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Coupling accuracy analysisPrecipitation simulation accuracyThe comparison between annual precipitation simulated by WRF-Hydro and measured precipitation is shown in the following Fig. 3a. From the Fig. 3a, we can get that the correlation between simulated precipitation and measured precipitation is 0.783, which is relatively high and the simulation is good. In addition, the simulated precipitation is less than the measured precipitation value in time. We guess that this error is caused by the precision and quality of precipitation products. WRF-Hydro can easily underestimate the duration of heavy rain when simulating precipitation, so the simulated precipitation is slightly smaller than the measured precipitation in long-term sequence, but the overall accuracy is good.Figure 3(a) Comparison between WRF-HYDRO simulation and measured annual precipitation in Daihai; (b) Comparison of runoff simulation and remote sensing estimation in Daihai Lake; (c) Modified runoff simulation and remote sensing estimation in Daihai Lake.Full size imageThe comparison between the simulated spatial distribution of annual precipitation and the verified products in the study area is shown in the Fig. 4. Generally speaking, the precipitation of interpolation products is slightly higher than the simulation value, which is consistent with the above analysis. In addition, the spatial distribution law of the two is consistent with each other, and the spatial variation law is basically the same. However, the transition of simulation results in areas with severe precipitation changes is relatively gentle, while the transition of interpolation products is more severe. The coverage of the maximum value in the simulation results is smaller than that of interpolation products. The guess is caused by the error of setting the precipitation boundary line. The boundary of interpolation products is China as a whole, and the boundary of simulation results is only Daihai Basin, which fundamentally determines that the precipitation simulation results will be slightly smaller than the interpolation products. Because the climate and hydrology mutual chamber is defined in the model setting from the surrounding grid points, the smaller the area causes some areas with mutual chamber cannot enter the boundary line, resulting in the precipitation simulation results less than the interpolation products. But in terms of the overall spatial differentiation law, the distribution of simulation results in interpolation products is not very different, which has good practical value.Figure 4Spatial comparison of WRF-HYDRO simulation and interpolation of annual precipitation in Daihai.Full size imageSimulation accuracy of runoff into LakeThe comparison between the WRF-Hydro simulation results and remote sensing estimation results of the runoff from Daihai Lake for many years is shown in the Fig. 3b. It can be seen from the figure that the correlation between simulation results and remote sensing estimation results is 0.629, which is better. But it is obvious that the simulation results are higher than those of remote sensing. The reason may be that the model does not set up the parameters of man-made water from the river entering the lake, including agricultural irrigation water and industrial water intake. So the simulation results are overestimated to the runoff into the lake. Therefore, the simulated runoff into the lake is modified in this study to reduce the water consumption ignored by the model.The comparison between the revised simulated runoff and remote sensing estimation is shown in the Fig. 3c. As can be seen from the figure, the correlation is increased to 0.650. Although not much improvement, the simulation results and remote sensing results are distributed evenly around the boundary.Analysis of coupling resultsPrecipitation analysisThe precipitation in Daihai Basin is relatively abundant. Except for some extreme drought years and humid years, the average annual precipitation is 300–600 mm (see Fig. 5a), and the average annual precipitation is about 400 mm. It can be seen from the figure that the minimum annual precipitation is less than 250 mm; The maximum annual diameter is higher than 750 mm. The difference between extreme dry year and extreme wet year is three times.Figure 5(a) Distribution curve of annual precipitation in Daihai Basin; (b) Distribution curve of annual mean monthly precipitation in Daihai Basin.Full size imageThe monthly average of precipitation in the Daihai Basin for many years is shown in the Fig. 5b. It can be seen from the figure that the precipitation in the Daihai Basin is unevenly distributed throughout the year, with the least in January at 1.73 mm and the most in July at 112.10 mm. The precipitation in July–August accounts for more than 50% of the total annual precipitation. In addition, it can be seen from the figure that the precipitation in the Daihai Basin is mainly concentrated in June to September, which is also the flood season in the Daihai Basin, accounting for more than 70% of the total annual precipitation.Combined with Table 3, overall, the average precipitation from 1980 to 1994 is 401.75 mm, with little fluctuation; During the period from 1995 to 2011, except for extreme precipitation in some years (more than 600 mm in both 1995 and 2003), the precipitation decrease, with an average value of 371.39 mm. There are several dry years and wet years, and the fluctuation range was sharp; From 2012 to 2020, the fluctuation range is small, and the average value rises to 451.75 mm.Table 3 Average precipitation (mm) in different periods in Dahai BasinFull size tableThe spatial distribution of annual precipitation in Daihai Basin is shown in the Fig. 6. It is obvious from the figure that the precipitation in 1990, 1995 and 2020 is abundant compared with other years. In addition, it is found that although the annual precipitation in Daihai Basin varies in size, its spatial distribution is basically the same.Figure 6Spatial distribution of annual precipitation in Daihai Basin.Full size imageThe spatial pattern of annual precipitation in Daihai Basin is as follows: the southeast of Liangcheng County and the north of Zuoyun County, the northwest of Liangcheng County and the northwest of Fengzhen county are the three precipitation centers, which gradually decrease outward. And the central effect of Fengzhen county is not obvious in some years. In addition, it is found that the area around Daihai Lake has the least precipitation in the whole Daihai Basin. This may be related to the terrain surrounding the Daihai Basin.In the whole study area, the annual precipitation in the north of Zuoyun County is larger than that in other regions. In some years, the annual precipitation reaches 800 mm, and the extension area is wide. In some years, it extends to the southeast of Liangcheng County. Therefore, it is speculated that mountain torrents, debris flows, rainstorms, snowstorms and other natural disasters are prone to occur here.In addition, combined with the topographic map, it is found that the southeast and northwest of Liangcheng County are the highest elevation in the study area, which coincides with the extreme precipitation. At the same time, it is found that the spatial consistency of precipitation distribution in the whole study area is higher than that of terrain distribution in the study area. Therefore, it is speculated that the precipitation in the study area is seriously affected by the terrain, in other words, the precipitation in the study area is mostly terrain rain or mountain convective rain.Runoff analysisThe Runoff Curve of Daihai Lake is shown in the Fig. 7a. It can be seen from the figure that the flow into the lake shows a downward trend from 1980 to 2020. Although it rebounded in 1996–1999 and 2005–2007, after 2010, the runoff into the lake decreased sharply below 8 × 106m3. From 1980 to 1990, the runoff into the lake decreased linearly with a larger slope and a faster speed; However, from 1990 to 2000, the runoff into the lake appeared the first vibration wave peak, and from 2000 to 2007, the second vibration wave peak. From 2008 to 2012, the decline rate was sharp, and the runoff into the lake had been reduced to 3.95 × 106m3 in 2012; Since 2013, the runoff into the lake tends to be flat, but it has not exceeded 10 × 106m3.Figure 7(a) Change of runoff in Daihai Lake over the years; (b) Changes of lake area in Daihai over the years; (c) Changes of lake water level in Daihai over the years; (d) Changes of volume water in Daihai Lake over the years.Full size imageThe change curve of Daihai Lake area is shown in the Fig. 7b. It can be seen from the figure that the area of Daihai Lake is declining in a straight line. In a short period of 40 years, the lake area has shrunk nearly 100 km2. In addition, we found that the shrinkage rate of Daihai Lake area slowed down from 1980 to 1985, but the lake area shrank sharply from 1995 to 2000. After 2005, the atrophy curve almost coincided with the fitting curve, and the overall fitting R2 was as high as 0.958.The water level variation curve of Daihai Lake is shown in the Fig. 7c. As can be seen from the figure, the variation trend of water level in Daihai Lake is very similar to that of lake area. However, the slope of lake water level change is less than the change rate of lake area. In the 40 years since 1975, the water level in Daihai has dropped by nearly 10 m. In addition, the water level rose slightly in 1995–1996 and 2003–2006. And after 2006, Daihai water level decline rate also accelerated. Since 2006, the water level of Daihai has dropped nearly 6 m, with a rate of 0.45 m/year.The trend of the volume water volume of the Daihai Lake is shown in the Fig. 7d. It can be clearly seen from the figure that the decline curve of the Daihai Lake water volume is close to a straight line, especially from 2005 to the present, the fitting degree is as high as 0.981. There should be some geometrical relationship among the lake area, water level and water volume, and this relationship should be related to the digital elevation model of the lake bottom. In addition, the changes of lake bottom topography are not linear, so there are still subtle differences between the three changes.The annual surface runoff of Daihai Basin is shown in the Fig. 8. It can be seen from the figure that the Gongba River, the Wuhao River, the Buliang River and the Tiancheng River in the south of Daihai Lake supply the Daihai Lake for a long time, and the Bantanzi River in the West also flows into the Dai sea in some years. Combined with the spatial distribution of annual precipitation, it can be concluded that surface runoff is seriously affected by precipitation. The annual distribution is uneven. The surface runoff from the southeast of Liangcheng County generally flows into Daihai Lake to the north, but in some drought years, it will be stopped and cannot flow into Daihai Lake. Bantanzi River in the west of Daihai Lake also supplies Daihai Lake in the year of more precipitation.Figure 8Spatial distribution of surface runoff in Daihai Basin.Full size imageTaking the surface runoff of Daihai Basin in January, April, July and October 2015 as an example, the distribution of surface runoff in different seasons of the year is analyzed, as shown in the Fig. 9. It can be seen from the figure that the rivers in Daihai Basin are seasonal rivers, which are prone to be cut off in autumn and winter. In winter (December–February), there will be different degrees of snowfall events in Daihai Basin, but due to the river freezing period and small snowfall, there will be no runoff. In spring (March to May), the precipitation in Daihai Basin began to increase, and the surface runoff also began to increase, mainly from the southeast and northwest of Liangcheng County. Gongba River, Wuhao River, buliang River, Tiancheng River and Bantanzi River in the south of Daihai Lake will supply Daihai Lake, but these rivers have small flow in spring, which is easy to break. Summer (June–August) is the main period of precipitation in Daihai Basin, and the surface runoff will also surge. In July 2015, the runoff in some areas reached 2000 mm, which was prone to flood disaster. The rivers in the west and south of Daihai Lake will supply it, but the runoff into Daihai Lake is not high, and most of the runoff is concentrated in the upper and middle reaches. In autumn (from September to November), the precipitation in Daihai Basin decreases. Before the freezing period, the precipitation may form runoff, but it is difficult to flow into Daihai Lake due to the small flow.Figure 9Spatial distribution of surface runoff in different seasons in Daihai Basin.Full size imageStatistical analysis of other factorsClimatic factors

(1)

Evaporation capacity

The variation curve of annual evaporation in Daihai is shown in the Fig. 10a. It can be seen from the figure that although the evaporation in Daihai Basin fluctuates, it shows an upward trend, with an upward slope of 8.855 and R2 of 0.560. From 1980 to 1986, the annual evaporation fluctuated around 1000 mm; From 1987 to 1992, the annual evaporation of Daihai Basin decreased sharply, but from 1993 to 2000, the annual evaporation increased sharply with a very high rate of increase; But after 2000, the annual evaporation fluctuated and remained at 1250 mm.

(2)

Average temperature

Figure 10Perennial (a) evaporation (b) annual average temperature (c) annual average wind speed change in Daihai Basin.Full size imageThe variation curve of annual average temperature in Daihai is shown in the Fig. 10b. It can be seen from the figure that the annual average temperature in Daihai Basin presents an obvious fluctuating upward trend, and the fitting upward slope is 0.040, R2 is 0.406. In addition, it can be observed that in a 10-year cycle, there will be two small fluctuations and one large fluctuation, and the fluctuation will rise.

(3)

Wind speed

The curve of annual average wind speed in Daihai is shown in the Fig. 10c. It can be seen from the figure that the annual average wind speed of Daihai Basin presents a fluctuating downward trend, and the fitting downward slope is 0.036, R2 is 0.368. In addition, it can be observed that the annual average wind speed fluctuated with a mean line of 6.2 from 1980 to 1987; In 1988 and 1990, it dropped sharply with a large slope; From 1990 to 2003, the fluctuation decreased. From 2003 to 2011, the fluctuation was stable at 4.5, and rose sharply in 2012. So far, the fluctuation has been stable at 5.2.Human factors

(1)

Cultivated land area

The change curve of cultivated land area in Daihai Basin is shown in the figure. It can be seen from the Fig. 11a that the annual average wind speed in Daihai Basin presents an upward trend, with the fitting rising rate of 0.017 and R2 of 0.970, almost in a straight line. In addition, it can be observed that from 1996 to 2005, the rising rate appeared a trough, that is, the rising rate first increased rapidly and then decreased. From 2000 to 2005, the rising rate was very slow and approached zero; But since 2006, it has returned to a straight-line rise.

(2)

Industrial water consumption

Figure 11Perennial (a) cultivated land area (b) industrial water consumption (c) total population change curve in Daihai Basin.Full size imageThe change curve of industrial water consumption in Daihai Basin is shown in the Fig. 11b. It can be seen from the figure that the industrial water consumption of Daihai Basin presents an upward trend, and the fitting rising rate is 0.433, R2 is 0.794. In addition, it can be observed that from 1975 to 1993, the industrial water consumption of Daihai Basin was below 3 × 106m3; From 1994 to 2005, except for the decrease in 1998–2000, it has been on the rise, and the rising speed is fast, which has increased five times in ten years; Since 2005, the industrial water consumption in Daihai Basin has been stable at about 15 × 106m3.

(3)

Total population

The change curve of total population in Daihai Basin is shown in the Fig. 11c. It can be seen from the figure that the total population of Daihai Basin presents an upward trend, and the fitting rising rate is 0.074, R2 is 0.864. In addition, it can be observed that the total population of Daihai Basin increased slowly from 1975 to 1985; From 1986 to 1990, the total population remained flat; It fluctuated from 1990 to 2000; Since 2000, the total population has risen sharply.Analysis of driving factors of hydrological informationIn this study, the average temperature, annual precipitation, annual evaporation, average wind speed in natural factors and cultivated land area, agricultural water consumption, industrial water consumption and population in human factors are considered as the influencing factors of runoff change in Daihai Lake. Therefore, the flow into the lake and the above elements constitute a variable sequence, and the correlation matrix is calculated. See the Table 4 for details.Table 4 Correlation matrix between lake inflow and influencing factors.Full size tableIt can be seen from the Table 4 that the cultivated land area has the highest correlation with the runoff into the lake, with a correlation of − 0.777, which is highly significant, followed by the wind speed, with a correlation of 0.690, which is highly significant; In addition, the total population, industrial water consumption, evaporation and average temperature were significantly correlated. Therefore, the discharge of Daihai Lake is influenced by both nature and human. It can be seen from the table that industrial water consumption, total population, cultivated land area, evaporation and annual average temperature have a negative impact on the flow into the lake, while wind speed has a positive impact.At the same time, the correlation between different factors can be obtained from the Table. For example, the correlation between industrial water consumption and population, cultivated land area and evaporation is as high as 0.8, which is highly significant; The correlation between population and cultivated land, cultivated land and wind speed and evaporation is also about 0.8, which is highly significant; In addition, the correlations between industrial water consumption and annual average temperature, population and annual average temperature, wind speed, evaporation, cultivated land, cultivated land and annual average temperature, evaporation and wind speed, wind speed and annual average temperature are all over 0.5.It can be clearly observed from the table that except for agricultural water consumption, precipitation and evaporation, the annual average temperature is significantly correlated with other factors, and the correlation is more than 0.5. The correlation between annual precipitation and other factors is small and not significant. Therefore, it can be determined that there is data redundancy between different elements. In order to eliminate the data redundancy and get the determinants of the discharge into the lake, the correlation analysis of the variable sequence is carried out, as shown in the table.It can be seen from the Table 5 that the cumulative variance of the first three principal components has reached 87.016%, and the eigenvalues of the first two principal components are greater than 1, which has met the standard. The variance contribution rate of the first principal component was 59.641%, and the order of load rate was cultivated land (0.967), industrial water (0.950), population (0.859), evaporation (0.856), wind speed (0.841), and the load rate was greater than 0.8; In the first principal component, the influence of human factors is greater than that of natural factors. In the second principal component, the variance contribution rate is 18.821%, in which the annual precipitation (− 0.875) and agricultural water consumption (0.736) have higher load rate, and the influence of natural factors is greater than that of human factors.Table 5 Component matrix of principal component analysis of different influencing factorsFull size tableFuture forecastAccording to the analysis in Sect. 3.4, we find that human factors have a huge impact on the lake inflow. In lake water balance, precipitation and evaporation are determined by climate. Now, the Inner Mongolian government has taken a series of measures to protect the Daihai Lake. Therefore, when we predict the future lake water volume, we consider two situations: (1) the future lake water volume in the natural state without any interference (protection or destruction) measures; (2) keeping the existing water volume unchanged future lake water volume in the case.Situation IFor the Situation I, we use two forecasting methods. Method I is to directly predict the future lake water volume by using the variation law of lake volume water volume with time. Method II is to use the lake water balance equation to estimate the change in lake water volume, and then estimate the future lake water volume. The results obtained by these two calculation methods are shown in the Table 6.Table 6 Future prediction of Daihai Lake in situation I.Full size tableWhen estimating the dry years of the Daihai Lake, the results obtained by using the time-varying laws of lake area, water volume and lake depth are inconsistent. Among them, the dry year of the Daihai Lake obtained by using the water volume is 2031, the lake area is 2047, and the water depth is 2096. The three are vastly different. The reason is the uncertainty of our modeling data. As Daihai Lake is a lake in an arid area, data is extremely scarce, and there is almost no continuous measurement of water level, depth, and water volume. The lake area is interpreted from remote sensing images and is an annual average, which results in neglect of inter-annual hydrological changes. Similarly, the water depth is also obtained by remote sensing. The resolution of the remote sensing image is 30 m. We use the interpolation method to control the accuracy to about 5 m. However, in the later stage of the prediction, when the lake depth is lower than 10 m, the results begin to become inaccurate. The modeling data of lake water volume were obtained from WRF-Hydro simulations, so the uncertainty of the data led to the inconsistency of the results. We choose the most recent year as the final result of method I, that is, the forecast result of water volume.From the Table 6, we can observe that the calculation results of the two methods are quite different. The reason is that in method I, we assume that the volume of water in the lake changes linearly, and there is only one variable; in method II, the number of variables increases and the uncertainty increases. However, the years when the Daihai Lake is predicted to dry up are basically the same. Method I predicts that the Daihai Lake will be depleted in 2031, and method II is 2033, which is not much different.Situation IIFor the situation II, we control the agricultural water consumption and industrial water consumption to remain unchanged, estimate the change of volume water at this time, and then estimate the future lake water volume. Among them, the change in water consumption is only evaporation, and the change in water replenishment is precipitation and runoff. The future lake inflow and lake water volume calculated by using the water balance equation are shown in the Table 7:Table 7 Future prediction of Daihai Lake in situation II.Full size tableFrom the Table 7, we can see that under human control, although the of lake inflow will continue to decline compared with no measures, the rate of decline will be significantly slower. And the lake inflow will drop to 0 in 2060. Similarly, the water volume in the Daihai Lake will decline. But the rate is significantly slower compared with situation I. And the water volume will drop to 0 in 2140, nearly 110 years later than 2032–3033 without any control. This shows that man-made protection of the Daihai Lake is extremely important. More

Biogeographic pattern of LOSSThe original forest plot data aggregated at 0.25 degree show large spatial variations (Fig. 1a) across the continents, with the greatest LOSS in Asia & Australia (mean ± 1 SE; 6.5 ± 0.5 Mg ha−1 y−1) > South America (4.9 ± 0.2 Mg ha−1 y−1) and Africa (4.6 ± 0.2 Mg ha−1 y−1) > North America (2.3 ± 0.1 Mg ha−1 y−1 in boreal and 2 ± 0.1 Mg ha−1 y−1 in temperate)36 (Fig. 1b; Supplementary Fig. 5a). This pattern was robust to bootstrapping (1000 iterations) to randomly select 90% of plots for estimating the probability distribution of the mean continental values (Supplementary Fig. 5b). The upscaled gridded LOSS maps generated by our random forest algorithm (see Methods) over the spatial domain of our full datasets shows hotspots of high LOSS in Southern Asia & Australia ( > 6 Mg ha−1 y−1), Northwestern South America (Amazon) ( > 5 Mg ha−1 y−1), and the western coast of North America ( >3 Mg ha−1 y−1)10,36,37,38 (Supplementary Fig. 6a). These patterns were robust to two bootstrapping approaches – based on the sampled biomes of each point feature and also randomly sampling 90% data with replacement (see Methods) (Fig. 2a; Supplementary Fig. 6b). The uncertainty (coefficient of variance – CV; %mean) was generally low ( 10%), despite the larger sample size (n  > 500 at 0.25 degree) (Fig. 2b; Supplementary Fig. 6c), likely because of potential effects of forest recovery or regrowth following past disturbance16 as well as the small plot size (i.e., 0.067 ha in each plot)39.Fig. 1: Map of sample locations and biomass loss to mortality (LOSS) data.a Sampling sites. A total of 2676 samples were collected and aggregated into 814 grids at 0.25 degree that were used for geospatial modeling. b The median and interquartile range of LOSS across continents—North America, South America, Africa, and Asia & Australia.Full size imageFig. 2: Map of biomass loss to mortality (LOSS) and its uncertainty across continents.a, b Ensemble mean of LOSS a and its uncertainty (coefficient of variation, b across continents at 0.25 degree derived from forest plot data using the bootstrapped (10 iterations) approach by randomly sampling 90% plots with replacement. c, d Ensemble mean of LOSS c and its uncertainty (coefficient of variation, d across continents at 0.5 degree derived from six dynamic vegetation models (DGVMs, ORCHIDEE, CABLE-POP, JULES, LPJ-GUESS, LPJmL, and SEIB-DGVM). Coefficient of variation was quantified as the standard deviation divided by the mean predicted value as a measure of prediction accuracy. e The difference of LOSS between ensemble mean of DGVMs and ensemble mean of LOSS derived from forest plots data across continents at 0.5 degree, quantified as difference between c and a, whereby LOSS in Fig. 2a is resampled at 0.5 degree.Full size imageDrivers of LOSSMean annual temperature (MAT), aridity index (the ratio of precipitation to potential evapotranspiration), and precipitation seasonality were identified as the dominant predictors of LOSS across continents (Supplementary Fig. 7a), with positive relationships with LOSS (Fig. 3a)10,36. In contrast to local-scale studies40,41, wood density, forest stand density, and soil conditions were poor predictors of LOSS when all data were used. These relationships were largely driven by the spatial pattern of LOSS and climate gradients, whereby LOSS and MAT, aridity index, and precipitation seasonality were high in tropical forests (Supplementary Fig. 8). This motivated us to examine the drivers of LOSS in tropical vs non-tropical biomes (Supplementary Fig. 7b, c; Fig. 3b–d). With a smaller gradient in climate within wet tropical forests, soil properties such as nutrient content and cation exchange capacity (CEC) were significant predictors of LOSS (Supplementary Fig. 7b; Fig. 3b)42. In wet tropical forests, the relationships between soil nutrient content and CEC and LOSS were positive (Fig. 3b) and thus appeared to support the pattern of higher mortality in more productive tropical forests growing over nutrient rich soils42,43. In non-tropical regions, basal area or a competition index based on the degree of crowding within stocked areas44 (see Methods) were the dominant predictors of LOSS, especially in extra-tropical North America (Supplementary Fig. 7c; Fig. 3c, d). This result highlights the role of stand competition in driving the spatial patterns of LOSS44,45. This pattern also supports the existence of a spatial tradeoff between faster growth and higher mortality because of resource limitations or younger death, whereby competition plays the fundamental role13,45. In contrast to other studies15,46, forest age (available in boreal and temperate forests in North America) was not a good predictor of LOSS (Supplementary Fig. 9), likely because of our focus on mature and old-growth forests (i.e., age > 80 and 100 years in boreal and temperate forests, respectively).Fig. 3: Standardized response coefficients (mean ± 95% CIs) between LOSS and dominant environmental drivers.The scales analyzed were at continents a, tropical regions b vs non-tropical regions c, d. The response coefficients were quantified by linear mixed model which account for each plot as a random effect. Panels c and d used basal area and stand density index (SDI) as competition index, respectively. SDI was defined as the degree of crowding within stocked areas and quantified as a function of tree density and the quadratic mean diameter in centimeters. Basal area is strongly correlated with total biomass and higher LOSS in higher basal area may be merely because of its correlations. Thus, we used another competition metrics – SDI to further confirm the role of competition in LOSS. The error bars denote the 95% confidence interval. *P  130%) in western boreal forests in North America (Fig. 2d).Conventional emergent constraintWe first used the conventional emergent constraint approach27 to constrain the projected (2015–2099) NPP and HR across continents. This approach was conducted by building the statistic (linear) relationship between the historical LOSS averaged at forest-plot scale (derived from original plot data of LOSS) or continental scale (derived from the map of LOSS) and projected NPP and HR summed across continents (see Methods and Supplementary Fig. 4 for details). We found that the emergent constraint approach worked well in North America, where the relationship between historical LOSS and projected NPP and HR was significant (the scenario of using original plot data of LOSS: R2 = 0.68 and P = 0.04 for grid-level NPP; R2 = 0.97 and P = 0.0001 for grid-level HR; the scenario of using map of LOSS at continent scale: R2 = 0.7 and P = 0.04 for grid-level NPP; R2 = 0.95 and P = 0.0008 for grid-level HR) (Supplementary Fig. 11a; Supplementary Fig. 12a). This emergent constraint approach was less effective, however, for other continents, where tropical forests are predominant (all P  > 0.05; Supplementary Fig. 11b, c, d; Supplementary Fig. 12b, c, d). These results suggest a weak linear relationships when observations are lumped or averaged at broad continental scales for tropical continents, thus highlighting the importance of spatial scale and non-linear relationships in emergent constraint25. We interpret the result that this LOSS emergent constraint works better in North America than in the tropical forests, by a better representation of forest plot distribution and couplings of LOSS and NPP and HR across space in North America.Machine learning constraintTo overcome this limitation, we trained a machine learning algorithm34 to reproduce the emerging relationship between historical LOSS and projected NPP and HR at grid level in each DGVM by incorporating all grid values without or with climate predictors, expressed as NPPpro or HRpro = f(LOSShis) or f(LOSShis, MATpro, MAPpro), respectively, where pro refers to projected variables, his refers to historical variables, and MAT and MAP is mean annual temperature precipitation, respectively (see Methods). The results show consistently positive non-linear relationships between LOSShis and NPPpro or HRpro across DGVMs (Supplementary Fig. 3). Our machine learning algorithms can surrogate well the results of process-based models between the historical LOSS and the projected NPP and HR (R  > 0.65 and R  > 0.9 in both scenarios without climate effects and with climate effects, respectively; see Methods) (Supplementary Fig. 13). After including the observed LOSShis (derived from LOSS) in the machine learning algorithm, we were able to generate spatially explicit constrained estimates34 of projected NPP and HR, and then compare them with the scenario without the constraint (Supplementary Fig. 14; Supplementary Fig. 15). These patterns essentially show a lower NPPpro or HRpro in locations of overestimated LOSShis in DGVMs, consistent with the positive relationship between LOSShis and NPPpro or HRpro (Supplementary Fig. 3).Our results show that most DGVMs overestimate tree mortality, particularly in tropical regions (Fig. 2c, e). Thus, if modeled mortality is over-estimated, we expect that NPP is over-estimated as well. Ultimately, we used a bootstrap approach to generate 100 maps of mean value of LOSS with its distribution following the values of the average and 2 times of standard deviation of LOSS maps as a conservative constraint (see Methods). Then the 100 maps of mean value of LOSS were used to constrain the projected NPP or HR as ensemble means in our ML constraint and the uncertainty of the constraint was assessed. Our bootstrapping constraint approach by LOSS reduces this common bias of models and decreases projected NPP down to 7.9, 2.3, 2 Pg C y−1 in South America, Africa and Asia & Australia, compared to original NPP values of 9, 2.4, 2.3 Pg C y−1 (Fig. 4a). The reason for this is that NPP or growth is strongly positively correlated with LOSS across space in both inventory data and DGVMs (Supplementary Figs. 2 and 3; Supplementary Fig. 16). The constant mortality parameter used in most models may be too large if modelers have tuned this parameter to obtain reasonable biomass stocks, thus compensating for an overestimate of NPP in absence of modeled competition between individuals and nutrients (e.g. phosphorus) limitations in tropical forests13. Likewise, HRpro showed similar patterns with NPPpro because of coupling of HR and NPP and LOSS at broad spatial and long term scales20,21, despite the likely decoupling of the instantaneous rate of HR and NPP and LOSS at local and short-term scales22,23. Thus, we also constrained a decrease in projected grid-level HR with values of 6.5, 1.9, 1.7 Pg C y−1 in South America, Africa and Asia & Australia compared to 7, 1.9, 1.8 Pg C y−1 in the original model ensemble (Fig. 4b). Taken together, our results constrain a weaker future tropical forest carbon sink from observation-based LOSS estimates down to 1.4, 0.4, 0.3 Pg C y−1 in South America, Africa and Asia & Australia as compared to 2, 0.5, 0.5 Pg C y−1 in the original models. The projected sink is reduced in particular over the Amazon basin, while North America showed an enhanced future carbon sink (1.1 and 0.8 Pg C y−1 after and before constraint, respectively). The constraint by the machine learning approach significantly reduced the model spread in grid-level NPPpro and HRpro generally in tropical regions and particularly in South America (Fig. 4; Table 1). This was in contrast to the case of constraint at the whole North America scale (Fig. 4; Table 1), presumably because of spatial trade-off or compensation from regions of mortality overestimation (i.e., eastern North America—temperate zones) vs underestimation (i.e., boreal zones). To this end, we further divided the whole North America into temperate and boreal forests and found the significant effects of the ML constraint (Supplementary Fig. 17). These results highlight the importance of spatial scale in the ML constraint approach. We thus recommend accounting for the role of spatial trade-off in our ML constraint approach or using our ML constraint approach at broad spatial scales whereby the effect of spatial trade-off is minimal. We also caution that the bootstrapping (100 times) approach used in our ML constraint increases the sample size and could have increased the significant difference with and without LOSS constraint. Overall, the uncertainty of the ML constraint was low in the bootstrapping approach (Supplementary Fig. 18).Fig. 4: Projected grid-level NPP and grid heterotrophic respiration (HR) across continents.a, b Projected (2015–2099) grid-level NPP a and grid-level HR b across continents quantified by six dynamic vegetation models—DGVMs (ORCHIDEE, CABLE-POP, JULES, LPJ-GUESS, LPJmL, and SEIB-DGVM). The y axes are the minimum, mean, and maximum values in six DGVMs. ‘DGVMs’ refers to the scenario before constraint and ‘DGVMs + Observation’ refers to the scenario after constraint without climate predictors. The constraint was achieved by using the observational maps (n = 100; through a bootstrapping approach; see Methods for details) of LOSS derived from forest plots data to feed into the trained ML (random forest) model. Reported are ensemble means of constraint. The constraint effect was significant when North America were divided into temperate and boreal forests (see results of Supplementary Fig. 17). *P  More

As well as the humanitarian catastrophe it is inflicting, Russia’s invasion of Ukraine in February is disrupting global flows of vital commodities such as fuel, food and fertilizer. This will affect biodiversity and the environment far beyond the war zones, with implications for sustainability and well-being worldwide.
Competing Interests
The authors declare no competing interests. More

Here at the Germplasm Bank of Wild Species of China at the Kunming Institute of Botany, we want to preserve the seeds of as many wild plants as possible from across China’s vast land area. I work on developing the best techniques to freeze plant seeds and tissues at ultracold temperatures, to maintain their viability for years. The idea is that if we plant these seeds again in hundreds of years, a plant will grow.The picture shows me taking a sample of embryos from the seeds of a magnolia tree out of a liquid-nitrogen cryopreservation tank to test whether they’ll regrow when thawed. I dress in protective equipment from head to toe to protect me from the nitrogen, which has a temperature of −196 °C.When I came to the institute in 2009 as a PhD student, it had just purchased its first liquid-nitrogen cryopreservation system, but no one knew how to operate it. I was the one to work it out.Over the years, human activities and climate change have had a negative impact on plant biodiversity. The ultimate goal of the plant seed bank is to collect and preserve all wild plant species in China that are endangered, rare or valuable. We want to save these species before they go extinct. We’ve collected seeds from nearly 11,000 plant species, but that’s only one-third of what grows in China.Many wild plants have genes that help them to survive in harsh environments and make them disease- or drought-resistant. In the future, we might need these genetic materials to breed new crops that can better adapt to the changing climate.I am constantly amazed by how diverse and beautiful seeds are. Some of them are brightly coloured and others are star-shaped. I feel proud when I see the unfrozen seeds germinate in test tubes and gradually grow into large plants. We have three plants in the seed-bank lobby that we cultivated from preserved tissues, and they are all now taller than me. More