Investigation into climate change effects on carbon and water fluxes, and water use efficiency of the temperate grassland ecosystems in Inner Mongolia of China Open Access

Water use efficiency (WUE), which is expressed by the ratio of the gross primary productivity (GPP) to the total ecosystem water consumption (represented by evapotranspiration; ET), is defined as the amount of carbon assimilated as biomass or grain produced per unit of water used by the crop, and it is a critical variable linking the carbon and water cycles (Zhou et al. 2013). According to Piao et al. (2013), carbon and water cycles have been greatly altered with climate change, and therefore, how climate change affects ecosystem GPP, ET and WUE has attracted wide attention, particularly in semi-arid regions where ecosystems are fragile. Since the estimation of GPP, ET and WUE are essential for investigation into the effects of climate change, many researchers have contributed to the estimation of GPP, ET and WUE. Currently, there are mainly three approaches for estimation of GPP, ET and WUE, namely field measurements, statistical models and process models. Field measurement is the most reliable method for the estimation of GPP, ET and WUE, but it is impossible to get long-term, large-scale observation data (Baldocchi 1994). The statistical models applied to estimate GPP, ET and WUE are simple and intuitive but lack a theoretical basis and these models cannot reveal the interaction between ecosystems and their environment (Ferguson et al. 2008). The process models, which incorporate the physiological and ecological processes for vegetation, such as the CENTURY (Kelly et al. 1997), TEM (Melillo et al. 1995), ORCHIDEE (Tum et al. 2016), and BIOME-BGC models (Raj et al. 2014), can better simulate the response of vegetation to climate change. Among process models, the BIOME-BGC model has been widely used to simulate ecosystem GPP and ET due to its detailed description of ecological and physiological processes of vegetation. Based on the simulated GPP and ET, WUE can be calculated as the ratio of the GPP to ET.

When estimating GPP, ET and WUE using a process model, the determination of model parameters which describe the physiological and ecological processes is a key issue, which can greatly affect the accuracy of model simulations. Therefore, it is important to choose a reasonable and efficient parameter optimization method. Recently, a number of methods have been proposed for model parameter optimization, including annealing algorithms, genetic algorithms and the PEST algorithm (Kim et al. 2007). However, it should be noted that these parameter optimization methods usually search optimal parameter values on an objective function surface, and consequently, the optimal values of parameters sought might be local optimal values rather than global optimal values (Bao et al. 2013). To avoid this problem, the System Response Parameter Calibration Method (SRPCM), which has been used only for parameter optimization of hydrological models so far, was tested in this study for the optimization of the parameters of the BIOME-BGC model.

In recent years, the responses of GPP, ET and WUE to climate change in different ecosystems have been extensively studied at various spatiotemporal scales. Ueyama et al. (2010) studied the response of GPP and ET to climate change in larch forests using a BIOME-BGC model with AsiaFlux data; Quan et al. (2018) studied the response of WUE to climate warming in an alpine meadow in a manipulative warming experiment. However, the influence of the same climate factors on the WUE in the same type of ecosystem may vary with geographical location (Mastrotheodoros et al. 2017). Huang et al. (2015) reported that ecosystem WUE increased with a rise in air temperature, while Bell et al. (2010) reported an opposite result. These phenomena reflect the complexity of factors affecting WUE, where a contributing factor may be the different responses of GPP and ET to environmental factors (Brümmer et al. 2012). Therefore, it is important to quantify the responses of ecosystem GPP and ET to changes in precipitation or temperature in order to quantify the changes to WUE under a changing climate.

As an important part of the terrestrial ecosystem, the impact of climate change on the temporal and spatial variations in carbon and water cycles in temperate grasslands have been the focus of many researchers in recent years. However, most studies have been carried out on a yearly scale, and more detailed investigation of changes to GPP, ET and WUE in response to climate change at the seasonal, monthly and daily scales is essential for understanding the impacts of climate change. Therefore, the primary objectives of this study were (i) to verify the applicability of SRPCM for parameter optimization of the BIOME-BGC model of a case study site; (ii) to quantify the annual, seasonal, monthly and daily variations of GPP, ET and WUE over the period 2003–2019 using a BIOME-BGC model; (iii) to explore the impacts of the changes to precipitation or temperature on GPP, ET and WUE over the period 2003–2019; and (iv) the quantify the responses of GPP, ET and WUE to different future climate-change scenarios.

For the calibration and validation of the BIOME-BGC model, the GPP and ET values recorded during the period 2004–2008 by the eddy correlation flux measurement system located in the Xilingol temperate grassland ecosystem were obtained from the ChinaFLUX Observation and Research Network (http://www.chinaflux.org/enn/index.aspx). Daily maximum temperature, daily minimum temperature, daily mean temperature, daily precipitation and daily solar radiation data for the period 2003–2019 were downloaded from the China Meteorological Data Service Center (http://data.cma.cn/). Vapor pressure deficit (VPD) and day length were obtained using Mountain Microclimate Simulation (MTCLIM) model. The soil data, including the thickness and composition for each type of soil, were obtained from the Resource and Environment Science and Data Center (https://www.resdc.cn/). The daily GPP and ET during the period 2003–2019 were simulated using a BIOME-BGC model with optimized parameters.

The BIOME-BGC model is a mechanistic biogeochemical model (Schmid et al. 2006), which is widely used to simulate the dynamics of carbon (C), nitrogen (N) and water (H₂O) into and out of an ecosystem on a daily timescale. It was developed following the FOREST-BGC model (Running & Gower 1991). Three types of input data files are required by the BIOME-BGC model: (i) site-specific parameter files, including site latitude, longitude, elevation, soil texture, effective soil depth, plant type, CO₂ concentration and biological fixation of N; (ii) meteorological data files, including maximum and minimum air temperature, daytime average temperature, precipitation, solar radiation, VPD and daylength; and (iii) eco-physiological parameter files, including vegetation type, stomatal conductance, leaf parameters, C:N of fine roots, canopy average specific leaf area, canopy light extinction coefficient and the fraction of leaf N in rubisco.

To calibrate and validate the BIOME-BGC model, the period 2004–2008 with daily observed GPP and ET was divided into two sub-periods: 2004–2005 for calibration and 2006–2008 for validation. The SRPCM was used to optimize the parameters of the BIOME-BGC model an a daily scale.

The optimal value of the parameter is obtained by iterative calculation of the initial parameter value ⁠.

If either one of the following conditions is satisfied, then it is considered that convergence is achieved, and the iterative calculation can be stopped:

• (i)

  function convergence principle: when the algorithm cannot significantly improve the objective function value in multiple iterations, the iteration ends; (⁠⁠), and ε is known as the convergence control constant; or

• (ii)

  parameter convergence principle: when the algorithm cannot significantly improve the parameter values in multiple iterations, then the iteration ends: ⁠.

R is used to indicate the degree of correlation between two variables. The larger R is, the higher the degree of correlation is. A t-test was carried out to detect if there is a significant correlation between the simulations and observations of GPP/ET.

After the BIOME-BGC model was optimized using the SRPCM, it was used to simulate daily GPP and ET for the period 2003–2019. Based on the daily GPP and ET, daily WUE = GPP/ET was computed, and monthly, seasonal and annual GPP, ET and WUE were obtained by summing their daily values. The BIOME-BGC model was also applied to simulate the daily GPP and ET under different climate-change scenarios (namely a rise of 1–2 °C in temperature and an increase in annual precipitation by 5%–15% by the end of the 21st century). The daily WUE and annual GPP, ET and WUE were also calculated under the climate change scenarios.

The Mann–Kendall (M-K) test (Zhu et al. 2021) was employed to analyze the trends of the annual, seasonal and monthly GPP, ET and WUE. These trends were tested at the confidence levels of 90%, 95% and 99%, respectively. The intra-annual distributions of GPP, ET and WUE were also plotted and analyzed. Based on the frequency of daily GPP, ET and WUE within different ranges, frequency curves were plotted respectively for growing and non-growing seasons to analyze any seasonal differences. The double accumulation curves for annual GPP and annual ET were plotted to analyze the impact of climate change on annual WUE.

To explore the impacts of historical variations of precipitation and temperature on WUE, GPP and ET during the period 2003–2019, the correlations of WUE/GPP/ET and precipitation/temperature were investigated at annual and monthly scales by use of a correlation analysis method.

To reveal the impacts of future climate change on WUE, GPP and ET, nine climate-change scenarios (see Supplementary Information Table A.1) based on the B2 emission scenario (namely a rise of 1–2 °C in temperature and an increase in precipitation by 5%–15%) developed by the IPCC Special Report on Emission Scenarios were assessed. The response of GPP, ET and WUE to the nine climate-change scenarios was simulated on a daily scale. The mean annual temperature and precipitation during the period 2003–2019 were adopted as the baseline. The annual GPP, ET and WUE values were also computed under the nine climate-change scenarios.

According to Figure 2, although there are some overestimations and underestimations by the BIOME-BGC model, the simulated and observed GPP and ET generally show similar variation patterns. This was also verified by the values of the correlation coefficient (R) and root mean square error (RMSE) for the correlation of the simulated and observed values of GPP and ET. As presented in Table 1, the correlation coefficients for both the calibration and validation periods are all higher than 0.557 with the values for GPP being higher than those of ET. The t-test also proved that a significant correlation existed between the simulated and observed values of GPP and ET at a significance level of 0.01 (p < 0.01). The RMSE for the simulated and observed GPP and ET during both the calibration and validation periods are all higher than 0.677 with the values of ET being higher than those of GPP. The values of both R and RMSE for the simulated and observed values of GPP and ET indicate that the model is in reasonable agreement with the observations for both GPP and ET.

Supplementary Information Figure A.2 presents the variations of monthly GPP, ET and WUE in May to September by year. GPP and ET play a decisive role in the annual total. In May, the GPP and ET demonstrated reversed variations in most of years, namely GPP locally increasing with ET locally decreasing. In June to July, the synchronization in variations of GPP and ET improved gradually. In August and September, GPP and ET illustrated very similar variations. The variations of WUE in May to September by year exhibited different trends.

The correlation between the simulated annual GPP, ET and WUE and the annual P and T is illustrated in Supplementary Information Figure A.3. From the figure, it can be found that there existed a significantly positive correlation between annual GPP and ET and the annual precipitation at a confidence level of 95% and 99% with their correlation coefficients being 0.602 and 0.772, respectively. However, the annual GPP and ET were not significantly correlated with annual temperature with their correlation coefficients being 0.232 and 0.07, respectively. The correlation between annual WUE and annual precipitation is weaker than that between annual WUE and annual temperature with their correlation coefficients being −0.156 and 0.396, respectively. It should be noted that the impacts of both precipitation and temperature on WUE were not significant. The fact that the double accumulation curve of annual GPP versus annual ET during the period 2003–2019 was almost a straight line (see Supplementary Information Figure A.4) also demonstrated that the changes in annual precipitation and temperature have limited influence on WUE. From Figure 4, it can also be found that the fluctuations of annual GPP and ET corresponded well with those of annual precipitation, but there existed poor synchronization in fluctuations between annual GPP and ET and annual temperature. The analysis above suggests that annual precipitation is a more important controlling factor than annual temperature for annual GPP and ET, while the annual temperature has a greater influence on annual WUE than annual precipitation.

The correlation coefficients between the seasonal GPP, ET and WUE and the seasonal P and T are summarized in Supplementary Information Table A.4. In growing seasons, there existed a significant positive correlation between seasonal GPP and ET and the seasonal P with their correlation coefficients being 0.671 and 0.736, respectively. The correlation between seasonal GPP and ET and seasonal T was not significant with the correlation coefficients being 0.303 and 0.209, respectively. The correlation between seasonal WUE and seasonal P was weaker than that between seasonal WUE and seasonal T with their correlation coefficients being −0.011 and 0.279, respectively. In non-growing seasons, the correlation between seasonal ET and P and between seasonal WUE and P was significant with the correlation coefficients being 0.9 and −0.667, respectively. The correlations between seasonal GPP and P and between seasonal GPP, ET and WUE and T were all not significant. From Figure 4, the fluctuations of seasonal GPP and ET corresponded well with those of seasonal P in growing seasons, but there existed poor synchronization in fluctuations between seasonal GPP and ET and seasonal T. In non-growing seasons, seasonal GPP and P showed very similar variations, but seasonal WUE and seasonal precipitation exhibited almost inverse variations. The analysis above suggests that seasonal P is a critically controlling factor for seasonal GPP and ET in growing seasons, and for seasonal ET and WUE in non-growing seasons.

Supplementary Information Table A.5 presents the correlation coefficients between monthly T_i, P_i and P_i−1 and monthly GPP, ET and WUE in 12 months during the period 2003–2019. Supplementary Information Figure A.2 presents the variations of monthly GPP, ET, WUE, P and T during May to September by year. Supplementary Information Table A.5 reveals that (i) the positive correlation between GPP and P_i in each month of May to September was stronger than between GPP and P_i−1 and (ii) the positive correlation between ET and P_i in each month was strong, and evidently stronger than the correlation between ET and P_i−1. The correlation between WUE and P_i in each month of April to October was negative, while a positive correlation between WUE and P_i−1 was found in each month of May to August and October. This implies that the precipitation in the previous month has a greater impact on the GPP and the WUE in a given month than the precipitation in the given month and less influence on ET in the given month than the precipitation in the given month.

GPP was positively correlated to T in April, May and August at a confidence level of 95% but their correlation was negative or weak in June and July with higher temperatures. A similar behavior was found for the correlation between ET and T. However, compared with the strong correlation between GPP and T in April, May, August and September, the correlation between ET and T in these months was much weaker. In contrast to GPP and ET, WUE was positively correlated with T in June and July but the correlation was weak. From May to September, WUE was all positively correlated with T in all months with a significant correlation at a confidence level of 99% appearing in May. Similar conclusions can also be drawn by the comparison of fluctuation synchronization of each month's GPP, ET and WUE with P and T.

Under the T0W5 and T0W15 scenarios, GPP, ET and WUE increased by 7.25%, 4.12% and 3.34%, respectively, and 18.06%, 12.09% and 5.68%, respectively. This indicated that an increase alone in precipitation of 5% and 15% still yielded an increase in GPP, ET and WUE. In contrast to precipitation increases, increases of 1 and 2 °C alone in temperature caused smaller increases in GPP, ET and WUE of 3.49%, 0.11% and 3.71%, respectively, and 1.68%, −0.76% and 2.76%, respectively. Compared with historical scenarios, under T1W5, T1W15, and T2W5, T2W15 scenarios the GPP increased by 3.66%, 17.20%, 8.07% and 19.93%, respectively, with WUE increasing by 2.19%, 5.25%, 4.98% and 8.11%, respectively. It was also found that ET was more sensitive to change in precipitation than in temperature. Under T1W5, T1W15, T2W5 and T2W15 scenarios, ET increased by 2.11%, 11.85%, 3.29% and 11.34%, respectively. The analyses indicate that the impacts on GPP, ET and WUE of a combined increase in temperature and precipitation are greater than the impact of a standalone increase in temperature or a standalone increase in precipitation under future climate-change scenarios.

The accuracy of model simulations is highly influenced by the determination of model parameter values, and as a result, the selection of appropriate model parameter optimization methods is vital to model simulations. In our study, the SRPCM was used to optimize the parameters of the BIOME-BGC model notwithstanding that its effectiveness in parameter optimization has been verified only for hydrological models. The SRPCM can directly search the optimal parameter values on the parametric function surface, while other available parameter optimization methods including the PEST algorithm usually search optimal parameter values on the objective function surface (Goegebeur & Pauwels 2007). In SRPCM, the non-linear parametric calibration problem is transformed into a linear parametric calibration problem by use of a differential system response relation between model output variations and parameter value variations, thus avoiding the local optimal value problem.

Since the PEST algorithm has been widely used to optimize the parameter values for BIOME-BGC models, it was also used to provide a comparison with the SRPCM optimization in this study. The results presented in Figure 2, Supplementary Information Figure A.1 and Table 1 indicate that the SRPCM performs better than the PEST algorithm.

On the basis that it was concluded that the SRPCM is able to optimize the parameter values in a BIOME-BGC model, then SRPCM could be considered when optimizing other ecological models.

Generally, the increased temperature can generate an increase in GPP. High temperature can also prolong the growing season of vegetation and thus improve the photosynthetic efficiency of vegetation (Jiao et al. 2021). Wan et al. (2005) reported that global warming could enhance GPP because plant photosynthesis would increase. However, the increased temperature can also have negative impacts on GPP. High temperatures increase water consumption, cause drought stress and can reduce vegetation productivity. Sang & Su (2009) found that increasing temperatures led to a reduction in the net ecosystem productivity (NEP) as soil respiration was boosted. Particularly, in semi-arid regions, where vegetation is always in a state of water shortage, an increase in temperature usually further aggravates the water shortage. To reduce water consumption, vegetation normally reduces its stomatal conductance or even closes its stomata, and consequently, a reduction in GPP occurs. Meanwhile, the water shortage induced by an increase of temperature can cause a reduction in soil evaporation (Wu et al. 2011). Since the study site is located in a semi-arid region, similar findings were obtained where GPP and ET were negatively correlated with the temperature in June and July, which are the months with the highest temperatures, but positively correlated with the temperature in other months with relatively higher temperature (see Supplementary Information Figures A.2 and A.3 and Table A.5). Berry & Björkman (1980) also considered that the response of photosynthesis to temperature is a parabolic curve having a peak at some intermediate temperature.

In semi-arid regions, precipitation is also a key factor affecting both vegetation productivity and transpiration. Jung et al. (2007) stated that the increase in GPP is more evident under wet and warm conditions than under dry and cold conditions. Weiwei et al. (2018) also confirmed that precipitation is the main limiting factor of vegetation change in arid and semi-arid regions, and that an increase in precipitation has a significant beneficial effect on GPP. Similar findings were found in this study where the impact on GPP of combined increases in temperature and enhanced precipitation were greater than for increased temperatures alone (see Figure 7). An upward trend in ET during the period 2003–2019 corresponding well with the increases in precipitation (see Figure 5 and Supplementary Information Figure A.2) indicated that precipitation is vital to ET. The strong positive correlation between the precipitation in the previous month and GPP in the current month and between the precipitation and ET in the same month (see Supplementary Information Table A.4) also verified that precipitation in the semi-arid region is a primary factor in promoting GPP and ET. Zhou et al. (2013) confirmed that precipitation has a stronger impact on ET than temperature.

At the same time, a negative correlation was determined between WUE and precipitation. Since the increase in precipitation can satisfy the water consumption induced by the rise in temperature, ET showed a greater increase than the vegetation carbon sequestration. As a result, WUE reduces with the increase in precipitation. Compared with precipitation, temperature was positively associated with WUE in May to September.

Using a BIOME-BGC model optimized by the SRPCM, the variations of GPP, ET and WUE at different time-scales and their responses to climate change have been explored. The results revealed that (i) the BIOME-BGC optimized by the SRPCM performed better than a mode optimized by the PEST algorithm when simulating daily GPP and ET processes; (ii) the GPP, ET and WUE annually and in growing seasons all showed an increasing trend but not significant with a confidence level of less than 90%, respectively; (iii) both GPP and ET in non-growing seasons demonstrated an increasing trend at a confidence level of 90% while the WUE presenting a slight decreasing trend; (iv) the intra-annual distributions of GPP, ET and WUE were very uneven with the highest GPP and ET observed in July and the highest WUE in September; (v) GPP and ET in the growing season had a decisive role in annual GPP and ET while a low daily WUE of less than 2 g/kg dominated in both growing seasons and non-growing seasons at the study site; (vi) annual GPP and ET were more sensitive to changes in precipitation than in temperature with little change of WUE with years; (vii) precipitation was a critical controlling factor for GPP and ET in growing seasons and for ET and WUE in non-growing seasons; (viii) monthly precipitation had a greater influence on GPP, ET and WUE than monthly temperature with the previous month's precipitation having a greater impact on GPP than the temperature in the current month; (ix) different climate-change scenarios had different impacts on GPP, ET and WUE, with the impacts of combined increases in temperature and precipitation on GPP, ET and WUE being greater than the impact of standalone increases in temperature or precipitation. The outputs from this study could provide a reference for the assessment of climate change impacts on carbon and water cycles of temperate grassland ecosystems.

This study was supported by the 111 Project under Grant No. BP0820018.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.