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Site descriptionThis experiment was conducted in two long-term P-trial grassland sites (Site A and Site B) situated in proximity (~ 350 m) to each other in the dairy farm at Johnstown Castle, Wexford, Co. Wexford, Ireland (6°49′ W, 52°29′ N). The sites were grazed permanent grasslands before establishment. When the experiment was established in 1995, 16 (10 m × 2 m) plots were formed in each site in a fully randomised block design with four replicates. The two sites established were selected to represent different soil types and drainage classes. Site A is a moderately drained brown earth and site B is an imperfectly drained gley soil31. Each year in February, each plot received one of the four phosphorous (P) fertilization rates (16% P superphosphate): 0 (P0), 15 (P15), 30 (P30), and 45 (P45) kg P ha−1 year−1. All plots were initially sown with Lolium perenne and reseeded in 2016 with the same species. However, plant species such as Poa trivialis, Agropyron repens, Trifolium repens were present to a lesser extent. Above-ground biomass is harvested each month between February and August followed by 40 kg N ha−1 fertilizer applications. In the year (2019) of this experiment and the years before, SulCAN as a solid was applied at the first or second week of each month during February-August and potassium (K) as muriate of potash (KCl) was applied in February at a rate of 125 kg K ha−1. SulCAN contains 26.7% N in the form of nitric and ammoniacal nitrogen and 5% water soluble Sulphur. For this study plots receiving P0, P15 and P45 at the two field sites were set up to carry out this experiment. The two sites were selected as they had slightly different soil properties and thus there was an opportunity to consider a soil × treatment effect in the experiment.Experimental designFertilizer N and substrate C were applied on 8 May and 12 June in the experiment undertaken between May and July 2019, which represents the main growing season in Ireland. Within each plot, an area of 1 m × 1 m was selected. Following N fertilizer application (40 kg N ha−1) to all plots, carbon substrate [mixture of glucose (40%), sodium acetate (30%) and methanol (30%)] was applied once within the selected area using a sprayer watering can. Labile C available in animal excreta usually contains carbohydrates, volatile fatty acids, and alcohols32; as such different carbon substrates were applied to mimic this. Our review of the literature also indicated that C source types could differentially affect denitrifying communities and consequently denitrification rate. Thus, a mixture of three C sources was used to decrease bias of one microbial group over another as a result of single substrate use. Carbon was supplied to alleviate C-limitations of denitrification and nitrification processes as observed by O’Neill et al.29 in soils from this trial and to ensure equal substrate availability across all soil P levels. Equivalent C input rate of 0.63 g C m−2 day−1 was added to represent a daily rate of plant carbon input from Lolium perenne dominated ecosystem33. Soil samples were collected on eight occasions throughout the experimental period. Soil was sampled from across each selected area to a depth of 10 cm, sieved through 4 mm sieve and analysed for soil mineral N and microbial biomass.Soil properties, plant biomass and climate parametersPhysico-chemical soil properties were characterized by taking samples from 10 cm depth from each plot in the two sites before the commencement of the experiment. Soil pH was measured in water (2:1, water volume:soil mass) using Sally pH Auto analyser Dilution System (Gilson 215, Gilson, Dunstable, England). Soil organic matter (SOM) content was determined from mass loss on ignition at 550 °C for 7 h. Total C and total N concentrations were measured using a TrueSpec C/N analyser (TruSpec, LECO Corporation, Michigan, USA). Plant available P, potassium (K), and magnesium (Mg) were estimated using Morgan’s extraction34 and analysed using a Lachat QuickChem 8500 Series 2 Flow injection Analyzer (Lachat, QuickChem, 5600 Loveland, Colorado, USA). Particle size analysis was performed using the Pipette method35, where 2 mm sieved dry soil (20 g) was pre-treated with 6% H2O2, 3% NH4OH, and 5% sodium hexametaphosphate before separating soil aliquots into particle sizes. Water Holding Capacity (WHC) was determined from the mass difference between water-saturated and then overnight dried (105 °C) soil. Bulk density was determined by dividing weight of oven-dried soil by the total soil volume.To determine the mineral N concentrations, ten gram fresh soil was extracted with 50 mL 2 M KCl (5:1 solution to soil ratio). The supernatant was filtered through Whatman No. 1 filter paper and filtrates were stored in a cold room at 4 °C for about a week until analysis. Ammonium (NH4+) and nitrate (NO3−) concentrations in the extracts were analysed by the Aquakem 600 discrete analyser.Above-ground plant biomass from each plot of both sites was harvested twice during the experiment period (June 10 and July 11, 2019) to a height of ~ 5 cm using a Haldrup plot harvester. The total harvested biomass weight from each plot was recorded and a 100 g sub-sample was taken for dry matter (DM) analysis. Each fresh herbage sub-sample was weighed and placed in an oven at 70 °C for 3 days, and dry weight of the biomass was determined after re-weighing.Rainfall records for the experiment period were obtained from a Met Éireann weather observing station located in Teagasc dairy farm in Johnstown Castle, Co. Wexford., situated within a 100 m distance from the experimental sites. Volumetric soil moisture content and temperature was measured to 5 cm depth on individual plots on each gas sampling occasion using a handheld theta probe (WET-2 WET Sensor, Delta-T Devices, Cambridge, England). Water-filled pore space (WFPS) were calculated from the soil moisture values, bulk density of the soils, and soil particle density (2.65 g cm−3).Microbial biomass, glomalin-related soil protein and potential denitrification activitySoils were analysed for microbial biomass nitrogen (MBN), phosphorus (MBP) and carbon (MBC) using the fumigation extraction method as described respectively in (Brooks et al.36,37, and Vance et al.38). Five gram fumigated (24 h) and non-fumigated soil samples were extracted with 100 mL 0.5 M NaHCO3 and analysed for P colorimetrically using an Aquakem 600 discrete analyser (Thermo Electron OY, Vantaa, Finland). In order to avoid the spike readings by the instrument due to the effervescent nature of NaHCO3, one millilitre of 10% HCl was added to 10 mL extracts and diluted to 50 mL using distilled water. Microbial P was calculated by subtracting the P concentration of non-fumigated samples from fumigated samples, and dividing the result by an extraction factor of 0.437.Microbial biomass C and N were determined similarly using chloroform fumigation method with extraction period of 48 h with 0.5 M K2SO438. The extracts of the fumigated and non-fumigated samples were analysed for total C and N using a TOC-L CPH/CPN analyser (Shimadzu, Tokyo, Japan), and the differences, divided by correction factors of 0.45 and 0.54, were used to estimate the microbial biomass C and N, respectively.Glomalin is a glycoprotein produced by AMF and can be used as an indicator of mycorrhizal colonization in the plant root-soil interface39. Total glomalin-related soil protein (GRPS) was extracted by 90 min of autoclaving (121 °C) of 1 g air-dried soil in 8 mL of 50 mM sodium citrate adjusted to pH 8.0 with HCl40. Three additional sequential extractions were performed with the sodium citrate solution by autoclaving for 60 min until no red-brown color was visible in the last supernatant. After autoclaving, the samples were centrifuged at 10,000 revolutions per minute (rpm) for 5 min. The amounts of glomalin in the extracts were quantified using the Bradford dye-binding assay with bovine serum albumin (BSA) as the standard (2 mg mL−1). In a 96-well plate, replicated 200 µL of standard or extracts and 50 µL of dye reagent were added in each well and mixed using a microplate mixer. The Bradford-reactive substance was determined by measuring absorbance at 600 nm using Microplate Reader (Modulus Microplate Multimode Reader, Turner BioSystems, Sunnyvale, California, USA). Sample concentrations were determined using the standard curve. Potential denitrification activity (PDA) was determined using the acetylene inhibition method, modified from Pell et al.41. Briefly, replicated 20 g fresh soils were added into two identical flasks from a sample of soil. The flasks were then sealed with a rubber stopper and flushed and filled with helium after evacuating the headspace air. In one of the replicas, 10% of the headspaces were removed and replaced by acetylene. All flasks were incubated at 15 °C on an orbital shaker at 175 rpm for 30 min followed by the addition of a nutrient solution containing 75 mmol L−1 KNO3, 37.5 mmol L−1 Na-succinate, 25 mmol L−1 glucose, and 75 mM Na-acetate. Gas samples were taken from the headspace every 1 h for 5 h. N2O concentrations were determined using a gas chromatograph (Bruker, Scion 456-GC, Livingston, Scotland), and PDA was calculated from the rate of change of N2O concentrations over time from acetylene amended flasks.N2O and CO2 flux measurementsGas samples (N2O and CO2 fluxes) were measured before and after the application of N fertilizer and C substrates, with a daily sampling for 10 days directly after C + N additions and 3–4 times a week in the third and fourth week and 2–3 times a week in the subsequent weeks. A rectangular (40 × 40 cm) static collar, made of stainless steel (opaque), was anchored 5 cm deep into the soil within the marked area of 1 m × 1 m in each of the selected plots. During gas sampling, a 10 cm tall chamber lid fitted with two septa on top was placed on the collar lined with neoprene rubber band. To ensure hermetic sealing of the headspace during sampling, the ring area of the collar was half-filled with water, and a 10 kg weight was placed on the top of the lid to compress the seal. Gas samples were collected between 09:30 and 11:30 local time using a 10 mL Luer lock syringe fitted with a hypodermic needle via one of the septa at 0, 20, and 40 min after chamber closure. Prior to transferring the final sample into a pre-evacuated 7 mL glass vial, air in the chamber headspace was mixed by flushing the syringe three times. Gas samples were analysed using a gas chromatograph (Bruker, Scion 456-GC, Livingston, Scotland) fitted with an electron capture detector to analyse for N2O concentrations and a thermal conductivity detector to analyse for CO2 concentrations. Daily Fluxes (F) were calculated for each plot using the following equation:$$ F = left( {frac{Delta C}{{Delta t}}} right) times left( {frac{M times P}{{T times R}}} right) times left( frac{V}{A} right) $$where ∆C is the change in gas concentration in the chamber headspace during chamber enclosure period in ppbv, ∆t is chamber closing period in minutes, so ∆C/∆t is the slope of the gas concentration with time. M is the molar mass of N2O-N (28 g mol−1) and CO2-C (12 g mol−1), P and T are the atmospheric pressure (Pa) and temperature (K). Atmospheric pressure values were obtained from the nearby weather station whereas for T, wet sensor values were used. V is the headspace volume of the closed chamber (m3) and A is surface are of the chamber (m3). R is the ideal gas constant (8.314 J K−1 mol−1). Daily flux for each treatment is reported as the average of the replicates.Cumulative N2O and CO2 emissions were calculated over each application period by multiplying the daily N2O and CO2 fluxes by the number of days between two consecutive measurements. A summation of the cumulative flux of each application period is reported as the total cumulative flux.Statistical analysisANOVAs with repeated measures were used to test for the C + N addition effect on N2O and CO2 emissions, MBC, MBN, MBP, NO3−, and NH4+ with P treatment, site, and day of measurement as fixed effects, and individual plots as a random effect. Two-way ANOVA was applied to test for main and interaction effects of P treatment and site on cumulative N2O and CO2 emissions, soil property parameters (Table 1), plant biomass, and GRSP. Prior to analysis, response variables were checked for normality (sphericity for repeated ANOVA) and homogeneity of variance, and log transformed when required. Tukey’s HSD post-hoc tests were conducted to identify pair-wise comparisons of significant effects at P  More

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The fourteenth-century pandemic known as the Black Death might not have been as devastating as was previously thought, an analysis of ancient pollen suggests1.

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doi: https://doi.org/10.1038/d41586-022-00435-6

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Study areaThe QTP is located in southwestern China (25° ~ 40°N, 75° ~ 103°E), with a total area of 2.5 million km2 and an average elevation above 4000 m (Fig. 7). The QTP is mainly covered with permafrost and grassland, with areas of glacier and desert48. The QTP, also known as the “Asian Water Tower”49, is the source of 13 major Asian rivers (e.g., the Indus, Ganges, Brahmaputra, Yangtze, and Yellow Rivers). The QTP has a clod, arid climate, with an annual average temperature below 0 °C and an annual mean precipitation of 400 mm. The seasonal distribution of precipitation is uneven, with most precipitation concentrated in the period June to September. There is a decreasing trend in precipitation from the southeast to the northwest of the plateau50. Known as the “Roof of the World” and “Third Pole”, the QTP is also an area that is sensitive to global climate change, showing increasing warming and humidification in recent decades51. In addition, the QTP contains a diversity of ecosystems and fosters a historic ecological security barrier, which nurtures the development of animal husbandry and diverse cultures.Figure 7Geographical location of the QTP. The map was created using ArcMap 10.2, URL: http://www.esri.com.Full size imageData sourcesRCP scenarios and climate change datasetThe RCP scenarios released by the IPCC 5th Assessment Report52 supply a forecasting standard for climate change research. RCP values ranging from 2.6 to 8.5 reflect radiation forcing values in 2100 relative to the beginning of the Industrial Revolution in 175053. Different radiative forcing scenarios represent different future climate scenarios. RCPs consist of one high-emission scenario (8.5 ({text{W}} cdot {text{m}}^{ – 2}), RCP8.5), two medium-emission scenarios (6.0 ({text{W}} cdot {text{m}}^{ – 2}), RCP6.0; 4.5 ({text{W}} cdot {text{m}}^{ – 2}), RCP4.5), and one low-emission scenario (2.6 ({text{W}} cdot {text{m}}^{ – 2}), RCP2.6)54. In this study, we adopted the RCP2.6, RCP4.5 and RCP8.5 climate change scenarios choosing RCP4.5 to represent the medium emission scenario in consideration of increasing activity through global initiatives in response to climate change. Specific descriptions of each scenario are shown in Table 1.Table 1 The characteristics of each RCP scenario.Full size tableWe adopted the climate change dataset outputs from five global circulation models(GCMs) (namely GFDL-ESM2M, HadGEM2-ES, IPSLCM5ALR, MIROC-ESM-CHEM, and NorESM1-M) within the fifth phase of the Coupled Model Intercomparison Project (CMIP5)55. The dataset outputs from GCMs were downscaled to a resolution of 0.5° and bias-corrected with Water and Global Change (WATCH) data (Integrated Project Water and Global Change, http:/www.eu-watch.org/data_availability)56. The baseline period of the dataset is 1950–2005 and the forecast period is 2006–2099.The climate change dataset included daily precipitation, air pressure, solar radiation, air temperature, maximum air temperature, minimum air temperature, wind speed, and relative humidity.Auxiliary dataThe auxiliary data for our research include the following. (1) The land use and land cover (LULC) map was obtained from the Resource and Environment Science and Data Center (RESDC), Chinese Academy of Sciences (https://www.resdc.cn) for 1980, 1990, 1995, 2000, 2005, 2010, 2015 and 2020 at a 1 km resolution. The LULC data have six major classes: cropland, grassland, forestland, water, built-up land and barren land. (2) The spatial distribution of soil type data, digital elevation model (DEM), watershed boundaries and normalized difference vegetation index (NDVI) data with a resolution of 1 km were obtained from the RESDC. (3) Soil physical and chemical property data (available soil water capacity, absolute depth to bedrock, silt content, clay content, sand content and soil organic carbon content) were obtained from the International Soil Reference and Information Centre (ISRIC Data Hub) (https://data.isric.org) with a 1 km spatial resolution. (4) During 1986–2005 and 1986–2098 (RCP2.6; RCP4.5; RCP8.5), the permafrost datasets in the Northern Hemisphere (https://doi.org/10.12072/ncdc.CCI.db0032.2020) and the response of the alpine grassland ecosystem to climate change (RCP2.6, RCP4.5, and RCP8.5) in the permafrost region of the Qinghai-Tibet Plateau from 1981 to 2099 (https://doi.org/10.12072/ncdc.CCI.db0006.2020) were provided by the National Cryosphere Desert Data Center (https://www.ncdc.ac.cn).Future land use simulation and validationIn this study, we used the Future Land Use Simulation model (FLUS) to simulate the LULC in 2030, 2050 and 2100 under the three RCP scenarios. This model was developed by57 and is available for download at (www.geosimulation.cn/flus.html). The FLUS model is an efficient land use simulation tool and has been widely used58,59. We selected the DEM, slope, precipitation, temperature, soil type, and permafrost distribution to calculate the suitability probability. Based on the land use transfer from 2010 to 2015, we calculated the total land use in 2030, 2050 and 2100 under three RCP scenarios by the Markov model. To validate the FLUS model, we set 2010 as the starting year and simulated the land use in 2015. The output results were compared with the real 2015 land use data, and we calculated the Kappa coefficient as follows:$$begin{array}{*{20}c} {Kappa = frac{{P_{0} – P_{C} }}{{P_{P} – P_{C} }}} \ end{array}$$
(1)
where (P_{0}) is the number of pixels converted correctly,(P_{C}) is the correct number of pixels to be converted in the random case, and (P_{P}) is the correct number of pixels to convert under ideal conditions.Assessment of ecosystem services under different RCP scenariosThis study assessed four ESs namely WY, SR, CS, and RMP, under climate change scenarios in 1980, 1990, 1995, 2000, 2005, 2010, 2015, and 2030 (short-term); 2050 (medium-term); and 2100 (long-term). We adopted the Integrated Valuation of Environmental Service and Tradeoffs (InVEST)60 model to assess the WY, SR, and CS ecosystem services. The InVEST model developed by the Natural Capital Project(www.naturalcapitalproject.org) is an effective model to evaluate ESs61 and is widely used in ES research on the QTP22,23,24,25. All spatial data were processed into a 1 km resolution and Albers projection by ArcGIS 10.2 before input into the InVEST model. The data requirements of the InVEST model and its processing are shown in Table S1. We use net primary productivity (NPP) to evaluate the RMP, and NPP can be used to represent the richness of biomass and the supply of organic materials. We adopted the Carnegie-Ames-Stanford Approach (CASA)62 model to estimate NPP.Water yieldWater yield is a key ecosystem service. It refers to the annual quantity of water available for human use, as measured by the supply of surface water per unit area63. We adopted the InVEST 3.9.0 water yield model to estimate WY services in the QTP region. The water yield model is based on the water balance principle64. The biophysical parameter table required by the model is shown in Table S2. The parameters in the biophysical table come from the published literature26,63,65. The annual WY is calculated as follows:$$begin{array}{*{20}{c}} {{Y_{xj}} = left( {1 – frac{{AE{T_{xj}}}}{{{P_x}}}} right){P_x}} end{array}$$
(2)
where (Y_{xj}) is the annual WY of land cover type j in pixel x; (P_{x}) is the annual average precipitation of pixel x; and (AET_{xj}) is the actual evapotranspiration of land cover type j in pixel x.$$begin{array}{*{20}c} {frac{{AET_{xj} }}{{P_{x} }} = frac{{1 + omega_{x} R_{xj} }}{{1 + omega_{x} R_{xj} + frac{1}{{R_{xj} }}}}} \ end{array}$$
(3)
where (omega_{x}) is a dimensionless nonphysical parameter representing soil properties under natural climate conditions. The calculation method is as follows:$$begin{array}{*{20}c} {omega_{x} = Zfrac{{AWC_{x} }}{{P_{x} }}} \ end{array}$$
(4)
where Z is a seasonal rainfall factor representing the regional precipitation distribution and other hydrogeological characteristics. The higher the Z value is, the less the seasonal constant Z affects the model results66. Since the QTP region belongs to the arid and cold climate zone in China, the Z value is set as 9. (AWC_{x}) is the soil effective water content of pixel X, which is determined by the soil depth and physical and chemical properties. (R_{xj}) is the Budyko dryness index, which is calculated as follows:$$begin{array}{*{20}c} {R_{xj} = frac{{K_{xj} cdot ET_{0} }}{{P_{x} }}} \ end{array}$$
(5)
where, (K_{xj}) is the reference crop evapotranspiration and (ET_{0}) is the reference evapotranspiration in pixel x. We adopted the modified Hargreaves method to calculate (ET_{0}).$$ET_{0} = 0.0013 times 0.408 times RA times (T_{av} + 17) times (TD – 0.0123P)^{0.76}$$
(6)
In the above formula, (T_{av}) represents the average daily maximum temperature and minimum temperature, (TD) represents the difference between the daily maximum temperature and minimum temperature, (RA) represents astronomical radiation (MJm-2d-1) and P represents precipitation (mm/month).Soil retentionSoil retention refers to the ability of various land cover types to prevent soil erosion. The InVEST 3.9.0 sediment delivery ratio (SDR) was employed to estimate SR services in the QTP region. The SDR model is based on the Revised Universal Soil Loss Equation (RUSLE)67, and the model is calculated as follows:$$begin{array}{*{20}c} {SR = R*K*LS – R*K*LS*C*P} \ end{array}$$
(7)
$$begin{array}{*{20}c} {L = left( {frac{gamma }{22.3}} right)^{{frac{beta }{1 + beta }}} } \ end{array}$$
(8)
$$begin{array}{*{20}c} {beta = frac{{sin frac{theta }{0.0896}}}{{left[ {3.0, *,left( {sin theta } right)^{0.8} +, 0.56} right]}}} \ end{array}$$
(9)
$$begin{array}{*{20}c} {S = 65.41*sin^{2} theta + 4.56*sin theta + 0.065} \ end{array}$$
(10)
where SR is the total amount of soil retention (tons ha-1 a-1), LS is the topographic factor, and LS is calculated from the slope length factor (L) and slope steepness factor (S). C is the vegetation and management factor. P is the support practice factor. C and P are shown in Table S2. R is the rainfall erosivity index(MJ mm ha-1 h-1 a-1), which was calculated via monthly precipitation28. K is the soil erodibility, which was calculated from the sand, silt, clay and organic soil moisture contents68. R and K are calculated as follows:$$begin{array}{*{20}c} {R = mathop sum limits_{i = 1}^{12} left( { – 1.5527 + 0.179P_{i} } right)} \ end{array}$$
(11)
$$begin{array}{*{20}c} {K = 0.1317*left{ {0.2 + 0.3*exp left[ { – 0.0256*SANleft( {1 – frac{SIL}{{100}}} right)} right]} right}} \ {*left( {frac{SIL}{{CLA – SIL}}} right)^{0.3} *left( {1 – frac{0.25*SOM}{{SOM + exp 3.72 – 2.95*SOM}}} right)} \ {quad quad*left( {1 – frac{{0.7*1 – frac{SAN}{{100}}}}{{begin{array}{*{20}c} {1 – frac{SAN}{{100}} + exp left( { – 5.51 + 22.9*left( {1 – frac{SAN}{{100}}} right)} right)} \ end{array} }}} right)} \ end{array}$$
(12)
where Pi is the precipitation in month i. SAN, SIL, CLA, and SOM are the contents of sand, silt, clay and organic moisture, respectively. Other parameters are shown in Table S1.Carbon storageCarbon storage services refer to the carbon that ecosystems store in vegetation, soil and debris. The InVEST 3.9.0 carbon model uses a simple method to estimate CS based on land use data. The carbon pools in this model include four categories: aboveground carbon, belowground carbon, soil organic carbon and dead organic matter. This model simplifies the carbon cycle, and the change in carbon storage is mainly caused by change in land use69. The carbon pools for land use types were set according to published literature70,71,72. The carbon storage is calculated as follows:$$begin{array}{*{20}c} {{text{C}}_{{{text{total}}}} = C_{above} + C_{below} + C_{soil} + C_{dead} } \ end{array}$$
(13)
where ({text{C}}_{{{text{total}}}}), (C_{above}), (C_{below}), (C_{soil}) and (C_{dead}) are the total carbon storage, aboveground carbon, belowground carbon, soil organic carbon and dead organic matter, respectively.Raw material provisionRaw material supply refers to the organic matter provided by the ecosystem for human production and life, such as pasture and wood. In this study, RMP was quantified by the annual NPP. The NPP in the QTP region is calculated by the CASA model, which is a light use efficiency model driven by climate and remote sensing data73,74. The CASA model has been widely used to estimate NPP in terrestrial ecosystems75,76. In the CASA model, NPP is calculated as follows:$$begin{array}{*{20}c} {NPPleft( {x,t} right) = APARleft( {x,t} right) times varepsilon left( {x,t} right)} \ end{array}$$
(14)
where, (APARleft( {x,t} right)) is the photosynthetically active radiation(MJ m-2) absorbed by pixel x in month t, (varepsilon left( {x,t} right)) is the actual light energy utilization rate(gC MJ-1), and the (APARleft( {x,t} right)) calculation method is as follows:$$begin{array}{*{20}c} {APARleft( {x,t} right) = SOLleft( {x,t} right) times FPARleft( {x,t} right) times 0.5} \ end{array}$$
(15)
In the formula, (SOLleft( {x,t} right)) is the total solar radiation in pixel x in month t(MJ M-2); (FPARleft( {x,t} right)) is the absorption ratio of photosynthetically active radiation by vegetation, which is determined by the normalized difference vegetation index (NDVI); and the constant 0.5 is the proportion of photosynthetically active radiation to the total radiation. (SOLleft( {x,t} right)) can be calculated by the solar shortwave radiation as follows:$$begin{array}{*{20}c} {SOLleft( {x,t} right) = a_{s} + b_{s} frac{n}{N}R_{s} } \ end{array}$$
(16)
where, (R_{s}) is the solar shortwave radiation(MJ M-2 d-1), n is the actual sunshine time(hours), N is the time of day(hours), and (frac{n}{N}) is the relative sunshine time; The constants (a_{s} = 0.25) and (b_{s} = 0.5).And the (varepsilon left( {x,t} right)) is calculated as follows:$$begin{array}{*{20}c} {varepsilon left( {x,t} right) = T_{varepsilon 1} left( {x,t} right) times T_{varepsilon 2} left( {x,t} right) times W_{varepsilon } left( {x,t} right) times varepsilon_{max} } \ end{array}$$
(17)
where, (T_{varepsilon 1}) and (T_{varepsilon 2}) are the stress factors of cold and heat, respectively; (W_{varepsilon }) is the water stress factor, reflecting the influence of water conditions; (varepsilon_{max}) is the maximum light use efficiency(gC MJ-1) under the optimal conditions, in this study, (varepsilon_{max}) is 0.389.Trend analysisThe Mann–Kendall nonparametric test and Sen’s slope estimator were used to analyze the trend of ESs in the QTP region. The Mann–Kendall method is widely used to analyze climatic and hydrological time series variation trends77. The advantage of the Mann–Kendall test is that it does not require the sample to follow a certain distribution, allows the existence of missing values, is not affected by a small number of outliers, and has strong quantitative ability78. The Mann–Kendall test is as follows:$$begin{array}{*{20}c} {S = mathop sum limits_{i}^{n – 1} mathop sum limits_{j = i + 1}^{n} sgnleft( {x_{j} – x_{i} } right)} \ end{array}$$
(18)
For time series data, i.e., {x1, x2, …, xn}, n is the length of the data, and (sgnleft( {x_{j} – x_{i} } right)) is derived as:$$begin{array}{*{20}c} {sgnleft( {x_{j} – x_{i} } right) = left{ {begin{array}{*{20}c} { + 1,x_{j} – x_{i} > 0} \ {0,x_{j} – x_{i} = 0} \ { – 1,x_{j} – x_{i} < 0} \ end{array} } right.} \ end{array}$$ (19) In this study, we set the significance level of (alpha = 0.05), when (left| Z right| le Z_{1 - alpha /2}) accepts the null hypothesis. Otherwise, the null hypothesis is rejected, and the trend is statistically significant.$$begin{array}{*{20}c} {Z = left{ {begin{array}{*{20}l} frac{S - 1}{{sqrt {VARleft( S right)} }},&quad S > 0 \ 0,&quad S = 0 \ frac{S + 1}{{sqrt {VARleft( S right)} }},&quad S < 0 \ end{array} } right.} \ end{array}$$ (20) $$begin{array}{*{20}c} {VARleft( S right) = left{ {nleft( {n - 1} right)left( {2n + 5} right) - mathop sum limits_{j = 1}^{p} t_{j} left( {t_{j} - 1} right)left( {2t_{j} + 5} right)} right} div 18} \ end{array}$$ (21) where p is the number of nodes in the dataset and (t_{j}) is the length of the nodes.Sen’s slope estimator is an estimation method based on the median and its insensitivity to outliers78.$$begin{array}{*{20}c} {beta = Medianleft( {frac{{x_{j} - x_{i} }}{j - i}} right)} \ end{array}$$ (22) Trade-offs and synergy analysisSynergies and trade-offs were used to describe the relationships among the ESs. A trade-off analysis was conducted to reflect the difference in ESs and their responses to climate change. Trade-offs are when ESs change in the opposite direction. Synergies are when ESs change in the same direction79. Correlation analysis is often used to evaluate trade-offs and synergies between ESs2. To analyze the trade-offs and synergies of ESs at different administrative and natural scales, we allocated the ES values at the 10 km (pixel), county and watershed scales by the “zonal statistic” module of ArcGIS 10.2, and conducted minimum–maximum normalization in R4.0.3 (www.R-project.com). To analyze the relationship between any two of the four ES types, the R package PerformanceAnalytics was adopted to measure the Spearman correlation matrix at different scales. More