input from CDC than from RS tended to result in a higher N balance in CDC-treated fields, with no statistically significant difference in N balance or soil total N between the treatments (Nguyen et al. 2020b). The higher P input from CDC than from RS allows farmers to apply lower amounts of P fertilizers in CDCtreated fields than in RS-treated fields, with P balance similar between the treatments (Nguyen et al. 2021). The effects of CDC application or RS recycling on K balance remain to be investigated, and how farmers manage K fertilizer application when RS is substituted with CDC is an open question.
Exchangeable K is the fraction of soil K that is electrostatically bound to the surface of minerals and organic matter and is readily available for plants. It has been used as an indicator to evaluate the K fertility of the soil (Dobermann and Fairhurst 2000). Plants can also take up non-exchangeable K from soil (Moritsuka et al. 2003), but its availability to plants is moderate or low because it is bound more strongly to minerals than exchangeable K. Non-exchangeable K is held between adjacent tetrahedral layers of intergrade clay minerals and is not bound covalently within the crystal structures of soil mineral particles (Helmke and Sparks 1996). Plants acquire considerable proportions of K that they need from this pool (Moritsuka et al. 2003;Moritsuka, Yanai, and Kosaki 2004). Therefore, both exchangeable and non-exchangeable K are important indicators of soil K fertility and soil K status.
Here, we investigated K inputs from RS or CDC and fertilizer, the K balance, and the soil K status (soil exchangeable and nonexchangeable K) in farmers' paddy fields under conventional RS recycling vs. RS removal followed by CDC application in mixed crop-livestock systems.

Study sites
The experiment was conducted in paddy fields in Mamurogawa town (38°51′N, 140°15′E; 374 km 2 ) in northern Yamagata Prefecture, Japan, in the 2017 and 2018 rice growth seasons. Paddy fields account for 88% of the total arable land in Mamurogawa (Ministry of Agriculture, Forestry and Fisheries 2019). Rice accounts for half of the gross agricultural production, and the other half comes from vegetables and livestock. Mixed crop-livestock systems have been practiced for many years in this area (see 2.2). Rice is cultivated once a year, from late April or early May to September or October. The fields are covered by snow from November to March; the average annual snowfall from 1982 to 2010 was 917 cm (Japan Meteorological Agency 2021). From 1981 to 2010, the mean annual temperature in the study area was 10.0°C and the average annual precipitation was 2711 mm (Japan Meteorological Agency 2021).

Field selection and treatments
In a previous study (Nguyen et al. 2020a), we investigated soil fertility of 79 paddy fields in which RS remained (RS treatment) or was taken to feed cows and then substituted with CDC (CDC treatment). From these fields, we chose 10 adjacent field pairs, one treated with RS and the other one with CDC. We selected the adjacent fields to reduce the variations in soil properties and environmental conditions between treatments. The mean distance between fields in each pair was 138.2 m (standard deviation 192.7). These field pairs were the same as in our previous studies conducted to evaluate nitrogen and phosphorus balance (Nguyen et al. 2020b(Nguyen et al. , 2021. In 2017, the data of only eight field pairs were fully collected due to miscommunication with farmers at harvesting time. In 2018, the data for 10 field pairs were collected. The duration of the RS treatments ranged from 10 to 43 years (avg. 33 years), and that of the CDC treatments ranged from 4 to 52 years (avg. 21 years) (Table S1). There were five main soil types in the study fields: Gray Lowland soils, Gley Lowland soils, Non-allophanic Andosols, Regosolic Andosols, and Wet Andosols (Table S1; NARO 2019; Obara et al. 2011). Edible, Sake, and Forage rice cultivars were grown in the study fields: 'Tsuyahime,' 'Haenuki,' 'Yukiwakamaru,' 'SD1,' 'Himenomochi,' 'Koshihikari,' 'Hitomebore'(edible rice), 'Dewasansan' (sake rice), and 'Yumeaoba' and 'Fukuhibiki' (forage rice) (Table S1).

The concept of K balance
The K balance was defined as the net change in the soil system's K content that results from all K inputs and outputs, including K gains and losses by the soil (Oenema, Kros, and Vries 2003). The K balance (kg K ha -1 yr -1 ) was calculated as follows: where K inputs is the annual K input (kg K ha -1 yr -1 ) to the field through organic matter (RS or CDC), K fertilizer, and irrigation water; K outputs is the annual K output (kg K ha -1 yr -1 ) from the field through K uptake by rice plants at harvesting and K leaching to the subsoil. Because water management of all fields followed the guidelines of Yamagata Prefecture for rice cultivation (Yamagata Prefecture 2010), K input from irrigation water was assumed to be 7.7 kg K ha -1 in all fields (averaged value for the Mamurogawa area; Matsuda and Kumagai 2017). We did not include K input through rainfall and K output through runoff in the above equation, because these amounts are reportedly small and have only negligible effects on K balance (Shibahara, Kawamura, and Kobayashi 1994;Dobermann et al. 1998).

Soil bulk density, exchangeable K, and nonexchangeable K
In each field, soil samples were taken from the plow layer with an auger (5 cm in diameter) at six positions and bulked together to make one sample in October 2017 and 2018 after rice harvesting. The position for soil sampling was determined following a modified diagonal-line soil sampling method (Anzai 1997). The boundary between the plow layer and the sublayer was found manually, and then the plow layer depth was measured with a ruler and recorded. Soil samples were dried in a forced-air oven at 35°C. Plant residues and stones were removed from soil samples manually. The forced-air dried soil was then ground in a ceramic mortar and passed through a 2mm sieve. Bulk density (BD) of soil was measured by taking 100cm 3 cores in the plow layer at three positions in each field. In the determination of BD, the gravel content was assumed to be negligible. Exchangeable K was extracted with 1 M ammonium acetate (pH 7.0; Harada 1984) and K concentration in the extract was determined by flame atomic absorption spectrometry (Spectr-AA 220-FS, Varian Australia Pty Ltd., Mulgrave, Australia). To determine the sum of exchangeable and nonexchangeable K, the soil was boiled with 1 M HNO 3 for 15 minutes (Helmke and Sparks 1996), and K concentration in the extract was determined by flame atomic absorption spectrometry (Spectr-AA 220-FS). To calculate the amount of nonexchangeable K, the amount of exchangeable K was subtracted from the amount of boiling 1 M HNO 3 -extractable K.
The amounts of exchangeable and non-exchangeable K (kg K ha -1 ) in plow layer soil were calculated as follows: K amount = K content × plow layer depth × BD × 0.1 where K content in mg kg -1 , plow layer depth in cm, BD in g cm -3 , and 0.1 is a unit-conversion factor.

Rice yield, K output by plant uptake, and K input from RS
To investigate the rice yield, 66 rice hills were sampled from each field at harvesting in October 2017 and 2018. In each field, plants samples were taken from three locations: one in the center and two near the two sides. At each location, two adjacent rows of 11 consecutive hills (22 hills in total) were collected at the soil surface. To determine brown rice yield, grain from 52 hills was dried until moisture content reached about 15% and threshed. Filled grain was separated from unfilled grain with a grain blower and husked. The brown rice was weighed and its moisture content was measured to adjust brown rice yield to 15% moisture.
The remaining 14 hills, which had a number of panicles per hill equal to the average number of panicles of 66 hills, were collected as in Kono (1975). A sub-sample of 4 hills from the 14 hills was used to determine the amount of K output by plant uptake and K input from RS. The aboveground parts of these four hills were separated into stems, panicles, and leaves. The samples were dried in a forced-air oven at 80°C, ground finely with a grinder (TI-100, Heiko Seisakusho, Ltd., Tokyo, Japan), and used to determine the total K content. A part of the ground sample was dried at 105°C and weighed to calculate moisture content; these data were used in the calculation of the dry weight of each plant part. Because stubble remains in the fields in both treatments, it was excluded from the calculation of plant K uptake and K input from RS. Plant K uptake was the sum of K uptake by the panicle, leaves, and stems (without stubble), and K input from RS was the sum of K amount in leaves and stems (without stubble). The sum of K amount in leaves and stem (without stubble) taken in 2017 and 2018 was assumed as the K input from RS in the 2017 and 2018 seasons, respectively. K uptake by the panicle, leaves, and stems (without stubble) was determined by multiplying the K content in each part of the plant by the corresponding dry weight. The weight of the stubble was calculated as 13% of the total weight of stem and leaves as in Ogawa, Takeuchi, and Katayama (1988) and Hayano et al. (2013).
To determine the total K content, ground samples were digested with concentrated H 2 SO 4 and H 2 O 2 (30%) (Mizuno and Minami 1980). The K concentration in the digestion solution was determined by flame atomic absorption spectrometry (Spectr-AA 220-FS).

K input from CDC
CDC samples were taken before application in April 2017 and 2018 from the storage of each farmer and divided into two parts. One part was dried at 60°C in a forced-air oven, ground finely with a grinder (TI-100), and then used to determine total K content that was used in the calculation of the K input from CDC. The other part was dried at 105°C in a forced-air oven to calculate the moisture content which was then used in the calculation of the application rate on a dry weight basis. The data of CDC application rate was obtained by asking the farmers.
The total K content in CDC was determined by the same method as for plant samples. Total K input from CDC was calculated by multiplying the total K content by dry weight. The total N, P, and C contents of the RS and CDC were also measured (Table S2).

K input from fertilizer
The application rate of K fertilizer was obtained by interviewing farmers about their fertilizer use in November 2017 and 2018. The types and amounts of fertilizer that were used in each season were recorded by farmers in their notebooks.

K output by leaching loss
The leaching water samples were collected by using a reducedpressure suction method (Toriyama and Ishida 1987;Kato 1997) with a ceramic tube (10-cm in length and 8-mm in diameter, sealed at one end) joined with a silicon tube (7-mm inner diameter, 9-mm outer diameter). The ceramic tube was set vertically at a depth of 30 to 40 cm under the soil surface in the middle of four rice hills at three locations in each field after transplanting. The silicon tubes were extended to 20 cm above the soil surface to prevent a flow of ponding water into the tube. To prevent the entering of insects or rainwater into the silicon tube, the end of tube was wrapped up with a plastic bag. The leaching water samples were firstly collected at 3 or 4 days after the installation of ceramic tube and continued at 1-or 2week intervals thereafter. A 50-mL plastic syringe was used to pump up the leaching water. The pH of the leaching water samples was determined using a glass electrode pH meter (TOA HM-20S pH meter, TOA Electronics Ltd., Tokyo, Japan), and adjusted to be between 2.0 and 3.0 by adding concentrated HCl and the sample was kept in a refrigerator. The K concentration in the samples was measured by flame atomic absorption spectrometry (Spectr-AA 220-FS).
The amount of leaching water was determined by using three pairs of 5.6-cm-diameter PVC pipes setting up near to the position of ceramic tube. In each pair, one pipe without a cap at the bottom was set up at depth of 35 cm under the soil surface to measure the amount of water loss by leaching and evaporation, and the other was capped at the bottom and set up at a depth of 15 cm under the soil surface to measure the amount of water loss by evaporation only. The tops of both pipes were set at 10 cm above the soil surface. The water level in the pipes was recorded several times per week. The total amount of K loss due to leaching was calculated by multiplying the K concentration by the volume of leaching water.

Statistical analysis
Welch's t-test was used to compare the K inputs, K outputs, K balance, and soil exchangeable and non-exchangeable K between the RS and CDC fields. Correlation analysis was used to analyze the correlation of K input with plant K uptake and K balance. The analysis was performed using the Analysis ToolPak in Excel for Office 365 (Microsoft, Redmond, WA, USA). A P value < 0.05 was considered to indicate a significant difference.

K input from fertilizer
The average amount of K fertilizer applied in the RS treatment was 61.5 kg K ha -1 in 2017 and 51.0 kg K ha -1 in 2018, and that in the CDC treatment was 58.4 kg K ha -1 in 2017 and 54.7 kg K ha -1 in 2018 (Table 1). It ranged from 14.7 to 91.3 kg K ha -1 in the RS treatment and from 24.9 to 98.8 kg K ha -1 in the CDC treatment (Fig. S1). Statistical analysis (Table 1) and the distribution of the data (Fig. S1) indicated no difference in K input from fertilizer between treatments. Most of the K fertilizer was inorganic or organic compound fertilizer and was applied as basal fertilizer before transplanting.

K input from RS and CDC
The amount of RS remaining in the field tended to be higher than that of CDC applied in 2017 and was significantly higher in 2018 ( Table 2). The K content in RS was 16.3 g K kg -1 in 2017 and 15.0 g K kg -1 in 2018, and that of CDC was 12.6 g K kg -1 in 2017 and 14.7 g K kg -1 in 2018. Statistical analysis indicated no significant difference in K content between RS and CDC ( Table 2). The K content of CDC varied greatly, from 2.29 to 26.75 g K kg -1 in 2017 and from 1.04 to 27.69 g K kg -1 in 2018 (data not shown).
The total K input from RS was 88.2 kg K ha -1 in 2017 and 82.7 kg K ha -1 in 2018, and that from CDC was 50.8 kg K ha -1 in 2017 and 63.0 kg K ha -1 in 2018. The difference in total K input between RS and CDC in both years was not statistically significant (Table 2), but in most field pairs (12 out of 18 field pairs), the values were higher in RS than CDC (Fig. S1). A large variation in the K content of CDC caused a large variation in K input from CDC: from 11.9 to 137.3 kg K ha -1 in 2017 and from 2.2 to 126.3 kg K ha -1 in 2018 (Fig. S1).

Plant K uptake and brown rice yield
At harvest, K content was highest in stems, followed by leaves and then grain ( Table 3). Most of the K taken up by plants went to stems, accounting for 69% of total K uptake in the RS treatment and 70% in the CDC treatment. There was no significant difference between treatments in K content or K uptake in each plant part, even though some values were higher in the CDC treatment than in the RS treatment. Total plant K uptake in the CDC treatment tended to be higher than in the RS treatment; the difference was not significant in both years (Table 3), but most of the values in 2017 (6 out of 8 field pairs) were higher in the CDC treatment (Fig.  S1). There was a positive correlation between total K input and plant K uptake in the RS treatment ( Figure 1).
As shown in Table S1, six field pairs (No. 1-5, and 9) in 2017 and five field pairs (No. 1, 2, 5, 6, and 8) in 2018 had the same cultivar. Field pairs No. 1, 2, and 5 with the same cultivar in both years were chosen to compare the brown rice yield, and no difference was found between the treatments in both years ( Figure 2). Values are mean ± SD. The P value is the probability level of two-tailed Welch's t-test. † Irrigation input was not measured and is indicated according to Matsuda and Kumagai (2017). Values are mean ± SD. The P value is the probability level of two-tailed Welch's t-test. All data are on a dry-matter basis.

K leaching loss
K concentration in leaching water ranged from 1.6 to 4.0 mg K L -1 (Figure 3). In 2017, K concentration in both treatments decreased continuously until 16 weeks after transplanting (WAT) from 4.0 to 1.6 mg K L -1 in the CDC treatment and from 3.5 to 2.0 mg K L -1 in the RS treatment. K concentration was higher in the CDC treatment than in the RS treatment in the first 8 weeks but was lower in the last 8 weeks. In 2018, K concentration in leaching water was 2.3 mg K L -1 at 2 WAT in both treatments, peaked at 8 WAT (RS: 3.4 K L -1 ; CDC: 3.0 mg K L -1 ), and then decreased continuously to 2.5 mg K L -1 in the RS treatment and 2.2 mg K L -1 in the CDC treatment. K concentration was the same in both treatments at 2-6 WAT but was higher in the RS treatment at 8-16 WAT. The total K leaching loss in the RS treatment (2017: 7.3 kg K ha -1 ; 2018: 7.0 kg K ha -1 ) was lower than in the CDC treatment (2017: 7.9 kg K ha -1 ; 2018: 7.3 kg K ha -1 ; Table 1). However, statistical analysis (Table 1) and the distribution of the data (Fig. S1) indicated no difference in K leaching loss amount between treatments.

K balance
K balance was positive in the RS treatment in both years and in the CDC treatment in 2018 (Table 1). Over the two years, K balance was negative in 2 of 18 fields in the RS treatment and in 9 of 18 fields in the CDC treatment (Fig. S1). K balance was Values are mean ± SD. The P value is the probability level of two-tailed Welch's t-test.  significantly higher in the RS treatment than in the CDC treatment in 2017 and tended to be higher in 2018 (Table 1). There was a strong positive correlation between total K input and K balance in both treatments (Figure 1).

Soil K status
Soil exchangeable K in the RS treatment was 189.3 mg K kg -1 in 2017 and 165.9 mg K kg -1 in 2018, and that in the CDC treatment was 174.0 mg K kg -1 in 2017 and 189.1 mg K kg -1 in 2018 (Table 4). Non-exchangeable K in the RS treatment was 594.3 mg K kg -1 in 2017 and 546.4 mg K kg -1 in 2018, and that in the CDC treatment was 711.1 mg K kg -1 in 2017 and 539.9 mg K kg -1 in 2018. The contents of exchangeable and non-exchangeable K in soil did not differ significantly between treatments in either year (Table 4). Also, the amounts of exchangeable and non-exchangeable K in the plow layer did not differ significantly between treatments in either year (Table 4).

K inputs in the RS and CDC treatments
In the RS treatment, K fertilizer application ranged from 14.7 to 91.3 kg K ha -1 (Fig. S1), and its contribution to total K input ranged from 16.3% to 47.8% (data not shown). In this treatment, 10 out of 18 fields had lower than the recommended amount of K fertilizer for paddy rice in the study area (from 37 to 83 kg K ha -1 depending on the cultivars; Yamagata Prefecture 2010). K input from RS was higher than that from fertilizer, ranging from 56.3 to 125.9 kg K ha -1 (Fig. S1); its contribution to total K input ranged from 48.1% to 78.2% (data not shown).
In the CDC treatment, K fertilizer application did not differ significantly from that in the RS treatment. It ranged from 24.9 to 98.8 kg K ha -1 (Fig. S1), and its contribution to the total K input ranged from 22.0% to 81.4% (data not shown). In this treatment, 10 out of 18 fields had a lower amount of K fertilizer than recommended for paddy rice in the study area. The high contribution of K fertilizer to total K input in some fields in the CDC treatment was due to the low input from CDC. The K input from CDC ranged from 2.2 to 137.3 kg K ha -1 (Fig. S1), and its contribution to total K input ranged from 6.4% to 73.5% (data not shown). In most field pairs, K input from CDC was lower than that from RS. We attribute the wide range of K input from CDC to the differences in K content in CDC, which was very low in some CDC samples but very high in others (Table S3). The dependence of the variation in K content on raw materials (Hashimoto and Ishikawa 1964;Kohyama et al. 2006;Ooya, Washio, and Ishibashi 2018) and storage methods (Hasegawa, Furukawa, and Kimura 2005) has been reported, so we  Values are mean ± SD. The P value is the probability level of two-tailed Welch's t-test.
tentatively attribute the large variation in K content in CDC to these factors. The materials used for making CDC differed among farmers and between years for the same farmers. The total K content in CDC stored indoors (25.1 g K kg -1 ) was much higher than in that stored outdoors (6.6 g K kg -1 ) (Table S3). Since about 70% of K in CDC is water soluble (Oyanagi et al. 2004), rainwater must have facilitated the leaching loss of K from CDC stored outdoors.

K outputs in the RS and CDC treatments
Plant K uptake accounted for 94% of the total output in both treatments (Table 1). It ranged from 75.3 to 151.1 kg K ha -1 in the RS treatment and from 73.5 to 162.1 kg K ha -1 in the CDC treatment (Fig. S1) and did not differ significantly between the treatments (Table 1). Plant K uptake in 2017 was slightly higher than that in 2018 in both treatments. Plant K uptake had strong positive correlation with brown rice yield, and the yield average for all study fields was higher in 2017 than in 2018 (data not shown). Rice cultivars, however, differed among field pairs and years. Comparison of brown rice yield in three field pairs with the same cultivar in both years revealed no difference between the years (Figure 2). Plant K uptake increased with an increase in total K input, although significant correlation was observed only in the RS treatment ( Figure 1). Stems at harvesting accounted for 69% of total K uptake in the RS treatment and 70% in the CDC treatment (Table 3). This result confirms that RS is an important K input to the field as reported by Dobermann and Fairhurst (2000) and Fageria et al. (2010). K leaching loss accounted for 6.4% of total K output in the RS treatment and 6.5% in the CDC treatment (Table 1). The range of K concentrations in leaching water and the amount of K leaching loss were similar to those in Katoh et al. (2003; estimated water leaching 0.5 cm day -1 ). The amount of K leaching was almost the same as a K input of 7.7 kg K ha -1 from irrigation water reported in this area by Matsuda and Kumagai (2017).

K balance in the RS and CDC treatments
In the RS treatments, K balance was positive in all fields in 2017 and 80% of the fields in 2018. It was positive in all fields when the data for each field was summed over the two years (data not shown), even when the amount of K fertilizer was lower than the recommended one. We attribute these results to the K input from RS. Exclusion of the K input from RS from the calculation of K balance would lead to a negative balance in all fields in the RS treatment. We confirmed that RS incorporation in the field is important to maintain K balance in paddy fields, as reported by Saha et al. (2009).
In the CDC treatments, negative K balance was observed in 63% of the fields in 2017 and in 40% in 2018 (data not shown). When K balance was summed for each field over two years, it was still negative in 60% of the fields. The negative K balance in CDC can be explained by the inadequate amount of K input from fertilizer or K input from CDC. The recommended amount of K fertilizer for paddy rice in the study area is 37 to 83 kg K ha -1 (Yamagata Prefecture 2010). If we applied 83 kg K ha -1 in all fields in CDC treatment, the percentage of negative-balance fields would be reduced from 63% to 50% in 2017, from 40% to 20% in 2018, and from 60% to 30% when the data for each field was summed over the two years. The rate of CDC application in the study field (10 to 20 t ha -1 in fresh weight) was higher than the recommended one in the study area (5 to 10 t ha -1 in fresh weight; Yamagata Prefecture 2010). However, due to the low K content in some CDC batches, the amount of K input was not enough for a positive K balance even if the recommended rate of fertilizer was applied. Therefore, to make K balance positive, the K content in CDC should be evaluated beforehand and the amount of co-applied K fertilizer should be adjusted as needed.
In 2017, the average value of K balance in the RS treatment was positive and significantly higher than that in the CDC treatment, in which the average value was negative (Table 1). In 2018, the average value of K balance in both treatments was positive and there was no significant difference between the treatments, even though the K balance of the CDC treatment was about half that of the RS treatment. The difference in soil types (Gray Lowland soils, Gley Lowland soils, Non-allophanic Andosols, Regosolic Andosols, and Wet Andosols; Table S1) may have caused a high variation of the data in each treatment, which masked the differences between the treatments. However, the comparison of soil K balance between the treatments in each soil type (Table S4) gave the same result as the comparison in all fields (Table 1). The intermingling of the soil types did not affect the comparison of K balance between the treatments.

Status of soil K in the RS and CDC treatments
Soil exchangeable and non-exchangeable K did not differ between the treatments or years, although non-exchangeable K decreased slightly in 2018 in comparison with 2017 in each treatment (Table 4). Soil exchangeable and nonexchangeable K were higher in Andosol than in Lowland soil, but the comparison of soil exchangeable and nonexchangeable K between the treatments in each soil type (Table S5) gave the same result as the comparison in all fields (Table 4). Therefore, the variation of soil types in the study fields did not affect the difference in soil K status between the treatments. The contribution of K balance to the sum of soil exchangeable K and non-exchangeable K was 4.4% (data not shown).
The amounts of exchangeable and non-exchangeable K in each Lowland soil and Andosol were within the range of standard values among agricultural soils that Kitagawa, Yanai, and Nakao (2018) collected from all over Japan. To evaluate soil K fertility, soil exchangeable K in the study fields was compared with the standard value of 125 mg K kg −1 reported by Tohoku Regional Agricultural Administration Office (1978) for paddy soil in the Tohoku region, where the study area is located. Exchangeable K was below 125 mg K kg −1 in both years in one field in the RS treatment and in three fields in the CDC treatments. Therefore, RS recycling could result in higher soil K fertility than RS removal and substitution with CDC.

Conclusion
In the study area (Mamurogawa, Yamagata), K fertilizer application varied widely among farmers in both RS recycling fields and fields where RS was replaced with CDC. The amount of K fertilizer applied did not differ significantly between the treatments. K fertilizer was applied at a rate lower than recommended in 56% of the fields (10 out of 18 fields) in both treatments. When RS remained in the field, K balance was positive even if K fertilizer application was lower than recommended. RS is an important K input to maintain K balance, because most K taken up by rice plants remains in the stem at harvest. When RS was substituted with CDC, K balance was negative in some fields because low K content in some CDC batches resulted in low K input from CDC. Therefore, in the fields where RS is substituted with CDC, the K content of CDC or K fertilizer amount should be adjusted to maintain K balance. In most of the RS-treated fields, soil exchangeable K was maintained higher than the standard value for fertile soil.