Ecology

Soil bacterial responses to salinityThe soil salt, EC, and BD values significantly increased, while significantly lower values of TC were observed as the salinization level increased (Table S1; p  More

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Oxygen minimum zones (OMZs) are unique oceanic regions with strong redox gradients. Anoxic zones in OMZs are hotspots for fixed nitrogen loss and production of the greenhouse gas N2O [1, 2]. Microbes in OMZs make important contributions to biogeochemistry, which motivates us to reconstruct metagenome-assembled genomes (MAGs) from the Eastern Tropical South Pacific (ETSP) OMZ (Fig. 1a, b). Among 147 recovered MAGs, we present 39 high- and medium-quality MAGs with completeness >50% and contamination 100 nM d−1) at the same station [6], where MAGs were recovered. Consistently, Thaumarchaeota MAGs (AOAs) were nearly absent (only AOA-2 had a relative abundance higher than 0.01%) and NOB MAGs (NOB-1 and NOB-2) were much more abundant than AOA in the anoxic core (Fig. 1d). MAGs in this study will provide opportunities to discover novel processes and adaptation strategies.Most MAGs had their highest relative abundances in the anoxic zone (Fig. 1c). Many of them contribute to the loss of fixed nitrogen, which occurs by denitrification (the sequential reduction of nitrate to nitrite, NO, N2O, and finally N2) and anammox (anaerobic oxidation of ammonium to N2). Measured nitrate reduction rates at this [5, 8] and other [16, 17] nearby stations were much larger than rates of any subsequent denitrification steps (e.g., nitrite reduction to N2O or to N2). Consistently, preliminary prediction of metabolisms shows that more than half of the MAGs found here contained nar, which encodes nitrate reduction, and one-third of those contained only nar and none of the other denitrification genes (i.e., they are nitrate-reducing specialists) (Fig. 2). Consistently, a previous study found that nar dramatically outnumbered the other denitrification genes in contigs from the Eastern Tropical North Pacific (ETNP) OMZ [18]. Indeed, four of the five most abundant MAGs in the anoxic core were nitrate-reducing specialists (Fig. 2). The fifth was an anammox MAG, which was only assigned to the genus level (Candidatus Scalindua) in GTDB and was not represented at the species level in the Tara Oceans dataset (Table S1). However, this anammox MAG was highly related to 20 anammox single-cell amplified genomes (SAGs) from the ETNP OMZ [19]. The anammox MAG had at least 90% average nucleotide identity (ANI) to the SAGs, with the highest ANI (98.8%) to SAG K21. Consistent with the previous work [19], the anammox MAG also encoded cyanase, indicating its potential of using organic nitrogen substrates. The most abundant nitrate reducer MAG here is Marinimicrobia-1 (Fig. 1), which belongs to the newly proposed phylum Candidatus Marinimicrobia [20]. Notably, one nitrate reducer can only be assigned to phylum level (Candidatus Wallbacteria) and was not present in the Tara Oceans MAGs (Table S1).We also identified a novel archaeal MAG possessing multiple denitrification genes. MG-II MAG-2 encoded Nar alpha and beta subunits, nitrate/nitrite transporters, copper-containing nitrite reductase, and N2O reductase (Fig. 2). Two MAGs from the Tara Oceans metagenomes (Table S1) were identified as the same species as MG-II MAG-2. TOBG_NP-110 (ANI to MG-II MAG-2 = 99.8%) from the North Pacific encoded Nar and nitrate/nitrite transporters, and TOBG_SP-208 (ANI to MG-II MAG-2 = 99.6%) from the South Pacific also contained the same denitrification genes as MG-II MAG-2 (Table S2). In addition, two MG-II SAGs (AD-615-F09 and AD-613-O09) were found at a different station of the ETSP OMZ sampled on the same cruise as this study [21]. Partial 16S rRNA genes of both SAGs are 100% identical to that of MG-II MAG-2 (alignment length = 200 bp for AD-615-F09 and 183 bp for AD-613-O09), but only AD-615-F09 might be the same species as MG-II MAG-2 based on ANI analyses (MG-II MAG-2 had 99.5% ANI to AD-615-F09, and 80.9% to AD-613-O09). Both SAGs also encoded Nar and nitrate/nitrite transporters [21]. The absence of other denitrification genes may be due to the low completeness of the two SAGs (completeness = 5.61% for both SAGs) [21]. Nitrite reductase and N2O reductase genes were located on the same contig in both MG-II MAG-2 and TOBG_SP-208 (Table S2). MG-II MAG-2 and TOBG_SP-208 had low contamination (1.9% and 0.8%, respectively), and their contigs with nitrite reductase and N2O reductase genes contained single-copy marker genes present only once in each MAG (Supplementary Methods). Although these results suggest a nearly complete denitrification metabolism in MG-II archaea, especially N2O consumption metabolism, methods besides metagenomics (e.g. reconstructing SAGs with high completeness) are highly recommended to rule out possible artifacts introduced by metagenomic binning and confirm the presence of these genes and their denitrification activity. Nonetheless, MG-II MAG-2 was present (Fig. 1e) and transcriptionally active in both Pacific OMZs (Fig. S2), indicating its adaptation to low oxygen environments. The MG-III MAG did not have any denitrification genes but was abundant in the anoxic zone (Figs. 1e and 2). It had a GC value (43.2%) distinct from all other known MG-III MAGs [22] and is the most complete (86.0%) and the least contaminated (0%) (Table S1) among all reported MG-III MAGs, indicating that MG-III is a novel archaeon in this group. Bacterial and archaeal MAGs recovered here implied that nitrogen metabolisms were present in more microbial lineages than previously thought. Further analyses of these MAGs will shed light on adaptation strategies in the unique OMZ environment and novel functions related to important element cycles. More

Data source and preprocessingConsidering factors such as amount of cloud and time intervals of image, four remote sensing images with a spatial resolution of 30 m, including Landsat 5 Thematic Mapper (TM) images for 08-21-2000, 09-04-2005 and 09-18-2010, and Landsat 8 Operational Land Imager (OLI) for 09-02-2016,were obtained from the Geospatial Data Cloud Platform (http://www.gscloud.cn). LULC information was extracted from these remote sensing images. In addition, the digital elevation model (DEM) with a spatial resolution of 30 m was obtained from the website. Elevation and slope information were derived from DEM data and used as terrain driving factors for scenario simulation. Other supporting data, such as Weishan County land use data, mine distribution data, general land use planing (2006–2020) and mineral resources planning (2008–2015), Jining City coal mining subsidence land rearrangement planning (2016–2030), were obtained from Weishan Natural Resources and Planning Bureau. These data were used for better data analysis.Considering severe ground subsidence and seeper in the study area, and referring to national standards: Current Land Use Classification (GB/T 21010-2017), remote sensing images were interpreted into six LULC types: farmland, other agricultural land, urban and rural construction land, subsided seeper area, water area, and tidal wetland.In the process of image interpretation, firstly, the remote sensing image was divided into two regions: one region were the lake and the surrounding tidal wetland, and the other region included farmland, other agricultural land, urban and rural construction land, subsided seeper area, etc.In region 1, decision tree classification, combined with the Modified Normalized Difference Water Index (MNDWI), was used to extract lakes. Then we masked them in region 1. The Normalized Difference Vegetation Index (NDVI) was calculated for the remaining image of region 1. Tidal wetland was mainly distributed along rivers and lakes, and NDVI value was higher than that of farmland and other vegetation. By analyzing its geographical distribution and NDVI value, and referring to Weishan County land use data, the appropriate threshold was selected to extract tidal wetland.The spectral signature of rivers, ditches and aquaculture ponds in other agricultural land in region 2 could be easily distinguished from other surface features. They could be extracted step by step by manual visual interpretation and empirical knowledge, referring to Weishan County land use data and water system data. Then we masked them separately in region 2. After extracting rivers, ditches, aquaculture ponds with high water content, the remaining LULC type with high water content in region 2 was subsided seeper area. According to the relationship of spectral signature of different LULC types, it was concluded that among the remaining LULC types in region 2, only TM3 band value of subsided seeper area was higher than TM5 band value. Using this characteristic, subsided seeper area could be distinguished from other LULC types. After extracting subsided seeper area, the remaining LULC types in region 2 were farmland and urban and rural construction land. The spectral characteristics of them were very different. Therefore, they could be distinguished using support vector machine (SVM) classification method, and their respective binary images were generated using decision tree method.The extracted six LULC types were shown in single layer and binary form respectively. Six LULC types were coded and synthesized into one image. We obtained 2000, 2005, 2010, 2016 LULC type maps (Fig. 2). Finally classification post-processing and accuracy evaluation were operated.Figure 2The LULC types maps of 2000, 2005, 2010 and 2016. Maps were generated using ArcGIS 10.1 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageThe accuracy of the interpretation results was verified by confusion matrix and kappa coefficient. The kappa coefficients of the four interpretation maps were 0.84, 0.85, 0.82 and 0.86, respectively (Table 1). The accuracy could meet the needs of further research.Table 1 Accuracy evaluation of the interpretation results (%).Full size tableBy reading previous research results37,38,39,40,41, based on the entropy theory, in the same study area, high spatial resolution data contains more entropy than low spatial resolution data, and reflecting more detailed information, but it will increase the uncertainty of prediction results and reduce the prediction accuracy. Although the prediction accuracy of low spatial resolution data increases, it will lose lots of detailed information. In order to ensure the accuracy of the simulation, considering the area of the study area and data requirement of the CLUE-S model, the interpreted LULC maps with a resolution of 30 m exceed the upper limit of the CLUE-S model data requirement, so the LULC maps were resampled to multiple scales including 60 m, 90 m, 120 m, and 150 m to facilitate logistic regression analysis of LULC types and driving factors.Selection and processing of driving factorsTo interpret the relationship between the LULC and its driving factors in the mining area, we not only need to identify the driving factors that have greater explanatory power for LULC change, but also need to quantitatively describe the relationship between driving factors and LULC types.Considering the accessibility, usability of the data and the actual conditions in the study area, seven driving factors were selected based on the land use map of Weishan County in 2005 and the DEM data5,10,11,13,26,28,29,30. The driving factors included: (1) terrain factors, including elevation and slope factors; (2) five accessibility factors, including the nearest distance between each grid pixel and the main roads, the major rivers, the residential area, the major mines, and the ditches. The 30 m grid data of each driving factor were resampled to 60 m, 90 m, 120 m and 150 m respectively.In this study, BLRM was used to explore the relationship between LULC change and the related 7 driving factors. BLRM is sensitive to multicollinearity. In order to eliminate the influence of collinearity on the regression results, the multicollinearity between independent variables was diagnosed before the regression model was established.The receiver operating characteristic (ROC) curve was used to evaluate the accuracy of regression analysis results at different scales. The results showed that using 60 m resolution provided more accurate regression analysis results and suffered less loss of LULC and driving factor information during resampling. Therefore, we used 60 m × 60 m grid cell data to driving forces analysis.Raster maps of each driving factor at a resolution scale of 60 m are shown in Fig. 3.Figure 3Raster maps of driving factors at a resolution scale of 60 m. Maps were generated using ArcGIS 10.1 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageLogistic regression analysis of LULC types and driving factorsBLRM is often used for regression analysis of explanatory binary variables. The presence and absence of a certain type of LULC in a specific area is set as 1 and 0, respectively, which is characteristic for binary variable. Therefore, we used BLRM to calculate the probability (P) of various LULC types in a specific spatial location, and its mathematical expression is:$$begin{aligned} ln left( frac{P}{1-P}right) = beta _0 + beta _1 X end{aligned}$$
(1)
where (frac{P}{1-P}) is the ’odds ratio’ of an event, abbreviated as ( Omega ), which represents the odds that an outcome will occur given a particular condition compared to the odds of the outcome occurring in the absence of that condition; (beta _0) is a constant; (beta _1) is the correlation coefficient of an explaining variable and an explained variable. Making mathematical transformation of the above expression, we get: (Omega = (frac{P}{1-P}) = e^{beta _0 + beta _1 X}).Regression analysis using BLRM, we divided the study area into many grid cells. Taking each LULC type as the explained variable, and the driving factor causing LULC change as the explanatory variable, we calculated the odds ratio of each LULC type in a specific spatial location, and analyzed the relationship between each LULC type and the driving factors. The calculating equation is:$$begin{aligned} mathrm{Logit} P = ln left( frac{P_i}{1-P_i}right) = beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i} end{aligned}$$
(2)
Making mathematical transformation of the above equation, we get:$$begin{aligned} P_i = frac{e^{(beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i})}}{1+e^{(beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i})}} end{aligned}$$
(3)
where: (P_i) is the probability of a certain LULC type i in a grid cell, (X_{1,i}sim X_{n,i}) are the driving factors of LULC type i, (beta _0) is the constant, (beta _1sim beta _n) are the correlation coefficients of each driving factor and LULC type i.The receiver operating characteristic (ROC) was used to evaluate the accuracy of regression analysis results. The accuracy can be measured by calculating the area under the ROC curve. The area value is between 0.5 and 1. The closer the value is to 1, the higher the accuracy is. In general, the area under the ROC curve is greater than 0.7, which indicates that the selected factor has good explanatory power27,42.CLUE-S simulation and accuracy validationBefore using the CLUE-S model for futural LULC scenario simulation in mining area, the prediction accuracy needs to be verified. Based on the data of LULC in 2005, the spatial distribution pattern of LULC in 2016 was predicted firstly.The modeling accuracy was evaluated based on the Kappa index by comparing the actual LULC map in 2016 with the simulated in 201627,43,44. Equation (4) gives one of the most popular Kappa index equations: i.e.,$$begin{aligned} mathrm{Kappa}=frac{P_o-P_c}{P_p-P_c} end{aligned}$$
(4)
where (P_o) is the observed proportion correct, (P_c) is the expected proportion correct due to chance, (P_c) =1/n, n is the number of LULC types, and (P_p) is the proportion correct when classification is perfect.In order to further verify the accuracy of the model simulation, we also calculated kappa for quantity (Kquantity).Scenario setting of futural LULC simulationDue to the continuous population growth and mineral exploitation in the study area, the land resources, especially farmland resources, have become increasingly scarce and the environment has been deteriorating. Based on the simulation and validated results during 2005-2016, we defined three scenarios—namely natural development scenario, ecological protection scenario, and farmland protection scenario—to predict LULC spatial patterns for 2025.Natural development scenarioIn this scenario, the land use demand of the study area was basically not restricted by policies in near future. We assumed that the change rate of each LULC type in near future was consistent with the change trend from 2005 to 2016. So it is defined as natural development scenario. Using Markov model to obtain the area transition probability matrix of each year from 2017 to 2025, and taking the proportion of each LULC type area in the total study area in 2005 as the initial state matrix, the area of each LULC type in 2025 under the natural development scenario was predicted.Based on the characteristics and trend of the LULC change from 2005 to 2016, after appropriately adjusting the transition probability matrix of different LULC types, we predicted the demands of each LULC type in 2025 under ecological protection scenario and farmland protection scenario using Markov model45,46.Ecological protection scenarioThis scenario emphasizes protecting the ecological environment, restricting the conversion of the LULC types that have more regulatory effects on the ecosystem, such as tidal wetland and water area, to other land use types. Garden land, woodland, grassland, and aquaculture land, belong to other agricultural land, which have regulatory effects on the local ecosystem, so their conversion to other LULC types should be restricted as well.Farmland protection scenarioAccording to the guidelines of “the general land use planning in Weishan County (2006-2020)”, we should maximize the potential use of current construction land, implement intensive and economical utilization of construction land, and use less or not use farmland to economical construction. So in order to ensure the dynamic balance of total farmland amount and the regional food supply security, in the farmland protection scenario, the conversion from farmland to other land use types should be restricted. The projected land use demands for 2025 under the three different scenarios are shown in Table 2.Table 2 Areas of LULC types in 2025 under different scenarios (ha).Full size table More

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The experiment was conducted at Agricultural and Bio-Systems Engineering Department, Faculty of Agriculture Moshtohor, Benha University, Egypt (latitude 30° 21′ N and 31° 13′ E), during the period of May to July, 2019 season under the university guidelines and legislation. Basil seedlings were sown in the plastic cups (7 cm diameter and 7 cm height) filled with peat moss. The cups were irrigated daily using water with nutrient solution (Ca(NO3)2, 236 g L−1, KNO3, 101 g L−1, K2SO4, 115 g L−1, KH2PO4, 136 g L−1, MgSO4 246 g L−1 and chelates for trace elements into preacidified groundwater (from the following ppm concentration are achieved in this formulation: N = 210, P = 31, K = 234, Ca = 200, Mg = 48, S = 64, Fe = 14, Mn = 0.5, Zn = 0.05, Cu = 0.02, B = 0.5, Mo = 0.01)). Two weeks old basil seedlings were planted at 9.0 plant m−2 in the experimental tanks. These seedlings were planted according to the permission of Benha university rules and legislation.Culture systems descriptionFigure 1a,b show the experimental setup. It shows the system which consists of hydroponic system, aeroponic system, soilless substrate, solution system and pumps.Figure 1(a) The experimental setup. (b) Images of system.Full size imageThe hydroponic system (Deep Water Culture (DWC)) consists of three rectangular polyethylene tanks that used for basil plants culture. Dimensions of each tank are 80 cm long, 40 cm wide and 30 cm high. The slope of hydroponic tanks was 2% and stand 1 m high above the ground. The hydroponic tanks were covered with foam boards to support the plants. Each hydroponic tank provided with an air blower (Model NS 780—Flow Rate 850 L h−1—Head 1.5 m—Power 15 W, China) to increase dissolved oxygen concentrations. The solution was circulated by a pump (Model First QB60—Flow Rate 30 L min−1—Head 25 m—Power 0.5 hp, China) from the solution tank to the upper ends of the hydroponic tanks. Small tubes (16 mm) were used to provide tanks with solution in a closed system.Aeroponic system consists of three rectangular polyethylene tanks that used for basil plants culture. Dimensions of each tank are 80 cm long, 40 cm wide and 50 cm high. The aeroponic tanks were established 1 m above the ground. Each aeroponic tank was divided into two parts, the lower part was made from polyethylene and the upper part was made from wood. The aeroponic tanks were covered with foam boards to support the plants. Each aeroponic tank was provided with two fog nozzles (Model M3MNWT5M – Orifice 2 mm – Discharge 8 L h−1, India) located at the bottom of the tank sprayed nutrient solution into the tank in order to keep the roots wet. Small tubes (16 mm) were used to provide aeroponic tank with solution in a closed system.Soilless substrates consist are placed in three rows are 2 m long. Each row consists standard peat moss slabs (1.00 m × 0.20 m × 0.075 m). Basil plants were placed on row peat moss slabs with a drip irrigation system. There were three plants per slab giving a mean density of 9.0 plant m−2. Each plant was fed by a single drip.The circular polyethylene tank of the nutrient solution system 500 L capacity was used for collecting the drained solution by gravity from the ends of the three systems. The nutrient solutions were prepared manually once per ten days17,18 by dissolving appropriate amounts of Ca(NO3)2, 236 g L−1, KNO3, 101 g L−1, K2SO4, 115 g L−1, KH2PO4, 136 g L−1, MgSO4 246 g L−1 and chelates for trace elements into preacidified groundwater (from the following ppm concentration are achieved in this formulation: N = 210, P = 31, K = 234, Ca = 200, Mg = 48, S = 64, Fe = 14, Mn = 0.5, Zn = 0.05, Cu = 0.02, B = 0.5, Mo = 0.01). pH and Electrical Conductivity (EC) were further adjusted to 6.5–7.0 and 1.4–1.8 dS m−1, respectively, after salt addition. The average air ambient temperature was 25.97 ± 4.37 °C and the average water temperature was 24.03 ± 3.92 °C. The average relative humidity was 65.4% and the light intensity was 338.55 ± 40.06 W m−2.MeasurementsThree plants sample were taken during the vegetative and flowering stages (four and seven weeks after transplanting, respectively) for growth measurement and chemical analysis. Plant height, root length and the fresh and dry weight of leaves, stems and roots were determined. After measuring fresh mass, the plants were oven dried at 65 °C until constant weight was reached19. Total content of macro elements was evaluated after being digested20. Nitrogen was determined by Kjeldahl digestion methods21. Potassium, Calcium and magnesium were determined by Photofatometer (Model Jenway PFP7—Range 0—160 mmol L−1, USA) and phosphorus (P) was determined colorimetrically method22. The content of oil was determined in different organs: leaves, stems and inflorescences according to23.Water samples were taken, at inlet and outlet of the culture units for measuring nitrogen (N), phosphorus (P), potassium (K), calcium (Ca) and magnesium (Mg) were measured every week at 10 am during the experimental period.Total production costThe cost calculation based on the following parameters was also performed:Fixed costs (Fc)Depreciation costs (Dc)$$D_{c} = frac{{P_{d} – S_{r} }}{{L_{d} }}$$
(1)

where Dc is the depreciation cost, EGP (Egyptian pound) year−1. ($ = 15.63 EGP). Pd is the system price, EGP. Sr is the salvage rate (0.1Pd) EGP. Ld is the system life, year.Interest costs (In):$$I_{n} = frac{{P_{d} + S_{r} }}{2} times {text{i}}_{{text{n}}}$$
(2)

where In is the interest, EGP year−1. in is the interest as compounded annually, decimal (12%). Shelter, taxes and insurance costs (Si).Shelter, taxes and insurance costs were assumed to be 3% of the purchase price of the automatic feeder (Pm).Then:$${text{Fixed,cost }} = {text{ D}}_{{text{c}}} + {text{ I}}_{{text{n}}} + 0.03{text{ P}}_{{text{m}}} /{text{ hour, of, use ,per ,year}}$$
(3)
Variable (operating) costs (Vc)Repair and maintenance costs (Rm):$${text{R}}_{{text{m}}} = 100% ;{text{deprecation,cost/hour,of,use,per,year}}$$
(4)
Energy costs (E):$${text{E }} = {text{ EC }} times {text{ EP}}$$
(5)

where E is the energy costs, EGP h−1. EC is the electrical energy consumption, kWh. EP is the energy price, 0.57 EGP kW−1.Labor costs (La):$${text{L}}_{{text{a}}} = {text{ Salary, of, one, worker }} times {text{ No}}{text{. ,of, workers}}$$
(6)

where La is the Labor costs, EGP h−1. Salary of one worker = 10 EGP h−1. No. of workers = 1.Then:$${text{Variable,costs }} = {text{ Rm }} + {text{ E }} + {text{ La}}$$
(7)
Total costs (Tc)$${text{Total ,costs }} = {text{ Fixed ,costs }} + {text{ Variable ,costs}}$$
(8)

Table 1 shows the input parameters of calculate total production costs of basil plants grown in different soilless systems.Table 1 The input parameters of calculate total production costs of basil plants grown in different soilless systems.Full size tableNutrients consumption rateThe Nutrients consumption rate were calculated as the differences between the nutrients at inlet and outlet of culture units by the following formula24:$$C_{{Nc}} = frac{{Nc_{{in}} – Nc_{{out}} }}{{{text{Number, of ,plants}}}} times Q times {text{24}}$$
(9)

where CNc is the nutrients consumption rate, mg day−1 plant −1. Ncin is the nutrients at inlet of the hydroponic unit, mg L−1. Ncout is the nutrients at outlet of the hydroponic unit, mg L−1. Q is the discharge, L h−1.Model development of nutrient consumptionModel assumptions:

N, P, K, Ca and Mg are the nutrients used in study.

The plants are uniformity distributed in the solution, so they work as a uniform sink for water and minerals with space at any time.

The root systems are uniformly dispersed in the solution with uniform root length density at any time.

The whole root system uptake characteristics are uniform.

Water losses by evaporation are negligible.

The simplest nutrient consumption models relate the nutrient consumption to the concentration gradient using some sort of proportionality factor such as root permeability or conductivity25,26. The nutrient consumption was determined by using the following equation:$$NC = a_{{NC}} cdot Delta {text{C }}$$
(10)

where NC is the nutrient consumption, mg plant−1 day−1. ∆C is the concentration gradient, mg plant−1 day−1. aNC is the proportionality factor, dimensionless.A similar model of nutrient consumption takes into consideration the differing effects caused by variations in root growth stage. Assuming that growth follows a first order differential equation and assuming that the root growth is exponential27, then Eq. (11) can be derived. This equation is presented in similar form to Eq. (10) and use the following equation:$$NC = left( {frac{{left( {C_{{plant}} – {text{C}}_{{{text{plant0}}}} } right)}}{{A_{r} – A_{{r0}} }}} right) cdot left( {frac{{{text{ln}}left( {frac{{{text{A}}_{{text{r}}} }}{{{text{A}}_{{{text{r0}}}} }}} right)}}{{{text{t}} – {text{t}}_{0} }}} right){text{.A}}_{{text{r}}}$$
(11)

where Cplanto is the concentration of the nutrients in the plant at time t0, mg plant−1. Ar is the root surface area at time t, cm2 plant−1. Ar0 is the root surface area at time t0, cm2 plant−1.Root surface area was calculated from root length and mean root radius using the following equation:$$A_{r} = {text{2}}pi {text{r}}_{{text{0}}} {text{L}}_{{text{r}}}$$
(12)
The root length increment using the following equation28:$$Delta L_{r} = Delta DW_{{root}} {text{v }}$$
(13)

where ∆Lr is the root length increment, cm day−1. ∆DWroot is the daily amount of root dry mass increment, g day−1. v is the ratio of root length and mass of roots, cm g−1.The daily amount of dry weight of roots is calculated from the following equation29:$$Delta DW_{{root}} = left{ {begin{array}{*{20}l} {{text{5LAI}}} hfill & {{text{for,LAI}} le {{0}}{{.5}}} hfill \ {{{2}}{{.5}} + {{23}}{{.9}}left( {{text{LAI-0}}{{.5}}} right)} hfill & {{text{for,LAI}} > {{0}}{{.5}}} hfill \ end{array} } right.$$
(14)

where LAI is the leaf area index.Leaf area index was changed in the same proportions as root length density to maintain a constant ratio between roots and shoots. The leaf area index is calculated from the following equation30:$$LAI = frac{{LAI_{{max }} }}{{1 + K_{2} e^{{left( { – k_{1} t} right)}} }}$$
(15)

where LAImax is the maximum leaf area index. K2 and k1 are the coefficients of the growth functions.All computational procedures of the model were carried out using Excel spreadsheet. The computer program was devoted to mass balance for predicting the nutrients consumption. The differences between the predicted and measured values were evaluated using RMSE indicator (root means square error) which is calculated using the following equation:$$RMSE = sqrt {frac{{sum {left( {Predicted-Measured} right)^{2} } }}{n}}$$
(16)
The parameters used in the model that were obtained from the literature are listed in Table 2. Figure 2 shows flow chart of the model.Table 2 The parameters used in the model.Full size tableFigure 2Flow chart of nutrients consumption rate.Full size imageStatistical analysisThree replicates of each treatment were allocated in a Randomize Complete Block Design (RCBD) in the system. Data were analyzed one-way ANOVA (analysis of variance) using statistical package for social sciences (spss v21). Means were separated using New Duncan Multiple Range Test (DMRT). Data presented are mean ± standard division (SD) of four replicates. More

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