###### Abstract
Of the various observations of soil dynamics, water content is the most commonly used observation, because it plays a significant role in the hydrological cycle, influencing infiltration, runoff, and groundwater recharge, and also because it can be measured with relative accuracy. However, it is indicated that soil water content data are not sufficient to provide accurate hydraulic characterization at the field scale [15]. The introduction of multivariate multi-objectives can provide a more comprehensive understanding of hydrological processes and obtain more rational hydrothermal parameters [9; 16; 17; 18; 19], especially in the case of arid and semi-arid soils where water-air-heat interactions are more pronounced. Here a number of studies have attempted to use multiple observations to estimate hydrothermal parameters. [PERSON] et al. [20] used multi-objective optimization to find the optimal hydraulic parameters by weighing soil pressure head and water content. [PERSON] et al. [21] used cumulative outflow and water content data to estimate the hydraulic properties of sandy soils. Some researchers used observed soil water content and temperature data to invert hydraulic and thermal parameters for calibrating models that study soil water movement and heat transfer [22; 23; 24; 25]. In recent years, many researchers have also utilized machine learning to invert parameters of the unsaturated zone [26; 27; 28]. However, studies on the simultaneous inversion of hydraulic and thermal parameters based on coupled hydrothermal models using multi-objective optimization methods are still limited. In particular, there is a lack of comprehensive and systematic study on the results of parameter inversion with different observed variables and combinations of variables as objectives. The interaction between different variables makes it difficult to effectively deal with complex multi-parameter systems. Multi-objective optimization provides a powerful framework for addressing such coupled flow processes with multiple observation types, allowing for the identification of an optimal solution set through the trade-off between different objectives. The Non-dominant Sorting Genetic Algorithm II (NSGA-II), an exploratory tool for solving multi-objective optimization problems using genetic algorithms proposed by [PERSON] et al. [29], remains one of the most commonly used and cited optimisation algorithms today. Considering the large computational consumption of this method [30; 31], [PERSON] and [PERSON] [32] proposed a multi-algorithm, genetically adaptive multiobjective based on the NSGA-II algorithm, namely AMALGAM. AMALGAM combines the advantages of different optimization algorithms and has been widely used in many fields due to its diverse optimization strategies and flexible adaptive characteristics, e.g., to calibrate hydrological models [33; 34; 35; 36; 37; 38], optimize resource allocation in ecological and environmental management [39; 40], improve irrigation efficiency and water resource utilization in agricultural irrigation and management [41; 42], and optimize the design of structure and system in engineering design [43]. This study employ multiobjective algorithms AMALGAM to evaluate the worth of different observation types in simultaneous estimations of the soil hydraulic and thermal properties within coupled hydrothermal processes quantified by HYDRUS-1D model. We select several possible commonly used types of observations in soil dynamics including soil water content, matrix potential, temperature, and heat flux as the objectives to investigate the results of the inversion of hydrothermal parameters based on these observations and different combinations of any of them. Thus, based on these four variables, the inverse simulations based on single, dual, triple, and quadruple objectives are generated, including totally 15 scenarios.