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Calculating Potential Evapotranspiration using Penman-MonteithAmong several equations used to estimate PET, an implementation of the Penman-Monteith equation originally presented by the Food and Agriculture Organization FAO-561, is considered a standard method3,12,13,49. FAO-561 defined PET as the ET of a reference crop (ET0) under optimal conditions, in this case with the specific characteristics of well-watered grass with an assumed height of 12 centimeters, a fixed surface resistance of 70 seconds per meter and an albedo of 0.231. Less specifically, “reference evapotranspiration”, generally referred to as “ET0”, measures the rate at which readily available soil water is evaporated from specified vegetated surfaces2,13, i.e., from a uniform surface of dense, actively growing vegetation having specified height and surface resistance, not short of soil water, and representing an expanse of at least 100 m of the same or similar vegetations1,13. ET0 is one of the essential hydrological variables used in many research efforts, such as study of the hydrologic water balance, crop yield simulation, irrigation system management and in water resources management, allowing researchers and practitioners to study the evaporative demand of the atmosphere independent of crop type, crop development and management practices2,4,13,49. ET0 values measured or calculated at different locations or in different seasons are comparable as they refer to the ET from the same reference surface. The factors affecting ET0 are climatic parameters, and crop specific resistances coefficients solved for reference vegetation. Other crop specific coefficients (Kc) may then be used to determine the ET of specific crops (ETc), and which can in turn be determined from ET01.As the Penman-Monteith methodology is predominately a climatic approach, it can be applied globally as it does not require estimations of additional site-specific parameters. However, a major drawback of the Penman-Monteith method is its relatively high need for specific data for a variety of parameters (i.e., windspeed, relative humidity, solar radiation). Zomer et al.18 compared five methods of calculating PET with parameters from data available at the time and settled upon using a Modified Hargreaves-Thornton equation50 which required less parametrization to produce the Global-AI_PET_v116,17,18. Several other attempts to produce global PET datasets with concurrently available global datasets came to similar conclusions51,52,53. The Modified Hargreaves-Thornton method required less parameterization with relatively good results, relying on datasets which were available at the time for a globally applicable modeling effort. The Global-AI_PET_v1 used the WorldClim_v1.420 downscaled climate dataset (30 arcseconds; averaged over the period 1960–1990) for input into the global geospatial implementation of the Modified Hargreaves-Thornton equation, applied on a per grid cell basis at approximately 1 km resolution (30 arcseconds). More recently, the UK Climate Research Unit released the “CRU_TS Version 4.04”, which now includes a Penman-Monteith calculated PET (ET0) global coverage, however at a relatively coarse resolution of 0.5 × 0.5 degrees. A number of satellite-based remote sensing datasets22,54,55,56,57 are now available and in use to provide the parameters for ET0 estimates, in some cases providing high spatial and/or temporal resolution and are likely to become increasingly utilized as the historical data record lengthens and sensors improve.The latest 2.0 versions of WorldClim58 (currently version 2.1; released January 2020), in addition to being updated with improved data and analysis, and a revised baseline (1970–2000), includes several additional primary climatic variables, beyond temperature and precipitation, namely: solar radiation, wind speed and water vapor pressure. The addition of these variables allowed that the global data now available was sufficient to effectively parameterize the FAO-56 equation to estimate ET0 globally at the 30 arc seconds scale (~1 km at equator).The FAO-56 Penman-Monteith equation, described in detail below, has been implemented on a per grid cell basis at 30 arc seconds resolution, using the Python programming language (version 3.2). The data to parametrize the various components equations required to arrive at the ET0 estimate were obtained from the Worlclim 2.158 climatological dataset, which provides values averaged over the time period 1970–2000 for minimum, maximum and average temperature; solar radiation; wind speed, and water vapor pressure. Subroutines in the program include calculation of the psychrometric constant (aerodynamic resistance), saturation vapor pressure, vapor pressure deficit, slope of vapour pressure curve, air density at constant pressure, net shortwave radiation at crop surface, clear-sky solar radiation, net longwave radiation at crop surface, net radiation at the crop surface, and the calculation of daily and monthly ET0. This process is described below. Geospatial processing and analysis were done using ArcGIS Pro v 2.9 (ESRI, 2020), Python (ArcPy) programming language (version 3.2), and Microsoft Excel for further data analysis, graphics and presentation.Global Reference Evapotranspiration (Global-ET0)Penman59, in 1948, first combined the radiative energy balance with the aerodynamic mass transfer method and derived an equation to compute evaporation from an open water surface from standard climatological records of sunshine, temperature, humidity and wind speed. This combined approach eliminated the need for the parameter “most difficult” to measure, surface temperature, and allowed for the first time an opportunity to make theoretical estimates of ET from standard meteorological data. Consequently, these estimates could also now be made retrospectively. This so-called combination method was further developed by many researchers and extended to cropped surfaces by introducing resistance factors. Among the various derivations of the Penman equation is the inclusion of a bulk surface resistance term60, with the resulting equation now called the Penman-Monteith equation3, as standardized in FAO-561 and subsequently by the American Society of Civil Engineers – Technical Committee on Standardization of Reference Evapotranspiration12,13,49,61. The FAO-56 Penman-Monteith form of the combination equation to estimate ET0 is calculated as:$$ETo=frac{Delta left({R}_{n}-Gright)+{rho }_{a}{c}_{p}frac{({e}_{s}-{e}_{a})}{{r}_{a}}}{Delta +gamma left(1+frac{{r}_{s}}{{r}_{a}}right)}$$
(1)
WhereET0 is the evapotranspiration for reference crop, as mm day−1Rn is the net radiation at the crop surface, as MJ m−2 day−1G is the soil heat flux density, as MJ m−2 day−1cp is the specific heat of dry airpa is the air density at constant pressurees is the saturation vapour pressure, as kPaea is the actual vapour pressure, as kPaes – ea is the saturation vapour pressure deficit, as kPa(Delta ) is the slope vapour pressure curve, as kPa °C−1(gamma ) is the psychrometric constant, as kPa °C−1rs is the bulk surface resistance, as m s−1ra is the aerodynamic resistance, as m s−1Psychrometric Constant (γ)The Atmospheric Pressure (Pr, [KPa]) is the pressure exerted by the weight of the atmosphere and is thus dependent on elevation (elev, [m]). To a certain (and limited) extent evaporation is promoted at higher elevations:$$Pr=101.3ast {left(frac{293-0.0065ast elev}{293}right)}^{5.26}$$
(2)
Instead, the psychrometric constant, [γ, kPa C−1] is expressed as:$$gamma =frac{{c}_{p}ast Pr}{varepsilon ast lambda }=frac{0.001013ast Pr}{0.622ast 2.45}$$
(3)
Where cp is the specific heat at constant pressure [MJ kg−1 °C−1] and is equal to 1.013 10−3, λ is the latent heat of vaporization [MJ kg−1] and is equal to 2.45, while ε is the molecular weight ratio between water vapour and dry air and is equal to 0.622.Elevation data has been obtained from the Shuttle Radar Topography Mission (SRTM) aggregated to 30 arc-second spatial resolution62 and combined with the USGS GTOPO3063 database for the areas north of 60°N and south of 60°S where no SRTM data was available (available at https://worldclim.org).Air Density at Constant Pressure [ρa]The mean Air Density at Constant Pressure [ρa, Kg m−3] can be represented as:$${rho }_{a}=frac{Pr}{{T}_{Kv}ast R}$$
(4)
While R is the specific heat constant (0.287, KJ Kg−1 K−1), the virtual temperature TKv can be represented as well as:$${T}_{Kv}=1.01ast ({T}_{avg}+273)$$
(5)
With Tavg as the mean daily air temperature at 2 m height [C°].Saturation Vapor Pressure [KPa]Saturation Vapor Pressure [KPa] is strictly related to temperature values (T)$${e}_{s_T}=0.6108ast ex{p}^{left[frac{17.27ast T}{T+237.3}right]}$$
(6)
Values of saturation vapor pressures, as function of temperature, are calculated for both Minimum Temperature [Tmin, C°] and Maximum temperature [Tmax, C°]. Due to nonlinearity of the equation, the mean saturation vapour pressure [es, KPa] is calculated as the average of saturation vapour pressure at minimum [es_min] and maximum temperature [es_max]$${e}_{s}=frac{{e}_{s_Tmax}+{e}_{s_Tmin}}{2}$$
(7)
The actual vapour pressure [ea, KPa] is the vapour pressure exerted by the water in the air and is usually calculated as function of Relative Humidity [RH]. Water vapour pressure is already available as one of the Worldclim 2.1 variables.$${e}_{a}=RH/100,ast ,{e}_{s}$$
(8)
The vapour pressure deficit (es-ea), [KPa] is the difference between the saturation (es) and actual vapour pressure (({e}_{a})).Slope of Saturation Vapor Pressure (Δ)The Slope of Saturation Vapor Pressure [Δ, kPa C−1] at a given temperature is given as function of average temperature:$$Delta =frac{4098ast 0.6108,ex{p}^{left(frac{17.27ast {T}_{avg}}{{T}_{avg}+237.3}right)}}{{left({T}_{avg}+237.3right)}^{2}}$$
(9)
Where Tavg [C°] is the average temperature.Net Radiation At The Crop Surface (R
n)Net radiation [Rn, MJ m−2 day−1] is the difference between the net shortwave radiation [Rns, MJ m−2 day−1] and the net longwave radiation [Rnl, MJ m−2 day−1], and is calculated using solar radiation (Rs). In Worldclim 2.1 solar radiation (Rs) is given as KJ m−2 day−1. Thus, for computation of ET0, its unit should be converted to MJ m−2 day−1 and thus its value should be divided by 1000. The net accounting of either longwave and shortwave radiation sums up the incoming and outgoing components.$${R}_{n}={R}_{ns}-{R}_{nl}$$
(10)
The net shortwave radiation [Rns, MJ m−2 day−1] is the fraction of the solar radiation Rs that is not reflected from the surface. The fraction of the solar radiation reflected by the surface is known as the albedo [α]. For the green grass reference crop, α is assumed to have a value of 0.23. The value of Rns is:$${R}_{ns}={R}_{s},ast ,(1-alpha )$$
(11)
The difference between outgoing and incoming longwave radiation is called the net longwave radiation [Rnl]. As the outgoing longwave radiation is almost always greater than the incoming longwave radiation, Rnl represents an energy loss. Longwave energy emission is related to surface temperature following Stefan-Boltzmann law. Thus, longwave radiation emission is calculated as positive in the outward direction, while shortwave radiation is positive in the downward direction. The net energy flux leaving the earth’s surface is influenced as well by humidity and cloudiness$${R}_{nl}=sigma ast left(frac{{T}_{max,,K}^{4}+{T}_{min,,K}^{4}}{2}right)ast left(0.34-0.14ast sqrt{{e}_{a}}right)ast left(1.35ast frac{{R}_{s}}{{R}_{so}}-0.35right)$$
(12)
Where σ represent the Stefan-Boltzmann constant (4.903 10-9 MJ K−4 m−2 day−1), Tmax,K and Tmin,K the maximum and minimum absolute temperature (in Kelvin; K = C° + 273.16), ea is the actual vapour pressure; Rs the measured solar radiation [MJ m−2 day−1] and Rso is the calculated clear-sky radiation [MJ m−2 day−1]. Rso is calculated as function of extraterrestrial solar radiation [Ra, MJ m−2 day−1] and elevation (elev, m):$${R}_{so}={R}_{a}ast (0.75+0.00002ast elev)$$
(13)
The extraterrestrial radiation, [Ra, MJ m−2 day−1], is estimated from the solar constant, solar declination and day of the year. It requires specific information about latitude and Julian day to accomplish a trigonometric computation of the amount of solar radiation reaching the top of the atmosphere following trigonometric computations as shown in Allen et al.1.Although the soil heat flux is small compared to Rn, particularly when the surface is covered by vegetation, changes of soil heat flux may still be relevant at monthly scale. However, accurate assessments of soil heat flux may require computation of soil heat capacity, related to its mineral composition and water content, which in turn may be rather inaccurate at global scale at resolution of 30 arc sec. Thus, for simplicity, changes in soil heat fluxes are ignored (G = 0).Bulk Surface Resistance (r
s)The resistance nomenclature distinguishes between aerodynamic resistance and surface resistance factors. The surface resistance parameters are often combined into one parameter, the ‘bulk’ surface resistance parameter which operates in series with the aerodynamic resistance. The surface resistance, rs, describes the resistance of vapour flow through stomata openings, total leaf area and soil surface. The aerodynamic resistance, ra, describes the resistance from the vegetation upward and involves friction from air flowing over vegetative surfaces. Although the exchange process in a vegetation layer is too complex to be fully described by the two resistance factors, good correlations can be obtained between measured and calculated evapotranspiration rates, especially for a uniform grass reference surface.A general equation for the bulk surface resistance (rs, [s m−1]) describes a ratio between the bulk stomatal resistance of a well illuminated leaf (rl) and the active sunlit leaf area of the vegetation:$${r}_{s}=frac{{r}_{l}}{LA{I}_{active}}$$
(14)
The stomatal resistance of a single leaf under well-watered conditions has a value of about 100 s m−1. It can be assumed that about half (0.5) of the total LAI is actively contributing to vapour transfer, while it can also be roughly generalized that for short crops there is a linear relation between LAI and crop height (h):$$LAI=24ast h$$
(15)
When the evapotranspiration simulated with the Penman-Monteith method is referred to a specific reference crop, denoted as ET0, a simplified computation of the method can occur that defines a priori specific variables into constant values. In this case, the reference surface is a hypothetical grass reference crop, well-watered grass of uniform height, actively growing and completely shading the ground, with an assumed crop height of 0.12 m, and an albedo of 0.23. The surface resistance for this hypothetical grass can be simplified to the following:$${r}_{s}=frac{100}{0.5ast 24ast h}$$
(16)
For such reference crop the surface resistance is fixed to 70 s m−1 and implies a moderately dry soil surface resulting from about a weekly irrigation frequency.Aerodynamic Resistance (r
a)The aerodynamic resistance [s m−1] verifies the transfer of water vapour and heat from the vegetation surface into the air, and is controlled by both vegetation status but also atmospheric turbulence under theoretical aspect as:$${r}_{a}=frac{lnleft[frac{{z}_{m}-d}{{z}_{om}}right]ast lnleft[frac{{z}_{h}-d}{{z}_{oh}}right]}{{k}^{2}{u}_{z}}$$
(17)
Zm [m] is the height [h] of wind measurements and Zh [m] is the height of humidity measurements. These are normally set at 2 meters height, although several climate models may provide them for higher heights (e.g. 10 m). The zero plane displacement (d [m]) term can be estimated as two thirds of crop height, while Zom is the roughness length governing momentum transfer, and can be calculated as Zom = 0.123 * h.The roughness length governing transfer of heat and vapour, Zoh [m], can be approximated as one tenth of Zom. k is the von Karman’s constant, equal to 0.41, and uz [m s-1] is the wind speed at height z.The reference surface, as stated, is a hypothetical grass reference crop, well-watered grass of uniform height, actively growing and completely shading the ground, with an assumed crop height of 0.12 m, and an albedo of 0.23. For such reference crop the surface resistance is fixed to 70 s m-1 and implies a moderately dry soil surface resulting from about a weekly irrigation frequency.When crop height is equal to 0.12 and wind/humidity measurements are taken at 2 meters height, then the aerodynamic resistance can be simplified as:$${r}_{a}=frac{208}{{u}_{2}}$$
(18)
Reference Evapotranspiration (ET
0)Given the above, and the specific properties of the standard reference crop, the FAO-56 Penman-Monteith method to estimate ET0 then can be calculated as:$$ETo=frac{0.408ast Delta ast left({R}_{n}-Gright)+gamma frac{900}{{T}_{avg}+273}ast {u}_{2}ast left({e}_{s}-{e}_{a}right)}{Delta +gamma left(1+frac{{r}_{s}}{{r}_{a}}right)}$$
(19)
Aridity Index (AI)Aridity is often expressed as a generalized function of precipitation and PET. The ratio of precipitation over PET (or ET0). That is, the precipitation available in relation to atmospheric water demand64 quantifies water availability for plant growth after ET demand has been met, comparing incoming moisture totals with potential outgoing moisture65.Geospatial analysis and global mapping of the AI for the averaged 1970–2000 time period has been calculated on a per grid cell basis, as:$$Al=MA_Prec/MA_E{T}_{0}$$
(20)
where:AI = Aridity IndexMA_Prec = Mean Annual PrecipitationMA_ET0 = Mean Annual Reference EvapotranspirationMean annual precipitation (MA_Prec) values were obtained from the WorldClim v 2.158, as averaged over the period 1970–2000, while ET0 datasets estimated on a monthly average basis by the Global-ET0 (i.e., modeled using the method described above) were aggregated to mean annual values (MA_ET0). Using this formulation, AI values are unitless, increasing with more humid condition and decreasing with more arid conditions.As a general reference, a climate classification scheme for Aridity Index values provided by UNEP64 provides an insight into the climatic significance of the range of moisture availability conditions described by the AI.
Aridity Index Value

Climate Class

0.65

Humid More

Site descriptionThe experiment was conducted at the Beef Cattle Research Center of the Institute of Animal Science/APTA/SAA, Sertãozinho, São Paulo, Brazil (21°08′16″ S e 47°59′25″ W, average altitude 548 m), during two consecutive years. The climate in this region is Aw according to the Köppen’s classification, characterized as humid tropical, with a rainy season during summer and drought during winter. The meteorological data is reported in Fig. 1. The soil in the experimental area is classified as an Oxisol42. Before the experiment, soil samples were collected for chemical characterization (Table 4), which was performed following the methodology described in Van Raij et al.43. Samples were collected in 18 experimental paddocks, at the depths of 0- to 10- and 10- to 20-cm layers, from 10 distinct sampling points in each paddock, in order to create one composite sample per unit, totaling 36 samples analyzed.Figure 1Meteorological data during the study period, obtained from the meteorological station located at Centro de Pesquisa de Bovinos de Corte, Instituto de Zootecnia/Agência Paulista de Tecnologia dos Agronegócios (APTA)/Secretaria de Agricultura e Abastecimento de São Paulo (SAA), Sertãozinho, São Paulo, Brazil.Full size imageTable 4 Chemical attributes of the soil in the experimental area, before installing the experiment (November 2015).Full size tableThe nitrogen total (Nt) content was determined by the micro-Kjeldahl method44, and the soil nitrogen stocks (SN) were calculated using the following equation below, according to Veldkamp et al.45.$${text{SN }}left[ {{text{Mg ha}}^{ – 1} {text{ at a given depth}}} right], = ,({text{concentration }} times {text{ BD}}, times ,{1}/{1}0),$$ where concentration refers to the Nt concentration at a given depth (g kg−1), BD is the bulk density at a certain depth (average 1.24 kg dm−3), and 1 is the layer thickness (cm).Description of treatments and managementsThe experiment was carried out in a 16-ha area, divided into 18 paddocks of 0.89 ha each (Fig. 2), organized in a randomized blocks design with three replicates and six treatments, namely conventional crop system with grain maize production (CROP), conventional livestock system with beef cattle production in pasture using Marandu grass (LS), and four ICLS for the production of intercropped maize grain with beef cattle pasture. All production systems were sowed in December 2015, under a no-tillage system. The fertilization recommendations in the systems were based on the recommendation presented in the Boletim 10046.Figure 2Localization and representation of the area of the experiment carried out in the study. Google Earth version Pro was used to construct the map (http://www.google.com/earth/index.html).Full size imageIn the CROP system, the maize Pioneer P2830H was cultivated, sowed in a spacing of 75 cm and sowing density of 70 thousand plants. Applications of 32 kg ha−1 of nitrogen (urea), 112 kg ha−1 of P2O5 (single superphosphate) and 64 kg ha−1 of KCl (potassium chloride) were performed. Complementarily, a topdressing fertilization was made using 80 kg ha−1 of nitrogen (urea) and 80 kg ha−1 of KCl. Sowing was carried out for two consecutive years (December 2015 and 2016), providing two harvests of maize grains (May 2016 and 2017), and between one harvest and the other, the soil remained in fallow without any cover crop. The total amount of fertilizer applied in two years was 224 kg ha−1 of nitrogen (urea), 224 kg ha−1 of P2O5 (single superphosphate) and 288 kg ha−1 of KCl (potassium chloride).For the LS treatment, Urochloa brizantha (Hoechst. ex A. Rich) R.D. Webster cv. Marandu (syn. Brachiaria brizantha cv. Marandu) was sowed in a spacing of 37.5 cm, with a density of 5 kg ha−1 of seeds (76% of crop value) for the pasture assemblage. Marandu grass seeds were mixed with the planting fertilizer, applying 32 kg ha−1 of nitrogen (urea), 112 kg ha−1 of P2O5 (as single superphosphate) and 64 kg ha−1 of KCl. Applications of 40 kg ha−1 of nitrogen, 10 kg ha−1 of P2O5 and 40 kg ha−1 of KCl were also performed as topdressing fertilization in October 2016 and March 2017. 90 days after sowing, the pasture was ready to be grazed (March 2016). Three grazing periods were carried out in continuous stocking systems, with the first period between March and April 2016, the second period between August and October 2016 and the third between November 2016 and December 2017. The total amount for 2 years was 112 kg ha−1 of nitrogen (urea), 132 kg ha−1 of P2O5 (single superphosphate) and 144 kg ha−1 of KCl (potassium chloride).The same cultivar, spacing, sowing density and fertilization rates described in the CROP treatment were used in all ICLS, as well as the same density of Marandu grass seeds and topdressing fertilization adopted in the pasture of the LS treatment. The total amount for two years was 192 kg ha−1 of nitrogen (urea), 132 kg ha−1 of P2O5 (single superphosphate) and 224 kg ha−1 of KCl (potassium chloride). In ICLS-1, Marandu grass was sowed in lines simultaneously with maize, while in ICLS-2, the sowing was also simultaneous, but the application of an under-dose of 200 mL of the herbicide Nicosulfuron was used, 20 days after seedlings emergence. In the ICLS-3, Marandu grass seeds were sown the time of topdressing fertilization of maize, thus the grass seeds were mixed with the fertilizer, and sowing was carried out in the interlines of maize, using a minimum cultivator. In ICLS-4, the sowing of Marandu grass was performed simultaneously with maize, but the grass seeds were sowed in both rows and inter-rows of maize, resulting in a spacing of 37.5 cm. In this treatment, the application of 200 mL of the herbicide Nicosulfuron was adopted, 20 days after seedlings emergence.In all ICLS treatments, maize harvest was carried out in May 2016. Ninety days after harvesting the plants, the pastures were ready to be grazed. Therefore, two grazing periods were made in continuous stocking, being the first period between August and October 2016 and the second period between November 2016 and December 2017. The method for animal stocking in treatments LS and ICLS was continuous with a stocking rate (put and take) being defined according to Mott47. Caracu beef cattle with 14 months of age were used at the beginning of the experiment, with an average body weight of 335 ± 30 kg.Estimations of the nutrient balance (NB) and nutrient use efficiency (NUE)In this study, the inputs and outputs of N were assessed at the farm level48,49. The NB was calculated by the equation below19,45,50.$${text{NB}}_{{text{N}}} = {text{ Input}}_{{text{N}}} {-}{text{ Output}}_{{text{N}}}$$As for the NUE, this parameter was evaluated as defined by the EU Nitrogen Expert Panel51, being calculated as the ratio between outputs and inputs of nitrogen.$${text{NUE}}_{{text{N}}} = , left[ {{text{Output}}_{{text{N}}} /{text{ Input}}_{{text{N}}} } right]$$where NB is the nutrient balance, N is nitrogen, Input is the N concentration in the mineral fertilizer (urea), Output is the nitrogen concentration in export (maize grain and animal tissue), and NUE is the use efficiency of the nutrient.The amount of N exported in maize grains, the grain production results (Table 2) were multiplied by the mean value of N, consulted in Crampton and Harris52.In order to estimate the amounts of nutrient exported by the animals in their tissues, the values of live weight gain were considered [kg ha-1 of live weight (PV)] (Table 2), as well as the nitrogen values of the tissue, according to the methodology proposed by Rasmussen et al.21. Those authors reported that for animals weighting less than 452 kg/PV, it represents 2.7%, while heavier animals have a 2.4% nitrogen content representation of their body weight.The inputs and outputs of N in each production system are represented in Figs. 3, 4 and 5. Biological N fixation, atmospheric deposition, denitrification, leaching, rainfall, and volatilization and absorption of ammonia were not considered in the calculation of NB.Figure 3Representation of inputs and outputs of nitrogen and organic residues generated in the crop system.Full size imageFigure 4Representation of inputs and outputs of nitrogen and organic residues generated in the livestock system.Full size imageFigure 5Representation of inputs and outputs of nitrogen and organic residues generated in the integrated systems.Full size imageData for animal tissue, animal excreta, and N concentration in grains were obtained from key manuscripts from the scientific literature in order to estimate the N balance.Calculation of nitrogen quantity and valuation of organic residuesThe amount of N in the organic residues was determined as a function of the system (Figs. 3, 4, 5). The residue considered in the CROP was the straw derived from maize, while for LS it was the litter deposited (LD) in the grass Marandu, and animal manure (feces and urine). The ICLS were considered as the straw, LD, and animal manure.The N concentration in straw and LD was determined following the methods of AOAC (1990). Straw was sampled immediately after maize grain harvest, using a 1-m2 frame in the field. The material was collected in two spots of the plot that were chosen randomly. All straw deposited on the soil was sampled, weighted and dried in an oven with air circulation (60 °C) until constant weight, for the determination of dry matter in kg of straw per hectare (Table 2). The LD in the pasture system (Table 2) was analyzed according to Rezende et al.53.In order to estimate the daily amount of excreta, we considered the stocking rate adopted in the experiment (Table 2) and the values proposed by Haynes and Williams54. According to those authors, adult beef cattle can defecate on average 13 times a day and urinate 10 times a day, totaling a daily amount of 28.35 kg of feces and 19 L of urine.The valuation was calculated based on the mean value of urea for the last 10 years in the fertilizer market55,56,57, namely $0.28 kg−1 ha−1 of urea, and considering the loss of nitrogen by volatilization, which according to Freney et al.58 and Subair et al.59 can reach up to 28%.Statistical analysisThe experiment was assembled in a randomized blocks design. The model adopted for the analysis of all response variables included the block’s and treatments fixed effects (3 blocks and 6 treatments), in addition to the random error. Statistical analysis were carried out by the function “dbc()” of the package “ExpDes.pt” of the software R Development Core Team60, and the mean values were compared by the Tukey’s test at a 5% probability level. More

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Climate and land cover dataOur study of tropical dry season dynamics required climatic variables with high temporal resolution (i.e., daily) and full coverage of tropic regions. To reduce uncertainties associated with the choice of precipitation (P) and evapotranspiration (Ep or E) datasets, we used an ensemble of eight precipitation products, three reanalysis-based products for Ep, and one satellite-based land E product. These precipitation datasets were derived four gauge-based or satellite observation (CHIRPS58, GPCC59, CPC-U60 and PERSIANN-CDR61), three reanalyses (ERA-562, MERRA-263, and PGF64) and a multi-source weighted ensemble product (MSWEP v2.865). The potential evapotranspiration (Ep) was calculated using the FAO Penman–Monteith equation66 (Eqs. (1, 2)), which requires meteorological inputs of wind speed, net radiation, air temperature, specific humidity, and surface pressure. We derived these meteorological variables from the three reanalysis products (ERA-5, MERRA-2, and GLDAS-2.067). Since PGF reanalysis lacked upward short- and long-wave radiation output and thus net radiation, we used available meteorological outputs from GLDAS-2.0 instead, which was forced entirely with the PGF input data.$${Ep}=frac{0.408cdot triangle cdot left({R}_{n}-Gright)+gamma cdot frac{900}{T+273}cdot {u}_{2}cdot left({e}_{s}-{e}_{a}right)}{triangle +{{{{{rm{gamma }}}}}}cdot left(1+0.34cdot {u}_{2}right)}$$
(1)
$${VPD}={e}_{s}-{e}_{a}=0.6108cdot {e}^{frac{17.27cdot T}{T+237.3}}cdot left(1-frac{{RH}}{100}right)$$
(2)
Where Ep is the potential evapotranspiration (mm day−1). Rn is net radiation at the surface (MJ m−2 day−1), T is mean daily air temperature at 2 m height (°C), ({u}_{2}) is wind speed at 2 m height (m s−1), ((,{e}_{s}-{e}_{a})) is the vapor pressure deficit of the air (kPa), ({RH}) is the relative air humidity near surface (%), ∆ is the slope of the saturation vapor pressure-temperature relationship (kPa °C−1), γ is the psychrometric constant (kPa °C−1), G is the soil heat flux (MJ m−2 day−1, is often ignored for daily time steps G ≈ 0).We derived the daily evapotranspiration data from the Global Land Evaporation Amsterdam Model (GLEAM v3.3a68), which is a set of algorithms dedicated to developing terrestrial evaporation and root-zone soil moisture data. GLEAM fully assimilated the satellite-based soil moisture estimates from ESA CCI, microwave L-band vegetation optical depth (VOD), reanalysis-based temperature and radiation, and multi-source precipitation forcings. The direct assimilation of observed soil moisture allowed us to detect true soil moisture dynamic and its impacts on evapotranspiration. Besides, the incorporation of VOD, which is closely linked to vegetation water content69,70, allowed us to detect the effect of water stress, heat stress, and vegetation phenological constraints on evaporation. Other observation-driven ET products from remote-sensing physical estimation and flux-tower are not included due to their low temporal resolution (i.e., monthly)71 or short duration72,73. ET outputs of reanalysis products are not considered in our analysis, because the assimilation systems lack explicit representation of inter-annual variability of vegetation activities and thus may not fully capture hydrological response to vegetation changes62,63,67.We used land cover maps for the year 2001 from the Moderate-Resolution Imaging Spectroradiometer (MODIS, MCD12C1 C574) based on the IGBP classification scheme to exclude water-dominated and sparely-vegetated pixels (like Sahara, Arabian Peninsula). All climate and land cover datasets mentioned above were remapped to a common 0.25° × 0.25° grid and unified to daily resolution. The main characteristics of the datasets mentioned above are summarized in Supplementary Table 1.Outputs of CMIP6 simulationsTo understand how modeled dry season changes compare with observed changes, we analyzed outputs from the “historical” (1983-2014) runs of 34 coupled models participating in the 6th Coupled Model Inter-comparison Project75 (CMIP6, Supplementary Table 3). We used these models because they offered daily outputs of all climatic variables needed for our analysis, including precipitation, latent heat (convert to E), and multiple meteorological variables for Ep (air temperature, surface specific humidity, wind speed, and net radiation). All outputs were remapped to a common 1.0° × 1.0° grid and unified to daily resolution.Defining dry season length and timingFor each grid cell and each dry season definition (P  More

The management of introduced species, whether kudzu or zebra mussels, is costly and complex. Now, a paper reports a workable, effective solution that harnesses network analyses of ecological phenomena.Invasive species can pose severe economic and environmental problems, costing more than US$1 trillion worldwide since 1970 (ref. 1). Yet managing this human-driven issue is difficult in itself. The regions involved can be vast — entire continents or countries, for instance — while budgets are typically limited. As well, the sites potentially affected and management options can be numerous. Real systems (for example, all the lakes in the United States) can have thousands of locations that could potentially be infested. By contrast, considering just 40 locations means dealing theoretically with over 1 trillion unique combinations (240) where management could be applied (for instance, to reduce the number of invasive species leaving infested areas or entering uninfested ones). Given these constraints, a key problem is how and where to deploy control measures such as invasive-species removal. While sophisticated optimization approaches exist2, which use mathematical rules to exclude most suboptimal combinations and quickly zoom in to which locations should be managed to minimize new invasions, these algorithms are generally unfeasible for very large systems. Now, writing in Nature Sustainability, Ashander et al.3 demonstrate that simpler network metrics revealing linkages between patches can provide solutions that are often comparable to the more complex optimization algorithms. More