**1. Introduction**

As a part of the Earth system, terrestrial ecosystems interact and couple with the atmosphere through water cycling and energy exchange, so terrestrial ecosystems have important impacts on weather and climate systems [1–3]. However, there are large uncertainties in current terrestrial ecosystem simulations and predictions, and these uncertainties affect our quantitative estimates of terrestrial ecosystem carbon flux and carbon storage and are an obstacle to the simulation and prediction of weather and climate events. Therefore, it is essential to conduct studies on uncertainties in terrestrial ecosystem simulations and predictions [4–8].

Model errors are one of the factors that contribute to uncertainties in the simulation and prediction of terrestrial ecosystems [9,10]. Model errors include climate forcing errors, uncertainties in the physical processes of models, and errors in the physical parameters of models. Climate change is an important factor that can induce variations in terrestrial

**Citation:** Sun, G.; Mu, M. Applications of CNOP-P Method to Predictability Studies of Terrestrial Ecosystems. *Atmosphere* **2023**, *14*, 617. https://doi.org/10.3390/ atmos14040617

Academic Editors: Alfredo Rocha, Xiaolei Zou, Guoxiong Wu and Zhemin Tan

Received: 9 February 2023 Revised: 16 March 2023 Accepted: 18 March 2023 Published: 24 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

ecosystems, especially under the background of global warming [11–13]. Climate change is reflected not only in variations in climatology but also in climate variability. However, in previous studies, linearly increased temperature and precipitation changes were employed to assess the impacts of uncertainties in climate change on uncertainties in simulated terrestrial ecosystems [14].

Recently, many studies have found that climate variability plays a key role in the variation in terrestrial ecosystems [15]. For example, Botta and Foley [16] demonstrated that climate variability resulted in changes in ecosystem structure, soil carbon, and vegetation carbon. Mitchell and Csillag [17] also emphasized that climate variability could influence the stability of grasslands and result in high uncertainty in estimating the net primary production (NPP) of grasslands. Zaghloul et al. [18] investigated the impact of climate change on river flow and showed that early spring warming caused water flow to increase in cold climate regions of Canada due to snowpack melting and gradual glacier melting. Li et al. [19] explored the climatic impact of vegetation spring phenology in China and provided important support for modeling vegetation phenology and growth in northern China. Dastour et al. [20] showed that the seasonal cycles of vegetation and climate were generally coherent but there was a time delay. Their wavelet methods also considered the observational uncertainties. Although the effects of climate variability change on terrestrial ecosystems have been investigated, the extreme effects of uncertainties in climate variability change on uncertainties in simulated terrestrial ecosystems are often neglected [21–23].

Moreover, the uncertainties of physical parameters in numerical models are a major factor contributing to the uncertainties in terrestrial ecosystem simulations and predictions. Reducing the errors of physical parameters in numerical models is an effective way to improve the simulation ability and forecasting skills of terrestrial ecosystems. The simulation ability and forecasting skill of terrestrial ecosystems can be improved by adjusting the model parameters. For example, by assimilating the parameters in the model, Rayner et al. [24] found that the model could match the seasonal cycle and annual variation in CO2 well with the observation with the Biosphere Energy Transfer Hydrology (BETH) model. Mo et al. [25] optimized the physical parameters of the boreal ecosystem productivity simulator (BEPS) model using the ensemble Kaman filter and found that the simulation abilities of total primary productivity, total ecosystem respiration, and net ecosystem productivity were improved. From these results, it was found that the simulation capability of terrestrial ecosystems could be improved by adjusting the parameters in numerical models.

Numerical models contain a large number of parameters in dynamic vegetation models, which simulate carbon storage and cycling in terrestrial ecosystems. There are three categories for the above parameters in numerical models. The first is related to the discrete format of the model, which is independent of observations; the second is for parameters that can be determined from direct observations; and the third is for parameters that can be determined from indirect observations. For example, the random number seed parameter in the Lund–Potsdam–Jena (LPJ) numerical model [26] belongs to the first type; the co-limitation shape parameter obtained directly from observations belongs to the second type [27]; and the temperature sensitivity parameter to the Q10 obtained from indirect observations belongs to the third type [28]. The latter two types of physical parameters determined by direct and (or) indirect observation (PDOs) are the focus of attention in the above studies.

The numerical model contains a large number of PDOs, and reducing the errors of all PDOs at the same time would be very costly. Identifying which PDO errors should be reduced first is critical, and this question involves identifying the sensitivity and importance of the physical parameters. There has been ample research on how to identify the sensitivities of physical parameters in numerical models. For example, Pitman [29] analyzed the sensitivities of 18 physical parameters in the Biosphere Atmosphere Transfer Scheme (BATS) model using the one-at-a-time (OAT) method. When the sensitivity of one of the parameters was analyzed, the remaining 17 physical parameters remained unchanged. However, the OAT approach ignores the interaction of physical processes characterized by physical parameters [30,31].

The above sensitivity analysis method was also used to analyze the sensitivity of the parameters. However, this method is based on the assumption of linearity and can be used to explore only small parameter errors and short integration times and is not valid for large parameter errors and long integration times. To consider the interaction of physical processes, some scholars have conducted sensitivity analysis of parameters with finite parameter error samples using the multiobjective generalized sensitivity analysis (MOGSA) method, Monte Carlo method, and extended Fourier amplitude sensitivity test (EFAST) method [32]. Zaehle et al. [28] applied the Monte Carlo hierarchical sample method to identify the sensitivity of model parameters. Bastidas et al. [33] used the MOGSA method to analyze the sensitivity of parameters according to different significance levels. These aforementioned methods were characterized by their low computational cost due to the use of limited samples in the parameter space to identify the sensitivities of physical parameters. However, there were certain limitations; for example, either the interaction among all physical parameters was not considered, or the sensitivity of physical parameters was identified within the parameter space using finite samples.

The responses of terrestrial ecosystems to uncertainties in climate change and physical parameters are a component of predictability studies. Although many studies have been conducted on the uncertainties of terrestrial ecosystem simulations and predictions in terms of uncertainties in climate change and physical parameters, the maximum extent of their uncertainty has rarely been determined. The conditional nonlinear optimal perturbation (CNOP) approach [34,35] is a powerful tool to study predictability. The CNOP approach is related to initial errors (CNOP-I) and model errors (CNOP-P) and has been widely applied to predictability studies in atmospheric and oceanic sciences [36–42].

In this study, the applications of the CNOP-P method to predictability studies of terrestrial ecosystems are introduced. The content includes the maximum extent of uncertainties in climate change on the simulation uncertainties in terrestrial ecosystems using the CNOP-P method. Second, key physical parameters and combinations of physical parameters that lead to uncertainties in terrestrial ecosystem simulations and predictions are identified using the CNOP-P method. Furthermore, the degree of improvement in terrestrial ecosystem simulations and projections is assessed by reducing the errors of sensitive physical parameter combinations identified by the CNOP-P method. These works are reviewed mainly to demonstrate the usefulness and adaptability of nonlinear optimization methods (e.g., the CNOP-P method) in terrestrial ecosystem predictability studies. Furthermore, it provides an outlook for more scholars to use this method to conduct uncertainty studies on numerical simulations and predictions of terrestrial ecosystems using the method.

This paper is organized as follows: studies on the influence of grassland ecosystem equilibrium on moisture index perturbation are introduced in Section 2.1. The impact of uncertainties in climate change on the uncertainties in simulated terrestrial ecosystems is presented in Section 2.2. In Section 2.3, the impact of uncertainties in physical parameters on the terrestrial ecosystem is introduced; in Section 3, the summary and conclusion are provided.

#### **2. Results of Reviews**

#### *2.1. The Impact of Moisture Index Perturbation on the Stability of Grassland Ecosystem Equilibrium*

To investigate the stability of grassland ecosystem equilibrium to climate perturbation, Sun and Mu [43] used the CNOP-P method and a five-variable grassland ecosystem model. For a grassland equilibrium state (GES) and a desert equilibrium state (DES) within the five-variable grassland ecosystem model, moisture index perturbations were generated using the CNOP-P method, and these perturbations represented the climate perturbation. They first found that the variations in the moisture index resulting from CNOP-P showed nonlinear characteristics. For instance, for the GES, the humidity index of CNOP-P gradually decreased when the amplitude of the moisture indices was small, while

when the amplitude of the moisture indices was large, the humidity index of CNOP-P showed a "decreasing–increasing–decreasing" pattern and changed sharply at the end of the period. The variation in the GES also exhibited nonlinear characteristics due to the above humidity index variations.

With the small amplitude of moisture indices, grassland ecosystems returned to the grassland equilibrium state under the influence of the CNOP-P-type humidity index. There were different times required for recovery for different amplitudes of moisture indices. However, grassland ecosystems gradually evolved toward the desert equilibrium state with abrupt changes in the larger amplitude of moisture indices. Numerical results indicated that grassland ecosystems eventually evolved toward a desert state with nonlinear instability when subjected to sufficiently large climate changes. For the DES, Sun and Mu [43] also demonstrated a nonlinear character similar to that of the GES.

To further explore the nonlinear characteristics of the stability of the GES and DES to different types of climatic disturbances, Sun and Mu [43] analyzed the nonlinear evolution of grassland ecosystems under the influence of nonlinear and linear climatic disturbances (Table 1). To interpret the differences between the two, they created two linear climate perturbations that could be distinguished in light of their linear slopes, which were zero or nonzero. For the GES, they found that nonlinear climate change had a severe impact on grassland ecosystems. Grassland ecosystems degraded to a desert equilibrium state and tended to be nonlinearly unstable under the influence of the CNOP-P-type moisture indices. For the DES, they found that nonlinear moisture indices had a severe impact on desert ecosystems. The desert ecosystem influenced by the CNOP-P-type moisture index degenerated into the grassland equilibrium state and became nonlinearly unstable. All of the above work suggests that nonlinear changes in climate variability play an important role in abrupt changes in the equilibrium state of grassland ecosystems.

#### *2.2. The Impact of Uncertainties in Climate Change on the Uncertainties in Simulated Terrestrial Ecosystems*

Soil carbon, as a large carbon sink, plays an important role in the carbon cycle in terrestrial ecosystems [14,44]. Changes in soil carbon can cause large changes in atmospheric CO2, which may further accelerate global warming. It is therefore necessary to determine the uncertainty in modeled soil carbon. Sun and Mu [45] used the CNOP-P method to analyze the maximum degree of uncertainty in the contribution of soil carbon to climate change uncertainty (both climatological change and climate variability) in China (Table 1).


**Table 1.** Summary of the studies of terrestrial ecosystem predictability using the CNOP-P method.

Under the background of global warming, they provided a nonlinear climate change, i.e., CNOP-P-type climate change, and a linear climate change. The key difference between the CNOP-P-type climate change and the linear climate change was whether there was a change in temperature or precipitation variability compared to a reference temperature or precipitation variability. Sun and Mu [45] showed that there were different regional responses to uncertainties in simulated soil carbon caused by CNOP-P-type and linear temperature changes.

By exploring three components of soil carbon in the LPJ model, namely, rapidly decomposing soil carbon, slowly decomposing soil carbon, and subsurface apoplastic material, they found that the decrease in subsurface apoplastic matter was probably the main reason for the decrease in soil carbon in arid and semiarid zones as a result of the two temperature climate changes. The different effects of the two temperature climate changes in southern China may be caused mainly by the rapid decomposition of soil carbon. The uncertainties in simulated soil carbon caused by the two precipitation climate changes were similar. In the arid and semiarid zones, both precipitation and climate changes led to increased uncertainty in the simulated soil carbon. This research implied that the variation in temperature variability played a crucial role in the variations in soil carbon and its components in the study region.
