Remote Sensing Data Assimilation in Crop Growth Modeling from an Agricultural Perspective: New Insights on Challenges and Prospects

Abstract

The frequent occurrence of global climate change and natural disasters highlights the importance of precision agricultural monitoring, yield forecasting, and early warning systems. The data assimilation method provides a new possibility to solve the problems of low accuracy of yield prediction, strong dependence on the field, and poor adaptability of the model in traditional agricultural applications. Therefore, this study makes a systematic literature retrieval based on Web of Science, Scopus, Google Scholar, and PubMed databases, introduces in detail the assimilation strategies based on many new remote sensing data sources, such as satellite constellation, UAV, ground observation stations, and mobile platforms, and compares and analyzes the progress of assimilation models such as compulsion method, model parameter method, state update method, and Bayesian paradigm method. The results show that: (1) the new remote sensing platform data assimilation shows significant advantages in precision agriculture, especially in emerging satellite constellation remote sensing and UAV data assimilation. (2) SWAP model is the most widely used in simulating crop growth, while Aquacrop, WOFOST, and APSIM models have great potential for application. (3) Sequential assimilation strategy is the most widely used algorithm in the field of agricultural data assimilation, especially the ensemble Kalman filter algorithm, and hierarchical Bayesian assimilation strategy is considered to be a promising method. (4) Leaf area index (LAI) is considered to be the most preferred assimilation variable, and the study of soil moisture (SM) and vegetation index (VIs) has also been strengthened. In addition, the quality, resolution, and applicability of assimilation data sources are the key bottlenecks that affect the application of data assimilation in the development of precision agriculture. In the future, the development of data assimilation models tends to be more refined, diversified, and integrated. To sum up, this study can provide a comprehensive reference for agricultural monitoring, yield prediction, and crop early warning by using the data assimilation model.

1. Introduction

Real-time monitoring and precise prediction of large-scale, long-term crop growth processes constitute a pivotal element in ensuring food security and optimizing agricultural production strategies [1]. While traditional empirical statistical models, regression models, and Markov models have provided some degree of support for agricultural production, their limitations in addressing extreme environmental stressors, evaluating crop variety adaptability, and predicting growth cycles have increasingly come to light [2,3]. In response, researchers are actively exploring the integration of Crop Growth Models (CGMs) with Remote Sensing (RS) technology to develop a monitoring and forecasting platform that closely approximates real-world conditions while offering fine-grained spatial information on crop growth [4].

This fusion strategy, integrating RS data with ground-based biomass predictions, enables cross-scale accurate estimation of critical parameters such as crop yield, pest, and disease thresholds [5,6]. This empowers agricultural decision-makers to swiftly respond to various risks and implement precision management measures, thereby enhancing both economic and ecological benefits of agricultural production [7]. Furthermore, delving deeper into the practical applications of such assimilation strategies in precision agriculture not only contributes to the transformation and upgrading of agricultural paradigms but also holds profound practical significance for refining agricultural production systems and fortifying the defense lines of food security [8].

Since the 1970s, RS technology has achieved remarkable advancements across numerous fields, particularly demonstrating immense potential in agricultural monitoring, crop yield estimation, and precision agriculture applications. This is largely due to its unique advantages such as synchronicity, timeliness, continuous coverage, and extensive observation ranges [9,10]. With further technological development, a series of quantitative inversion products closely related to crop physiological and biochemical parameters have emerged, providing rich and valuable data resources for agricultural early warning, monitoring, and yield assessment [11,12,13,14,15]. For example, in agriculture, horticulture, plant science, and other fields, the use of remote sensing data for plant growth modeling can significantly improve the accuracy and efficiency of the model [16,17,18,19].

Moreover, studies have shown that RS technology also exhibits broad application value in revealing environmental change dynamics, agricultural forecasting, and monitoring [20,21,22,23,24]. However, it still faces significant limitations in deeply uncovering crop growth mechanisms and intricately characterizing the complex interactions between crops and their environment [14]. Externally, this manifests as issues with poor temporal and spatial continuity, limited model fitting accuracy, and insufficient generality [4,25]. Additionally, the substantial costs and time required to process vast amounts of RS data represent a major challenge hindering its widespread application in the agricultural sector.

Compared to RS technology, CGMs operate within a rigorous mathematical framework, enabling them to meticulously track the dynamic physiological and ecological processes of crops [26]. Studies demonstrate that CGMs, through their deep understanding of the intertwined effects of intrinsic crop growth patterns and environmental factors, have become effective tools for simulating crop growth dynamics and multi-dimensional yield prediction [27]. Different from models that simply rely on meteorological statistics, CGMs comprehensively consider atmospheric conditions, soil characteristics, crop genetic traits, and field management practices, which can more accurately simulate the actual growth trajectory of crops and effectively solve the shortcomings of complex system modeling [28]. The process-oriented nature, mechanism analysis, and temporal dynamics of CGMs are crucial for understanding the intricate behaviors of agricultural production systems [25]. To delve further into the latest developments concerning CGMs’ application in data assimilation, we conducted a literature review focusing on key terms like “data assimilation”, “Crop Growth Models”, and “precision agriculture”. The results revealed the frequency distribution of various models in agricultural applications, as depicted in Figure 1. Evident from the figure, the SWAP model occupies a leading position in assimilation applications with an adoption rate exceeding 30%, while EPIC, WOFOST, and APSIM models are also widely used.

On another front, the most recent CGMs research in agricultural Data Assimilation (DA) emphasizes the focus on precise, detailed, and integrated simulation of crop growth processes, aiming to achieve meticulous operations for crop growth status, yield, and even the entire agricultural production system [29].

Table 1. Crop growth models commonly used for data assimilation and list of precision agriculture applications.

Model Name	Application of Agricultural Assimilation	References
APSIM	Simulate crop growth, soil water, and nutrient dynamics and crop management practices (suitable for crops such as wheat, corn, and soybeans)	[33]
Agromet Shell	Simulated crop growth and yield (Prediction of crop growth and yield changes based on meteorological data)	[34]
Aquacrop	Response of simulated crops to water stress and yield prediction (Suitable for arid and semi-arid areas)	[35]
CERES-wheat	Simulate the growth and yield of wheat (Taking into account a variety of environmental and regulatory factors)	[36]
CROPGRO-Soybean	Simulate crop growth and yield, such as soybeans (The physiological and ecological processes of crops, soil conditions, and management measures were considered.)	[37]
Cropsyst	Simulate the growth, development, and yield of a variety of crops (Suitable for different climate and soil conditions)	[38]
DAISY	Simulate the interaction between soil moisture, nutrients, and crop growth (Suitable for farmland and paddy field management)	[39]
DSSAT	Simulate the growth, yield, and soil dynamics of many crops (Taking into account the impact of climate change and management practices on crops)	[40]
EPIC	Simulate crop growth, soil erosion, nutrient cycling (Sustainable management of agro-ecosystem)	[34]
GLAM	Simulated crop growth and yield are affected by global climate change (The effects of climate change on crop physiological and ecological processes were considered)	[41]
HERMES	Simulation of crop growth and water balance (It is especially suitable for crop management in the Mediterranean climate region)	[39]
STICS	Simulate crop growth, soil moisture, and nutrient dynamics (Suitable for wheat, corn, and other crops and different soil types)	[42]
SUCROS	Simulate the growth and yield of sugar crops, such as sugarcane (The physiological and ecological processes of crops and climatic factors were considered)	[43]
SWAP	Simulation of water cycle and crop growth in farmland system (Suitable for arid and semi-arid areas)	[44]
WOFOST	Simulation of crop growth, yield, and soil moisture dynamics (Crop physiological and ecological processes and climate change are considered)	[45]

summarizes several common CGMs, showcasing their exceptional applicability in the domain of precision agriculture. To a certain extent, CGMs successfully complement the limitations of RS technology in acquiring and processing crop parameter information, especially in elucidating crop growth mechanisms, simulating crop responses under complex environmental conditions, and improving the accuracy and consistency of data interpretation [12,30]. For instance, multiple studies explicitly highlight that in critical areas such as grain yield forecasting, crop fine-scale management, and regional optimization of agricultural resource allocation, CGMs are gradually emerging as vital instruments for assessing and investigating the performance of agricultural production systems [25,26,31,32].

However, despite their excellent performance in theoretical explorations and small-scale applications, CGMs encounter considerable challenges when scaling up to broader geographical or regional levels. Many CGMs are initially designed with a focus on crop growth at the level of individual plots or fields, and their parameter settings and structures tend to be relatively simplified, which makes it difficult to fully capture the complex uncertainties and interactions of meteorological conditions, soil characteristics, and agricultural management practices at the regional scale [46,47]. Therefore, how to overcome these limitations while maintaining the model prediction accuracy, so that CGMs can be effectively applied in precision agriculture scale, is a key research topic in this field.

Fortunately, DA strategies offer a promising solution to effectively integrate the strengths of RS and CGMs and address the aforementioned challenges. DA methods ingeniously combine multisource RS observational data with CGMs simulation outputs, aiming to harness the full potential of both to achieve a more precise and comprehensive understanding of crop growth processes [30,48]. Compared with the methods using RS technology or crop model alone, the data assimilation method has greater flexibility, computational efficiency, and versatility. RS data have injected rich spatial information into CGMs, filling the spatial dimension gap that models usually lack. On the other hand, CGM can take advantage of the rich details of RS to perform more accurate simulations and predictions [49]. This complementary relationship significantly improves the accuracy of crop yield prediction and agricultural situation monitoring and provides a strong technical basis for the transformation of agricultural production to precision and high efficiency [4,30,50]. Therefore, in-depth study of the application of data assimilation in precision agriculture not only helps to overcome the limitations of existing technologies in agricultural monitoring and yield prediction but is also an important driving force to promote the modernization of agricultural production system.

In view of this, we rely on Web of Science, Scopus, and Google Scholar tools to carry out in-depth retrieval around keywords such as “Data assimilation”, “Crop simulation”, and “assimilation algorithm”. The results are shown in Figure 2. We find that the research situation of DA in the field of agriculture presents the following remarkable characteristics. From the time dimension, the research heat of DA in the field of agriculture shows a continuous upward trend, reaching an historical peak in 2022 (see Figure 2a). This shows that with the progress of science and technology and the growth of the demand for agricultural modernization, the application research of DA technology in agriculture is receiving more and more attention and investment. From the spatial dimension, China, the United States, Canada, and other countries are particularly active in the field of agricultural DA research, with fruitful results (see Figure 2b) that may be related to the advantages of agricultural scientific research strength, technological innovation, and policy support in these countries. However, the current research on the DA method in the field of agriculture is still relatively limited, which may be closely related to the consideration of assimilation cost, the difficulty of technology implementation, the complexity and variability of agricultural production itself, and so on. Although some scholars have combed and summarized the progress of the application of DA in agriculture in detail, and achieved a series of important research results [30,51,52], it is undeniable that there are still significant gaps in the following aspects:

• The choice of emerging RS platform DA: in the face of an endless stream of new generation RS data (such as satellite constellation, UAV, new RS platform, high space-time resolution, etc.), how to make use of the characteristics of multi-source data, consider application scenarios and cost-effectiveness and other factors, select and effectively integrate these data, and further solve the data source problem of DA is an urgent need for the current research.
• In-depth understanding of the internal mechanism of DA model: there is a lack of discussion on parameter selection and optimization, uncertainty quantification, multi-model fusion, and fine management of the DA model in existing precision agriculture research, which restricts the further improvement of DA model performance and the expansion of agricultural application.
• The applicability of new challenges to DA: under the background of extreme climate change, precision agriculture, and the rise of the agriculture 4.0 digital era, challenges such as the processing of new RS sources of DA, multi-dimensional application scenarios, robust models, and new requirements for high-precision DA have not been fully studied and addressed.

Based on the above analysis, this study will focus on the above issues and provide new ideas for the future development of DA in the field of precision agriculture. Through multi-dimensional literature retrieval and strengthening case analysis, this paper summarizes and analyzes the possible new applications of DA in order to promote the wide application of DA in precision agriculture and help to realize the precision, intelligence, and sustainability of agricultural production.

The structure of the rest of this paper is as follows: the Section 2 describes the remote sensing data source, platform, and framework of data assimilation in detail. The Section 3 systematically analyzes the latest development of precision agriculture data assimilation model strategy. The Section 4 discusses the main challenges and future prospects of data assimilation. The Section 5 part is the conclusion. Finally, there is a list of references.

2. Materials and Methods

2.1. Assimilation of Agricultural Data Sources by Remote Sensing

In recent years, DA has made remarkable progress in agricultural practice fields such as crop monitoring, yield prediction, and evaluation [53,54,55,56]. On the one hand, RS data, as an important data source of DA, play an important role in promoting scientific agricultural decision-making; on the other hand, RS data quality, acquisition, management, full chain error, and scale effect all constitute a key bottleneck restricting the effectiveness of DA [48]. This means that selecting and evaluating the universality of RS data is very important to maximize the accuracy of crop yield prediction and agricultural management decision-making. Fortunately, with the rapid development of RS technology, the spatial resolution has leapt from several hundred meters in the past to several meters or even better today, which not only brings unprecedented spatial detail richness and feature recognition refinement to DA but also greatly broadens its depth and breadth in agricultural applications (see Figure 3). In this context, Multispectral data [57,58,59], Hyperspectral data [60,61], Visible light and near-infrared spectra [62,63,64,65,66], as well as various types of RS data such as LiDAR [67,68], are being widely and creatively integrated into the DA process to more comprehensively and accurately characterize the interaction between crop growth status and the environment [69].

2.2. A New Multi-Source Remote Sensing Platform DA

As a new type of RS with the most potential, satellite constellation plays an indispensable role in key fields such as fine water resources management, disaster early warning, and crop yield prediction because of its excellent environmental adaptability, strong comprehensive resolution of multi-parameters, and dual characteristics of wide area coverage and fine monitoring, and provides unprecedented spatial information support for DA work [71]. The satellite constellation consists of a set of carefully planned satellite units that orbit the Earth in a specific orbital layout and configuration, ensuring seamless global coverage and efficient revisit capabilities [72]. It is particularly worth mentioning that the constellation integrates a wide range of sensor devices, including optical cameras (such as panchromatic, multispectral, and hyperspectral cameras), thermal infrared sensors, and microwave radar (such as synthetic Aperture Radar, SAR), etc., which can capture land surface information in an omni-directional and multi-band manner, laying a rich and accurate data foundation for various DA applications [71,73].

Assimilation research in recent years has shown great potential in improving the accuracy and refinement of data analysis. For example, Bouras et al. effectively assimilated Sentinel-2 satellite LAI data into the SAFY model by using ensemble Kalman filtering method, which significantly improved the estimation accuracy of spatial variability of winter wheat yield by more than 70% [74]. Meanwhile, Manivasagam et al. innovatively combined PlanetScope and Sentinel-2 imagery to create a high-density time-series LAI dataset, accurately simulating the dynamic changes in crop yields within fields with notable research outcomes. Additionally, the sub-meter to tens-of-meters high spatial resolution provided by satellite constellations meets the demanding requirements for precise identification of subtle agricultural features [75]. Gilardelli et al. adeptly used remote sensing LAI data to realize fine-grained simulation of rice yields at the sub-field scale [76]. Moreover, Ogweno et al. leveraged the high-resolution datasets from PlanetScope and Sentinel-2, along with advanced machine learning (ML) algorithms such as Random Forest, Support Vector Machines, and Regression Trees, to conduct large-scale Land Use and Land Cover (LULC) mapping with striking classification accuracies, reaching up to 93% and 91%, respectively [77].

Looking ahead, with the successful deployment of Landsat-9 and the anticipated efficient operation of its successor Landsat-Next, coupled with the extensive integration of Dove small satellites from Planet Labs into the DA field, we can reasonably anticipate near-real-time, daily global coverage of RS monitoring, offering timely insights into crop growth conditions [78]. Such advancements will not only elevate the timeliness and accuracy of DA but also substantially bolster the capacity of agriculture and environmental sectors to tackle global challenges, providing robust data support for informed decisions toward sustainable development.

As an important part of modern remote sensing technology, unmanned aerial vehicles (UAVs) have significant advantages compared with remote sensing satellite sensors in terms of mobility, flexibility, safety, cost, ease of operation, response speed, and high-resolution image acquisition ability, and can efficiently capture high-precision details of farmland microtopography, vegetation structure, and water status. UAVs have brought significant innovation and development to the field of data analysis [79,80]. For instance, Yamagishi et al. demonstrated the enormous potential of UAV imaging technology in rapid and non-destructive field phenotyping [81]. Gu et al. utilized a high spatio-temporal resolution UAV-based point spectrometer to significantly improve the accuracy of Sun-Induced Chlorophyll Fluorescence (SIF) measurements at the field scale, opening up a new technological pathway for refined monitoring in agriculture [82]. Concurrently, Xie et al. leveraged UAV multispectral technology to accurately estimate SPAD values across multiple growth stages of lychees, providing a powerful tool for rapid assessment of crop nutritional status [83].

New DA research reveals that the assimilation application value of UAVs is especially pronounced in small-scale, refined agricultural management scenarios. Philippe et al. integrated DA with UAV monitoring and plant parameter estimation techniques to enable real-time monitoring of vegetation health status, providing a scientific basis for precision agricultural management [84]. Additionally, Zhang et al. proposed partial least square method and random forest method to estimate winter wheat grain filling rate (GFR) by using leaf chlorophyll content (LCC) and LAI extracted from UAV images, providing a new perspective for dynamic monitoring of crop growth [85]. Numerous studies have also relied on key parameters related to crop growth status and health obtained via UAVs to provide timely and effective guidance for crop management, propelling DA towards increased intelligence and refinement [86,87,88]. It is worth noting that UAVs possess the capability to rapidly cover vast areas of surface information and can operate in complex terrains and hazardous areas, greatly enhancing the efficiency and accuracy of RS data acquisition [34,89,90]. In summary, the application prospects of UAVs in the precise agriculture DA domain are set to become increasingly broad, and their role in promoting agricultural modernization and boosting agricultural productivity will be even more pronounced.

It is worth noting that the latest technological innovation of the RS platform has injected a strong impetus into the research of DA. The emergence of diversified devices such as ground observation stations, vehicle mobile platforms, and handheld spectrometers greatly expands the breadth and depth of RS data sources, which can effectively make up for the lack of satellite and UAV data and provide near-surface information closer to the actual state of crops, thus significantly improving the accuracy of model assimilation. For example, some researchers have creatively proposed a method of combining multi-sensor ground mapping and representation, which skillfully integrates a variety of heterogeneous but complementary sensor data carried on unmanned rovers to generate a multi-level three-dimensional map of the environment [91]. This technique not only significantly enhances the resolution of mapping texture details, but also opens up a new research approach for DA research. At the same time, Kursch et al. successfully achieved accurate estimation of outdoor vineyard yield by using a consumer-grade RGB-D camera mounted on a mobile robot platform. In addition, they discussed the potential of handheld mid-infrared spectrometers in field fresh soil sampling and real-time analysis, providing strong technical support for soil science research and agricultural precision management [92].

Looking ahead, we can expect greater results from these methods, with the emergence of more high-quality ground observation station data, such as the high-resolution satellite-driven automatic soil observation network SONTE-China, and the multi-spectral sensor system DIEGO deployed on the International Space Station [93]. Zhang et al.’s ground-based RS platform will play an increasingly important role in the field of DA research, starting a new upsurge of scientific research and helping to achieve comprehensive and accurate monitoring and management of agro-ecosystems [94].

2.3. High Spatio-Temporal Resolution Remote Sensing DA

The rise of high temporal resolution satellite constellations has ushered in a stream of high-frequency revisit data, enabling the continuous generation of time series for critical biophysical parameters such as VIs, LAI, and phenology, thereby facilitating seamless and dynamic tracking of crop growth processes [95,96]. This groundbreaking advancement provides an unprecedented level of detailed time series inputs for model assimilation, significantly enhancing the precision modeling capabilities of agricultural ecosystems. In cutting-edge high spatio-temporal resolution DA research, scientists employ Enhanced Spatio-Temporal Adaptive Reflectance Fusion Model to skillfully merge Landsat and MODIS data, yielding composite products with both high spatial and temporal resolutions. These are further combined with models like SAFY to accurately quantify crop yields [97]. Additionally, by leveraging RS, reanalysis, and in-situ datasets, advanced point-to-surface fusion techniques like GRASPS create high-resolution, accurate, and seamless maps of surface SM distribution, significantly improving monitoring accuracy of agricultural water status [98].

Of particular note, high spatial resolution satellites demonstrate unparalleled advantages in revealing within-field heterogeneity, rapidly identifying crop disease patches, and precisely assessing the effects of management practices [99,100,101]. This suite of achievements suggests that continuously exploring and innovating in multi-source RS data fusion methods holds the promise of continually enhancing spatial and temporal resolution, thus pushing the application of DA in the agricultural sector into deeper realms [102,103,104]. Specifically, recent studies have proposed a series of innovative models and frameworks, such as Dual-Branch Convolutional Neural Networks (DB-CNN), the Cascade-PSPNET model integrating Bayesian theory with deep learning (DL) algorithms, and the Spatio-Temporal Fusion (STF) framework, all of which have achieved remarkable results in practical applications [105,106,107]. Fundamentally, it is the continuous innovation and progress of RS data sources that provide unprecedented high spatiotemporal resolution data support for DA research, driving the innovation and application leap of agricultural RS technology in the field of DA.

2.4. The Mechanism and Framework of DA

In recent years, the deep integration of RS technology and CGMs has brought significant innovation power to the DA method in the agricultural field and has shown great potential for application is undoubtedly worthy of recognition [44,108,109,110]. The core mechanism of DA is to use mathematical theory and advanced model algorithms to combine the multi-dimensional and high spatio-temporal resolution observation data from RS platform with the internal biophysical process simulation of CGMs so as to bridge the gap between model simulation and actual observation and enhance the simulation accuracy and predictive behavior of the model to complex agricultural systems [52,111]. To some extent, based on proficiency in RS data analysis, CGMs, and other professional skills, and a deep understanding of the internal mechanism of DA, building an efficient and adaptable assimilation framework is the top priority of DA. A simple assimilation framework is shown in Figure 4.

The DA framework encompasses four core steps: RS observation acquisition and processing, model simulation and parameter setting, assimilation algorithm application, and cyclic iterative updating [112]. RS observation focuses on acquiring high-resolution RS images, involving the integration of multi-source RS data, preprocessing (including radiometric calibration, atmospheric correction, geometric correction, and error elimination), and data fusion techniques (such as super-resolution, multi-scale fusion, and spatio-temporal filtering) to inversely derive vegetation bio-chemical parameters for assimilation input. In the model simulation stage, suitable numerical models and observation operators are selected based on input parameters, generating an integration of bio-chemical parameters, establishing model and parameter errors, and employing diverse assimilation strategies to assess the feasibility of observational data, which, when available, are incorporated into the CGMs. The assimilation algorithm stage employs statistical methodologies (e.g., Kalman filtering, variational methods) or physically-based approaches (like 4D-Var, Ensemble Kalman Filtering) to identify the optimal state estimate via the model’s internal residuals, constructing the framework of the assimilation process system. Lastly, during the iterative updating cycle of assimilation, key state variables are selected and updated by the assimilation algorithm, driving the CGMs to update according to the new state until all updates conclude, yielding the final predictive outcome [111,113].

3. Results

Exploring the DA model with low cost, strong versatility, and strict mechanisms has become one of the research hotspots in the field of precision agriculture assimilation. Therefore, by combing the literature, we summarize the mechanism process and evolution trend of the DA model, as shown in Figure 5. The development track of the DA model gradually develops from simplification to refinement, diversification, and integration. From the initial simple forcing method, which is slightly rough due to the accumulation of model errors due to over-reliance on observations, to the innovation of DA model under Bayesian paradigm, such as Markov chain Monte Carlo (MCMC) algorithm, Variational Bayes, and Bayesian coupling, it undoubtedly marks a great improvement in the theoretical framework and a great leap in domain performance. In addition, the development of the DA model continues to expand in the direction of computational efficiency and parallelization, multi-source data fusion and multi-assimilation strategy coupling, model universality enhancement, and so on.

3.1. Forcing Method

Forced mode assimilation, as a straightforward and simple DA approach, has been extensively adopted in crop growth monitoring [114]. Its fundamental principle involves directly utilizing RS observational data as external driving forces for CGMs, bypassing complex mathematical optimizations or probabilistic statistical treatments. Instead, it relies on the model’s inherent dynamical mechanisms to respond to these external signals, aiming to align model outputs with actual observations [30], as shown in Figure 6. The assimilation model has the advantages of intuition, high efficiency, and no iteration, and plays an important role in the study of early crop DA. Its achievements are mainly focused on the accurate simulation of aboveground biomass and yield [115,116,117,118].

Simultaneously, these studies have vividly exposed the limitations of the Forced mode assimilation; for instance, it is highly sensitive to external driving factors but tends to overlook fluctuations in the model’s internal states. Furthermore, it heavily depends on RS observational data and has limited capacity to deal with uncertainties in the model’s internal states. These constraints are evident in the context of precision agriculture applications [119]. Thus, facing potential nonlinear and non-Gaussian processes in future large-scale and complex application scenarios, it is imperative to explore the integration and innovation of the forced mode assimilation with more advanced DA methods, such as variational assimilation and filtering assimilation. Through such integration, we can effectively enhance the accuracy and robustness of DA, thereby addressing the challenges in the agricultural domain in the future [120].

Figure 6. The assimilation strategy framework of yield prediction is driven directly by assimilation model based on crop canopy temperature as input. Notes: DBA is dry biomass accumulation, kg ha⁻¹; FBA is fresh biomass accumulation, kg ha⁻¹; RDBA is relative DBA; RFBA is relative FBA [121].

Figure 6. The assimilation strategy framework of yield prediction is driven directly by assimilation model based on crop canopy temperature as input. Notes: DBA is dry biomass accumulation, kg ha⁻¹; FBA is fresh biomass accumulation, kg ha⁻¹; RDBA is relative DBA; RFBA is relative FBA [121].

3.2. Model Parameter Optimization DA

In contrast, model parameter optimization methods (also known as continuous assimilation methods) are more suitable for complex and refined agricultural scenarios. At the heart of this approach lies the iterative adjustment of model initial parameters within a given reanalysis time window T, where all available observation data and model state values are used as a foundation to strive for the best possible fit between the model trajectory and observed data [109,122,123,124]. Particularly noteworthy among these methods is the Four-Dimensional Variational (4D-Var) algorithm, which builds upon the three-dimensional version by incorporating temporally evolving background information. It transforms the assimilation problem into a search for the optimal solution of the dynamic model, effectively integrating all observational results over a specified time period [125,126,127]. The core mechanism of 4D-Var is shown in Formulas (1)–(3) [128,129]:

$$J\left(X_0\right)={\displaystyle \frac{1}{2}}{\left[X_0-X_0^b\right]}^T{B}^{-1}\left[X_0-X_0^b\right]+{\displaystyle \frac{1}{2}}{\sum }_{i=1}^n{\left[H\left(X_i\right)-Y_i\right]}^T{R}_i^{-1}\left[H\left(X_i\right)-Y_i\right]$$

(1)

where $J\left(X\right)$ is the cost function of 4D-Var, X and Y represent the model state variable and observation, respectively, $X_0$ represents the initial value of the state variable, $X_0^b$ is the background field of the state variable, $X_0^b$ is the prior estimate of $X_0$, B and R represent the covariance matrix of the background field and the observation field, respectively, and H is the observation operator. $X_i$ is the model prediction value at time i and $Y_i$ is the observation vector at time i. $X_i$ is obtained from the integral prediction equation M:

$$X_i=M_{i-1}\left(X_{i-1}\right)$$

(2)

In 4D-Var, the minimum objective function J is solved to obtain the optimal $X_0$. First, the gradient information of the objective function is required:

$$\nabla J\left(X_0\right)=B^{-1}\left(X_0-X_0^b\right)+{\sum }_{i=0}^n{M}_{0\to i}^T{H}^T{O}^{-1}[Y_i-\left(H_i\right)]$$

(3)

where the adjoint of the second term on the right solves the gradient through the inverse integral of the adjoint equation, and the following assumptions are made in the calculation process:

• $M_{0\to i}^T$ represents the mode prediction operator from 0 to i, and has $X_i=M_{0\to i}^T{X}_0$, and the forward prediction mode can be expressed as the product of the intermediate prediction mode, that is, $X_i=M_{i-1\to i}\cdots M_{0\to 1}{X}_0$.
• Under the tangent linearity hypothesis, the pattern operator and the observation operator are linearized, that is, $X_i-X_0\approx M_{0\to i}^{\prime }(X_i^b-X_0^b)\approx H^{\prime }(X_i^b-X_0^b)$, where $M_{0\to i}^{\prime }$ and $H^{\prime }$ are the tangent operators of the pattern operator and the observation operator, respectively, and the minimum value of J is solved by gradient descent or conjugate gradient method. The obtained $X_0$ is the optimal solution of the initial state.

The current 4D-Var research either focuses on the selection of assimilation parameter variables [44,62,130] or on the optimization of cost function [108,131]. As shown in Figure 7, the assimilation framework based on the 4D-Var model is shown in detail. Based on this model, many scholars have achieved satisfactory results. However, the latest research shows that there are challenges in the application of precision agriculture [132,133,134,135].

First, based on the statistical normal distribution hypothesis and tangent linear hypothesis, 4D-Var simplifies the complexity of the model, but when dealing with strong nonlinear or significant model errors, linearization approximation may lead to gradient information distortion and increase the uncertainty in the process of assimilation [135]. Second, 4D-Var is extremely sensitive to the selection of initial conditions, and improper initial values may cause the algorithm to fall into local optimization or face difficulties when trying to converge, so it is necessary to carefully evaluate the effectiveness of initial values and seek more robust optimization algorithms. Although some scholars consider using Jacobian matrix to optimize the initial conditions and parameters of the model, it controls the gradient information, determines the search direction and step size, and then considers the model continuity [136]. However, for large-scale, high-resolution models, the calculation of the Jacobian matrix often requires significant computing resources and memory, and the effect is not always as expected. Sparsity and parallel computing technology can alleviate this problem to some extent, but for extremely large-scale problems, the computing cost is still high. At the same time, although the finite difference method is often used in gradient approximation, it may have adaptability problems in high-dimensional cases [137,138]. Therefore, the dimensions and characteristics of the data should be fully considered when selecting and applying the gradient approximation method [139]. As the selection of assimilation parameters also has an impact on the results, the selection of parameterization schemes and physical processes will also bring uncertainty to the data analysis results [140]. Based on this, we extract the following possible solutions:

• Explore the advantages of optimization algorithms such as conjugate gradient method and quasi-Newton method in solving gradient problems. Global optimization techniques such as multiple startup, simulated annealing, and genetic algorithm were used to improve the initialization and optimization strategy of the algorithm and improve the convergence and stability of the algorithm [113]. Try to calibrate the sensitivity error of the initial conditions based on the model.
• Search for nonlinear framework: To solve nonlinear uncertainty, explore and develop nonlinear variational assimilation frameworks, such as manifold embedding variational method (ME-Var), four-dimensional variational filtering (4D-VARF), etc. For example, the anisotropic background error and time-window four-dimensional variation algorithm constructed by Wu et al. provides us with valuable reference experience [141].
• Focusing on uncertainty characterization and quantification. Introducing set members to model uncertainty: set Kalman filtering idea, and developing assimilation methods such as set four-dimensional variational (En-4D-Var) [142]. In terms of physical and chemical parameters, we need to pay attention to the quantification of the uncertainty, reduce the uncertainty through the integration of assimilation methods, and improve the adaptability and scalability of assimilation algorithms.
• Using ML and AI to improve DA efficiency: Using advanced technologies such as GPU acceleration and distributed parallel computing to develop low-rank or reduced-order models to improve computing efficiency and reduce computing costs [143,144,145,146].

3.3. Model Status Update DA

Ensemble Kalman filter (EnKF) is an assimilation algorithm that combines the advantages of ensemble prediction and Kalman filter. It was first proposed by Evensen and later described in detail by Burgers et al. [147,148]. The model state update assimilation process is shown in Figure 8. Its core operational mechanism involves two main stages: prediction and update [149,150]. Its core mechanism is shown in Formulas (4)–(9) [74,151,152]:

• Forecast

$$X_{i,k+1}^f=M_{k,k+1}\left(X_{i,k}^{\mu }\right)+{\omega }_{i,k}, {\omega }_{i,k}~N\left(0,Q_k\right)$$

(4)

where, $X_{i,k+1}^f$ represents the predicted value of the i th state variable at time k + 1, $X_{i,k}^{\mu }$ represents the estimated value of the ith state variable at time k, $X_{i,k}^{\mu }$ represents the state transition matrix from time k to time k + 1, ${\omega }_{i,k}$ represents the model error, which obeys the Gaussian distribution with mean 0 and covariance matrix $Q_k$.

• Update

$$X_{i,k+1}^{\mu }=X_{i,k+1}^f+K_{k+1}\left[Y_{k+1}^o-H_{k+1}\left(X_{i,k+1}^f\right)+v_{i,k}\right], v_{i,k}~ N\left(0,Q_k\right)$$

(5)

$${\overline{X}}_{k+1}^{\mu }={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{X}_{i,k+1}^{\mu }$$

(6)

$$K_{k+1}=P_{k+1}^f{H}^T{\left(H{P}_{k+1}^f{H}^T+R_k\right)}^{-1}$$

(7)

$$P_{k+1}^f={\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left(X_{i,k+1}^f-H\left({\overline{X}}_{k+1}^f\right)\right){\left(X_{i,k+1}^f-\left({\overline{X}}_{k+1}^f\right)\right)}^T$$

(8)

$$H{P}_{k+1}^f{H}^T={\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left[H\left(X_{i,k+1}^f\right)-H\left({\overline{X}}_{k+1}^f\right)\right]{\left[H\left(X_{i,k+1}^f\right)-H\left({\overline{X}}_{k+1}^f\right)\right]}^T$$

(9)

where $X_{i,k+1}^{\mu }$ is the updated estimate of the ith state variable, $K_{k+1}$ represents the Kalman gain, $Y_{k+1}^o$ is the new observation value, $H_{k+1}$ is the observation matrix, and $v_{i,k}$ is the observation error, which follows the Gaussian distribution with the mean of 0 and the covariance matrix of $Q_k$. ${\overline{X}}_{k+1}^{\mu }$ represents the average estimate of all state variables, $P_{k+1}^f$ represents the prediction error variance matrix, and $R_k$ is the observed noise covariance.

It is found that the EnKF model is most widely used in precision agriculture assimilation, especially in combination with WOFOST, CERES, and SAFY swb models [153]. In addition, the model is often assimilated as physicochemical parameters (such as LAI, SM, NDVI) for yield prediction, and more results have been achieved [154]. Recent DA studies show that EnKF focuses on in-depth exploration of uncertainties associated with multi-source RS assimilation and model blending errors. Some researchers have integrated diverse RS data sources, such as MODIS, Landsat-8, HJ-1 A/B, and Sentinel-2, into the EnKF framework to optimize CGMs simulation performance [155,156]. Other studies have combined MCMC algorithms [157] or hybrid complex evolutionary algorithms with EnKF to recalibrate CGMs parameters and assimilate time-series data like LAI into the models, significantly enhancing simulation accuracy [135]. Li et al. effectively improved the estimation method for winter wheat yields by employing an EnKF strategy to assimilate spatiotemporal LAI into the CERES wheat model, considering factors such as observation error, assimilation stage uncertainty, and temporal-spatial scale variability [5]. Despite these advancements, EnKF still faces several challenges in the field of precision agriculture that require resolution.

In general, EnKF is built upon the assumption of Gaussian distributions for system state and observation errors. However, in practical applications, nonlinear factors such as extreme weather, pests and diseases, light, temperature, moisture, and fertilizer may cause state variables to deviate from Gaussian distributions, exhibiting non-Gaussian characteristics like heavy tails or sharp peaks and leading to inaccurate covariance calculations. Although EnKF can calculate the covariance of prior state vectors using samples from the prior distribution, its effectiveness can be limited when dealing with non-Gaussian properties. Consequently, non-parametric methods like Particle Filtering and Iterative Expectation-Maximization (EM) algorithms, all Gaussian assumptions, emerge as strong alternatives to EnKF [158,159].

Furthermore, EnKF usually estimates the covariance matrix by the differences between the set members. However, when dealing with high-dimensional systems, smaller integration sizes can lead to underestimation or overestimation of covariance, manifested by filter divergence or over-reliance on observed data [160,161]. To address this problem, common strategies include introducing an inflation factor to increase Kalman gain and adopting an adaptive mechanism to dynamically adjust covariance matrix parameters based on historical filter performance and observed data characteristics [162]. In the future, the Schur product (also known as the Hadamard product), which refers to a new matrix formed by the product of the corresponding elements of two matrices in the context of data assimilation, can be used to localize the covariance matrix, that is, to preserve only the covariance between the observation points and the model states that are spatially close. The covariance between distant points is set to zero (or smaller) or the Gaspari-Cohn function (Gaspari and Cohn proposed a smooth truncation function in 1999), which is often used as a localized kernel, that is, the smooth decay from the center (i.e., the observed position) outward to zero, ensuring that the covariance of the neighboring region is fully utilized, and the covariance of the distance between the two points is set to zero. Distant covariances are gradually ignored, and other methods are expected to reduce the number of conditions in the covariance matrix, thereby improving the estimation accuracy [163].

In addition, EnKF faces challenges in dealing with discontinuous processes such as threshold effects, saturation phenomena, or discrete events [164], as the assimilation results are no longer significantly updated or improved despite the input of new observational data after the data reach a certain threshold. There are two main coping strategies: the first is to convert non-Gaussian observations to approximate Gaussian distributions through techniques such as piecewise linearization, logarithmic transformations, Box-Cox transformations, and TPCM pairing [165]. The second option is to take the non-Gaussian process model directly and solve for the Kalman gain using the Jacobian matrix or Newton iterative methods, although this may increase the computational cost [136]

It is noteworthy that recent EnKF research highlights that enhancing its scalability and adaptability is crucial when confronted with complex nonlinearity, non-stationarity, uncertainties, and model errors arising from high-resolution RS, unmanned aerial vehicle hyperspectral data, and extreme climates and changing farming systems [166]. Specific strategies include explicitly incorporating model error terms, implementing weighted fusion of multiple models, adopting advanced smoothing-filtering algorithms like Ensemble Square Root Filter (EnSRF) [167], and exploring ML-based automatic parameter adjustment algorithms and feedback mechanisms [168,169]. These measures hold promise to bolster EnKF’s performance in complex agricultural RS applications, preparing it to tackle future challenges.

3.4. Bayesian Normal Form DA

Particle filtering (PF), as a recursive Bayesian filtering algorithm, has gained significant attention due to its superior capabilities in handling non-Gaussian and nonlinear systems [30,60,170]. PF generates a set of particles through random sampling, representing the probability distribution of the system state, and approximates the posterior probability of state variables by weighting and summing these particles [171]. Its core mechanism is shown in Formulas (10)–(15):

Hypothesis from the posterior probability distribution of the state variables $P\left(x_k\right|z:k)$ to extract the N particles ${\left\{x_K^i,{\omega }_k^i\right\}}_{i=1}^N$, the state of the posterior probability density distribution by the following formula approximation obtained [5]:

$$P\left(x_k\right|z_{1:k})\approx {\omega }_k^i{\sum }_{i=1}^N\delta \left(x_k-x_k^i\right)$$

(10)

where, $\delta$ represents the Dirac function, k represents the time, $x_k^i$ represents the particle’s state value, $x_k^i$ represents the particle’s weight, $z_k$ represents the observed value, and $P\left(x_k\right|z_{1:k})$ represents the posterior probability distribution. Generally speaking, the posterior probability density of the state variable is unknown, so it is difficult to obtain the posterior distribution density function by direct sampling. To solve this problem, this study adopts Sequential Importance Sampling (SIS), that is, sampling from an importance distribution function $q\left(x_k\right|z_{1:k})$ whose probability distribution is the same as $P\left(x_k\right|z_{1:k})$, whose probability distribution is known and easily sampled. The importance weight of the particle is [172]:

$${\omega }_k^i\infty {\displaystyle \frac{P\left(x_k\right|z_{1:k})}{q\left(x_k\right|z_{1:k})}}$$

(11)

The method mainly uses recursive ideas to calculate the weight of particle importance [173]:

$${\omega }_k^i={\omega }_{k-1}^i{\displaystyle \frac{P\left(z_k\right|x_k^i\left)P\right(x_k^i\left|x_{k-1}^i\right)}{q\left(x_k^i\right|x_{k-1}^i,z_k)}}$$

(12)

Which $q\left(x_k^i\right|x_{k-1}^i,z_k)$ is the importance sampling function, $P\left(z_k\right|x_k^i)$ is the likelihood function, and $P\left(x_k^i\right|x_{k-1}^i)$ is the prior probability distribution function. In order to calculate simply, we usually choose to render $q\left(x_k^i\right|x_{k-1}^i,z_k)=P(x_k^i\left|x_{k-1}^i\right)$, there are [174]:

$${\omega }_k^i={\omega }_{k-1}^{i}P\left(z_k\right|x_k^i)$$

(13)

Therefore, the updated particle weights can be as follows [5]:

$${\omega }_k^i={\displaystyle \frac{{\omega }_k^i}{\sum _{i=1}^N{\omega }_k^i}}$$

(14)

Through this processing, the estimation of the final state variable is the weighted average of all the state values of the particles [172,173,174].

$${\widehat{x}}_k={\sum }_{i=1}^N{\omega }_k^i{x}_k^i$$

(15)

In agricultural research, PF has been widely applied in various CGMs (e.g., WOFOST, CERES-Wheat, APSIM, etc.) and the assimilation of key parameters such as LAI, significantly improving the accuracy of simulating crop yield, biomass, SM, and hydraulic parameters [175,176,177,178,179,180,181], as depicted in Figure 9, which shows a framework for assimilation based on PF. Meanwhile, research efforts have focused on the improvement and optimization of PF technology, including residual resampling, residual remapping, sensitivity analysis, PF-MCMC methods, and utilizing rigorous evaluation metrics such as RMSE and normalized RMSE [179,182,183,184].

It is important to note that several assimilation methods mentioned above either rely on analytical equations, cost function minimization, or solving covariance matrices, and often depend on a series of assumptions, such as the tangent linearity assumption, initial values following normal distributions, and Gaussian error structures [186]. When confronted with explicit non-Gaussian and nonlinear processes, adhering to Gaussian assumptions can not only result in suboptimal performance but can also lead to misleading results [187]. Against this backdrop, the importance of MCMC-based stochastic sampling methods becomes evident, offering a more flexible and effective solution. MCMC methods excel at drawing samples from complex posterior distributions, particularly demonstrating their strengths when dealing with problems involving non-normality and multimodality that are difficult to sample directly. By constructing a Markov chain and iteratively updating it according to predefined transition rules (such as the Metropolis–Hastings algorithm or Gibbs sampling), these methods ensure that the stationary distribution of the chain aligns with the target posterior probability distribution [188]. In theory, once the Markov chain reaches its stationary state, the sampling comprehensively covers the support region of the posterior distribution. However, in high-dimensional spaces, the Markov chain might require a long “burn-in period” and numerous iterations to converge, resulting in decreased sampling efficiency, commonly referred to as the “curse of dimensionality” [189]. To verify convergence to the target distribution, diagnostic indicators such as Gelman–Rubin statistic (R-hat) and effective sample size are usually employed [190]. In practice, combining MCMC with other methods or algorithmic improvements might be necessary to enhance efficiency and practicality. As shown in Figure 10, the basic steps of the Metropolis–Hastings MCMC method alongside the PF algorithm illustrate the operational framework of this methodology.

Consider that if the PF is placed in a high-dimensional and long-running scene, most of the particles may have very little weight, and only a few particles have significant weights, resulting in the decrease of the effective coverage of the filter to the state space and the loss of particle diversity, which is the so-called “particle degeneration” problem [192,193]. To deal with this problem, researchers have proposed a series of strategies, such as increasing the number of particles, introducing dynamic particle proliferation or an elimination mechanism, and using adaptive particle number adjustment in order to maintain the diversity of particle systems [194]. However, although these methods can improve the uncertainty estimation, they also increase the computational burden accordingly. To reduce the computational overhead while maintaining the diversity of particles, the researchers also tried to dynamically adjust the resampling threshold, resampling method [195], or migration distribution according to the current particle distribution characteristics (such as entropy and effective number of particles). It is worth noting that the traditional resampling techniques (such as system sampling, importance sampling, etc.) may fail in high-dimensional complex environments [30,124]. It is therefore necessary to employ more complex and computationally expensive strategies such as multivariate kernel density estimation and stratified sampling [196].

On the other hand, the performance of PF depends largely on the choice of initial particle distribution [197]. To avoid particle degradation or falling into local optimization, a priori knowledge, historical data, or model simulation results can be used to intelligently select or generate the initial particle distribution. In addition, PF involves multiple parameter adjustments, and the development of adaptive parameter adjustment algorithms, such as joint probabilistic data association-particle filter, can help to better meet these challenges [171,198]. Although these optimization methods do improve the performance of PF, they also increase the complexity and computational requirements of the algorithm. However, the core advantage of PF in dealing with non-Gaussian processes is always the key to gain a foothold in practical applications [199]. Therefore, in practical applications, we should comprehensively weigh various factors according to the specific situation and select the most appropriate algorithm and optimization strategy.

Hierarchical Bayesian Methods (HBMs), pioneered by Wikle et al. and Berliner et al. [200], are particularly adept at handling complex agricultural datasets with hierarchical or nested structures. Their essence lies in decomposing problems into distinct levels and employing conditional probability distributions to precisely describe the inherent relationships between these levels. This approach transforms the daunting task of solving a complex joint probability distribution into a series of more manageable posterior probability calculations, significantly streamlining the process [201]. HBMs typically consist of three components: a lower-level data model, a mid-level dynamic model, and a top-level parameter model [202]. Its core mechanism is shown in Formulas (16)–(21): In order to ensure the observation error, $ϵ$ is introduced to represent the error term [203].

$$y=\mathrm{H}x+ϵ$$

(16)

In the formula, y represents the observation vector, which contains a series of observations for the real state x, which represents the actual state of the system at a certain time or space (temperature, wind speed), and H is the observation operator (or observation matrix). On the questions of how the observed data are generated from the real state, it can be a case of simple scalar multiplication (for example, a single observation point directly corresponds to a state variable), or it can be a more complex function (for example, RS observation is associated with the real state through the sensor response function). $ϵ$ is the observation error vector, which represents the deviation between the observed data and the real state. In general, we assume that $ϵ$ obeys multivariate normal distribution.

$$ϵ~\mathrm{N}\left(0,\mathrm{R}\right)$$

(17)

Among them, R is the observation error covariance matrix, which reflects the correlation between observation errors and their respective variances. Then we give two expressions of the middle dynamic layer, including as many different application scenarios as possible. The first one represents the dynamic model as a set of partial differential equations [53]. That is:

$${\displaystyle \frac{\partial T}{\partial t}}=D\left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}\right)+f\left(x,y,t\right)$$

(18)

In the formula, $T\left(x,y,t\right)$ is expressed as a temperature field, D is a heat conduction coefficient, and $f\left(x,y,t\right)$ represents an external heat source or boundary condition. This kind of equation is usually solved by finite difference and finite element method discretization. In the second way, we regard dynamic behavior as a random walk process (considering one-dimensional random walk model), and consider the trend and fluctuation of state variables, whose state evolution follows [204]:

$$d{x}_t=\mu dt+\sigma d{\mathrm{W}}_t$$

(19)

where $x_t$ is the state variable of $t$ at the time point, $\mu$ is the drift rate (long-term trend), $\sigma$ is the diffusivity (fluctuation amplitude), and ${\mathrm{W}}_t$ is the standard Brownian motion (Wiener process), indicating random disturbance. The top-level parameter model is mainly used to describe the parameter uncertainty (the error term of the data model and/or the coefficient of the dynamic model). It usually satisfies a certain prior distribution, based on our preliminary understanding or empirical estimation of them. For example, the coefficient $\theta$ of the dynamic model satisfies [203,204]:

$$\theta ~p\left(\theta \right)$$

(20)

Note: $p\left(\theta \right)$ is not only Poisson distribution, but may be uniform distribution, normal distribution, or Gamma distribution, which depends on prior knowledge. For the observation error covariance matrix $\mathrm{R}$ in the data model, if there is a correlation between its elements, the inverse Wishart distribution may be used as its a priori.

$$\mathrm{R}~\mathrm{I}\mathrm{W}\left(\nu ,\mathrm{S}\right)$$

(21)

where $\nu$ represents the degree of freedom parameter and $S$ represents the status matrix.

In practical DA procedures, initial prior distributions of parameters, combined with observational data, are updated through a Bayesian theorem to yield posterior distributions, thereby obtaining optimal parameter estimates or their probability distributions [205]. Thanks to its flexibility, efficiency, strong explanatory power, and robust handling of uncertainties, HBM has found wide application in fields including environmental science, oceanography, meteorology, and others [206,207,208,209,210]. However, its adoption in precision agriculture remains nascent, with numerous challenges still to overcome. For instance, dealing with multi-level uncertainties and computing high-dimensional posterior distributions within HBMs often employs MCMC sampling techniques. Hadley et al., within an HBM framework for assimilating IMTA models, successfully estimated the posterior distributions of state variables and parameters along with their uncertainties using Particle MCMC [211]. Nonetheless, when models have numerous parameters and dense observation data, this can significantly escalate computational costs during assimilation [212,213]. Addressing this, Zhang et al. employed Hamiltonian Monte Carlo (HMC) sampling to effectively mitigate such high computational expenses [214]. Moreover, gradient-based inference methods like variational inference, approximate Bayesian computation, and rapid assimilation algorithms such as PF are also worth exploring and applying [215,216].

In practice, while simplifying assumptions are often made based on linear problems, the presence of nonlinearity, non-stationarity, and multi-scale effects can, in reality, lead to intricate prior distributions and covariance structures in parameter models, complicating model construction and solution [217,218]. Techniques such as mode averaging and Principal Component Analysis (PCA) for dimensionality reduction are commonly used to decrease the number of parameters and alleviate computational loads [219]. With advancements in computational power and deeper understanding of physical processes, emerging methods like Bayesian analysis based on DL and Approaches combining Visual Salience with Hierarchical Bayesian hold promise to further advance HBM assimilation techniques in precision agriculture, ushering in new application opportunities [220,221].

4. Discussion

4.1. Challenges Faced by DA in Agricultural Application

4.1.1. Deep Fusion and Uncertainty Management of Multi-Source Heterogeneous Data

The issue of assimilation accuracy, to some extent, stems from data challenges, and the integration of multi-source heterogeneous data (such as RS, meteorological data, field observations, drone inspections, model simulations, etc.) offers a potential solution to this challenge [222]. However, the discrepancies in RS data currently used in agriculture are among the primary obstacles limiting the deep fusion of such multi-source and heterogeneous datasets. RS data with varying spatial, temporal, and spectral resolutions, as well as scale differences, when used as inputs to drive CGMs, can steer the evolution of model simulation accuracy and reliability in different directions [223,224,225]. Figure 11 vividly illustrates the disparities among different satellite sensors in terms of spectral, spatial, temporal, and radiometric resolution and scale. Generally, for regional-scale applications like regional water-saving irrigation, global climate change monitoring, and earth resource surveys, medium to low-resolution data from sources like MODIS and Sentinel-3 is sufficient [226,227]. Conversely, for local, real-time scale applications such as environmental monitoring and disaster emergency response, the demand for high precision and real-time data is extremely high, necessitating high-resolution RS data [228,229]. It is noteworthy that the acquisition and utilization of RS data in actual agricultural applications are not proactive processes and often overlook the significance of the differences in RS data (resolutions, time steps, observation modes, error characteristics, etc.), thereby increasing the complexity of integrating multiple RS datasets [230,231].

On the one hand, errors in observational data are inevitable, and even when actual crop growth data are obtained, they often suffer from sparsity in both space and time, potentially leading to insufficient fused information and degradation of data precision and quality [232]. For instance, in large-scale SM monitoring, due to resource constraints, only a limited number of monitoring stations can be established, with considerable distances between them, making data points across the entire farmland appear sparse. Additionally, instrument inaccuracies, environmental factors (like wind direction and cloud thickness), and human operational errors all introduce biases [140,162]. On the other hand, during data fusion, there is a lack of consideration for how well CGMs adapt to the data, as there are no visual references, leading to the natural absorption of correlation errors introduced by the diversity in RS data. Models may fail to fully represent crop conditions, especially when ground practices and climate impacts are not reliably understood, focusing more on critical parameter inputs and direct replacements. If certain CGMs data are not suitable for the current study area or climatic conditions, they can introduce substantial errors, propagating uncertainties in multi-source integration, which highlights the importance of incorporating a development agenda aimed at refining imperfect models to align with actual crop development, thereby mitigating uncertainties and errors [233,234]. With the rapid advancement and broad application of precision agriculture assimilation, fully considering and implementing a development agenda to guide precise decision-making, cross-sectoral resource integration, and addressing new scenario challenges is of vital importance.

Moreover, data quality control and uncertainty quantification are crucial considerations in the multi-source integration process. The quality of RS data from diverse sources and structures may vary greatly, and if rigorous selection of RS data quality is not performed, the fused outcome could potentially be less accurate than the original datasets [235,236]. This necessitates emphasis on steps such as data cleaning, deduplication, transformation, and validation to eliminate or reduce noise, outliers, and errors in the data [237]. For example, when studying the impact of climate change on crop yields, sensitivity analysis of parameters and uncertainty analysis should follow modeling to ensure decisions are made within controllable ranges, enhancing the accuracy and reliability of the fused results [238,239].

Nonetheless, the deep integration of multi-source heterogeneous data and uncertainty management in CGMs assimilation also confronts numerous challenges [240,241,242]. Some studies strive to optimize data fusion algorithms, theoretically providing higher quality data for assimilation, but many existing methods overlook complementarity and potential conflicts among datasets, potentially leading to failed fusion in practical agricultural contexts [243,244]. Hence, the development of more sophisticated inter-source relational modeling algorithms, such as those based on ML and DL fusion algorithms (e.g., SWPanGA super-resolution, MSFF, DB-CNN, etc.), to deeply reveal and capture the complex interactions among datasets, holds promise for future DA [82,106,143,144,245,246]. Meanwhile, other studies focus on quantifying and managing uncertainties in both CGMs and the data fusion process, employing methods such as Bayesian Model-Data Fusion (MDF) and Semantic Segmentation Networks [247,248,249]. Furthermore, building an end-to-end uncertainty model based on systems engineering represents another major focal point for future DA research.

4.1.2. Refinement and Dynamic Updating of Complex Crop Growth Models

Current CGMs often face limitations when simulating complex nonlinear physicochemical processes, ultimately due to incomplete understanding of crop growth mechanisms and constraints imposed by data quality and availability. On the one hand, models frequently fail to accurately replicate crop growth processes, which are influenced by various factors such as soil properties, water supply, nutrient uptake, light conditions, and pest infestations [250,251]. On the other hand, studies may lack sufficient and precise input of model parameters, encounter difficulties in measurement, or be hampered by transmission constraints [252]. The input parameters themselves are inherently uncertain and are usually defined within ranges based on prior knowledge and historical calibrations. There is ongoing debate about whether the focus should be on tracing the sources of uncertainty or on qualitatively analyzing the impact of these uncertainties on DA. Regardless of the emphasis, Bayesian frameworks offer effective means for quantifying both the sources of uncertainty and their impacts, providing not only optimal parameter estimates but also a standardized method to evaluate the magnitude and variability of uncertainties [253]. However, the use of advanced sampling techniques like MCMC often requires substantial computational resources and prolonged run times, which remains a topic of discussion [254]. By contrast, the integration of Gibbs sampling with Hierarchical Bayesian DA is seen as an ideal strategy for addressing complexities in model uncertainties [213], leveraging Gibbs sampling’s efficiency in univariate conditional probability distributions and the HBA’s capacity to handle multilevel uncertainties, although considerations for computational resources in agricultural contexts remain crucial.

Model refinement and dynamic updating are enabled by deepening our understanding of physical processes, such as precisely modeling changes in SM, evaporation, infiltration, and crop water uptake in fields, which are vital for realistic representations of crop growth environments. Recent studies highlight the significant benefits of enhanced grid resolution in capturing spatial heterogeneity in farmland, facilitating a more nuanced understanding of crop growth distribution and dynamics [255]. These advancements bring simulations closer to actual crop growth. Furthermore, refined parameter estimation is another advantage, exemplified by improvements to the YOLOv5s algorithm that reduce errors from parameter uncertainties [256]. High-resolution observations and advanced inversion algorithms allow for uncovering local structures and nonlinear relationships in the parameter space, with dynamic updates and adjustments to parameter estimates directly influencing outcomes as new observations are incorporated [257]. Studies have shown that dynamically estimating observation error covariances is more accurate than traditional methods for quantifying observation uncertainties, and, where necessary, assigning weights can help mitigate the impact of observational errors to some extent [258]. These advancements all revolve around quantitative and qualitative analyses of parameter uncertainties to enhance CGMs simulation accuracy; exploring ensemble methods that combine refined models rather than relying on a single optimal model leverages the strengths of multiple models and mitigates biases [259]. Inspired by online learning in ML, frameworks that dynamically adjust model parameters based on new observations are being designed to improve models’ timeliness and adaptability to complex scenarios [260,261].

However, it must be acknowledged that model refinement and dynamic updating can increase the complexity of model structures, leading to more state variables and parameters. This poses challenges for optimizing state estimation and parameter calibration, as these processes can involve solving nonlinear and non-Gaussian problems or managing uncertainty and error quantification [262]. Technical challenges in implementing dynamic updates cannot be overlooked, necessitating models with robust learning capabilities and adaptability to evolving environmental conditions. Innovative algorithms, such as the highly adaptive DL-Crop algorithm, have been proposed to support dynamic updates [146,263]. As we advance CGMs’ sophistication and dynamism, integrating precision agriculture and exploring DL applications in parameter automation and dynamic updating are essential. DL methods like multi-variable time-attention networks and U-nets have proven advantageous in fitting complex nonlinear relations [264]. Bayesian frameworks, including HBMs, HMC, and Bayesian Neural Networks, continue to offer promising avenues for solving nonlinear problems and quantifying uncertainties [264,265]. Hybrid assimilation methods, such as integrated Kalman and Bayesian filters, should also be considered for their advantages in tackling similar challenges [266]. The synergistic application of these methods holds potential for delivering comprehensive and accurate solutions.

4.1.3. From Univariate Assimilation to Multivariable and Multiscale Assimilation

Current DA primarily focuses on the assimilation of individual key variables such as LAI and NDVI, largely due to mismatches in scales between observations and models [267]. Satellite or sensor observations typically provide information at the pixel level, reflecting vegetation status over larger spatial scales and encapsulating complex, mixed ground information. Conversely, models operate based on simplified assumptions and interpret single variables, struggling to precisely capture all relevant biophysical processes when dealing with interconnected micro-scale variables like SM, nutrient content, and pest pressure. These variables are not directly measurable by RS, and model simplifications may not adequately represent their collective influence. Consequently, DA often prioritizes parameters that are easily extracted and have a significant impact on model predictions, overlooking the synergistic effects of multiple interrelated variables during crop growth. While this approach may suffice for broader tasks such as land cover classification, vegetation monitoring, and crop area estimation on a macroscopic scale [268,269], it can prove disastrous for precision operations, leading to intensified drought and flooding, environmental pollution, yield impacts, delayed pest management, and economic losses [270,271,272]. Although simpler to implement, this approach lacks versatility, especially in refined agricultural practices.

A promising solution lies in developing multi-variable, multi-scale integrated assimilation techniques to tackle key issues related to data fusion, model coupling, and uncertainty handling. This necessitates addressing scale transformation problems across different spatial and temporal dimensions, particularly when non-linear transformations and landscape heterogeneity are involved. Adjusting the spatial scale of agricultural landscapes from satellite RS to field scale typically involves averaging satellite (LAI/NDVI) data over fields to represent overall vegetation health [273,274], which may not adequately capture landscape variability [275]. More sophisticated downscaling techniques, such as ML-based methods trained to predict high-resolution parameter values, can be employed. Researchers have linked high-resolution ground measurements with RS (LAI/NDVI) to establish relationships with field-scale crop growth parameters, subsequently applied to low-resolution satellite data to estimate crop conditions at the field scale [276]. Furthermore, CNNs have been used to enhance the resolution of satellite RS images, improving the estimation accuracy of vegetation parameters at the field scale [277].

Adjusting for the time scale requires careful consideration, especially when converting daily data to decadal or monthly averages to match model time steps. Simple averaging or statistical downscaling may not suffice given the inherent nonlinear dynamics of time series data [176,278]. Adopting assimilation strategies that couple space and time and incorporating dynamic models to capture nonlinear temporal dynamics presents a promising avenue. For instance, in predicting pest outbreaks, spatiotemporal assimilation techniques can be designed to integrate forecasting systems seamlessly, enhancing the accuracy and timeliness of disease warnings [279]. Notably, future research may concentrate on dynamic windowing and adaptive filtering techniques [280], as well as ML-based multi-scale assimilation models [281,282], marking a focal point for advancing multi-variable, multi-scale integrated assimilation.

4.2. The Future Development Prospect of DA

4.2.1. Intelligent and Integrated DA

DA applications in agriculture are trending towards greater intelligence and precision, with efficiency and accuracy continually enhanced by the rapid development of multi-sensor integration, cloud computing, Internet of Things (IoT), and artificial intelligence technologies—a consensus among agricultural practitioners [283,284]. In the context of smart greenhouse and field management studies, IoT technology facilitates real-time monitoring and collection of microscale data, including SM, temperature, crop growth status, and soil chemical properties, which are then efficiently consolidated via cloud platforms [285]. The Copernicus Sentinel satellite constellation, offering high-resolution optical and thermal sensing data, combined with high-resolution RS and in-field sensor data revolutionizes Earth observation, enabling agricultural managers to adjust irrigation and fertilization strategies in real-time and with precision through advanced DA algorithms processed in parallel on cloud servers. This results in enhanced accuracy of crop yield forecasts [286,287]. In addition, the assimilation of spatial scale and time dimension and the tradeoff and fusion application of their integration methods are important development directions in the field of data assimilation in the future [288,289,290]. For example, we could explore a more adaptive spatial scale assimilation method, which can deal with the differences of data characteristics and model requirements in different regions and different environmental conditions. In addition, the introduction of time series analysis and sliding window technology can realize the real-time tracking and assimilation of the dynamic process and improve the ability of the model to support short-term prediction and real-time decision-making. Simultaneously, AI technologies have transformative potential, optimizing model parameter estimation and reducing response times through historical data analysis, thereby enhancing agricultural adaptability and resilience under complex climatic and environmental changes [291]. Nevertheless, the integration of smart technologies with precision DA in agriculture must navigate the unique complexities and variability of agricultural systems [292]. For example, data limitations, such as heterogeneity, singularity, scale differences, and uncertainties, often pose significant barriers to progress [74]. Yet technological advancements, like the Planet-Scope, Planet Labs Dove satellite constellations, and UAVs, facilitate the integration of multi-source data, overcoming challenges related to data uniformity and scale [86,87]. High-resolution satellites like Landsat-9 significantly contribute to discerning subtle variations in agricultural landscapes, complementing ground observations [78].

For complex CGMs, whether simulating crop development, processing data, or tracking growth stages dynamically, DA incurs significant costs, especially at larger spatial and temporal resolutions for regional or national scale simulations. The trade-off between model accuracy and complexity is often skewed towards simplicity for predictive power, neglecting modular design. CGMs typically treat simulation units as independent entities, allowing different modules to be assigned to separate units for parallel processing in cloud servers, a strategy facilitated by advances in CUDA, distributed storage, and multi-GPU systems [293]. Considering computational time and cost, Genetic Algorithm-based Task Scheduling (GA-TP), GPU clusters, and computer clusters, alongside AI technologies, are leveraged for their ability to distribute computational loads and expedite processing [294,295].

Large-scale parallel infrastructures like Google Earth Engine (GEE) offer a platform for redesigning DA algorithms with its immense computational power and data storage, presenting new possibilities [296]. Future developments should account for interactions and dependencies among modules, incorporating physical modeling with ML methods like ML-4D-Var, environmental stress indices, and crop variety traits, leveraging ML’s capacity for nonlinear modeling to improve adaptability to varied conditions and crop types [297,298].

While complex CGMs offer accuracy and performance advantages, their computational complexity and demands can hinder DA research. Thus, approximated models or emulators are proposed to simplify computational requirements while preserving model accuracy. Emulators simulate key growth parameters like LAI, biomass, and transpiration rates, combining these with observations and utilizing variational approximation or Gaussian process estimation for model parameterization, leading to more accurate crop growth status predictions and yield estimates [299,300]. Such approaches propel DA towards greater intelligence and service-oriented applications.

4.2.2. DA Applicability of Decision Support for Precision Agriculture

DA, serving as a crucial link between observational data and CGMs, has been extensively demonstrated through cutting-edge research to hold immense potential and application value in supporting precision agriculture decision-making, such as precision irrigation, detailed yield estimation, targeted monitoring, and precision pest control [83,223,301]. Despite these advancements, there remain gaps to bridge before DA fully aligns with the practical requirements of precision agriculture. First and foremost, the practice of precision agriculture imposes stricter demands on the quality and integration of observational data, likely tied to the necessity for high-quality agricultural decisions. Persistent challenges include cloud coverage, sensor errors, resolution disparities, and scale integration. Researchers have thus focused on constructing advanced data fusion frameworks, such as those based on Bayesian theory, designed to simultaneously address complex nonlinear issues arising during the fusion process. These frameworks typically incorporate multi-source RS platforms like LiDAR, SAR, hyperspectral imagery, and high-resolution data from drones to enhance spatial-temporal resolution and data continuity [302,303]. The EU Horizon 2020 project “SEN4CAP” exemplifies this approach. Additionally, for cloud detection and gap filling, ML algorithms, notably CNNs and transfer learning techniques, have emerged as promising solutions, validated by tools like FMask on GEE [304] and the Sen2Cor cloud detection algorithm developed by the European Space Agency (ESA) [305].

Second, the suitability of CGMs in precision agriculture DA necessitates addressing issues related to model optimization and quantification of parameter uncertainties. Approaches range from rule-based expert systems to ML-driven black-box simplifications of models, such as the simplified version of FAO’s AquaCrop model, AquaCrop-OS [223], and the USDA ARS’s Excel-based simplified EPIC model, which greatly facilitate farmer and consultant use [306]. Deeper explorations might involve modular and component-based methodologies, with initiatives like the US DOE’s Agricultural Model Intercomparison and Improvement Project (AgMIP) [307] indicating a promising path forward. The discourse on parameter uncertainty quantification revolves around MCMC and Bayesian parameter estimation under a Bayesian framework, with future developments potentially leaning towards data-driven adaptive CGMs.

Lastly, the choice and adaptability of DA algorithms as core components of precision agriculture decision support systems are critical to ensuring the full exploitation of DA in precision agriculture scenarios. Different DA methods, including forcing methods, 4D-Var, EnKF, PF, and HBM, each have distinct applicability and performance characteristics in precision agriculture. Forcing methods are primarily suited for parameter optimization and observational correction [308], whereas variational and Bayesian assimilation methods are better equipped for large-scale, global, or complex uncertainty handling tasks, such as refined yield prediction [309,310]. HBM particularly excels in integrating multi-source RS data and assessing model uncertainties [119]. Conversely, EnKF and PF show advantages in addressing medium-sized, localized issues, such as precision irrigation decisions, SM forecasting, and decision management [173,311]. Studies also propose hybrid assimilation strategies, e.g., EnKF-Variational assimilation and EnKF-SSPE [312,313], and emphasize the potential of leveraging GPU, cloud computing, and parallel platforms like GEE to enhance assimilation efficiency through large-scale parallel computations, a highly prospective research direction [314].

5. Conclusions

Data assimilation has obvious advantages, great potential, and broad space for development in agricultural applications. However, the quality, resolution, and applicability of assimilation data sources are still the key bottlenecks affecting the development of data assimilation precision agriculture. In the future, the assimilation applications of emerging satellite constellation remote sensing, UAV, ground station data, high spatio-temporal resolution remote sensing, and multi-source remote sensing fusion technology should be vigorously promoted. It is worth noting that in light of the quantification of remote sensing integration errors and uncertainties, the introduction of the development agenda has an efficient and significant effect and is an effective means to promote the future development agenda of precision agriculture. The assimilation application of crop growth model is uneven. The SWAP model stands out in the application of agricultural data assimilation because of its wide applicability. The development trend of Aquacrop, WOFOST, and APSIM models is also quite positive, but the applications of Cropsyst and GLAM models are relatively few. The potential of multi-model fusion and assimilation mechanism is worthy of further study. LAI is the mainstream assimilation parameter selection, and the progress of multi-parameter data assimilation in precision agriculture is worth looking forward to. Model parameter optimization and uncertainty quantification mainly depend on the quantitative calibration method under the Bayesian framework. With the rise of ML technology, automatic parameter adjustment methods and integrated assimilation strategies based on ML, such as EnKF, variational assimilation, Bayesian filtering, and so on, show broad research prospects. In the application trend of precision agriculture assimilation model strategy, the data assimilation research based on EnKF is the most active, while the Bayesian system assimilation strategy shows a trend of rapid development. The development of multi-level assimilation or multi-model integrated assimilation is worth exploring.

The data assimilation model is developing in the direction of refinement, diversification, and integration. Its mechanism framework has been continuously deepened and improved, resulting in a significant improvement in the overall performance. In the future, advances in GPU technology, GEE platform, cloud computing technology, and artificial intelligence will make large-scale parallel assimilation possible and release the great application potential of precision agriculture. However, the current research literature shows that it needs to be strengthened in the field of agricultural data assimilation. In order to meet the growing demand of data assimilation in precision agriculture, future research should focus on the optimization of assimilation data sources, the refinement of crop growth models, and the upgrading of assimilation model strategies to improve adaptability, accuracy, and efficiency. At present, there is an imbalance in spatial and regional distribution in the research of agricultural data assimilation, so it is very important to strengthen the sharing and exchange of international data assimilation results. It is necessary to promote cooperative research between countries and regions, share advanced experience and technological innovations, and promote the innovative development of global agricultural data assimilation.