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Literature values of R
To and Q10 of leaf respirationData of RTo were read from texts, tables, and figures in all available literature (18 species; Supplementary Tables 1, 2) when measured more than once within a period of darkness in lab- and field studies where measurement temperature, To, was kept constant. The RTo-initial was defined as the initial measurement of RTo for each study/species, and further values of RTo at later points within the same night of the same study were read as well.Apparent- and inherent temperature sensitivities (Q10, Equation 1; Fig. 2b) were obtained from all available literature (ten species; Supplementary Table 2) where in the same study/species, both nocturnal values of Q10,app and of Q10,inh were obtained in response to long-term natural T-changes in the environment during the night (hours) and nocturnal values were obtained in response to short-term artificial T-changes (max 30 min), respectively.Measurements of R
To and Q10 of leaf respirationIn the field (United Kingdom, Denmark, Panama, Colombia and Brazil), RTo (µmol CO2 m−2 s−1) in 16 species (Supplementary Tables 1, 3) was measured through nocturnal periods at constant To (controlled either by block-T or leaf-T) with infra-red gas analysers (Li-Cor-6400(XT) or Li-Cor-6800, Lincoln, Nebraska, USA). Mature, attached leaves positioned in the sunlight throughout the day were chosen. Target [CO2] in the leaf cuvette was set to ambient, ranging from 390 to 410 ppm, depending on when measurements were made, and target RH = 65 ± 10%, with a flow rate of 300 µmol s–1. The RTo-initial was defined as RTo at first measurement after darkness 30 min after sunset (to conservatively avoid light-enhanced dark respiration, LEDR50,51. Leak tests were conducted prior to measurements52. The temporal resolution of measurements varied between every three minutes to once per hour for the different species. Data were subsequently binned in hourly bins.Measurements to derive Q10,inh and Q10,app were conducted in two species in a T-controlled growth cabinet and in six species in the field (Supplementary Table 2), where Q10,inh was measured in response to 10–30 min of artificial changes in T and Q10,app was calculated from measurements of RT in response to T of the environment (growth cabinet or field) at the beginning of the night and again at the end of the night (hours apart).Tree level measurements in whole-tree chambersThe night-time respiratory efflux of the entire above-ground portion (crown and bole) in large growing trees of Eucalyptus tereticornis was measured in whole-tree chambers (WTCs) in Richmond, New South Wales (Australia, (33°36ʹ40ʺS, 150°44ʹ26.5ʺE). The WTCs are large cylindrical structures topped with a cone that enclose a single tree rooted in soil (3.25 m in diameter, 9 m in height, volume of ~53 m3) and under natural sunlight, air temperature and humidity conditions. An automated system measured the net exchange of CO2 between the canopy and the atmosphere within each chamber at 15-min resolution. During the night, we used the direct measurements of CO2 evolution (measured with an infra-red gas analyser; Licor 7000, Li-Cor, Inc., Lincoln, NE)53,54 as a measure of respiration.Due to the high noise-to-signal ratio in the CO2-exchange measurements from this system when analysing the high-resolution temporal variation through each night, we chose to only analyse temporal variation in tree-RT for the nights when tree-RT-initial were amongst the top 10% of CO2-exchange signals for the entire data set. The resulting data spanned 62 nights and included hourly average measurements from three replicate chambers.Data analysis of R
To
Measurements of nocturnal leaf respiration under constant temperature conditions (RTo) were divided by the initial rate of respiration (RTo-initial) at the onset of each night. Hourly means of RTo/RTo-initial were calculated for each leaf replicate to remove measurement noise and reduce bias due to the measurement of some species at more frequent intervals throughout the night. For species with multiple leaf replicates, these hourly means of RTo/RTo-initial were then combined to create hourly averages of RTo/RTo-initial at the species level. For each species, these values were plotted as a function of time to demonstrate how RTo/RTo-initial decreases with time since the onset of darkness, from sunset until sunrise (Supplementary Fig. 1). For each species, hourly means of RTo/RTo-initial plotted as a function of time were linearised by log-transforming data and the slope of the relationship determined. To test whether the slopes of the lines differed significantly within plant functional groups (woody, non-woody), species originating from the same biome (temperate, tropical) or species measured under the same conditions (lab, field), the slopes of the lines for all species from a given functional group, biome or measurement condition were tested pairwise against each other using the slope, standard error and sample size (number of points on the x-axis) for each line and applying a 0.05 cut-off for p values after Bonferroni correction for multiple testing. 11 out of 701 comparisons came out as being significantly different, which is why within-group slope differences were considered to be overall non-significant for this analysis. t-tests were used to test whether the slopes differed between plant functional groups (tree, non-woody), species originating from different biomes (temperate, tropical) and species measured under different environmental conditions (lab, field). In these tests, the degrees of freedom varied according to the different sample sizes. Since RTo/RTo-initial plotted as a function of time always starts at 1, the intercepts do not differ between species. t-tests were performed on linearised power functions by log-transforming data in order to test potential differences between lab and field, origin of species, between woody and non-woody species and between temperate and tropical biomes. Since these functions were statistically indistinguishable in each pairing, all measurements of nocturnal leaf respiration under constant temperature conditions (n = 967 nights, 31 species) were collated into a single plot. The data were binned hourly since some studies had very few measurements on half-hourly steps. A power function was fitted with a weighting of each hourly binned value using 1/(standard error of the mean). The power function was chosen as it, better than the exponential- or linear function, can capture both sudden steep- as well as slower decrease in RTo/RTo-initial in different species. The 95% confidence interval of the power function, following the new model equation, overlaps with all the 95% confidence intervals of the hourly binned values (Fig. 1a). All data analysis, including statistical analysis and figures were performed using Python version 3.9.4.Evaluation of new equationWe performed four sets of simulations (S1-S4) using different representations of leaf and plant respiration as outlined in Supplementary Table 4. Evaluation of Equation 4 (S2; Equation 3 from Fig. 1a merged with Equation 1) in comparison with Equation 1 (S1) and Equation 5 (S4) in comparison with Equation 2 (S3), respectively, for predictions of nocturnal variation in response to natural variation in temperature, was conducted by use of independent sets of leaf level data and tree scale data. The effect of including variable nocturnal RTo is estimated as the difference between S1 and S2 and between S3 and S4, respectively.The first data set used for the evaluation consists of nine broad-leaf species for which spot measurements of leaf respiration under ambient conditions were taken at sunset and before sunrise in the field (Fig. 1b and Supplementary Fig. 2a). Of these nine species, three species (Fig. 1c) were further measured throughout the night at ambient conditions. Further, whole-tree measurements measured throughout the night at ambient conditions (Supplementary Fig. 3a–d) were also used for evaluation. Finally, comparisons of Q10,inh with Q10,app in another ten species were used to test if RTo appeared constant as assumed in Equation 1 (Supplementary Tables 2, 3 and Fig. 2b).To validate the suitability of Equation 4 and Equation 5 over equations with full temporal control, modelled respiration values were compared against observed measurements for three species at the leaf level (Supplementary Fig. 2b–d) and for Eucalyptus tereticornis at the whole-tree level using three chamber replicates and during 62 nights using hourly measurements (Supplementary Fig. 3a–d). Linear fits were applied, using ordinary least squares regressions, to plots of normalised respiration (({R}_{T}/{R}_{{T}_{0}})) predicted by the four models against the observed values. The first measurements of the night were excluded from the fits, as these were necessarily equal to unity. The standardised residuals (S) in Supplementary Figs. 2c, 3b are calculated using the equation ({S}_{i}=({R}_{{{{{{{rm{modelled}}}}}}}_{i}}/{R}_{{{{{{{rm{Modelled}}}}}}}_{0}}-{R}_{{T}_{i}}/{R}_{{T}_{0}})/sqrt{(mathop{sum }nolimits_{i}^{N}{({R}_{{{{{{{rm{modelled}}}}}}}_{i}}/{R}_{{{{{{{rm{Modelled}}}}}}}_{0}}-{R}_{{T}_{i}}/{R}_{{T}_{0}})}^{2})/{df}}), for the residual of the ith measurement, where the sum is over all measurements, df is the number of degrees of freedom, and Rmodelled are the respiration values modelled by the four equations in Supplementary Table 4.Evaluation is done by comparing observed and simulated RT/RT, initial. We evaluate the nocturnal evolution of RT/RT, initial and use (i) one-to-one line figures that include fitted regression line, R2, p value and RMSE, (ii) Taylor diagrams and (iii) use plots of standardised residuals against temperature and hours since darkness for a qualitative assessment of the simulations, to identify whether there are any model biases at specific times or temperatures. Model evaluation, statistical analysis and figures were done using python version 3.9.4.Global scale modelling of plant R and NPP
We applied the novel formulation derived in this study (Equation 4 and Equation 5) to quantify the impact of incorporating variable RTo on simulated plant R and NPP globally using the JULES land surface model32,33 following simulations outlined in Supplementary Table 4.Plant respiration in JULES and simulations for this study: The original leaf respiration representation in JULES follows either eqn 1 ({{R}_{T}={R}_{{T}_{0}}{Q}}_{10}^{(T-{T}_{0})/10}) with Q10 = 2 and To = 25 oC or Equation 1 with an additional denominator ({{R}_{T}={R}_{{T}_{0}}{Q}}_{10}^{(T-{T}_{0})/10}/leftlfloor left(1+{e}^{0.3(T-{T}_{{upp}})}right)times left(1+{e}^{0.3({T}_{{low}}-T)}right)rightrfloor) (Equation 6). For the purpose of this application, we have used Equation 1 to represent leaf respiration in standard JULES simulations. The remaining components of maintenance respiration in JULES, i.e. fine root and wood are represented as a function of leaf to root and leaf to wood nitrogen ratios and leaf respiration rates following RT (β + (Nr + Ns)/Nl) (Equation 6) with RT as leaf respiration, Nr, Ns and Nl as root, stem and leaf Nitrogen content respectively and β as a soil water factor (Equation 42 in ref. 32). This implies that any variation in leaf respiration is passed to root and wood respiration as well30,31,35. Growth respiration is estimated as a fraction (25%) of the difference between GPP and maintenance respiration (Rm) expressed as Rg = 0.25 (GPP-Rm).JULES version 5.2 was modified to simulate leaf and plant respiration using the various descriptions (Equations 1–5) outlined in the modelling protocol in Supplementary Table 4. JULES uses standard astronomical equations to calculate the times of sunrise and sunset on a given day at each grid point. We used the model leaf temperature and RT at the timestep at or immediately preceding sunset to represent Tsunset, and RT,sunset and at every timestep through the night, the time since sunset (h) was updated. We performed global simulations for the period 2000–2018 with JULES, using the global physical configuration GL8, which is an update from GL755. We used WFDEI meteorological forcing data56 available at 0.5-degree spatial resolution and 3-h temporal resolution, and disaggregated and run in JULES with a 15 min timestep. Simulations were performed using nine plant functional types (PFTs)33. To isolate the effects of the new formulation on simulated Rp and NPP from possible impacts on leaf area index (LAI) or vegetation dynamics, we prescribed vegetation phenology via seasonal LAI fields and vegetation fractional cover based on the European Space Agency’s Land Cover Climate Change Initiative (ESA LC_CCI) global vegetation distribution57, processed to the JULES nine PFTs and re-gridded to the WFDEI grid. Annual variable fields of CO2 concentrations are based on annual mean observations from Mauna Loa58. JULES was spun up using the three cycles of the 2000–2018 meteorological forcing data to equilibrate the soil moisture stores. The mean annual output of Rp and NPP over the study period (2000–2018) is computed for all simulations and the effect of the new formulation is presented as the difference between the temporal mean of simulations with and without nocturnal variation in whole plant RTo for NPP and vice versa for Rp and as percentage respect to simulations without nocturnal variation in RTo. Results are presented for grid cells where grid level NPP is >50 g m−2 yr −1 in the standard simulations to avoid excessively large % effects at very low NPP. Output from JULES was analysed and plotted using python version 2.7.16.PermitsNo permit was required in Denmark as measurements were taken in private land (of author) and public land and measurements were non-destructive. Data were collected under the Panama Department of the Environment (current name MiAmbiente) research permit under the name of Dr Kaoru Kitajima. Permit number: SE/P-16-12. Data in Brazil were collected under the minister of Environment (Ministério do Meio Ambiente—MMA), Instituto Chico Mendes de Conservação da Biodiversidade—ICMBio, Sistema de Autorização e Informação em Biodiversidade—SISBIO permit number 47080-3. No permit was required in Colombia as measurements were taken on private land, no plant samples were collected, and trees were part of an existing experiment for which one of the co-authors is the lead. No access permits were required in the UK as they were conducted on the campus of own university plus in their own private garden.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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Experimental designA 2-year field experiment was conducted at the Modern Agricultural Research and Development Base of Henan Province (113° 35′–114° 15′ E, 34° 53′–35° 11′ N). In order to enhance the diversity of LAI data, a split-plot design with a variety of field management measures and three replications was selected for the experiment (Fig. 1). The size of each experiment plot was 40 m2, the soil texture was predominantly sandy loam and sandy clay loam, as determined by textural analysis of soil samples collected before planting. Maize cultivar Dedan-5 was used in the experiment, which was planted on June 12, 2019, and June 20, 2020, with a row spacing of 42 cm and a planting density of 7 seedlings·m−2. The soil and cultivar in field experiments were representatives of those in the region. The irrigation, pesticide, and herbicide control practices followed local management for maize production.Figure 1The experimental design.Full size imageLAI measurements and UAV-based image acquisitionThe measurements of LAI were conducted at four growth stages including the tasseling stage (TS), flowering stage (FS), grain-filling stage (GS), and milk-ripe stage (MS) of maize in 2019 and 2020, a total of 264 LAI data of maize were collected during the 2-year field trial (Table 1). In order to reduce the impact of plant variability, the random sampling method was used to collect LAI samples. For each plot, three plants were randomly selected to measure the total green leaf area with the non-destructive portable leaf area meter (Laser Area Meter CI-203; CID Inc.). And the average leaf area of selected plants represented the single plant leaf area in each experiment plot. The LAI of each plot wasTable 1 Description of samplings.Full size table$$mathrm{LAI}=mathrm{LA}*mathrm{D}$$
(1)
where (mathrm{LA}) is the leaf area of a single plant in each plot; (mathrm{D}) is the planting density in one square meter.PHANTOM 4 PRO (DJI-Innovations Inc., Shenzhen, China) is a multi-rotor UAV equipped with a 20-megapixel visible-light camera that was employed to capture digital images. Aerial observations were conducted on the same dates as the LAI measurements, which was between 10:30 a.m. and 2:00 p.m. local time when the solar zenith angle was minimal. The UAV was flown automatically based on preset flight parameters and waypoints, with a forward overlap of 80% and a side overlap of 60%. A three-axis gimbal integrated with the inertial navigation system stabilized the camera, the automatic camera mode with fixed ISO (100) and a fixed exposure was used during the flight. Altogether, 4192 images were taken in eight flights from a flight height of 29.36 m above ground, with a spatial resolution of 0.008 m.The measurements of maize LAI were carried out with permission from the Modern Agricultural Research and Development Base of Henan Province. All experiments were carried out in accordance with relevant institutional, national, and international guidelines and legislation.Image pre-processingDJI Terra (version 2.3.3) was used to generate ortho-rectified images based on the structure from motion algorithms and a mosaic blending model. The main procedures are as follows: (1) extract feature points and match features according to the longitude, latitude, elevation, roll angle, pitch angle, and heading angle of each image; (2) build dense 3D point clouds by using dense multi-view stereo matching algorithm; (3) build a 3D polygonal mesh based on the vector relationship between each point in the dense cloud; (4) establish a 3D model with both external image and internal structure by merging the mosaic image into the 3D model; (5) generate digital orthophoto map (DOM).Vegetation indices (VIs) derived from the UAV-based digital imageryDigital imagery records the intensity of visible red (R), green (G), and blue (B) bands in individual pixels24. In order to enhance the vegetation parameters contained in the digital image, fourteen commonly used RGB-based VIs were collected, and their correlation with the LAI of maize at different growth stages was evaluated. Table 2 shows the detailed information of the selected RGB-based VIs.Table 2 RGB-based VIs for LAI estimation.Full size tableCentered on the point where LAI was measured, regions of interests (ROIs) with a size of 100*100 were clipped from the digital image. Python 3.7.3 was used for extracting the R, G, B information of maize and computing the RGB-based VIs from ROIs. In order to reduce the effects of light and shadow, the R, G, B color space of the image was normalized according to the followings:$$mathrm{r}=frac{R}{R+G+B}$$
(2)
$$g=frac{G}{R+G+B}$$
(3)
$$b=frac{B}{R+G+B}$$
(4)
where r, g, and b are the normalized values. R, G, B are the pixel values from the digital images based on each band.Pearson correlation analysisBefore regression analysis, the Pearson correlation analysis was performed to determine the relationship between maize LAI and different RGB-based VIs extracted from the digital image. Pearson correlation coefficient ((mathrm{r})) reflects the degree of linear correlation between two variables, which is between − 1 and 1. The calculation formula of Pearson correlation coefficient was expressed as follows:$$mathrm{r}= frac{sum_{i=1}^{n}left({X}_{i}-overline{X }right)left({Y}_{i}-overline{Y }right)}{sqrt{sum_{i=1}^{n}{left({X}_{i}-overline{X }right)}^{2}}sqrt{sum_{i=1}^{n}{left({Y}_{i}-overline{Y }right)}^{2}}}$$
(5)
where (X), (mathrm{Y}) are variables, (n) is the number of variables.Regression methodsLinear regression (LR)Linear regression is an approach for modelling the relationship between dependent and independent variables. The case of one independent variable is called unary linear regression (ULR), the expressions can be expressed as follows:$$mathrm{y}={beta }_{0}+{beta }_{1}x+varepsilon $$
(6)
where (varepsilon ) is deviation, which satisfies the normal distribution. (x), (mathrm{y}) are variables. ({beta }_{0}), ({beta }_{1}) are the intercept and slope of the regression line, respectively.For more than one independent variable, the regression process is called multiple linear regression (MLR), the expressions can be expressed as:$$mathrm{y}={beta }_{0}+{beta }_{1}{x}_{1}+{beta }_{2}{x}_{2}+dots +{beta }_{n}{x}_{n}$$
(7)
where ({x}_{1}),( {x}_{2}), …, ({x}_{n}), (mathrm{y}) are variables, ({beta }_{0}), ({beta }_{1}), ({beta }_{2}), …, ({beta }_{n}) are coefficients that determined by least square method and gradient descent method38.The RGB-based VIs with the highest Pearson correlation coefficient was used to establish the ULR model, and VIs with a correlation coefficient higher than 0.7 were used to establish the MLR model. In each growth stage, 70% of observation data were randomly selected for establishing models, and the remaining 30% of data were used as the testing dataset to assess the model performance.Back propagation neural networks (BPNN)In this study, a three-layer BPNN model was established for LAI estimation (Fig. 2). RGB-based VIs with a correlation coefficient higher than 0.7 were selected as the input variables. Tan-Sigmoid activation function was used in the hidden layer, and the Levenberg–Marquardt algorithm was selected as the training function. The maximum epoch of BPNN training was set to 1000, the learning rate was set to 0.005, and the MSE was set to 0.001. The observation data set was split into the training set and the testing dataset with a ratio of 7:3. The training dataset was used to fit the weights and bias of the BPNN model, the testing dataset was used to evaluate the model performance. Before training, data normalization was conducted for the input and output variables, and the denormalization was required to convent the output variable back into the original units after training.Figure 2Three-layer BPNN model.Full size imageRandom forest (RF)RF is a non-parametric ensemble ML method that operates by constructing a multitude of decision trees at training time and outputting the average prediction of the individual trees (Fig. 3). The bootstrapping approach was used to collect different sub-training data from the input training dataset to construct individual decision trees.Figure 3Random forest model.Full size imageThe construction process of RF regression model is as follows:

(1)

The value of (mathrm{n}_mathrm{estimators}) was tested from 50 to 1000 in increments of 50, and the value of 500 was finally selected according to higher R2 and lower RMSE.

(2)

At each node per tree, (mathrm{m}_mathrm{try}) RGB-based VIs was randomly selected from all 14 vegetation indices, and the best split was chosen according the lowest Gini Index. (mathrm{m}_mathrm{try}) was tested from 3 to 10, and the final value was 6.

(3)

The other parameters in the RF model were kept as default values according to the (mathrm{RandomForestRegressor}) function in (mathrm{Scikit}-mathrm{learn library}).

(4)

For each tree, the data splitting process in each internal node was repeated from the root node until a pre-defined stop condition was reached.

(5)

Similar with LR and BPNN model, the RGB-based VIs with a correlation coefficient higher than 0.7 were selected as the input variables, and the output variable is LAI.

Data analysis and performance evaluationThe repeated random sampling validation method was used to evaluate the generalization performance of different models. The training and testing dataset were randomly split 500 times. For each split, the LR, BPNN, and RF models were fitted to the training dataset, and the estimation accuracy was evaluated using the testing dataset. The coefficient of determination (R2), root mean square error (RMSE), and Akaike information criterion (AIC) of the training dataset were used for the assessment of models39, and the estimation accuracy was evaluated by R2 and RMSE of the testing dataset. Mathematically, a higher R2 corresponds to a smaller RMSE, and thus represents better model performance. The procedures of LAI inversion using UAV-based digital imagery and ML methods were shown in Fig. 4.Figure 4Flowchart of LAI inversion using UAV-based remote sensing and ML methods.Full size imageThe construction and evaluation of models was performed using Python 3.7.3 in Windows 10 operating system with Intel Core i7-9700 processor, 3.00 GHz CPU, and 32 GB RAM. The processing software is Spyder. The statistical analysis and figure plotting were performed in R × 64 4.0.3. More

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