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Gamma source and dose modelingThe general literature contains conflicting results on whether the energies of photons interacting with fungi affects the radiotrophic response. As such, we sought to control critical variables while irradiating the fungi with ionizing radiation from a sealed Cs-137 source and a UV source. The Cs-137 source emitted a photon at 662 keV along with other lower energy photons near 30 keV (Table S1).A review of previous studies was conducted to identify the gamma dose rate and total dose that should be targeted for exposure (Table S2). Those dose rates ranged from 600,000 rad delivered in 1.5 h to 0.08 rad delivered in 16 h. Even among studies examining the same fungi attributes, the total dose varied dramatically. For the present study, we used a Health Physics code to target a 50-rad dose over a one-week exposure. This dose was selected as it changes blood count observed in most humans24. We hypothesized that this dose would induce physiological changes in the fungi without causing a high rate of lethality. A MicroShield (Grove Software, Inc.) model was created to identify the quantity of radioactive material and distance between source and sample necessary to achieve the dose of 50 rad in seven days. From a sensitivity analysis of the MicroShield model, it was determined that ~ 350 µCi of Cs-137 would create a dose rate of ~ 50 rad in seven days (Fig. 1; Table S3), if placed 1.8 cm from the surface of the fungi. It should be noted that Microshield values are often conservative and likely underestimate the actual dose on target. In addition, 50 rad falls in the middle of the large range for energies previously reported in the general literature (Table S2).Figure 1Time required on target to achieve an exposure of 50 rad determined in MicroShield and based on an activity of ~ 350 µCi for Cs-137 source and the vertical distance between the source and fungus.Full size imageThe dose from the Cs-137 source on the fungal mycelium is also dependent on the radial growth of the fungus from the center plug used to initiate growth. As the fungus grows away from the source, the leading edge will experience a lower total dose of radiation. Although a uniform dose would have been ideal, a source with activity sufficient to create a uniform radiation field would have initiated a variety of safety controls deemed impractical for this experiment. The background radiation dose at the testing site in Albuquerque is approximately 10 µrem h−1; the dose at the outermost area of the Petri dish was measured at 65,553 µrad h−1. As this dose was primarily from gamma emissions, rad and rem can be considered equivalent. To validate the simulation, a dose rate study was performed using thermoluminescent dosimeters (TLD) placed at varying distances from the center of the source. The TLD placed directly under the source measured ~ 100 rad over the seven-day exposure, which is double the prediction from the simulation (50 rad; Fig. 2A). However, at a radial distance of 3.5 cm, the measured and estimated total dose over seven days were much closer, 12.3 and 11.4 rad, respectively. A comparison of the measured and estimated dose on target demonstrated a non-linear correlation (Fig. 2B), in which the simulation better approximated the dose at larger radial distances from the source.Figure 2(A) The total gamma dose on the fungal mycelial at 7 days as a function of the radial distance from the central mycelium plug based on empirical measurements (-●-) and estimated from simulations (-○-). (B) Observed correlation between the measured and estimated doses at varying radial distances.Full size imageIn order to normalize the energy deposited in the fungi from Cs-137 and the UV lamp sources, the units of MeV g−1 s−1 were selected for additional simulations. Monte Carlo N-Particle transport code (MCNP) simulations were used to determine this quantity for the Cs-137. The materials and geometry of the Petri dish and fungus used for these simulations are shown in Fig. 3. The Cs-137 was simulated as a point source located 1.5 cm from the top of the fungi. The Petri dish was set on a bakelite table. The setup was located in the center of a notional 5 m × 5 m × 5 m room with 30 cm thick concrete walls and filled with air. Leads bricks set on the table surrounded the petri dish and source. The International Commission on Radiological Protection (ICRP) material definitions did not contain data for fungal mycelia. Thus, we selected for skin as the closest approximation of the properties of the fungal mycelium25. This simulation gave a result for the energy deposited per particle as 6.53 × 10–4 MeV g−1, which for a 350 μCi activity, the rate of energy deposition was determined to be 7907 MeV g−1 s−1.Figure 3Top (upper left) and side (upper right) view of the Petri dish and fungi materials and distances used to determine energy deposition rates in MCNP. The overall geometry used for the radiation transport simulations, including the lead bricks, is shown from the top down (lower left) and from the side (lower right).Full size imageUV source and irradiationOur intent was to match the energy absorbed by the fungi to control for all variables except the photon energy difference between the Cs-137 source and UV lamp. The spectrum of energies emitted from the Cs-137 source varied significantly from those of the UV lamp, which in this case was a 30 W deuterium lamp that emitted from 185 to 400 nm (Fig. S1). This wide bandwidth represented photon energies ranging from 3.1 to 6.7 eV. The bandwidth of the UV exposure was limited to 300–350 nm using a 50-nm bandpass filter centered at 325 nm to ensure that incident photons would be in the UV energy range and not form ozone. Because we chose to match the overall energy deposited from the UV source to the gamma source it was necessary to attenuate the beam to the right power level. We assumed that all the UV energy would be absorbed near the surface rather than in the bulk since the fungi were melanized. This simplified the calculations and reduced risk, given the challenge of accurately estimating the absorbance of the fungi. The power deposited by the gamma source was calculated as the rate of energy deposition was determined to be 7907 MeV g−1 s−1 (1.3 nW g−1 s−1). Given the initial size of the plug was 1 cm in diameter, the desired lamp fluence needed to be ~ 2.8 nW cm−2. Across the spectrum of interest, the lamp power was determined to be 3.202 × 10–4 mW, thus requiring an attenuation of 8.7 × 10–9 (OD 8.06), reducing the lamp power to ~ 3 pW cm−2 and achieving a reasonably close power density to the target. Due to the sensitivity of UV detectors, the required power densities could not be measured directly. Alternatively, we measured the neutral density filters to verify the prescription was indeed correct.Response of P. variotii to irradiationUniform plugs (~ 5-mm in diameter) of actively growing mycelia of P. variotii were cut using the end of a Pasteur pipette and transferred a Petri plate containing potato dextrose agar (PDA) one day prior to initiating exposure experiments. The diameter of the mycelium was measured from four images, separated by precisely six hours, over the course of seven days and used to measure the growth rate. Differences in the pigmentation of the fungi under the different conditions was quantified in Fiji26 through analysis of grayscale images collected at day seven, following the method described by Brilhante et al.27 A ratiometric value was derived from the grayscale values and the white background, which corrected for variations in lighting across or between images.Significant differences in the pigmentation but not growth rates of P. variotii were associated with exposure to UV and gamma to irradiation, based on One-Way ANOVA analyses (Fig. 4A; Table S4). P. variotii is a ubiquitous filamentous fungus commonly inhabiting soil, decaying plants, and food products and was reported to be present on the surface of the walls of Unit-4 at ChNPP22,28. P. variotii is also a common food contaminant and is resistant to high temperature and metals29,30, despite being more sensitive to gamma irradiation than other fungi such as Aspergillus fumigatus31. In the present study, we hypothesized that positive radiation-induced effects in P. variotii would result in enhanced growth rates due to gamma irradiation. Across all conditions, the average growth rate of P. variotii was ~ 5.6 ± 0.9 mm d−1 (mean ± standard deviation). While the growth rate of P. variotii exposed to gamma irradiation was greater compared with the control and UV-irradiated samples (Fig. 4A), the difference in the mean growth rates was not significant (P = 0.255) by ANOVA.Figure 4(A) Growth rate and pigmentation of control (orange square), gamma- (blue square), and UV- (red square) irradiated cultures of P. variotti (mean ± standard deviation). (B) Estimated total irradiation dose experienced by the mycelial as a function of the distance from the central source. Exponential decay fit: − 3.6 + 105.7*exp(− 0.75*x); Adjusted R2 = 0.998. (C) Graphical representation of the irradiation dose based on the growth rate and duration of exposure for zones of mycelia as a function of radial distance from the central plug.Full size imageWe also hypothesized that the pigmentation of P. variotii would increase with exposure to gamma and UV irradiation. While P. variotti does not produce melanin, it does produce a pigment, Ywa1, from a polyketide synthesis (PKS) gene cluster and has been shown to protect the fungus against UV-C irradiation28. In some melanized fungi, Ywa1 serves as precursor and can be hydrolyzed to 1,3,6,8-tetrahydroxynaphthalen (T4HN). T4HN may then be converted to 1,8-dihydroxynaphthalene (1,8-DHN) melanin through the DHN pathway32. However, Lim et al.28 concluded that P. variotii does not produce true melanin as the pigmentation was maintained when the DHN-melanin pathway was inhibited. Significant differences in the pigmentation of P. variotii were observed among the three different sample types (P  More

Overall characteristics of air pollutantsThe results of previous studies indicated that local pollution is highly important in determining the emissions of air pollutant. Therefore, in this study, we estimated the changes in pollution and the AQI between the pre-COVID and COVID lockdown periods and among the different regions in Ji’nan. A comparison of the different pollutant concentrations analysed in this study shows that the concentrations of almost all pollutants decreased during the COVID lockdown period; only the concentration of O3 increased continuously as the COVID lockdown period progressed (Fig. 1).Figure 1Spatial distributions of the different observation sites and industrial enterprises above a designated size threshold in Ji’nan city. JCE, machine tool factory No. 2; LSX, technical college; JNS, Ji’nan fourth building group; KFQ, economic development zone; KGS, Kegansuo; LWZ, Laiwu memorial hall; NKS, Agricultural Scientific Institute; SZZ, Seed warehouse of Shandong Province; SJC, Ji’nan monitoring station; TXG, Taixing company; CQD, Changqing school. Red circles, red triangles and red squares represent stations in urban, urban-industrial and suburban regions, respectively. The map of Observation site was completed by the geostatistical analysis module of ArcGIS (version 10.3, https://developers.arcgis.com/).Full size imageDuring the observation period, the daily average mass concentrations of PM10, PM2.5, SO2, NO2, CO, and O3 in Ji’nan were 137.09 µg/m3, 101.35 µg/m3, 22.70 µg/m3, 39.77 µg/m3, 1.28 mg/m3, and 71.84 µg/m3, respectively (Fig. 2). The mass concentrations of PM10 and PM2.5 exceeded the daily average Grade I values (50 µg/m3 and 35 µg/m3) of the Ambient Air Quality Standard of China (CAAQS, GB 3095-2012) during the whole observation period. In contrast, the mass concentrations of NO2, SO2, CO and O3 were substantially lower than the daily average Grade I values (80 µg/m3, 50 µg/m3, 4 mg/m3 and 100 µg/m3, respectively) of the CAAQS each day. During the pre-COVID period, the daily average mass concentrations of PM10, PM2.5, SO2, NO2, CO, and O3 in Ji’nan were 177.03 µg/m3, 125.94 µg/m3, 26.39 µg/m3, 54.52 µg/m3, 1.59 mg/m3, and 60.72 µg/m3, respectively. The mass concentrations of all these pollutants, except NO2, CO and O3, exceeded the daily average Grade I values of the CAAQS. The mass concentration trends during the COVID lockdown period were consistent with those during the pre-COVID period, but there were significant differences in the concentrations between the periods. In summary, the air quality in Ji’nan was generally good from January 24 to February 7, 2020, mainly due to the strict prevention and control measures for COVID-19.Figure 2Temporal variations in the mass concentrations of air pollutants (PM10, PM2.5, NO2, SO2, CO and O3) at the urban site in Ji’nan during the observation period.Full size imageEffects of regional differences and lockdown on air pollutantsOur results reveal that the PM10, PM2.5, NO2, SO2, CO and O3 concentrations in the urban, suburban and urban-industrial regions differed significantly between the COVID lockdown and pre-COVID periods (Figs. 3, 4).Figure 3Mean concentrations (± SD, mg/m3) of PM10, PM2.5, NO2, SO2, CO and O3 during the pre-COVID and COVID lockdown periods in 2020; the values were determined by combining the urban, suburban and urban-industrial areas at the regional scale. *, ** and *** represent significant differences between the pre-COVID and COVID lockdown periods in the same region (Duncan test, *p = 0.05; **p = 0.01; ***p = 0.001), with nonsignificant results being excluded.Full size imageFigure 4General reductions in the concentrations of major air pollutants.Full size imageNOx, one of the most important pollutants and a major health hazard, was studied in different countries across the world during COVID-19-related lockdowns. In all three regions studied herein, the highest rate of reduction in NO2 concentrations was observed during the COVID lockdown period (Fig. 4), with the NO2 levels in the COVID lockdown period being 54.02% on average lower than those during the pre-COVID period (53.07% in urban area, 48.31% in the suburban areas and 55.74% in the urban-industrial area) (Fig. 4); this reduction is greater than that reported at other sites by 26–42%11 and 14–38%18 but lower than that (50–62%) in Barcelona and Madrid in Spain33. As shown in Fig. 3E, the NO2 concentrations in the urban, suburban and urban-industrial areas were significantly higher in the pre-COVID period than in the COVID lockdown period, with the pre-COVID the NO2 levels in the urban area being 13.46% and 27.63% higher than those in the suburban and urban-industrial areas, respectively. During the COVID-19 lockdown period, the NO2 levels in urban areas were 4.69% and 31.75% higher than those in the suburban and urban-industrial areas, respectively. Blocking and controlling the air pollution associated with COVID-19 has helped reduce ground NO2 levels34 and this effect might be correlated with the tropospheric NO2 column density27. Among all sources of NO2, automobile emissions and power generation are the most important5. A systematic review confirmed that a short-term increase in the NO2 concentration in urban areas correlates to an increase in the number of pneumonia hospitalizations5,35.The trends in the CO concentration were similar to those in the NO2 level. During the COVID-lockdown period, the average CO mass concentrations in the urban, suburban and urban industrial areas were 1.08 mg/m3, 1.16 mg/m3 and 1.14 mg/m3, respectively, which decreased by 27.78%, 29.46% and 36.61%, respectively, compared with those during the pre-COVID period. The highest levels of PM10 were also observed during the pre-COVID period in the urban, suburban, and urban-industrial areas in Ji’nan (Fig. 4). The reductions in PM2.5 and CO emissions in urban and urban-industrial areas are generally higher than those in suburban areas25, supporting our findings. Notably, PM2.5 and CO are generated mainly by construction activities and from road dust, natural soil dust and dust from urban-industrial activities36. In contrast, the differences in the PM10 concentrations among the three regions were not significant during either the pre-COVID period or the COVID-lockdown period (Fig. 3A), which suggests that particles in Ji’nan are strongly diffused. However, the COVID lockdown period had a significant effect on the PM10 concentrations, with 42.86%, 44.26% and 50.60% differences in the PM10 concentration between the pre-COVID and COVID lockdown periods in the urban, suburban and urban-industrial areas, respectively (average of 44.92%, Fig. 4). The main reasons for the decreases in the concentration of PM were the severe restrictions on vehicle traffic, the cessation of industrial activities, and the stopping of construction projects, which are important sources of floating dust in the urban air37. Despite the overall consistency among the observed changes in all regions for the different air pollutants (except O3), at the regional level, some differences were statistically significant, while others were not due to the variability among stations, with the differences being more pronounced at the urban, suburban and urban-industrial stations.O3 is a secondary pollutant involved in different atmospheric reaction mechanisms and acts as both a source and sink. Generally, the impact of lockdowns on O3 was mixed, with its levels generally falling within ± 20%38, but total O3 levels remained relatively stable18. In this study, by comparing the regional mean concentrations throughout the COVID-19 period, we found that O3 concentrations were higher during the COVID lockdown period than during the pre-COVID period, especially in the urban regions (Fig. 3). Furthermore, the mean O3 concentration at all stations during the COVID lockdown period was 37.42% higher than that during the pre-COVID period (46.84% in the urban areas, 18.27% in the suburban area, and 19.84% in the urban-industrial areas) (Fig. 4); this finding is consistent with the outcomes of other studies, which reported that O3 concentrations increased by (on average) 20% during lockdowns39, potentially due, in part, to atmospheric reactivity37. The higher lockdown O3 concentrations can be attributed to the following three reasons: (1) low PM concentrations can result in more sunlight passing through the atmosphere, encouraging increased photochemical activities and thus higher O3 production40; (2) a reduction in NOx emissions increases O3 formation41; and (3) lower PM2.5 concentrations means their role as a sink for hydroperoxy radicals (HO2) is less effective, which would increase peroxy radical-mediated O3 production42. During the pre-COVID period, the O3 levels were not significantly different among the region, and the same results were observed during the COVID lockdown period. However, in the urban and urban-industrial areas, the O3 levels during the COVID lockdown period were significantly higher than those in the pre-COVID period (p  More

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

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