Abstract
Background and aims
It is so far a gap in knowledge to assess nitrate (NO3 −) leaching loss linking with crop yield for a given cereal cropping system.
Methods
We conducted a meta-analysis on 32 published studies reporting both NO3 − leaching losses and crop yields in the maize (N = 20) and wheat (N = 12) systems.
Results
On average, 22 % and 15 % of applied fertilizer N to wheat and maize systems worldwide are leached in the form of NO3 −, respectively. The average area-scaled NO3 - leaching loss for maize (57.4 kg N ha−1) was approx. two times higher than for wheat (29.0 kg N ha−1). While, if scaled to crop yields, the average yield-scaled NO3 − losses were comparable between maize (5.40 kg N Mg−1) and wheat (5.41 kg N Mg−1) systems. Across all sites, the lowest yield-scaled NO3 − leaching losses were observed at slightly suboptimal fertilization rates, corresponding to 90 % and 96 % of maximum maize or wheat yields, respectively.
Conclusions
Our findings suggest that small adjustments of agricultural N management practices can effectively reduce yield-scaled NO3 − leaching losses. However, further targeted field experiments are still needed to identify at regional scale best agricultural management practices for reducing yield-scaled NO3 − leaching losses in maize and wheat systems.
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Introduction
Nitrogen (N) addition to agricultural systems is an essential facet of modern agriculture, which currently feeds 7 billons people in the world (Erisman et al. 2008; Tilman et al. 2002). N fertilizer applications remain essential and are contributing about 30–50 % to crop yield increase (Erisman et al. 2008). The major cereal crops (maize, wheat and rice) provide close to 60 % of all human calories, either directly as human food or indirectly as feed for livestock production (Cassman et al. 2003; Linquist et al. 2012). With further increases in global population and changing human diets the major challenge remains to meet the huge food demand of 9 billion people by 2050 (Godfray et al. 2010; Tilman et al. 2011). Intensification of agricultural production and increasing use of N fertilizers was so far the key to meet global yield demands. However, high production cropping systems are always associated with substantial hydrological and gaseous N losses (e.g., Ju et al. 2009; Zhou et al. 2013) mostly due to the difficulty in accurately predicting site-specific N requirements (e.g., Cassman et al. 2003). Consequently, nitrogen surpluses are a common feature for most cropping systems in the world (e.g., Sutton et al. 2011; Vitousek et al. 2009). On average, annual grain crops take up less than 50 % of applied N worldwide (Cassman et al. 2002). A large proportion of excessive N is lost into the environment through unmanaged hydrological and gaseous pathways (Vitousek et al. 2009). Nitrate (NO3 −) leaching is the main N loss pathway from cropping systems (e.g., Robertson and Vitousek 2009; Zhou et al. 2012; Zhu et al. 2009) and is the dominant source of NO3 − in the hydrosphere (He et al. 2011). Globally, NO3 − leaching losses from agricultural systems are estimated to account for 19 % of total applied N in the world (Lin et al. 2001). The large amount of NO3 − leaching losses into the hydrosphere can not only induce groundwater quality degradation and surface water eutrophication (Carpenter et al. 1998; Sutton et al. 2011) but also increase the risk of cancer for humans, especially, when excessive NO3 − is ingested in drink water (Rivett et al. 2008). NO3 − leaching losses have been intensively measured in various cropping systems (Basso and Ritchie 2005; Gheysari et al. 2009; Huang et al. 2011; Sepaskhah and Tafteh 2012; Zhou et al. 2012). However, besides a well-documented positive correlation between NO3 − leaching losses and N fertilizer application rates (e.g., Huang et al. 2011), consistent patterns between the magnitude of NO3 − leaching losses and agricultural management practices, such as N fertilizer type, tillage method and irrigation management, could so far not be demonstrated (Bakhsh et al. 2005; Zavattaro et al. 2012).
To meet future demands of grain crops of an increasing global population, the concept of sustainable intensification has been proposed. This widely acknowledged concept (Grassini and Cassman 2012; Mueller et al. 2012; Tilman et al. 2011) postulates that higher crop yields can be achieved while environmental impacts such as NO3 − leaching can be minimized (Cassman et al. 2003; Matson and Vitousek 2006; Smith and Gregory 2013; Tilman 1999). That this is feasible has been shown in the study by Mueller et al. (2012). It shows that meeting the global challenges of food security and environmental sustainability for the coming decades could be achieved through carefully considering nutrient and water managements (Mueller et al. 2012). By conducting actual field experiments, Grassini and Cassman (2012) achieved high crop yields and improved environmental performances in terms of greenhouse gases emissions from an irrigated maize system in Nebraska through better management of water and N fertilizer inputs.
Linking crop yield and environmental performance with regard to greenhouse gas emissions has been identified as a valuable approach to evaluate a given cropping system in the framework of sustainable intensification (e.g., Linquist et al. 2012). Moreover, the yield-scaled approach has been intensively applied to evaluate emissions of greenhouse gases from cropping systems (Grassini and Cassman 2012; Linquist et al. 2012; Shang et al. 2011; Van Groenigen et al. 2010), while to our knowledge no studies used such an approach to assess NO3 − leaching losses from cereal cropping systems.
To close this gap in knowledge we conducted a meta-analysis of published studies in order to (1) assess NO3 − leaching loss on a yield-scaled basis from maize and wheat systems; (2) illustrate that yield-scaled NO3 − leaching loss, rather than the conventionally reported NO3 − leaching loss as a function of area, is a more suitable integrated metric to evaluate NO3 − leaching loss for a given cereal system; (3) explore the implications to minimize yield-scaled NO3 − leaching loss from maize and wheat systems.
Materials and methods
Data
An exhaustive literature survey of peer-reviewed publications that reported NO3 − leaching losses from the major cereal systems (wheat, maize and rice) was carried out using the ISI-Web of Science research database for articles published before January 2013. We only included studies that simultaneously reported both NO3 − leaching loss and crop yield. Furthermore, NO3 − leaching loss must have been measured under field conditions at least for an entire season, i.e. from planting to harvest. Since we only found one study meeting the criteria for rice (Zhang et al. 2011), we needed to drop the idea to also include rice systems in our analysis. In addition to (area-scaled) NO3 − leaching loss, another four variations characterizing N fertilizer dynamics were taken into account: (a) yield-scaled NO3 − leaching loss, (b) the N surplus (here defined as N application rate minus crop N uptake), (c) crop grain yield and (d) crop nitrogen use efficiency (NUE). It is noteworthy that crop NUE (%) here was calculated by using the N difference method which is based on the difference in N uptake between a given crop that receives a given amount of applied N and N uptake in the unfertilized treatment.
The amount of N applied as inorganic fertilizer, manure or green manure was determined for each study treatment. We did not include the amount of N inputs from either previous crop residues or applied crop residues since these data were rarely reported or N contents of crop residues were not available. The final dataset consisted of 20 (136 observations) and 12 (69 observations) studies for maize and wheat, respectively (Table 1). Estimates of NO3 − leaching losses included in this analysis were obtained by measuring soil water NO3 − concentrations with suction cups or plates (52 %) in combination with soil water hydrological modeling or by using lysimeters (48 %). In several studies NO3 − leaching losses were measured at various soil depths. For our study we only used those data of NO3 − leaching losses as given for the deepest soil layer. For maize, the majority of studies were from Europe (9), six studies from Asia and five studies from the USA. For wheat, seven studies were from Europe, four studies from Asia, and one from South America (Fig. 1). Prior to starting meta-analysis, we calculated yield-scaled NO3 − leaching loss (kg N Mg–1 grain), N surplus (kg N ha–1) and crop nitrogen use efficiency (%) for each individual treatment. In order to further examine the relationship between N application rate and the four selected variations, such as NO3 − leaching loss, yield-scaled NO3 − leaching loss and crop yields, the included studies were divided based on N fertilizer application rates into five categories for both maize (0–100, 100–200, 200–300, 300–400, and >400 kg N ha–1) and wheat (0–100, 100–150, 150–200, 200–250 and >250 kg N ha−1) systems.
Data analysis
For every study, the NO3 − leaching, yield-scaled NO3 − leaching, N surplus, crop yield and NUE for each individual treatment combination were included as a separate data point (observation) in our meta-analysis. We performed meta-analysis using a nonparametric weighting function and generated confidence intervals (CIs) using bootstrapping. The observations were weighted by replicates. Note that inter-annual variations of NO3 − leaching losses have been intensively observed for wheat as well as for maize systems (e.g., Syswerda et al. 2012; Zhou et al. 2012), with annual NO3 − leaching values over a six years observation period ranging in the study by Zhou et al. (2012) from 19 to 53 kg NO3-N ha−1 year−1. Therefore, to avoid bias toward multi-year measurements, multi-year observations were averaged over experimental years. We used the software of MetaWin 2.1 to generate mean observations and the corresponding 95 % bootstrapped CIs (4999 iterations) (Rosenberg et al. 2000). Mean observations for the categories of studies (i.e. the two types of cereal crops (maize and wheat), and the categories according to N application rate within each crop type) were considered significantly different if their 95 % CIs did not overlap. To assess the potential of mitigating yield-scaled NO3 − loss, we identified the treatment with the lowest yield-scaled NO3 − leaching loss for each study, and repeated all meta-analysis by using the identified data set. Linear regression analysis were performed to obtain the mean values of NO3 − leaching lost per kg N applied in the maize and wheat cropping systems across study sites. Also, quadratic regression analysis between N application rates and relative yield (i.e. a percentage of maximum yield obtained at each study site) to identify the average optimum N application rates. In order to assess the implications for reducing NO3 − leaching loss, we tested the relationships between area-scaled and yield-scaled NO3 − leaching losses and N surplus in both maize and wheat cropping systems. Before exploring relationships between area-scaled and yield-scaled NO3 − leaching loss and N surplus across study sites, these corresponding values for each study site were normalized to values ranging between 0 and 1 by using Origin 7.0 (Origin Lab Corporation, USA). This is needed, since each study site has its own edaphic characteristics, climate conditions as well as agricultural management. All above regression analysis were performed by using SPSS 17.0 (SPSS, Inc., USA).
Results
Crop grain yield and NUE
Crop yields ranged between 3.4 and 13.5 Mg ha−1 (mean value: 10.1 Mg ha−1) for maize and 3.1 and 7.6 Mg ha−1 (mean value: 5.9 Mg ha−1) for wheat (Table 2). The corresponding average N application rates for maize and wheat were 249 and 171 kg N ha−1, respectively. Crop yields positively responded to N application rates and the quadratic model was appropriate for describing grain yields response to increasing N application rates in both maize and wheat systems (Fig. 4). Crop nitrogen use efficiency (NUE) ranged from 12.4 % to 64.1 % (mean value: 40.8 %) and 14.2 % to 74.6 % (mean value: 50.9 %) for maize and wheat systems, respectively (Table 2). The highest average crop NUE for maize (56.9 %) and wheat (66.7 %) systems were obtained with the corresponding average N application rates of 234.2 kg N ha−1 (ranging from 200 to 300 kg N ha−1) and 174.6 kg N ha−1 (ranging from 150 to 200 kg N ha−1), respectively.
Area-scaled NO3 − leaching loss
The NO3 − leaching losses across all sites ranged from 0.3 to 325.0 kg N ha−1 and 1.0 to 82.5 kg N ha−1 for maize and wheat systems, respectively (Table 2). The average NO3 − leaching loss for maize was 57.4 kg N ha−1 and, thus, approx. two times higher than that for wheat (29.0 kg N ha−1; Fig. 2a). For wheat as well as maize systems a significant linear relationship between NO3 − leaching losses and N fertilization could be determined (P < 0.05; Fig. 3). The linear regression reveals that on average 22 % and 15 % of N applied were lost through NO3 − leaching from maize and wheat systems, respectively. Moreover, average NO3 − leaching losses increased rather slowly along with N fertilizer rates if N fertilization rates were <150 kg N ha−1. However, if N application rates were >150 kg N ha−1 NO3 − leaching losses sharply increased to values >33.0 kg N ha−1 (Table 1).
Yield-scaled NO3 − leaching loss
The yield-scaled NO3 − leaching losses ranged from 0.3 to 25.6 kg N Mg−1 and 0.3 to 15.1 kg N Mg−1 for maize and wheat systems, respectively (Fig. 2b). In spite of higher area-scaled NO3 − leaching losses for maize cropping systems, the average yield-scaled NO3 − leaching loss was comparable between maize (5.40 kg N Mg−1) and wheat (5.41 kg N Mg−1) systems which is due to higher crop yields for maize (Table 2). On average the rather low yield-scaled NO3 − leaching losses (2.6–4.0 kg N Mg−1, mean: 3.2 kg N Mg−1,) in maize cropping systems were observed in studies with N fertilization rates being in the range of 100 to 200 kg N ha−1 (mean: 143 kg N ha−1) (Table 2). Similarly, for the wheat systems average yield-scaled NO3 − leaching losses were rather low (3.1–5.8 kg N Mg−1, mean: 4.5 kg N Mg−1) if N fertilization rates were in the range of 150 to 200 kg N ha−1 (mean: 175 kg N ha−1).
Discussion
Crop yield and area-scaled NO3 - leaching loss
Since achieving high crop yield has so far been the top priority of cereal production systems, the N fertilizers have been excessively applied to insure that crop yields are not limited by N supplies. However, has also shown in this analysis (Fig. 4) crop yields do not linearly respond to inputs of N fertilizer (e.g., Cassman et al. 2002; Sawyer et al. 2006). As closer N supply approaches optimum fertilization rates and specifically if N supply exceeds the optimum N supply, environmental losses of N such as in form of N2O or NH3 will increase exponentially (Van Groenigen et al. 2010; Sutton et al. 2011).
In converse to crop yields, our analysis revealed a linear relationship between NO3 − leaching loss and N application rates for both maize and wheat cropping systems (Fig. 3). Similar trends between N application rates and NO3 − leaching losses have been documented in several case studies (Dauden et al. 2004; Perego et al. 2012). For example, Dauden et al. (2004) reported a significantly positive correlation between NO3 − leaching losses and N application rates for a Spanish irrigated maize system. Moreover, our meta-analysis showed that across different studies with their specific-site features such as soil characteristics and agricultural management or climatic conditions, 25 % and 13 % of applied N were lost by NO3 − leaching to the hydrosphere from maize and wheat systems, respectively (Fig. 3). The values obtained in our study are close to the global value as derived by process based modeling as given by Lin et al. (2001) for leaching losses from cropland (19 %), but lower than the value of 30 % as suggested by IPCC (IPCC 2006). Nevertheless, the different values suggest that simply applying a “fractionation factor” (i.e. the proportion of applied N fertilizer to soils is leached) approach for estimating regional N fertilizer induced NO3 − leaching loss is questionable because NO3 − leaching loss is highly dependent on site-specific management practices, soil conditions and meteorological conditions during the measurements. Further site-specific field NO3 − leaching measurements, ideally, from various field treatments—well covering the local management practices—in various regions differing in climate and soil conditions, are still needed to decrease the uncertainties in estimate of global and regional NO3 − leaching losses during maize and wheat productions.
Our meta-analysis clearly shows that NO3 − leaching losses for maize systems are higher than those for wheat systems (Fig. 2, mean value: 57.4 vs. 29.0 kg N ha−1), a conclusion which is consistent with several previous case studies (e.g., Ju et al. 2009; Zhou et al. 2012). However, our database may be regional biased, since out of 69 observations for wheat which simultaneously provided data on NO3 − leaching as well as crop yields, 16 came from Denmark. Here, wheat fields were additional fertilized in autumn with solid manure, and on average 27 % of applied N was lost through NO3 − leaching (Sorensen and Rubaek 2012). In contrast, Huang et al. (2011) observed only 3.0 kg N ha−1 NO3 − leaching losses from a wheat production system at a N application rate of 180 kg N ha−1 in the north China. Nevertheless, differences in NO3 − leaching losses between maize and wheat systems are incontestable and can be primarily explained by in average higher N application rates for maize (249 kg N ha−1) as compared to wheat (171 kg N ha−1). Moreover, specifically in regions with two crops per year such as in most subtropical regions in China, maize is cropped during the warm and moist season (in China the monsoon season), while wheat is preferable cropped during the colder and dryer winter season (Fang et al. 2006; Zhou et al. 2012; Zhou et al. 2013; Zhu et al. 2009). For that reason NO3 − leaching losses in those regions are higher for maize as compared to wheat. For example, Zhou et al. (2012) conducted a six-year field experiment monitoring crop yields and NO3 − leaching of a rain-fed wheat-maize rotation system in the southwest China. They observed that approx. 21.9 % of applied N was lost through NO3 − leaching in the maize seasons, while in the wheat seasons no NO3 − leaching occurred.
Yield-scaled NO3 − leaching loss: a valuable integrated metric
Since crop yields as well as NO3 − leaching losses are up to optimum yields positively correlated with N application (Figs. 3 and 4) it remains challenging how to define a sustainably intensification of maize and wheat cropping systems, i.e. maintaining or increasing crop yields while reducing NO3 − leaching losses. Here we suggest to directly link NO3 − leaching losses and crop yields, rather than to solely use only values of NO3 − leaching losses (i.e. assess NO3 − leaching loss as a function of area). The major advantage of a yield-scaled approach is that it directly links crop yields with parameters describing environmental pollution. I.e. rather than the common metric as a function of area, a yield-scaled approach reflects negative environmental impacts per unit of product, and, thus, reflects the dual goals of sustainable intensification (i.e., reducing negative environmental impacts and maintaining or increasing crop yields). The yield-scaled approach has been intensively applied for assessing greenhouse gases (GHGs) emissions from agricultural systems by either meta-analysis or actual field case studies (Grassini and Cassman 2012; Linquist et al. 2012; Van Groenigen et al. 2010) but has never been used for describing NO3 − leaching losses from maize or wheat systems.
Our meta-analysis shows that the yield penalties when optimizing for lowest yield-scaled NO3 − leaching losses were rather low and close to the optimum yield. Table 3 shows that for the given agricultural N practices accepting yield losses of 4 % for maize and 10 % for wheat systems would decrease the NO3 − leaching losses per kg product to a minimum. This shows that minor changes in agricultural N management practices are likely to result in a significant reduction of NO3 − leaching losses from cereal systems, an approach which have been suggested before (Robertson and Vitousek 2009; Tilman et al. 2011; Tilman et al. 2002) but never been demonstrated in the frame of a cross-system and region meta-data analysis. Also for China Ju et al. (2009) suggested that reducing current N application rates (550–600 kg N ha−1 year−1) by 30–60 % will not significantly affect crop yields, but most likely would reduce N losses and here specifically NO3 − leaching losses to the environment by 50 %.
Implications to reduce NO3 − leaching loss
Note that here in this analysis we only discussed the implications of agricultural N management practices to reduce NO3 − leaching loss, even though irrigation management has been evidenced as another regulator of NO3 − leaching loss in cereal systems (e.g., Sepaskhah and Tafteh 2012; Tafteh and Sepaskhah 2012). The core of better agricultural N management for reducing NO3 − leaching loss is related to either improving crop NUE or reducing N surplus (e.g., Robertson and Vitousek 2009). On average area-scaled and yield-scaled NO3 − leaching losses for maize systems decreased along with increasing nitrogen use efficiency (NUE, here defined as the fraction of applied N taken up in the above-ground biomass at physiological maturity relative to the non-fertilized treatment) in this meta-analysis (Table 2), indicating that improving NUE can reduce NO3 − leaching loss in maize system. Similarly, Li et al. (2007) on the basis of a three-year field experiment in the North China Plain—where over 20 % of the national grain productions of China is produced—concluded that agriculture management practices which increase crop NUE will also significantly reduce NO3 − leaching losses from maize systems. However, as shown in Table 2, improving crop NUE may not always reduce NO3 − leaching loss from wheat systems. For example, manure N fertilizers applied prior to sowing winter wheat increased NO3 − leaching losses to 23–35 % of applied N, though 60 % of applied N was taken up by the crops in this study (Sorensen and Rubaek 2012). Therefore, synchronizing N applications with crop residue and soil N stock mineralization dynamics and actual crop N requirements are a prerequisite to mitigate NO3 − leaching loss from cropping systems (Ju et al. 2009; Li et al. 2007; Meisinger and Delgado 2002).
In our meta-analysis we show a positive relationship between N surplus (defined as N application minus crop N uptake) and area-scaled and yield-scaled NO3 − leaching losses (Fig. 5). It demonstrates that NO3 − leaching losses substantially increase when N applications are exceeding crop N uptake, which has been observed by several previous studies (Ju et al. 2004; Ju et al. 2006; Ju et al. 2009; Li et al. 2007; Perego et al. 2012; Robertson and Vitousek 2009). For example, Perego et al. (2012) observed substantial NO3 − leaching losses associated with large N surplus for maize systems in the Po Valley, Italy. This can be explained by the accumulation of NO3 − in the soil profile and subsequent leaching of NO3 − following heavy rainfall or major irrigation events (e.g., Ju and Christie 2011; Zhou et al. 2012). It is of interest that both area-scaled and yield-scaled NO3 − leaching losses varied little if systems received N fertilization in the range of 85–113 % of crop N requirements but increased sharply when N surplus exceeded 50 kg N ha−1 or >115 % of the optimal N fertilization rate (Table 2). This further indicates that application of N fertilizer in accordance with crop N requirements is key to reduce NO3 − leaching losses from the cereal cropping systems.
Though the identification of agricultural N management practices with lowest yield-scaled NO3 − leaching loss is not the main objective of this analysis, we show that lowest yield-scaled NO3 − leaching losses can be achieved if yield losses—as compared to optimal yields—of 10 % for maize and 4 % for wheat systems will be accepted (Table 3). Moreover, our ‘best N rate’ (i.e., the N application rates with lowest yield-scaled NO3 − leaching loss) for either maize (178 kg N ha−1) or wheat (162 kg N ha−1) cropping systems are much lower than the rate which results in highest crop yields as identified by curve fitting in Fig. 4 (maize: 400 kg N ha−1; wheat: 244 kg N ha−1). Therefore, reducing the excessive N application rates towards rates which are better matching crop N requirements is not only a way to decrease N surplus while maintaining optimal crop yields, but also to avoid substantial NO3 − leaching losses. However, the recommended N rates with lowest yield-scaled NO3 − leaching loss identified in this analysis can not be simply applied to a site-specific cropping system. Our meta-analysis integrated observations across sites, thereby smoothing site-specific factors such as landscape positions, meteorological and soil conditions, which are on the other hand responsible for variations in NO3 − leaching losses across study sites (e.g., Perego et al. 2012; Sepaskhah and Tafteh 2012; Zhou et al. 2012; Zhu et al. 2009). Moreover, different methodology used for NO3 − leaching measurement also may induce large variations in reported estimates of NO3 − leaching losses (e.g., reviewed by Weihermuller et al. 2007). One of the major limitations of the current analysis is that many studies reported NO3 − leaching losses without reporting crop yields. That is somehow surprising since crop yields can be determined more easily and inexpensively as compared to NO3 − leaching measurements. Since there are increasing concerns about the tradeoff between crop yields and environmental performances (e.g., NO3 − leaching loss) for cereal productions, it is important to report both NO3 − leaching losses and crop yields in order to provide more insight to the relatively complex relationships among agricultural management practices, NO3 − leaching losses and crop yields. It is noteworthy that we only discussed the implications of regulating N application rates to reduce yield-scaled NO3 − leaching losses. NO3 − leaching losses are not only controlled by crop N immobilization or biogeochemical processes, but also by hydrological processes. Importantly, we were not able to evaluate water management effects on yield-scaled NO3 − leaching losses in this analysis due to limited data, though one can expect that irrigation is a major driver of NO3 − leaching losses.
Conclusions
We conducted for the first time a comprehensive meta-analysis which links NO3 − leaching losses and crop yields in maize and wheat cropping systems. The area-scaled NO3 − leaching losses for maize cropping systems were approx. two times higher than for wheat cropping systems. The higher area-scaled NO3 − leaching losses from maize cropping systems were largely driven by higher nitrogen fertilizer applications and wetter and warmer climate conditions during the maize growing seasons. However, yield-scaled NO3 − leaching losses were comparable between maize and wheat cropping systems. The lowest yield-scaled NO3 − leaching losses can be achieved at near optimal yields in both the maize and wheat cropping systems, highlighting that appropriate agricultural N management practices will not only result in near optimal crop yields but will also significantly reduce NO3 − leaching loss per kg product to a minimum.
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Acknowledgments
This study was gratefully supported by the Natural Science Foundation of China (Grant No. 41271321), the Helmholtz-CAS Joint Laboratory ENTRANCE and is part of the Climate Change, Agriculture and Food Security programme (CCAFS) of CGIAR institutes.
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Zhou, M., Butterbach-Bahl, K. Assessment of nitrate leaching loss on a yield-scaled basis from maize and wheat cropping systems. Plant Soil 374, 977–991 (2014). https://doi.org/10.1007/s11104-013-1876-9
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DOI: https://doi.org/10.1007/s11104-013-1876-9