Data from: Integrating continuous stocks and flows into state-and-transition simulation models of landscape change

1.State-and-transition simulation models (STSMs) provide a general framework for forecasting landscape dynamics, including projections of both vegetation and land-use/land-cover (LULC) change. The STSM method divides a landscape into spatially-referenced cells and then simulates the state of each cell forward in time, as a discrete-time stochastic process using a Monte Carlo approach, in response to any number of possible transitions. A current limitation of the STSM method, however, is that all of the state variables must be discrete.

2.Here we present a new approach for extending a STSM, in order to account for continuous state variables, called a state-and-transition simulation model with stocks and flows (STSM-SF). The STSM-SF method allows for any number of continuous stocks to be defined for every spatial cell in the STSM, along with a suite of continuous flows specifying the rates at which stock levels change over time. The change in the level of each stock is then simulated forward in time, for each spatial cell, as a discrete-time stochastic process. The method differs from the traditional systems dynamics approach to stock-flow modelling in that the stocks and flows can be spatially-explicit, and the flows can be expressed as a function of the STSM states and transitions.

3.We demonstrate the STSM-SF method by integrating a spatially-explicit carbon (C) budget model with a STSM of LULC change for the state of Hawai'i, USA. In this example, continuous stocks are pools of terrestrial C, while the flows are the possible fluxes of C between these pools. Importantly, several of these C fluxes are triggered by corresponding LULC transitions in the STSM. Model outputs include changes in the spatial and temporal distribution of C pools and fluxes across the landscape in response to projected future changes in LULC over the next 50 years.

4.The new STSM-SF method allows both discrete and continuous state variables to be integrated into a STSM, including interactions between them. With the addition of stocks and flows, STSMs provide a conceptually simple yet powerful approach for characterizing uncertainties in projections of a wide range of questions regarding landscape change.

1. 状态转移模拟模型（State-and-transition simulation models, STSMs）提供了一套通用框架，用于预测景观动态，包括植被与土地利用/土地覆被（Land-use/land-cover, LULC）变化的投影。该方法将景观划分为带空间参考的单元格，随后以离散时间随机过程为基础，采用蒙特卡洛方法，针对各类可能的转移过程，逐一对每个单元格的状态进行时间向前模拟。但状态转移模拟模型现有局限在于，所有状态变量必须为离散型。
2. 本文提出一种用于拓展状态转移模拟模型的新方法，可适配连续型状态变量，该方法被称为含存量与流量的状态转移模拟模型（State-and-transition simulation model with stocks and flows, STSM-SF）。STSM-SF方法允许为状态转移模拟模型中的每个空间单元格定义任意数量的连续存量，同时配套一组连续流量，用以明确存量水平随时间变化的速率。随后针对每个空间单元格，以离散时间随机过程为基础，对每个存量的水平变化进行时间向前模拟。该方法区别于传统系统动力学的存量流量建模范式：其存量与流量可实现空间显式表达，且流量可表示为状态转移模拟模型的状态与转移过程的函数。
3. 我们通过将空间显式碳（Carbon, C）收支模型与美国夏威夷州土地利用/土地覆被变化的状态转移模拟模型相整合，对STSM-SF方法进行了演示。在本示例中，连续存量为陆地碳库，而流量则为这些碳库之间可能发生的碳通量。尤为关键的是，其中部分碳通量由状态转移模拟模型中对应的土地利用/土地覆被转移过程触发。模型输出结果涵盖，在未来50年土地利用/土地覆被的投影变化驱动下，景观中碳库与碳通量的时空分布变化情况。
4. 新型STSM-SF方法可将离散型与连续型状态变量整合至状态转移模拟模型中，同时涵盖二者之间的交互作用。通过引入存量与流量模块，状态转移模拟模型可提供一套概念简洁却功能强大的方法，用于量化表征各类景观变化相关问题的投影预测中的不确定性。