*2.3. The Impact of Uncertainties in Physical Parameters on the Terrestrial Ecosystem* 2.3.1. The Sensitivity Analysis Method Based on CNOP-P

The numerical model contains a large number of physical parameters. Finding the key physical processes and physical parameters in the numerical model is an important way to improve simulation capabilities and prediction skills. To find the most sensitive physical parameters, Sun and Mu [46] proposed a sensitivity analysis (SA) method based on CNOP-P (Figure 1, Table 1). For the SA method based on CNOP-P, there were two steps. First, some insensitive physical parameters were eliminated using the CNOP-P method. Next, among the remaining physical parameters, the combination of relatively sensitive and important physical parameters was judged using the idea of combination and the CNOP-P method. In the second step, the sensitivity of a single parameter was identified using the CNOP-P approach, which in theory was the optimal way to ensure the ranking of every parameter in terms of its sensitivity. Obviously, this method fully considered the nonlinear synergistic effects between physical parameters. Moreover, this method identified relatively sensitive and important combinations of physical parameters in the whole physical parameter space.

**Figure 1.** Flowchart depicting the steps involved in the SA method based on CNOP-P (From research findings by Sun and Mu [46]).

#### 2.3.2. Identification of Sensitive Physical Parameters

Model errors are a critical source affecting the uncertainty in simulated terrestrial ecosystems. It is important to determine which parameter errors should be reduced to improve the simulation ability of terrestrial ecosystems. Sun and Mu [47] used the SA method based on CNOP-P to identify the most sensitive physical parameters to soil carbon. To compare the sensitivity of the parameter combination, the one-at-a-time (OAT) approach was also applied to judge the sensitivity of each parameter.

Sun and Mu [47] noted that the most sensitive parameters to soil carbon varied between plant functional types (Figure 2, Table 1, and the physical meanings of the parameters can be found in Table S1). For example, for C3 perennial grasses under semiarid conditions, the uncertainty in hydrological processes was also critical for modeling soil carbon.C3 perennial grasses are cool season grasses and are great at fixing CO2 at cooler temperatures. However, at higher temperatures, e.g., above 90 degrees F, they are not as efficient. The most sensitive parameter combinations using the SA method based on CNOP-P differed from the highest rank of sensitivity for each parameter using the OAT method. This difference suggested that the nonlinear effects of parameter combinations were key to determining sensitive parameter combinations (Figure 3, and the physical meanings of the parameters can be found in Table S1).

**Figure 3.** The sensitive parameter combination for the simulated soil carbon using the SA method based on CNOP-P (From research findings by Sun and Mu [47]. Parameter corresponding to the number can be found in studies by Sun and Mu [47] and Table S1 in Supplementary Materials).

Numerical simulations and predictions of carbon fluxes (net primary production, NPP) on the Qinghai–Tibet Plateau (TP) are still subject to large uncertainties. To reduce the uncertainty in numerical simulations and improve the predictive power of simulated NPP, Sun et al. [48] identified the key physical processes associated with uncertainty at nine stations on the TP using the SA method based on CNOP-P. In the mid-precipitation region of the Tibetan Plateau, the parameters related to photosynthesis were the main factors contributing to the large uncertainty in the NPP simulations; in regions with low and high precipitation on the Tibetan Plateau, the combined effects of the parameters related to hydrological processes and photosynthesis played an important role (Figures 4 and 5, and the physical meanings of the parameters can be found in Table S2). All the above results showed that the SA based on the CNOP-P method could reasonably identify relatively sensitive and important combinations of parameters and was more physically meaningful.

**Figure 4.** The sensitivity of each parameter using CNOP-P method over the TP (From research findings by Sun et al. [48]. Parameter corresponding to the number can be found in studies by Sun et al. [48] and Table S2 in Supplementary Materials).

2.3.3. Evaluation of Simulation Ability and Prediction Skill by Reducing the Errors of Sensitive Physical Parameters

An important objective of finding the sensitive parameter subset is to improve the simulation ability and prediction skill of terrestrial ecosystems. Sun et al. [48] designed an ideal numerical experiment to reduce the uncertainty in the simulation of NPP over the TP (Table 1). To explore the benefits of modeling NPP while reducing the parameter errors associated with the most sensitive parameter subset, an experiment was implemented as follows:

$$\tau = \frac{\|M\_T(\mathbf{U}\_{0\prime}, P + p) - M\_T(\mathbf{U}\_{0\prime}, P)\| - \|M\_T(\mathbf{U}\_{0\prime}, P + (1 - a)p) - M\_T(\mathbf{U}\_{0\prime}, P)\|}{\|M\_T(\mathbf{U}\_{0\prime}, P + p) - M\_T(\mathbf{U}\_{0\prime}, P)\|} \times 100\% \tag{1}$$

where *τ* represents the benefit of modeling NPP based on reducing the parameter errors of the sensitive parameter subset. A larger *τ* value indicates a better improvement in the NPP simulation. *P* is the reference state of the sensitive parameter subsets. *p* is the CNOP-P, which is related to the errors of five sensitive parameter subsets. *α* (=0.2, 0.4, 0.6, and 0.8) represents the extent of the error reduction for the correct parameters due to data assimilation or observation.

Sun et al. [48] demonstrated that eliminating the errors associated with the most sensitive and important parameter subset with the SA method based on CNOP-P led to the maximum benefit in terms of reducing the uncertainty of simulated NPP when compared to that obtained using the traditional method. For all cases over the TP in the studies of Sun et al. [48], the numerical results showed that the simulation abilities of NPP were improved by reducing the uncertainties in sensitive physical parameters identified by the CNOP-P method compared to the OAT method. In addition, for some cases, the extent of improvement in the simulated NPP by reducing the uncertainties in sensitive physical parameters identified by the CNOP-P method was distinctly better than that by the OAT method [48]. For example, for the Ngari site, the extent of the improvement in the simulated NPP was 34.3% using the CNOP-P method and 28.6% using the OAT method. This study suggested that we should prioritize reducing the uncertainty of relatively sensitive parameter combinations among all physical parameters to improve the prediction or simulation ability of NPP over the TP. Sun et al. [48] also emphasized the importance of nonlinear interactions among sensitive parameter sets for uncertainties in the simulation ability and prediction skill of terrestrial ecosystems.

#### **3. Discussion**

Although the CNOP-P method has been studied in terms of uncertainties in terrestrial ecosystem modeling and prediction, more research should be conducted. It is not enough for studies to consider only the effects of a 2 ◦C temperature increase on terrestrial ecosystem variations. Climate change with multimodel prediction results should be considered. Additionally, ideal numerical experiments are implemented when studying sensitive combinations of physical parameters. In the future, studies of sensitive physical parameter combinations can be conducted with observational data. Finally, the study of the CNOP-P method in terrestrial ecosystem predictability is not limited to the above two aspects.

On the one hand, ensemble forecasting is one of the methods that can be used to improve the simulation and prediction of terrestrial ecosystems, and research on the CNOP-P method is worth exploring land carbon cycle ensemble predictions (LEPS). On the other hand, the impacts of extreme events (e.g., droughts, high temperatures, and fires) on terrestrial ecosystems have received increasing attention from scholars. Studies of terrestrial ecosystem responses to climate change imply that this approach can be used to carry out research on the effects of extreme events on terrestrial ecosystems.As the underlying surface of the Earth system, terrestrial ecosystems affect local and global climate change through land–atmosphere interactions. The impact of terrestrial ecosystems on regional and global climate change will be discussed in the future using the CNOP-P method, especially for studies of extreme events. The results reviewed in this article may not be sufficient to conclude significant findings that are part of uncertainties in simulated and predicted terrestrial ecosystems over multiple years. In this study, uncertainties in simulated and predicted terrestrial ecosystems were shown using the nonlinear optimization method (CNOP-P method). These results encourage us to further research the uncertainty and predictability of terrestrial ecosystems.

### **4. Conclusions**

In this paper, the applications of CNOP methods in terrestrial ecosystem predictability studies are reviewed. The paper contained two main parts. First, using the CNOP method, climate changes were given where both climate state changes and climate variability changes were considered. The numerical results showed that the nonlinear changes in climate variability were considered to show more significant changes in terrestrial ecosystems. This result shows the important role of nonlinear variations in climate variability in terrestrial ecosystem changes.

Additionally, to overcome the limitations of traditional methods in studying the identification of key physical parameters for terrestrial ecosystem simulation and prediction uncertainty, a CNOP-P-based SA method for identifying combinations of sensitive physical parameters was proposed. This method can consider both the nonlinear interactions among physical parameters and the sensitivity of the parameters in the whole physical parameter error space. The sensitive physical parameter combinations identified by the CNOP-Pbased SA method for identifying sensitive physical parameter combinations were more sensitive than those identified by the traditional methods. Furthermore, reducing the errors of sensitive physical parameters identified by the CNOP-P-based SA method resulted in a higher degree of improvement in terrestrial ecosystem simulation and prediction. All of

these applications imply that the CNOP method is an important theoretical tool that can be used to study the uncertainties in terrestrial ecosystem simulations and predictions.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/atmos14040617/s1, Table S1: The chosen physical parameters in studies of Sun and Mu [46,47]; Table S2: The chosen physical parameters in studies of Sun et al. [48].

**Author Contributions:** Conceptualization, M.M.; methodology, M.M.; software, G.S.; validation, M.M.; formal analysis, G.S.; investigation, M.M. and G.S.; resources, G.S.; data curation, G.S.; writing original draft preparation, G.S.; writing—review and editing, M.M.; visualization, G.S.; supervision, M.M.; project administration, M.M.; funding acquisition, M.M. and G.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** Funding was provided by the National Natural Science Foundation of China (Nos. 42288101), by the Guangdong Major Project of Basic and Applied Basic Research (No. 2020B0301030004), and by the National Natural Science Foundation of China (Nos.41975132, 42175077).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to acknowledge the helpful and constructive comments that improved the manuscript substantially from Editor and three anonymous reviewers.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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